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The Royal Docks Community School Medium Term Plan AUTUMN Resources: Maths Frame-working Textbooks: 1.1, 1.2, 1.3 Keywords Literacy Assessment Numeracy TERM 1 Differentiation: 1-2 Induction & Testing Numeracy Work Problem solving using the four operations, Decimals, negative numbers, Angles, Perimeter & Area. Numeracy Work Numeracy Work Problem solving using the four operations, negative numbers, Angles, Perimeter & Area. Problem solving using the four operations, Decimals, negative numbers, Angles, Perimeter & Area. HW: Once a week lasting 45 minutes Understanding of the common keywords used in maths. Problem solving using the four operations, Decimals, negative numbers, Angles, Perimeter & Area. Testing in the 2nd week of term 3 Place value, Integers, Ordering & Rounding. -Understand negative numbers as positions on a number line; order, add and subtract integers in context. Support: Extension: -Read and write whole numbers in figures and words. -Understand negative numbers as positions on a number line. -Order positive and negative integers. -Calculate a temperature rise and fall across 0C. -Round positive whole numbers to the nearest 10, 100 or 1000 -Understand and use decimal notation and place value. -Read and write any number for 0.001 to 1 000 000, knowing what each digit represents. -Add and subtract 0.1 and 0.01 to or from a decimal number. -Multiply and divide integers and decimals by 10, 100 and 1000 and explain the effect. -Multiply and divide integers and decimals by 10, 100 and 1000 and explain the effect. Week Learning outcomes: Success Criteria: (Key Questions :) You have 44 eggs, and each egg-box can hold six eggs. How many boxes would you need? What would happen if you rounded to the nearest 10 in order to estimate a solution? 1 Keywords are used and spelt Correctly. Writing the meaning for the keywords Units, tenths, hundredths, thousandths, digit, decimal point, decimal, unit, addition, subtraction, multiplication, division, operation, commutative, bracket, powers, column method, estimate, rounding, carrying, decimal place, squared. Real –life problems (worded problems) Times Tables TenQQ (Starter & plenaries Number Bonds Powers, integers, roots Negative numbers (To check link ) Mymaths KS3 Assessment http://www.mymaths.co.uk/indexLo g.asp?h=74272 4. Sequences -Describe integer sequences. - Generate terms of a simple sequence, given a rule (e.g. finding a term from the previous term, finding a term given its position in the sequence). -Generate sequences from patterns or practical contexts. - Describe the general term in simple cases. 5-6. Perimeter, Area and Volume - Deduce and use the formula for the perimeter of a rectangle. • Deduce and use the formulae for the areas of a rectangle and a right-angled triangle. - Know and use the formula for the area of a rectangle. - Calculate the perimeter and area of shapes made from rectangles. - Solve problems in everyday contexts involving length and area. - Use 2-D representations to visualise 3-D shapes. - Deduce some of their properties. - Calculate the surface area of cubes and cuboids. -Be able to make a sensible estimate of the surface area of everyday objects. What is the next term, what is the 10th term? Why? -Show me an example of a number sequence: with an increasing pattern with a decreasing pattern? -What is the same/different: 4, 7, 10, 13, ... and 13, 10, 7, 4, True/Never/Sometimes: A sequence always goes up in equal steps. Convince me that the number '___' is in this sequence. -Show me: a sequence that has the term-to-term rule of +2. the sequence that has the position-toterm rule of +2. the sequence that has the nth term of i) n+2 ii) 3n+2 -Convince me that: the nth term of the sequence 5, 8, 11, 14, … is 3n+ 2 that the nth term of the sequence 15, 11, 7, 3, … is 19 – 4n -How do you know which is the base and height? -Find shapes with a perimeter of 11cm -Find another measurement that is the same as 3m -How we decide what each division on the scale represents? -Draw two different rectangles with an area of 8 squares? How about 7 squares? Why not? -Why is the area of a rectangle given by length times width? -A shape made from two rectangles has area 10cm2. Draw the shape. - 50g of plasticene? -How do you know which is the base and height? -Find six triangles with an area of 12cm2 -Find six parallelograms with an area of 48cm2 Support: Extension: -Understand the definition of a multiple and generate multiples of whole numbers. -Recognise and extend number sequences from any number in steps of constant size extending beyond zero when counting backwards. -Generate and describe simple integer sequences Generate terms of a simple sequence, given a rule. -Generate sequences from practical contexts. -Generate and describe simple integer sequences. -Explore and predict terms in sequences generated by counting in regular steps. -Recognize that sequences of multiples can be generated in two ways. -Generate terms of a simple sequence given a rule for finding each term from the previous term. -Explore term-to-term and position-to-term relationships. -Generate sequences from practical contexts and describe the general term in simple cases. -Measure and draw lines to the nearest millimetre. -Know and use the names and abbreviations for units of length -Understand measure and calculate perimeters of rectangles and regular polygons. -Understand that area is measured in square units. -Use appropriate methods to measure and estimate area. -Understand, count and calculate the area of a rectangle. -Understand, count and calculate the surface area of cubes and cuboids -Deduce and use the formula for the perimeter of a rectangle. -Deduce and use the formulae for the areas of a rectangle and a right-angled triangle. -Calculate the perimeters and areas of shapes made from rectangles. -Solve problems in everyday contexts involving length and area. - Deduce and use the formulae for the area of a triangle, parallelogram and trapezium. -Derive and use a formula for the surface area of a cube and cuboid. -Calculate the surface area of shapes made from cubes and cuboids. 2 Describing sequences using the keywords. Researching keywords Sequence, term, consecutive, infinite, finite, generate, term-toterm rule, term number, rule, input, output, general term, relationship TenQQ (Starter & plenaries Kangaroo Assessment (level ladders). Sequences, functions and graphs Mymaths http://www.mymaths.co.uk/indexLo g.asp?h=74272 Keywords are used and spelt Correctly. Writing the meaning for the keywords Metre {m}, centimetre {cm}, kilometre {km}, millimetre {mm}, perimeter, square centimetre {cm2}, square metre {m2}, square millimetre {mm2}, square kilometre {km2}, area, face, edge, vertex, vertices, cube, cuboid, 3-D, surface area, net. Real –life problems (worded problems) TenQQ Starter & plenaries Making sensible estimates of the surface area of everyday objects. Kangaroo Assessment (level ladders). Measures Beyond the Classroom Area and Perimeter Mymaths http://www.mymaths.co.uk/indexLo g.asp?h=74272 7. Decimal Numbers -Understand and use decimal notation and place value. - multiply and divide integers and decimals by 10, 100, 1000, and explain the effect. -Compare and order decimals in different contexts. -know that when comparing measurements the units must be the same. -Round positive whole numbers to the nearest 10, 100 or 1000, and decimals to the nearest whole number or one decimal place. What would happen if you rounded to the nearest 10 in order to estimate a solution? How many numbers are there between 1 and 2? Give me some numbers between 7.1 and 7.2 Use decimal notation for tenths. -Use decimal notation for hundredths. -Know what each digit represents in numbers with up to two decimal places. -Multiply and divide whole numbers and decimals by 10, 100 and 1000. -Understand and use decimal notation and place value. -Read and write any number for 0.001 to 1 000 000, knowing what each digit represents. -Add and subtract 0.1 and 0.01 to or from a decimal number. -Multiply and divide integers and decimals by 10, 100 and 1000 and explain the effect. -Multiply and divide integers and decimals by 10, 100 and 1000 and explain the effect. 8. Creating & Manipulating Algebraic. Expressions - Use letter symbols to represent unknown numbers or variables. -Know the meanings of the words term, expression and equation. - Understand that algebraic operations follow the rules of arithmetic. - Simplify linear algebraic expressions by collecting like terms; multiply a single term over a bracket (integer coefficients). The answer is 2x+5y. What is the question? The answer is 4n-12. What is the question? Find five expressions equivalent to 2y = 6x+4 Why are x, x2, x3 not like terms? Consider m, m2, m3. Show me a formula involving a and b such that when you substitute a = 2 and b = 7 into the formula you get 18. What is wrong: 3(b+1) = 3b + 1 10(p -4) = 10p - 6 -2 (3 - f) = -6 -2f 8 – (n – 1) = 7 – n Show me a formula involving a and b such that when you substitute a = -2 and b = 3 into the formula you get 18. Convince me that: 2(x+7) = 2x + 14 5(y -4) = 5y - 20 Support: - Understand and use the relationships between the four operations. -Understand the meaning of and begin to use simple expressions with brackets. -Understand the principles of the arithmetic laws. - Use brackets. -Use letters and symbols to represent unknown numbers. - Use letter and symbols to represent unknown numbers Extension: - Recognise that algebra follows the same conventions and order as arithmetic operations. -Simplify or transform linear expressions by collecting like terms. -Substitute positive integers into simple linear expressions and formulae. -Begin to multiply a single term over a bracket. -Understand that algebraic operations follow the same conventions and order as arithmetic operations. -Begin to distinguish the different roles played by letter symbols in equations, formulae and functions. - Know the meaning of the words formulae and function. - Substitute integers into simple formulae including examples that lead to an equation to solve. 3 Keywords are used and spelt Correctly. Writing the meaning for the keywords Units, tenths, hundredths, thousandths, digit, decimal point, decimal, unit, addition, subtraction, multiplication, division, operation, commutative, bracket, powers, column method, estimate, rounding, carrying, decimal place, squared. Real –life problems (worded problems) Times Tables TenQQ (Starter & plenaries Place value, rounding Keywords are used and spelt Correctly. Writing the meaning for the keywords Term, expression, equivalent, like terms, unknown, algebraic, substitution, brackets, operation, simplify, expand, equation, solve Real –life problems (worded problems) TenQQ (Starter & plenaries Equations, formulae, identities Mymaths http://www.mymaths.co.uk/indexLo g.asp?h=74272 Week AUTUMN Learning outcomes: Success Criteria: (Key Questions :) TERM 2 1-3 Fractions, Decimals, Percentages -Express a smaller whole number as a fraction of a larger one. -Simplify fractions by cancelling all common factors and identify equivalent fractions. -Change an improper fraction to a mixed number, and vice versa -convert terminating decimals to fractions, e.g. 0.23=23/100. -Convert simple fractions to decimals, using division -Convert simple fractions to decimals, using a calculator -Order fractions by converting them to decimals -Use diagrams to compare two or more simple fractions. -Add and subtract simple fractions and those without common denominators. -Calculate simple fractions of quantities and measurements (whole-number answers). - Multiply a fraction by an integer. -Understand percentage as the ‘number of parts per 100’. -Calculate simple percentages. -Use percentages to compare simple proportions. -Recognise the equivalence of percentages, fractions and decimals. -Convert a percentage to a decimal -Convert a percentage to a fraction -Recognise the equivalence of percentages, fractions and decimals. -Calculate a number or amount as a percentage of another. -Break up a complex calculation into simple steps. -Number line fractions: where should I place 3/4? What tells you that it is greater than 1/2? -Show this fraction as part of a square / rectangle / number line. -Explain mental methods for finding common percentages of a quantity – e.g. 10%, 5%, 20% etc . -How many different ways can you shade a 2x3 rectangle of squares to show 1/3? -Find six fractions equivalent fractions to ___ -Explain mental methods for finding common percentages of a quantity – e.g. 331/3%, 17½%, 20% -Which percentages/ decimals / fractions are easiest to convert? Why? -To find 10% you divide by 10. Why don’t you divide by 20 to find 20%? --80 pupils go on a school trip. 25% are girls. How can you work out the number of boys? -If you know that 1/5 = 0.2, what else can you deduce? -If you know that 1/8 = 0.125, what else can you deduce? -Camel problem - 3 sons to have 1/2, 1/3 and 1/9 of dad’s 17 camels. Bloke offers 1 camel, splits them and bloke gets camel back. How? (nice plenary!) -Extend sequences of + and fractions from Y7 – e.g. 1/2 +1/3 + 1/6 = 1. -Can you predict the result of 1/4 + 1/6 + 1/12? Further predictions? -Show me a pair of fractions which have a sum / difference of 4/7. Extend to fractions which do not have the same denominator -Convince me: o that 4/7 + 3/8 = 53/56 that 4 ÷ 2/5 = 10. Resources: Maths Frame-working Textbooks: 1.1, 1.2, 1.3 Keywords Literacy Assessment Numeracy Differentiation: HW: Once a week lasting 45 minutes Support: -Use fraction notation to describe parts of shapes. - Recognise when two simple fractions are equivalent, including relating hundredths to tenths. -Use a diagram to compare simple fractions -Begin to simplify fractions by cancelling -Use fraction notation to describe parts of shapes -Change an improper fraction to a mixed number, and vice versa -Calculate simple fractions of whole-number quantities -Multiply a fraction by an integer -Use decimal notation for tenths and hundredths -Convert terminating decimals to fractions -Compare and order decimals in different contexts -Understand percentage as the number of parts per hundred. -Recognise the equivalence of percentages, fractions and decimals 4 Extension: -Use fraction notation to describe parts of a shape -Express a smaller whole number as a fraction of a larger one -Change an improper fraction to a mixed number, and vice versa =Identify equivalent fractions -Simplify fractions by cancelling all common factors -Reduce a fraction to its lowest terms -Use a diagram to compare simple fractions -Convert terminating decimals to fractions -Convert simple fractions to decimals, using division -Convert simple fractions to decimals, using a calculator -Order fractions by converting them to decimals. -Recognize recurring decimals. -Add and subtract simple fractions and those without common denominators. -Break up a complex calculation into simple steps -Calculate simple fractions of quantities and measurements -Multiply a fraction by an integer -Understand percentage as the ‘number of parts per 100’ -Convert a percentage to a decimal -Convert a percentage to a fraction -Recognize the equivalence of percentages, fractions and decimals. -Calculate a number or amount as a percentage of another. Keywords are used and spelt Correctly. Writing the meaning for the keywords Fraction, denominator, numerator, proper fraction, improper fraction, mixed number, equivalent fraction, cancel, lowest terms, decimal, convert, expressions, per cent, percentage, hundredths, equivalent, recurring decimal. Real –life problems (worded problems) Kangaroo Assessment (level ladders). Fractions Percentages Beyond the Classroom Fractions Proportional sets 1 Proportional sets 2 Use of a calculator Comparing proportions Proportions of a whole Simplifying fractions Mymaths http://www.mymaths.co.uk/indexLo g.asp?h=74272 3/ 4 Coordinate Geometry -Use conventions and notation for 2-D coordinates in all four quadrants. -Find coordinates of points determined by geometric information. Coordinates: ‘x is a cross, wise up’. What does this mean?! Does it help you? Find a pair of points with a mid-point of (1,4:) and another… and another Find a point which is a three units from (1,4): and another… and another A square has sides parallel to the x and y axes. What relationships exist between the coordinates of the four corners? Is it always possible to find the coordinates of the third and fourth corners of a square if you know the first and second? Is there a unique answer? Support: -Use conventions and notation for 2-D coordinates in the first quadrant (positive). Extension: -Use conventions and notation for 2-D coordinates in all four quadrants. -Find coordinates of points determined by geometric information in the first quadrant (positive). -Find coordinates of points determined by geometric information. 4–5 - Function and Graphs -Express simple functions in words, then using symbols. -Represent them (functions) in mappings. -Generate coordinate pairs that satisfy a simple linear rule. -Plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT. -Recognize straight-line graphs parallel to the x-axis or y-axis. -Plot and interpret the graphs of simple linear functions arising from real-life situations, e.g. conversion graphs. -Coordinates: ‘x is a cross, wise up’. What does this mean?! Does it help you? -I want to plot the graph of y=2x. What shall I do? -Give me the co-ordinates of some points which can be joined to form a straight line -Find three lines that pass through 1 on the y-axis -Is the point (2, 4) on the line y=x+1? Explain your answer -Find another line that is parallel to this one. How do you know they are parallel? -Find another line with the same yintercept -Which of these are parallel: y = 2x+1, y = x+2, 2y = 4x – 10? What happens when the gradient gets bigger / smaller / negative? Give set of equations and set of graphs to match. How did you work it out? Using equations of straight lines, can you create a square? Explain what happens when two lines are perpendicular? -Express simple functions in words, then using symbols. -Express simple functions in words, then using symbols. -Represent simple functions in mappings -Read and plot coordinates in all four quadrants. -Plot the graphs of simple linear functions. -Using function machines to explore mappings. -To calculate input, output and missing operations -Understand and use inverse operations. -Begin to apply inverse operations where two successive operations are involved. -Recognise that equations of the form y = mx + c correspond to straight-line graphs. -Consider the features of graphs of simple linear functions. -Begin to plot the graphs of simple linear functions arising from real-life problems. -Read values from a straight-line graph. -Plot and interpret the graphs of simple linear functions arising from real-life problems. -Find the equations of straight-line graphs. -Plot and interpret linear graphs that occur in real life 5 Exploring mathematical concepts -Describing visualisations of shapes, movements and constructions coordinates, origin, quadrant, xaxis, y-axis, Cartesian plane. -Beyond the Classroom Coordinates in four quadrants Coordinates in the first quadrant Mymaths http://www.mymaths.co.uk/indexLo g.asp?h=74272 Keywords are used and spelt Correctly. Writing the meaning for the keywords. rule, input, output, function machine, mapping diagram, generate, variable, straight –line graphs, y-axis, x-axis, plot, equation, Y-intercept, gradient, coordinates, parallel, square, square roots, quadrant. Kangaroo Assessment (level ladders). Sequences, functions and graphs Graphs of linear functions 5–6 Planning Statistical Projects -Suggest possible answers, given a question that can be addressed by statistical methods. -Decide which data would be relevant to an enquiry and possible sources. -Plan how to collect and organise small sets of data from surveys and experiments. -Design data collection sheets or questionnaires to use in a simple survey. -Construct frequency tables for gathering discrete data, grouped where appropriate in equal class intervals 6-7 Processing and Representing Data -Collect small sets of data from surveys and experiments, as planned. -Construct, on paper and using ICT, graphs and diagrams to represent data, including: • bar-line graphs • frequency diagrams for grouped discrete data • simple pie charts -Interpret diagrams and graphs (including pie charts), -Draw simple conclusions based on the shape of graphs and simple statistics for a single distribution What is an appropriate graph / chart for this? Why? Can the mean = median = mode? What do the scales mean? Is it more efficient to use ICT here? Are scatter diagrams appropriate for these data? What does the graph tell you? Why would you choose to use ICT here? Why is this graph misleading? Does this piece of data fit the trend. If not, can you think of a reason why it doesn’t? What is an appropriate graph / chart for this? Why? Can the mean = median = mode? What do the scales mean? Is it more efficient to use ICT here? Are scatter diagrams appropriate for these data? What does the graph tell you? Why would you choose to use ICT here? Why is this graph misleading? Does this piece of data fit the trend. If not, can you think of a reason why it doesn’t? -Decide which data would be relevant to an enquiry and suggest possible sources. -Plan how to collect and organise data. -Design a data collection sheet. -Construct frequency tables Collect and record a small set of data from an experiment. -Understand the concept of grouped data. -Collect small sets of data from surveys and experiments, as planned. -Construct frequency tables for discrete data, grouped where appropriate in equal class intervals. -Collect and record small sets of data from experiments. -Draw graphs and diagrams to represent data. -Categorise data into discrete or continuous types. -Given a problem that can be addressed by statistical methods, suggest possible answers. -Decide which data would be relevant to an enquiry and determine the degree of accuracy needed. -Plan how to collect the data, including sample size. -Design a data collection sheet and questionnaires to use in simple experiments. -Collect and record small sets of data from experiments. -Construct frequency tables for discrete and continuous data, grouped where appropriate in equal class intervals -Construct frequency tables for discrete data, grouped where appropriate in equal class intervals. -Construct pie charts for categorical data on paper and using ICT; Interpret pie charts Read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Data -Discussing and interpreting data and drawing conclusions -Writing short and extended responses -Presenting their findings to an audience Class interval, modal class, sector, pie chart, survey, experiment, primary source, secondary source, frequency tables, data collection sheet, axes, bar chart, pictogram, bar-line graph, continuous, discrete, class, time series. Kangaroo Assessment (level ladders). Collecting data Read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Data -Discussing and interpreting data and drawing conclusions -Writing short and extended responses -Presenting their findings to an audience Data, mode, median, range, average, mean, sum, frequency, event, frequency table, pictogram, bar chart, bar-line graph, pie chart, compound bar chart END OF AUTUMN TERM TEST (1 lesson) 6 SPRING Week Learning outcomes: Success Criteria: (Key Questions :) TERM 1 1–3 Number Operations and Calculation Methods -Understand and use the rules of arithmetic and inverse operations in the context of positive integers and decimals. -Use the order of operations, including brackets. -Recall number facts, including positive integer complements to 100 and multiplication facts to 10 × 10, and quickly derive associated division facts -Strengthen and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings. - Solve simple problems mentally -Make and justify estimates and approximations of calculations. -Use efficient written methods to add and subtract whole numbers and decimals with up to two places -Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by singledigit whole numbers -Carry out calculations with more than one step using brackets and the memory; use the square root and sign change keys -Enter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures) -Check results by considering whether they are of the right order of magnitude and by working problems backwards. -Understand how to solve real life problems with or without calculator. Can division ever make a number larger? Can multiplication ever make a number smaller? How can you check if your answer makes sense? [Last digits / estimating] What are the steps to: Multiply Divide By a two numbers? Find a number between 4.35 and 4.362. And another, and another… 4x6 = 24. What else does this tell you? Can division ever make a number larger? Can multiplication ever make a number smaller? How can you check if your answer makes sense? [Last digits / estimating] Show me an amount and a percentage increase that gives the answer £33 What is the same/different about: 17/100 × 37 = 629/100 = 6.29 0.17 × 37 = 6.29 1% of 37 = 0.37 so 17% of 37 = 0.37 × 17 = 6.29 Resources: Maths Frame-working Textbooks: 1.1, 1.2, 1.3 Keywords Literacy Assessment Numeracy Differentiation: HW: Once a week lasting 45 minutes Support: -Use informal written methods to subtract whole numbers. -Make and justify estimates and approximations of calculations. -Check a result by considering whether it is of the right order of magnitude. -Understand and use the rules of arithmetic and inverse operations in the context of positive integers. - Check a result by performing an inverse operation. -Use informal pencil and paper methods and standard written procedures to add whole numbers. - Recall number facts, including positive integer complements to 100 and multiplication facts to 10 × 10, and quickly derive associated division facts -Check a result by performing an inverse operation. -Multiply a two-digit number by a one-digit number, using an informal written method, and the standard written method. -Multiply a three-digit number by a one-digit number. -Understand how to solve real life problems with or without calculator. Extension: -Know and use the order of operations. -Understand the commutative law. -Interpret the meaning of a bracket. -Develop the order of operations to include brackets and powers. -Know that a horizontal line acts as a bracket in expressions. -Calculator methods: Know how to use the bracket and x² key of a calculator. -Use standard column procedures to add, subtract & multiply whole numbers and numbers with up to 2 decimal places. - Strengthen and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings. - Solve simple problems mentally. -Make and justify estimates and approximations of calculations. -Use known facts to derive unknown facts. -Calculator methods: Enter numbers and interpret the display in different contexts (decimals, money). -Understand how to solve real life problems with or without calculator. Keywords are used and spelt Correctly. Writing the meaning for the keywords digit, decimal point, decimal, unit, addition, subtraction, multiplication, division, operation, commutative, bracket, powers, column method, estimate, rounding, carrying, decimal place, squared. grid method, standard method, estimate. Real –life problems (worded problems) Kangaroo Assessment (level ladders). Written calculations Mental calculations Beyond the Classroom Decimals and negative numbers Mymaths http://www.mymaths.co.uk/i ndexLog.asp?h=74272 7 3-4 Units of Measurement -Choose and use units of measurement to measure. -Estimate, calculate and solve problems in everyday contexts. -Convert one metric unit to another, e.g. grams to kilograms. -Read and interpret scales on a range of measuring instruments 4-5 Ratio & Proportion -Understand the relationship between ratio and proportion. -Use direct proportion in simple contexts. -Use ratio notation, simplify ratios and divide a quantity into two parts in a given ratio. -Solve simple problems involving ratio and proportion using informal strategies. Support: What unit would you use to measure______? -Read and interpret scales on a range of Show me pairs of metric units that can measuring instruments. complete the statements below: i) 1 ______ = 1000 ______ -Convert one metric unit of length to another. ii) 1 ______ = 100 ______ iii) 1 ______ = 10 ______ -Recognize the relationship between metric units of mass. What is the same/different about: -Convert one metric unit of mass to another. mm, cm ,m,km mg, g, kg, -Recognize the relationship between metric units km, kg, l Convince me how to read a scale on of capacity and convert them. measuring equipment. What unit would you use to measure______? Does every year have a Friday the 13th? What is the greatest number of Friday the 13th’s you can have in a single year? What is the difference between bearings and angles? ne metric unit to another The answer is ‘£350 and £450’. What Support: is the question? -Understand the idea of proportion. Draw a golden rectangle (sides are in -Understand the idea of ratio. the ratio 1:1.618) Divide into the -Use ratio notation. largest square possible and a -Simplify a ratio to an equivalent ratio by rectangle. What do you notice about cancelling. the resulting rectangle? -Understand the relationship between ratio and Is a 10% increase on £300 the same proportion. as 30% increase on £100? Why? If you increase by e.g. 20% then by a further 20% is this the same as inc by 40%? Explain your answer Ratio of squash to water is 1:3. Is 2:5 stronger or weaker? Are these number sets in proportion? What if the recipes were for 12 people, 3 people, 15 people, etc. How do you know? Explain and identify key information. If I had a litre of orange juice… If I needed five litres of squash… how many people, what ingredients? 8 Extension: -Read and interpret scales on a range of measuring instruments. -Recognize the relationship between metric units of length. -Convert one metric unit of length to another. -Begin to know rough metric equivalents of common imperial measures. -Recognize the relationship between metric units of mass and capacity. -Convert one metric unit of mass and capacity to another. -Begin to know rough metric equivalents of common imperial measure. Keywords are used and spelt correctly. -Writing the meaning for the keywords Extension: -Solve problems involving proportions. -Use the unitary method to solve problems. -Use ratio notation. -Reduce a ratio to its simplest form by cancelling. -Solve simple problems about ratio and proportion using informal strategies. -Divide a quantity into two or more parts in a given ratio. -Check a result by considering whether it is of the right order of magnitude and by working the problem backwards. Keywords are used and spelt Correctly. Writing the meaning for the keywords. Fraction, ratio, simplify, equivalent fraction, unitary method. Writing the meaning for the keywords -Read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Data Kangaroo Assessment: Level Ladders Fractions Percentages Beyond the Classroom Ratio and proportion Proportional reasoning Mymaths http://www.mymaths.co.uk/i ndexLog.asp?h=74272 TenQQ measuring instrument, inch, foot, yard, mile, capacity, litre, centilitre, millilitre, pint, gallon, mass, gram, kilogram, pound, ounce -Describing visualisations of shapes, movements and constructions -Discussing which mathematical equipment and materials to use Kangaroo Assessment (level ladders). Measures Mymaths http://www.mymaths.co.uk/i ndexLog.asp?h=74272 6 Angles and Polygons - -Identify and use angle, side and symmetry properties of triangles and quadrilaterals. -Explore geometrical problems involving these properties. -Explaining reasoning orally, using step-by-step deduction supported by diagrams. -Use correctly the vocabulary, notation and labeling. -Conventions for lines, angles and shapes. -Distinguish between and estimate the size of acute, obtuse and reflex angles. -Identify parallel and perpendicular lines. -Know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles. Support: Classify these quadrilaterals Which regular polygons tessellate? -Distinguish between and estimate the size of (Using Geostrip triangles) can you acute, obtuse and reflex angles. make a different triangle from the -Identify parallel and perpendicular lines. same three strips? Repeat for a -Use correctly the vocabulary, notation and quadrilateral. labeling. Find 2 shapes with an area of ___ but -Calculate angles on a straight line and around a with different perimeters. point Can parallel lines be curved? -Calculate angles in a triangle. Can you have an obtuse / reflex angle in a triangle? Can you cut a triangle into 4 quadrilaterals and a triangle? Can you cut a triangle into quadrilaterals only, without putting new corners on the sides of the triangle? Extension: -Review, identify and use angle, side and symmetry properties of triangles and quadrilaterals. -Solve geometric problems using side and angle properties of equilateral, isosceles and rightangled triangles and special quadrilaterals. -Visualize and sketch 2-D shapes in different orientations using ICT -Identify and use the geometric properties of triangles, quadrilaterals and other polygons to solve problems. -Explain and justify inference and deductions using geometric reasoning Keywords are used and spelt Correctly. Writing the meaning for the keywords. Polygons, hexagon, octagon, line of symmetry, adjacent, perpendicular, acute, obtuse, reflex and right angles, parallel lines Describing visualisations of shapes, movements and constructions -Writing short and extended responses TenQQ Level Ladders Geometrical reasoning Beyond the Classroom Angles Mymaths http://www.mymaths.co.uk/i ndexLog.asp?h=74272 AUTUMN HALF TERM TEST (1 lesson) Week SPRING Learning outcomes: Success Criteria: (Key Questions :) TERM 2 1 Angles and Polygons Continuation from Spring Term 1 week 6. Continuation from Spring Term 1 week 6. Resources: Maths Frame-working Textbooks: 1.1, 1.2, 1.3 Keywords Literacy Assessment Numeracy Differentiation: HW: Once a week lasting 45 minutes Support: Continuation from Spring Term 1 week 6. 9 Extension: Continuation from Spring Term 1 week 6. See Spring Term 1 week 6. 2-4 Interpreting Data 5-6 Equations and Formulae -Review of Planning Statistical Projects & Processing and Representing Data from Autumn Term 2 weeks 5 – 7 must be done before mini-investigation. -Calculate statistics for small sets of discrete data: • find the mode, median and range, and the modal class for grouped data • calculate the mean, including from a simple frequency table, using a calculator for a larger number of items. -Compare two simple distributions using the range and one of the mode, median or mean. -Interpret pie charts. -Given a problem that can be addressed by statistical methods, suggest possible answers. -Decide which data would be relevant to an enquiry and suggest possible sources. -Write a short report of a statistical enquiry, including appropriate diagrams, graphs and charts, using ICT as appropriate; justify the choice of presentation. -Construct and solve simple linear equations with integer coefficients (unknown on one side only) using an appropriate method (e.g. inverse operations). -Use simple formulae from mathematics and other subjects; substitute positive integers into linear expressions and formulae and, in simple cases, derive a formula What is an appropriate graph / chart for this? Why? Can the mean = median = mode? What do the scales mean? Is it more efficient to use ICT here? Are scatter diagrams appropriate for these data? What does the graph tell you? Why would you choose to use ICT here? Why is this graph misleading? Does this piece of data fit the trend? If not, can you think of a reason why it doesn’t? Give examples of discrete / continuous / primary / secondary data What do these words mean: hypothesis, discrete, continuous, sample? What is an appropriate graph / chart for this? Why? What do the scales mean? Is it more efficient to use ICT here? What does the graph tell you? What is wrong with this graph/chart? Why is this graph misleading? Does this piece of data fit the trend? If not, can you think of a reason why it doesn’t? The answer is 2x+5y. What is the question? The answer is 4n-12. What is the question? Find five expressions equivalent to 2y = 6x+4 Why are x, x2, x3 not like terms? Consider m, m2, m3. Show me a formula involving a and b such that when you substitute a = 2 and b = 7 into the formula you get 18. Show me a formula involving a and b such that when you substitute a = -2 and b = 3 into the formula you get 18. What is wrong: 3(b+1) = 3b + 1 10(p -4) = 10p - 6 -2 (3 - f) = -6 -2f 8 – (n – 1) = 7 – n Convince me that: 2(x+7) = 2x + 14 5(y -4) = 5y - 20 Support: Extension: -Review of Planning Statistical Projects & -Review of Planning Statistical Projects & Processing and Representing Data from Processing and Representing Data from Autumn Autumn Term 2 weeks 5 – 7 must be done Term 2 weeks 5 – 7 must be done before minibefore mini-investigation. investigation. -Find the mode, median and range of a small set of -Find the mode and range of a small set of discrete data. discrete data -Find the median for a small set of discrete data -Recognise when it is appropriate to use the -Begin to find the mean of a small set of discrete median or the mode. -Calculate the mean for a small set of discrete data data. -Use tally charts and frequency tables to record -Calculate statistics and solve problems involving non-grouped data the mean. -Understand the concept of grouped data -Record non-grouped data in frequency tables. -Interpret pie charts. -Calculate the mean for a frequency table of non-Decide which data would be relevant to an grouped data. enquiry and suggest possible sources. -Interpret diagrams and charts, including pie -Decide how to collect and organise data. charts. -Design a data collection sheet. -Draw simple conclusions based on the shape of -Construct frequency tables. the graphs and find simple statistics for a single -Collect and record a small set of data from an distribution. experiment. -Given a problem that can be addressed by -Draw bar charts, bar-line graphs and statistical methods, suggest possible answers. pictograms to represent data. -Decide which data would be relevant to an enquiry and determine the degree of accuracy needed. Data, mode, median, range, average, mean, sum, frequency, event, frequency table, pictogram, bar chart, bar-line graph, pie chart, compound bar chart Support: -Understand that algebraic operations follow the same conventions and order as arithmetic operations. -Substitute positive integers into simple linear expressions. -Recognize that algebraic operations follow the same conventions and order as arithmetic operations. -Solve simple linear equations with integer coefficients using inverse operations. -Solve simple linear equations with integer coefficients using inverse operations Keywords are used and spelt Correctly. 10 Extension: -Begin to solve simple linear equations with the unknown on one side only. -Solving simple linear equations with integer coefficients with the unknown on one side only. -Solve simple equations with brackets. -Solve simple linear equations with integer coefficients with the unknown on both sides. -Derive simple algebraic expressions and formulae. -Explore ways of constructing simple equations to express relationships TenQQ Level Ladders Processing, representing and interpreting data Beyond the Classroom Line graphs Selecting and constructing graphs and charts Mymaths http://www.mymaths.co.uk/i ndexLog.asp?h=74272 Writing the meaning for the keywords. Substitute, simplify, expression, expanding brackets, equation, solve, equals, inverse operations, balancing, unknown, balance, formula, formulae, variable Level Ladders Equations, formulae, identities Mymaths http://www.mymaths.co.u k/indexLog.asp?h=74272 SUMMER Week Learning outcomes: TERM 1 1 Powers and Roots - Recognise the squares of numbers to at least 12 × 12 and the corresponding roots. -Use squares and positive and negative square roots. -Use the function key for sign change, powers and roots. -Use a calculator to find a square root. -Find square roots of multiples of 100 and 1000 by factorizing. -Recognise the first few triangular numbers Success Criteria: (Key Questions :) Resources: Maths Frame-working Textbooks: 1.1, 1.2, 1.3 Keywords Literacy Assessment Numeracy Differentiation: HW: Once a week lasting 45 minutes Support: What happens when you raise a number to a negative / fractional -Use a calculator to find the squares of whole power? numbers up to 10. Can every cube of a number be -Recognise the square root as the inverse of the written as the difference of two square. squares? -Find a square roots both mentally, and using a Multiply the triangular numbers by 8 calculator. and add 1. What numbers do you get? Why? Is there a pattern in the prime numbers? Which is bigger ab or ba? How do you decide? Which numbers have an odd number of factors. Why? What numbers multiplied by themselves give 36? Can a square have area 45? Extension: -Recognise squares of numbers 1 to 12, and their corresponding square roots. -Find square roots of multiples of 100 and 1000 by factorizing. -Know how to work out squares of numbers greater than 12. -Use a calculator to find a square and a square root. -Use squares and positive and negative square roots. -Use the function key for sign change, powers and roots Keywords are used and spelt correctly. -Writing the meaning for the keywords -explaining calculation strategies and talking about methods for the solution of problems -reasoning in working towards a solution and justifying results -comparing different mathematical processes for their efficiency and effectiveness -talking about mathematical expressions using mathematical and nonmathematical language Integer, positive, negative, square, power, square root, cube, cube root, index, indices. Mymaths http://www.mymaths.co.uk/in dexLog.asp?h=74272 http://www.mymaths.co.uk/ta sks/library/loadLesson.asp?tit le=powers/squareNumbers&t askID=1053 11 2-3 Factors, Multiples and Primes -Recognise and use multiples. -Find the lowest common multiple of two numbers. -Understand the significance of a counter example. -Use simple tests of divisibility. -Find the factors of a number by checking for divisibility. -Find all the pairs of factors of a number. -Find the highest common factor of two numbers. -Recognise prime numbers up to 100. -Explore links between factors and primes. -Recognise the first few triangular numbers. What patterns arise when you multiply Support: consecutive pairs / triples? -Know simple test for divisibility. 182 is the product of 2 consecutive -Recognise and use factors. integers, but the answer is not unique. -Find all the pairs of factors of whole numbers. Find both products -List the factors of a number. Are the prime factors of a number -Understand the concept of a prime number. unique? -Know the prime numbers up to 30. Is the prime factor decomposition of a -Explore links between factors, primes, number unique? multiples. When finding prime factor decompositions using the ‘tree’ method, does it matter how you break down the starting number? 12 Extension: -Recognise and use multiples. -Find the lowest common multiple of two numbers. -Use simple tests of divisibility. -Use knowledge of common multiples to test for divisibility by numbers greater than 10. -Understand the significance of a counter example. -Find the factors of a number by checking for divisibility -Find all the pairs of factors of a number. -Find the highest common factor of two numbers. -Use factors to make multiplications simpler. -Recognise prime numbers up to 100. -Explore links between factors and primes. -Find the prime number decomposition of a number. Keywords are used and spelt Correctly. Writing the meaning for the keywords Multiple, common multiple, lowest common multiple, divisible, divisibility, factor, factor pairs, common factors, highest common factor, prime number, squared, square number, square root, power, inverse, estimate, subtraction, tenths, hundredths, division, divisor, remainder, counter example. Real –life problems (worded problems) Kangaroo Assessment (level ladders). Powers, integers, roots Mymaths http://www.mymaths.co.uk/in dexLog.asp?h=74272 4-5 Transformations (To extend to Enlargements and Scale Factors) -Use accurately the language and notation associated with reflection. -Recognise and visualise reflection in given mirror lines of a 2-D shape. -Explore the line symmetry of 2-D shapes. -Use accurately the language and notation associated with rotation. -Recognise and visualise rotation about a given point of a 2-D shape. -Explore the rotation symmetry properties of 2-D shapes. -Use accurately the language and notation associated with translation of 2-D shapes. -Recognise and visualise translation of a 2-D shape. -Enlarge 2-D shapes given a centre of enlargement and a positive whole number scale factor. -Define transformations of shapes on a coordinate grid. -Draw simple transformations on a coordinate grid. -Explore transformations using ICT. Where do you think the enlargement will be? What is wrong with this enlargement? What does the centre of enlargement mean? What is the scale factor of this enlargement? Does a rectangle have four lines of symmetry? When enlarging on a coordinate grid: What connections are there between the coordinates of corresponding vertices? Find a shape with ‘x’ lines of symmetry and ‘y’ order of rotational symmetry What effect does enlargements have on angles? Why are plugs in sinks circular? What shapes do babies learn to put in shape-sorters first? Why? What are the key pieces of information needed to complete the following: -a rotation; -a reflection; -a translation; - an enlargement. Support: -Recognise reflection symmetry. -Explore the line symmetry of 2-D shapes. -Use accurately the language and notation associated with reflection. -Recognise and visualise reflection in given mirror lines of a 2-D shape. -Use accurately the language and notation associated with rotation. -Recognise and visualise rotation about a given point of a 2-D shape. -Explore rotation using ICT. -Explore the rotation symmetry properties of 2-D shapes. -Use accurately the language and notation associated with translation of 2-D shapes. -Recognise and visualise translation of a 2-D shape. -Define simple transformations of shapes on a coordinate grid (first quadrant only). 13 Extension: -Understand and use the language and notation associated with reflection and rotation. -Recognise and visualise reflection in given mirror lines of a 2-D shape. -Recognise and visualise rotation about a given point of a 2-D shape. -Explore reflection and rotation using ICT. -Explore the line symmetry of 2-D shapes. -Explore the rotation symmetry properties of 2-D shapes. -Use accurately the language and notation associated with translation of a 2-D shape. -Transform 2-D shapes by simple combinations of reflections, rotations and translations, on paper and using ICT. -Understand and use the language and notation associated with enlargement. -Enlarge 2-D shapes given a centre of enlargement and a positive whole number scale factor. -Make simple scale drawings. -Define transformations of shapes on a coordinate grid. -Draw simple and combined transformations on a coordinate grid. Keywords are used and spelt Correctly. Writing the meaning for the keywords. Equivalent points, perpendicular bisector, mirror line, reflection, symmetrical, line of symmetry, reflection symmetry, rotate, rotation, centre of rotation, clockwise, anticlockwise, order of rotation, translation, object, image, inverse, transformation, tessellation, enlargement, scale factor, centre of enlargement, scale drawing Level Ladders Transformations Geometrical reasoning Beyond the Classroom Coordinates in four quadrants Transforming shapes Enlargement (positive integer scale factor) Transformations Mymaths http://www.mymaths.co.uk/in dexLog.asp?h=74272 SUMMER Week Learning outcomes: Success Criteria: (Key Questions :) TERM 2 1-2 Probability -Use vocabulary and ideas of probability, drawing on experience. -Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts; identify all the possible mutually exclusive outcomes of a single event -Estimate probabilities by collecting data from a simple experiment and recording it in a frequency table; - compare experimental and theoretical probabilities in simple contexts. The probability it will rain tomorrow is ½ - True or False? Why? How can you decide how many outcomes there will be? If I flip a coin 1000 times will I get 500 heads? If you repeat an experiment, will you always / sometimes / never get the same result? Design an experiment that will give probabilities of 1/3, 1/2, 2/5 etc. Selection (say 10) of different coloured counters in a bag. Pick and replace several times. At each pick, what do you think the colours of the 10 counters are? How can we be even more sure? How can you make a game fair? A coin is flipped 10 times and you get 2H and 8T, is this coin biased? Resources: Maths Frame-working Textbooks: 1.1, 1.2, 1.3 Keywords Literacy Assessment Numeracy Differentiation: HW: Once a week lasting 45 minutes Support: -Use vocabulary and ideas of probability, drawing on experience. -Understand and use the probability scale from 0 to 1. -find and justify probabilities based on equally likely outcomes in simple contexts. -Relate the frequency of an outcome to its probability. -Decide if an experiment or game is fair or unfair. 14 Extension: -Find and record all possible mutually exclusive outcomes for two successive events using tree diagrams. -Collect data from a simple experiment and record in a frequency table. -Estimate probabilities based on this data. -Understand that if an experiment is repeated there may be, and usually will be, different outcomes. -Compare experimental and theoretical probabilities in simple contexts. -Understand that increasing the number of times that an experiment is repeated generally leads to better estimates of probability. Keywords are used and spelt Correctly. Writing the meaning for the keywords outcome, random, estimated probability, frequency, expected probability, experimental probability Real –life problems (worded problems) (level ladders). C:\Users\ahall11.316\App Data\Local\Microsoft\Wind ows\Temporary Internet Files\Content.Outlook\N6U 6YZ5I\resources\other\cor nwall_progression\sow_pr obability.docProbability Beyond the Classroom Probability The probability scale Experiments Mymaths http://www.mymaths.co.uk/in dexLog.asp?h=74272 3-4 Construction and Loci -Use a ruler and protractor to: • measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree. - construct a triangle, given two sides and the included angle (SAS) or two angles and the included side (ASA). -Use ICT to explore constructions: Explore transformations and symmetries using ICT. -Use a ruler and protractor to construct quadrilaterals. Show me an estimate of an angle. -Show how you can construct an angle of 30 / 45 / 75 with just a straight edge and compasses. -What regular polygons can you construct just using straight edge and compasses? -Show me an example of: A point equidistant from these two points, and another and another …. A point a metre from …. 5 REVISION & END OF YEAR EXAM WEEK Revision & Exams. 6 -7 - - 3D Shapes -Use squares and rectangles to visualise cubes and cuboids. -Use other 2-D representations to visualise 3-D shapes and deduce some of their properties. -Draw 2-D representations of 3-D shapes. -Know what the nets of cubes, cuboids and tetrahedrons look like. -Investigate the nets of cubes and cuboids. -Calculate the surface area & volume of shapes made from cubes and cuboids (review of area & volume). -Use ruler and protractor to construct simple nets of 3-D shapes, e.g. cuboid, regular tetrahedron, square-based pyramid, triangular prism Show me a net of a i) cube ii) cuboid iii) prism iv) pyramid -True/Never/Sometimes: 3-D shapes have more than one net -Convince me that: a cube has at least five different nets a cuboid has at least five different nets a triangular prism has at least two different nets -Given 2 elevations (or 1 elevation and a plan) of a 3-D shape, what could the shape be? -Show me: a solid with a plan that is square. a solid with front and side elevations that are all triangles. a solid with front and side elevations that are all triangles and a square plan Draw a solid with an volume of 12cm³ and another… and another Find a cuboid with a surface area of 24cm³ and another… and another What unit would you choose to measure ______? Why? Support: -Review, identify and use angle, side and symmetry properties of triangles and quadrilaterals. -Review conventions and notation for 2-D coordinates in all four quadrants. -Review coordinates of points determined by geometric information. -Use a ruler and protractor to: • measure and draw lines to the nearest millimetre and angles, including reflex angles, to the nearest degree. -Use Logo to explore constructions of triangles and quadrilaterals. -Explore transformations and symmetries using ICT. Extension: -Use ICT to explore constructions: Explore transformations and symmetries using ICT. -Construct a triangle, given two sides and the included angle (SAS) or two angles and the included side (ASA). -Draw quadrilaterals, given two sides and an angle, or two angles and a side, using a ruler and protractor. -Draw quadrilaterals, given three sides of their constituent triangles, with a ruler and compasses. Support: Revision & Exams. Extension: Revision & Exams. Support: -Use squares to visualise cubes and shapes made from cubes. Extension: -Use other 2-D shapes to visualise 3-D shapes and deduce some of their properties. -Use other 2-D representations to visualise 3-D shapes and deduce some of their properties. -Draw 2-D representations of 3-D shapes. -Investigate the nets of cubes and cuboids. -Draw 2-D representations of 3-D shapes. -Identify nets for a closed cube and cuboid. -Calculate the surface area & volume of shapes made from cubes and cuboids (review of area & volume). -Construct nets for a closed cube and cuboid. -Identify different nets for an open cube and a cuboid. -Use a ruler, protractor and compasses to construct simple nets of 3-D shapes The Royal Docks Community School Medium Term Plan 15 Describing visualisations of movements and constructions -Discussing which mathematical equipment and materials to use - Solve worded problems involving Construction and Loci Equilateral, isosceles, right angled, scalene, symmetrical, parallelogram, rhombus, kite, arrowhead, trapezium, protractor, acute, obtuse, reflex, vertex, construct, draw, sketch, clockwise, anticlockwise, exterior, interior, alternate, corresponding, vertically opposite, bisector, compasses, equidistant Kangaroo Assessment (level ladders). Construction, loci Beyond the Classroom Properties of shapes Mymaths http://www.mymaths.co.uk/in dexLog.asp?h=74272 Keywords are used and spelt Correctly. Writing the meaning for the keywords. area, face, edge, vertex, vertices, cube, cuboid, 3-D, surface area, net. Mini- investigation on polygons & 3-D shapes. Mymaths http://www.mymaths.co.uk/in dexLog.asp?h=74272 Unit Title: Numbers 1, Algebra1, Geometry1, Statistics1 Length of Unit: 32 Hours (8 weeks) Unit Aims: To develop numbers and algebra skills. Unit Outcomes: Week Learning outcomes: Success Criteria: Differentiation: Assessment opportunities: Literacy opportunities / Functional Skills Keywords: Numeracy Opportunities/ Core Skills Resources: Kangaroo Assessment (level -Multiply and ladders) stage 3 divide integers Place value, and decimals by rounding 0.1 and 0.01 -Recognise the effect of multiplying and dividing by a number less than 1. -Multiply and divide by any integer power of 10. -Understand the effect of multiplying and dividing by numbers between 0 and 1. -Round positive numbers to any given power of 10. -Round decimal numbers to the nearest whole number or to one, two or three decimal place. -Keywords are used and spelt correctly. Integer, positive, negative, number line, inverse, product, index, indices, Multiplying, dividing, decimals, Round. TenQQ (Starter & plenaries) -Rounding Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension Extension: -Keywords are used and spelt correctly. (Key Questions :) Term 1A Week 1 and 2 Place value, Integers, Ordering & Rounding . -Add and subtract, multiply and divide integers -Read and write positive integer powers of 10; -multiply and divide integers and decimals by 0.1, 0.01 -Order decimals -Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal places Support: True / Never / Sometimes: To multiply by 100, you move the digits two places to the left To multiply by 100, you move the digits two places to the right To divide by 100, you move the digits two places to the left To divide by 100, you move the digits two places to the right To divide by 100, you move the decimal point two places to the left To divide by 100, you move the decimal point two places to the right What is the same/different about 46 10, 4600 ÷ 10, 46 100 and 4600 ÷ 100 Find a number between 4.35 and 4.362. And another, and another Convince me: that 7900 ÷ 10 = 790 that 250 ÷ 10 and 2500 ÷ 100 give the same answer. how to multiply a number by 10. -how to divide a number by 100. Week 3 Powers and roots -Use squares, positive and negative square - Why are square numbers called square numbers? -Understand negative numbers as positions on a number line. -Add and subtract positive and negative integers in context. -Order decimals by comparing digits. -Order decimals by positioning them on a number line. -Round positive numbers to any given power of 10. -Round decimal numbers to the nearest whole number or to one or two decimal places. -Multiply and divide integers and decimals by 10, 100 and 1000, and explain the effect. Support: - Recognise square Extension: Kangaroo Assessment (level ladders) stage 1 16 -Writing the meaning for the keywords -Level Up Texts 3-5 4-6 5-7 -Real –life problems (worded problems) -Using talk to Mathswatch Worksheets explain and present ideas -Active listening to understand 10 ticks -Reading for information TenQQ (Starter & plenaries) Kangaroo worksheets Integer, positive, negative, square, power, square TenQQ (Starter & plenaries) Collins Maths Frameworking: Pupil Books Homework: roots, cubes and cube roots, -index notation for small positive integer powers -Use a calculator to find squares and cubes, know that 100 =102, 1000 = 103, 1 million = 106 -Use the cube and cube root keys on a calculator if available. Week 4 and 5 Angles and polygons -Identify alternate angles and corresponding angles; understand a proof that: the angle sum of a triangle is 180°and of a quadrilateral is 360° the exterior angle of a triangle is equal to the sum of the two interior opposite angles -Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties -Know that if two 2-D shapes are congruent, corresponding sides and angles are equal -Which is bigger ab or ba? How do you decide? -Which numbers have an odd number of factors. Why? -Can a square have area 45? -Give me three factors of 26? -What numbers multiplied by themselves give 36? -Which has the greatest value (23)4 or (24)3 ? -What happens when you raise a number to a negative power? -What happens when you raise a number to a fractional power? -Why are these called alternate angles? -Why are these called corresponding angles? -How do you know this is true? -Can you cut a triangle into 4 quadrilaterals and a triangle? -Can you cut a triangle into quadrilaterals only, without putting new corners on the sides of the triangle? -What reasoning links 'Angles on a straight line are 180°' to 'Vertically opposite angles are equal'? -Are there other links? -Why are the geometrical facts organised in this particular order, starting at the top and working down the chart? -What are the links and arrows intended to show? -Can you explain how to use the given facts to deduce that (a) vertically opposite angles are equal (b) alternate angles are equal? numbers and their corresponding square roots. -Use a calculator, including the square root key, to find square roots, rounding as appropriate. Support: -Know the sum of angles at a point, on a straight line and in a triangle. -Use angle measure; distinguish between and estimate the size of acute, obtuse and reflex angles. -Use a ruler and protractor to measure and draw lines to the nearest millimeter and angles, including reflex angles, - Use index notation for integer powers. -Use simple instances of the index laws. -Use a calculator to find squares and cubes, know that 100 =102, 1000 = 103, 1 million = 106 -Use the cube and cube root keys on a calculator if available. Extension: -Explain how to find, calculate and use: the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons. -Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons. -Explain how to find, calculate and use: the interior and exterior angles of regular polygons. -Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons. -Know that if two 2-D shapes are congruent, corresponding Powers, integers, roots http://www.myma ths.co.uk/tasks/lib rary/loadLesson.a sp?title=powers/s quareNumbers&ta skID=1053 Kangaroo Assessment (level ladders) stage 3 Geometrical reasoning Angles -Writing the meaning for the keywords -explaining calculation strategies and talking about methods for the solution of problems -reasoning in working towards a solution and justifying results -comparing different mathematical processes for their efficiency and effectiveness -talking about mathematical expressions using mathematical and non-mathematical language -Keywords are used and spelt correctly. root, cube, cube root, index, indices. Acute, right, obtuse, reflex, protractor, line segment, ruler, -Writing the parallel, alternate, meaning for the corresponding, keywords opposite, interior, exterior, -Describing parallelogram, visualisations of rhombus, shapes, isosceles, movements and trapezium, kite, constructions arrowhead, -Writing short and pentagon, hexagon, extended polygon. responses http://www.mymat hs.co.uk/tasks/libra ry/loadLesson.asp?t itle=powers/square Numbers&taskID= 1053 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets TenQQ (Starter & plenaries) http://www.mymat hs.co.uk/gold/angle s/Angler.html?guid ={911FFA5A5E78-410A-AE226961647055A7} Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets 17 sides and angles are equal. -Solve geometric problems using congruent triangles. Week 6 Probabilit y Week 7 and 8 Fractions and decimals -Interpret the results of an experiment using the language of probability; appreciate that random processes are unpredictable -Know that if the probability of an event occurring is p then the probability of it not occurring is 1 − p; use diagrams and tables to record in a systematic way all possible mutually exclusive outcomes for single events and for two successive events -Compare estimated experimental probabilities with theoretical probabilities, recognising that: • if an experiment is repeated the outcome may, and usually will, be different • increasing the number of times an experiment is repeated generally leads to better estimates of probability. -The probability it will rain tomorrow is ½ - True or False? Why? -How can you decide how many outcomes there will be? -If I flip a coin 1000 times will I get 500 heads? -If you repeat an experiment, will you always / sometimes / never get the same result? -Design an experiment that will give probabilities of 1/3, 1/2, 2/5 etc. -Selection (say 10) of different coloured counters in a bag. Pick and replace several times. At each pick, what do you think the colours of the 10 counters are? How can we be even more sure? -How can you make a game fair? -A coin is flipped 10 times and you get 2H and 8T, is this coin biased? -Give me examples of mutually exclusive events. -Convert fractions to decimals with or without a calculator, and vice-aversa -Recognise that a recurring decimal is a fraction; use division to convert a fraction to a decimal; -order fractions by writing them with a common denominator or by converting them to decimals -Add and subtract fractions by writing -If you know that 1/5 = 0.2, what else can you deduce? -If you know that 1/8 = 0.125, what else can you deduce? -Find a unit fraction that is the sum of two other unit fractions. How many can you find -Find a fraction that is between ½, and ¾. How did you find this? -Show me a pair of fractions which have a sum / difference of 4/7. Extend to fractions which Support: -Understand and use the probability scale from 0 to 1. -Find and justify probabilities based on equally likely outcomes in simple contexts. -Find and record all possible mutually exclusive outcomes for single events and two successive events, using diagrams and tables. -Collect data from a simple experiment and record in a frequency table. -Compare experimental and theoretical probabilities in simple contexts. Support: -Identify equivalent fractions. -Simplify fractions by cancelling all common factors. -Convert terminating decimals to fractions. -Use division to convert a fraction to a decimal, with Extension: -Use the language of probability when interpreting the results of an experiment. -Identify all the mutually exclusive outcomes of an experiment. -Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems. -Appreciate that random processes are unpredictable. -Compare experimental and theoretical probabilities in a range of contexts. -Appreciate the difference between mathematical explanation and experimental evidence. Kangaroo Assessment (level ladders) stage 3 -Keywords are used and spelt correctly. Probability The probability scale Experiments Finding outcomes Using mutually exclusive outcomes -Writing the meaning for the keywords Extension: -Recognise that a terminating decimal is a fraction -Convert decimals (up to 3pl) to fractions, Recognise that a recurring decimal is a fraction. -Interpret the display on a calculator. -Use division to convert a fraction to a decimal, Kangaroo Assessment (level ladders) stage 2 Fractions Percentag es Ratio Ratio and proportio n -Read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Data -Writing short and Event, probability scale, random, theoretical, outcome, sample space, diagram, tally, frequency, estimate, biased, experimental, tree diagram, theoretical probability, estimated probability, unpredictable, reliable, mutually exclusive, bias. TenQQ (Starter & plenaries) http://www.mymat hs.co.uk/tasks/libra ry/loadLesson.asp?t itle=probability/pro babilityRevision&t askID=1263 Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks extended TenQQ (Starter & plenaries) responses Kangaroo worksheets 18 -Exploring mathematical concepts -Explaining calculation strategies and talking about methods for the solution of problems -Reasoning in working towards a solution and justifying results Equivalent fractions, numerator, denominator, cancel, simplify, simplest form, decimal, fraction, improper/mixed fraction, recurring decimal. Equivalent fraction, common denominator, improper fraction, mixed number, fraction, per cent, percentage, http://www.mymat hs.co.uk/tasks/libra ry/loadLesson.asp?t itle=fractions/equiv alentFractions&tas kID=1042 Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets them with a common denominator; -calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction -Multiply a fraction by a fraction using cancelling. -Use cancellation to simplify the product of two fractions. -Divide a fraction by a fraction, interpreting division as a multiplicative inverse. Term 1B Week 1 and 2 Percentag es -Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another; -Calculate percentage of numbers, quantities and measurements using written methods. -Calculate percentages of numbers, quantities and measurements using a calculator. -calculate percentages and find the outcome of a given percentage increase or decrease do not have the same denominator -Show me: o a pair of fractions with a sum of 4/7 o a pair of fractions with a difference of 3/8 o a fraction and a quantity such that the answer is 8cm -Convince me: o that 4/7 + 3/8 = 53/56 that 4 ÷ 2/5 = 10 -Which percentages/ decimals / fractions are easiest to convert? Why? -To find 10% you divide by 10. Why don’t you divide by 20 to find 20%? -80 pupils go on a school trip. 25% are girls. How can you work out the number of boys. -Explain mental methods for finding common percentages of a quantity – e.g. 331/3%, 17½%, 20% and without a calculator. -Order fractions by writing them with a common denominator. -Order fractions by converting them to decimals. -Add and subtract fractions by writing them with a common denominator. -Calculate fractions of quantities (including fraction answers). -Multiply an integer by a fraction. without and with a calculator. -Add and subtract fractions by writing them with a common denominator -Calculate fractions of quantities -Multiply a fraction by a fraction -Divide an integer by a fraction -Use cancellation to simplify the product of a fraction and an integer. -Divide a fraction by a fraction, interpreting division as a multiplicative inverse. Support: -Understand percentage as the ‘number of parts per 100’. Convert percentages to decimals -Calculate simple percentage of quantities -Find the outcome of percentage changes. -Solve problems involving percentage changes using (a) a unitary method, (b) inverse operations. hundredths, cancel, numerator, decimal, 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets Kangaroo Assessment (level ladders) stage 2 Fractions Percentag es Ratio Ratio and proportio n -Exploring mathematical concepts -Explaining calculation strategies and talking about methods for the solution of problems -Reasoning in working towards a solution and justifying results -Comparing different solutions in order to arrive at a correct solution Percentage, decimal, amount, unitary method, percentage increase, percentage decrease. http://www.mymat hs.co.uk/tasks/libra ry/loadLesson.asp?t itle=fractions/equiv alentFractions&tas kID=1042 -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks -Use the multiplication grid to find other ratios in the family 8:12 and 14:42. What do the ratios have in common? Week 3 and 4 -Use the equivalence of fractions, decimals and percentages to compare proportions -Ratios related to age and Support: how they change over -Use direct time: e.g. if Josh and Beth proportion in are 1 and 4, £200 will be Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension TenQQ (Starter & plenaries) Extension: -Solve simple problems Kangaroo Assessment (level ladders) stage 2 Fractions 19 -Keywords are used and spelt correctly. Direct proportion, proportion, ratio, cancel, strategy, multi-step, NRICH Kangaroo worksheets Collins Maths Frameworking: Pupil Books 2.1Support Ratio and proportio n Week 5 Units of measure ments Week 6 and 7 Perimeter , area, surface area and Volume -Apply understanding of the relationship between ratio and proportion; -simplify ratios, including those expressed in different units, recognising links with fraction notation; -divide a quantity into two or more parts in a given ratio; -use the unitary method to solve simple problems involving ratio and direct proportion -Choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts; know rough metric equivalents of imperial measures in common use, such as miles, pounds (lb) and pints -Derive and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound shapes -Know and use the formula for the volume of a cuboid; calculate split in the ratio 1:4 now. simple What about next year etc. contexts etc.? -Understand the idea of ratio and use ratio notation. -Simplify a ratio -Understand the relationship between ratio and proportion. -Use ratio and proportion to solve simple problems. -Divide a quantity into two parts in a given ratio. -How do you know which is the base and height? -Find shapes with a perimeter of 11cm -Find another measurement that is the same as 3m -How we decide what each division on the scale represents? -Draw two different rectangles with an area of 8 squares? How about 7 squares? Why not? -Why is the area of a rectangle given by length times width? -A shape made from two rectangles has area 10cm2. Draw the shape. -How do you know which is the base and height? -Find six triangles with an area of 12cm2 -Find six parallelograms with an area of 48cm2 -How do you know which is the base and height? -Find shapes with a perimeter of 11cm -Find another measurement that is the same as 3m Support: -Read and interpret scales on a range of measuring instruments. -Solve problems in everyday contexts involving length, mass and time involving direct proportion. -Use proportional reasoning to solve a problem -Divide a quantity into two or more parts in a given ratio. -Solve simple problems using a unitary method. -Simplify a (three-part) ratio to an equivalent ratio by cancelling. -Recognise links between ratio and fraction notation. -Simplify as ratio expressed in different units -Compare two ratios of the form 1: m or m:1 Extension: -Choose and use units of measurement to measure, estimate, -know rough metric equivalents of imperial measures in common use, such as miles, pounds (lb) and pints -calculate and solve worded problems involving metric and imperial Percentag es Ratio Ratio and proportio n -Writing the meaning for the keywords -Read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Data efficient, unitary method, multiplier, conjecture, prove, justify, counter example, cancelling. Mixing Lemonade 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets Kangaroo Assessment (level ladders) stage 2 Measures Area and perimeter -Keywords are used and spelt correctly. -Writing the meaning for the keywords -Describing visualisations of shapes, movements and constructions -Discussing which mathematical equipment and materials to use tonne, metric, imperial, square millimetre (mm2), square centimetre (cm2), square metre (m2), square kilometre (km2), NRICH Estimating Angles On the Edge Fence It Hidden Dimensions Warmsnug Double Glazing Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Support: -Know and use the formula for the area of a rectangle. -Calculate the perimeter and area of shapes Extension: -Know and use the formulae for the circumference and area of a circle, including definitions of a circle. Kangaroo Assessment (level ladders) stage 2 Measures Area and perimeter 20 -Keywords are used and spelt correctly. -Writing the meaning for the keywords Area, perimeter, formula, base, height, perpendicular, circle, centre, circumference, arc, radius, diameter, NRICH Estimating Angles On the Edge Fence It Hidden Dimensions Warmsnug Double Kangaroo worksheets Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 volumes and surface areas of cuboids and shapes made from cuboids -How we decide what each division on the scale represents? -Draw two different rectangles with an area of 8 squares? How about 7 squares? Why not? -Why is the area of a rectangle given by length times width? -A shape made from two rectangles has area 10cm2. Draw the shape. made from rectangles. -Deduce and use a formula for the area of a triangle. -Calculate surface areas of cubes and cuboids. -Know and use Area and the formula for volume the area of a Circumference circle. and area of a -Solve problems circle involving circles. -Know and use the formulae for finding the area of triangles, parallelograms and trapezium, and compound shapes. -Know and use the formula for the volume of cuboids; calculate volumes of shapes made from cuboids. -Calculate the volume of right prisms. -Solve problems involving area and volume. -Discussing semicircle, sector, which radii. mathematical equipment and materials to use -Describing visualisations of shapes, movements and constructions -Writing short and Glazing 4-6 5-7 Mathswatch Worksheets 10 ticks extended TenQQ (Starter & plenaries) responses Kangaroo worksheets Term 2A Week 1 and 2 Creating & Manipula ting Algebraic Expressio ns -Recognise that letter symbols play different roles in equations, formulae and functions; know the meanings of the words formula and function -Understand that algebraic operations, including the use of brackets, follow the rules of arithmetic; use index notation for small positive integer powers -Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket -The answer is 2x+5y. What is the question? -The answer is 4n-12. What is the question? -True / Never / Sometimes: n2 = 2n -Show me an example of a formula expressed in words -What is the same/different about '£5 standing charge plus 5p for every minute' and ,Cost of phone bill = £5 standing charge plus 5p for every minute' -How can you change ‘Plumber’s bill = £40 per hour’ to include a £20 call-out fee -True/Never/Sometimes: A formula should have an equals sign in it -Convince me that there is only one solution to 'I think of a number and add 12. The answer is 17.' -Find five expressions equivalent to 2y = 6x+4 Support: -Understand that algebraic operations follow the same conventions and order as arithmetic operations Simplify algebraic expressions. -Multiply a single term over a bracket. -Know and use the distributive law. -Know how multiplication is represented in algebraic expressions. Extension: -Recognise that letter symbols play different roles in equations, formulae and functions; know the meanings of the words formula and function -Use index notation for integer powers and simple instances of the index laws. -Know how multiplication and division are represented in algebraic expressions. -Simplify or transform linear expressions by collecting like terms, multiply a single term over a bracket (to include unknown Kangaroo Assessment (level ladders) stage 2 Equations, formulae, identities Simple formulae -explaining calculation strategies and talking about methods for the solution of problems -reasoning in working towards a solution and justifying results -comparing different mathematical processes for their efficiency and effectiveness -talking about mathematical expressions using mathematical and non-mathematical language Expression, term, like terms, simplify, expand, brackets, More Number Pyramids Crossed Ends Number Pyramids Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets 21 Week 3 Planning Statistica l Projects -Discuss a problem that can be addressed by statistical methods and identify related questions to explore -Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources; consider appropriate sample size -Plan how to collect the data; construct frequency tables with equal class intervals for gathering continuous data and two-way tables for recording discrete data -Why are x, x2, x3 not like terms? Consider m, m2, m3. -Show me a formula involving a and b such that when you substitute a = 2 and b = 7 into the formula you get 18. -Show me a formula involving a and b such that when you substitute a = -2 and b = 3 into the formula you get 18. -What is wrong: 3(b+1) = 3b + 1 10(p -4) = 10p - 6 -2 (3 - f) = -6 -2f 8 – (n – 1) = 7 – n -Convince me that: 2(x+7) = 2x + 14 5(y -4) = 5y - 20 -What does average mean? -Why do we have more than one way of working out an average? -How can we represent a group of numbers, with a single number? -Can the mean = median = mode? -What do the scales mean? -What does the graph tell you? -Why would you choose to use ICT here? -Why is this graph misleading? outside the bracket) and two sets of brackets. -Use the equals sign appropriately and correctly. -Know and use the distributive law for multiplication. i.e. a(b+c) = ab+bc -Simplify or transform algebraic expressions by taking out single term common factors. Support: -Discuss a problem that can be addressed by statistical methods and identify related questions to explore. -Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources. -Plan how to collect the data, including sample size. -Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources. -Design and use simple two-way tables. -Discuss a problem that can be addressed by statistical methods and identify related questions to explore. -Plan how to collect data, including sample size. -Design a survey or experiment to capture the necessary data from 1 or more sources. -Determine the sample size and degree of accuracy needed Design, trial and refine Data collection sheets. -Classify data as discrete and continuous data. -Know how to group data. -Design, use & interpret 2-way tables. Kangaroo Assessment (level ladders) stage 2 Averages Processing, representing and interpreting data Graphs and diagrams NRICH Searching for (Mean)ing -Keywords are used and spelt correctly. -Writing the meaning for the keywords -Read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Data -Discussing and interpreting data and drawing conclusions -Writing short and extended responses -Presenting their findings to an audience 22 Two-way table, mode, frequency, median, mean, range, event, frequency table, distribution, statistics, class interval, modal class, modal group, stem-and leaf, scatter graph, assumed mean, compound barchart, pie chart, trend, discrete, continuous, primary source, secondary source. Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets Week 4 and 5 Function and Graphs Week 5 and 6 Coordin ate Geometr y -Generate terms of a linear sequence using term-to-term and position-to-term rules, on paper and using a spread sheet or graphics calculator -Use linear expressions to describe the nth term of a simple arithmetic sequence, justifying its form by referring to the activity or practical context from which it was generated -Express simple functions algebraically and represent them in mappings or on a spread sheet -Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT; recognise that equations of the form y = mx + c correspond to straight-line graphs -Construct linear functions arising from real-life problems and -Coordinates: ‘x is a cross, wise up’. What does this mean?! Does it help you? -I want to plot the graph of y=2x. What shall I do? -Find three lines that pass through 1 on the y-axis -Is the point (2, 4) on the line y=x+1 ? Explain your answer -What happens when the gradient gets bigger / smaller / negative? -Give me the co-ordinates of some points which can be joined to form a straight line Support: -Generate sequences from practical contexts and describe the general term in simple cases. -Generate terms of a simple sequence, given a rule -Generate terms of a simple sequence, given a rule for finding a term given its position in the sequence. -Express simple functions in symbols and words. -Draw mapping diagrams of linear functions. -Identify functions from mapping diagrams. -Know some of the properties of mapping diagrams. - Support: Recognise that equations of the form y = c and x = c correspond to straight-line graphs parallel to the x- and y- axes. -Generate coordinate Extension -Use linear expressions to describe the nth term of an arithmetic sequence justifying its form by referring to the activity or practical context from which it was generated. -Introduce the general term. -Know that an arithmetic sequence is generated by starting with a number a and adding a constant number d to the previous term. Continue familiar sequences (square numbers, powers of 10, 2 etc.) (Link to work on integers, powers and roots) Generate sequences by multiplying or dividing by a constant factor. -Draw mapping diagrams for linear functions. -Extend the mappings to include negative integers and fractional values. -Know some of the properties of mapping diagrams. . Extension: -Know and explain the reasons for m representing the gradient and c the y-intercept and y = mx + c a straight-t line graph. -Recognise that graphs of the form y=mx+c Sequences, functions and graphs -Give set of equations and set of graphs to match. How did you work it out? Using equations of straight lines, can you create a square? Explain what happens when two lines are perpendicular? Sequences, functions, graphs Graphs of linear functions -Discussing and interpreting data and drawing conclusions Sequences, nth term, term, term to term rule, Mapping, -Writing short and mapping diagram, extended coordinates, responses origin, x-axis, y-axis, graphs, points, equation, y-intercept, straight-line graphs, Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets Graphs of linear functions Coordinat es in the first quadrant Coordinat es in four quadrants 23 -Exploring mathematical concepts -Describing visualisations of shapes, movements and constructions gradient, parallel, quadrant, xcoordinate, ycoordinate, distance-time graph, rearrange, axis, distance, time, plot, speed Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 plot their corresponding graphs; discuss and interpret graphs arising from real situations, e.g. distance–time graphs Term 2B Week 1 and 2 -Understand and use the rules of arithmetic and inverse operations in the Number context of integers and Operation fractions s and -Use the order of Calculati operations, including on brackets, with more Methods complex calculations -Recall equivalent fractions, decimals and percentages; use known facts to derive unknown facts, including products involving numbers such as 0.7 and 6, and 0.03 and 8 -Use efficient written methods to add and subtract integers and -How can you check if your answer makes sense? [Last digits / estimating] -Can division ever make a number larger? -Can multiplication ever make a number smaller? -How do you choose an estimate to use? -In which order would you calculate 4 x 7 x 5? Why? -How would you work out 537 x 24? What would be the answer to 53.7 x 24? -This division calculation is incorrect 219.3 ÷ 8 = 274.125 How can you tell? pairs and plot graphs of simple linear functions using all four quadrants. -Read other coordinate pairs from a drawn graph. -Recognise that on graphs of the form y = mx + c, the values of the coordinates of each point satisfy the equation. -Plot graphs of linear functions using ICT. Recognise that graphs of the form y = mx + c intercept the y-axis at c. -Begin to identify the role of m in equations of the form y = mx + c. Plot graphs of simple linear functions on paper and using ICT. correspond to straight-line graphs and represent an infinite set of points. -Plot graphs of linear functions using ICT. -Find the gradient of straight-line graphs and the yintercept and hence find the equation of a straight-line graph. -Plot graphs of linear function (given y implicitly in terms of x i.e ay + bx = 0 or y + bx + c = 0) on paper and using ICT. -Construct linear functions arising from real-life problems and plot their corresponding graphs. -Read values off a graph and discuss trend and shape of the graphs. -Discuss and interpret distancetime graphs Support: -Recognise square numbers and their corresponding square roots. -Use a calculator, including the square root key, to find square roots, rounding as appropriate. -Know and use the order of operations, Extension: -Recognise inverse operations. -Use inverse operations to check results with and without a calculator. -Use the order of operations, including brackets, with more complex calculations. -Use the bracket keys on a calculator. Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets Kangaroo Assessment (level ladders) stage 2/3 Written methods Solving problems Multiplying and dividing Checking solutions 24 -explaining calculation strategies and talking about methods for the solution of problems -reasoning in working towards a solution and justifying results -comparing different mathematical processes for their efficiency and effectiveness -talking about mathematical expressions using Divisible, divisibility, multiple, factor pair, common multiple, tenths digit, hundredths digit, Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks decimals of any size, including numbers with differing numbers of decimal places -Use efficient written methods for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations including brackets. -Use the bracket keys on a calculator. -Consolidate standard column procedures for addition and subtraction of integers and decimals with up to 2 places. -Make and justify estimates and approximation s of calculations. -Develop standard written methods to divide a 3digit number by a 2-digit number. -Make and justify estimates and approximation s of calculations. -Check a result by considering whether it is of the right order of magnitude. -Develop standard written methods to divide decimals with 1 or 2 places by a 1-digit number. -Check a result by considering whether it is of the right order of magnitude. -Use factors to simplify -Evaluate expressions using nested brackets -Understand the effect of powers when evaluating an expression. -Calculate with complex mixed operations, including using the brackets keys on a calculator. -Consolidate standard column procedures for addition and subtraction of integers and decimals of any size, including a mixture of large and small numbers with differing numbers of decimal places. -Use standard column procedures for multiplication of decimals involving threedigit and twodigit numbers. -Understand where to position the decimal point for the answer. -Check a result by considering whether it is of the right order of magnitude and by working the problem backwards; Use inverses to check results. -Use standard column procedures for division of decimals. -Understand where to position the decimal point by considering equivalent calculations. -Check a result by considering whether it is of mathematical and non-mathematical language TenQQ (Starter & plenaries) Kangaroo worksheets 25 mental calculations. -Use partitioning to simplify mental calculations. Week 3 Transfor mations -Transform 2-D shapes by rotation, reflection and translation, on paper and using ICT -Try out mathematical representations of simple combinations of these transformations -Find a shape with ‘x’ lines of symmetry and ‘y’ order of rotational symmetry -Does a rectangle have four lines of symmetry? Support: -Understand and use the language and notation associated with reflections. -Recognise and visualise the reflection of a 2-D shape in given mirror lines. -Understand and use the language and notation associated with rotations. -Recognise and visualise the rotation of a 2-D shape about a given point. -Recognise and explore reflection symmetry. -Recognise and explore rotation symmetry. -Understand and use the language and notation associated with translations. -Recognise and visualise the translation the right order of magnitude and by working the problem backwards. -Use inverses to check results. -Consolidate and extend mental methods of calculation. -Use factors to simplify mental calculations. -Use doubling and halving strategies. Extension: -Transform 2-D shapes by simple combinations of rotations, reflections and translations on paper and using ICT. - Identify all the symmetries of 2D shapes. Kangaroo Assessment (level ladders) stage 3/4 Transforming shapes Transformation s -Keywords are used and spelt correctly. -Writing the meaning for the keywords -Exploring mathematical concepts -Describing visualisations of shapes, movements and constructions -Discussing which mathematical equipment and materials to use -Writing short and extended Reflect, mirror line, object, image, equivalent point, perpendicular bisector, rotation, angle of rotation, centre of rotation, clockwise, anticlockwise, symmetrical, line of symmetry, reflection symmetry, order of rotation, symmetry, transformation, translation, NRICH http://nrich.maths.o rg/5461/index http://nrich.maths.o rg/5459 http://nrich.maths.o rg/5461/index Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) responses Kangaroo worksheets 26 of a 2-D shape. -Transform 2D shapes using repeated reflections, rotations and translations, on paper and using ICT. Week 4 Enlarge ments and Scale Factors -Understand and use the language and notation associated with enlargement; enlarge 2D shapes, given a centre of enlargement and a positive integer scale factor; explore enlargement using ICT What effect does enlargement have on angles? -Why are plugs in sinks circular? What shape to babies learn to put in shape-sorters first? Why? -What are the key pieces of information needed to complete the following: - a rotation; - a reflection; - a translation; - an enlargement. -Where do you think the enlargement will be? -What is wrong with this enlargement? -What does the centre of enlargement mean? -What is the scale factor of this enlargement? -When enlarging on a coordinate grid: What connections are there between the coordinates of corresponding vertices? Support: Extension: Understand and use the language and notation associated with enlargement. Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor. -Understand and use the language and notation associated with enlargement; enlarge 2-D shapes, given a centre of enlargement and a positive wholenumber scale factor. -Identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments; recognise that enlargements preserve angle but not length. -Within the context of enlargement consolidate understanding of the relationship between ratio and proportion; -Reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation. -Understand the implications of enlargement for perimeter. -Know that if two 2-D shapes are congruent, corresponding Kangaroo Assessment (level ladders) stage 3/4 Transforming shapes Transformation s -Keywords are used and spelt correctly. -Writing the meaning for the keywords -Exploring mathematical concepts -Describing visualisations of shapes, movements and constructions -Discussing which mathematical equipment and materials to use -Writing short and extended enlargement, scale factor, centre of enlargement, similar, ratio, simplest form, proportion, congruent. NRICH http://nrich.maths.o rg/5461/index http://nrich.maths.o rg/5459 http://nrich.maths.o rg/5461/index Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) responses Kangaroo worksheets 27 sides and angles are equal. -Know that translations, rotations and reflections preserve length and angle and map objects on to congruent images. Week 5 and 6 Equations and Formulae -Construct and solve linear equations with integer coefficients (unknown on either or both sides, without and with brackets) using appropriate methods (e.g. inverse operations, transforming both sides in same way) -Use graphs and set up equations to solve simple problems involving direct proportion -Use formulae from mathematics and other subjects; substitute integers into simple formulae, including examples that lead to an equation to solve; -substitute positive integers into expressions involving small powers e.g. 3x2 + 4 or 2x3; derive simple formulae -Model incorrect solutions to equation solving: What is wrong with this? -Give me six equations with the same solution? How do you work this out? -If x3 + 2x = 30, give me two numbers x is between -How can you decide which is closest? How long would you continue this process? -Can an equation have more than one solution? -Can an equation have no solutions? -Why does the point of intersection show the solution to a pair of simultaneous equations? Link graphical and algebraic representations. Support: -Derive simple algebraic expressions. -Solve linear equations with integer coefficients (unknown on one side only). -Simplify expressions by collecting like terms. Solve linear equations of the forms x/a = b and ax/b = c, where a, b and c are positive integers. -Explore ways of constructing simple equations to express relationships. -Use formulae from mathematics and other subjects. -Substitute positive integers into simple formulae and find an unknown subject. -Derive algebraic expressions and formulae. Extension: -Construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equations, positive or negative solutions). -Solve equations involving a divisor both numerical and algebraic. -Understand and use inverse operations in terms of recognising a+i = c is the same as a= c – b. -Write different equivalent statements for real-life problems. -Explore general algebraic relationships for real-life problems. -Rearrange formula by making different unknowns the subject of the equation. -Explore the meaning of and substitute numbers into formulae. -In simple cases find an unknown where it is not the subject of the formula. Kangaroo Assessment (level ladders) stage 1-5 Equations, formulae, identities Simultaneous linear equations Inequalities in one variable -explaining calculation strategies and talking about methods for the solution of problems -reasoning in working towards a solution and justifying results -comparing different mathematical processes for their efficiency and effectiveness -talking about mathematical expressions using mathematical and non-mathematical language Expression, term, like terms, simplify, expand, brackets, substitution, equation, equal, solve, inverse operations, balance, formula, substitute, unknown, Index notation, squared, power, cubed, collecting, simplified, indices, analyse, factorise, formulae. NRICH Arithmago ns Negatively Triangular Mind Reading Think of Two Numbers Number Tricks Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets 28 Term 3A Week 1 and 2 Processi ng and Represen ting Data -Collect data using a suitable method (e.g. observation, controlled experiment, data logging using ICT) -Calculate statistics for sets of discrete and continuous data, including with a calculator and spreadsheet; recognise when it is appropriate to use the range, mean, median and mode and, for grouped data, the modal class -Construct graphical representations, on paper and using ICT, and identify which are most useful in the context of the problem. Include: • pie charts for categorical data • bar charts and frequency diagrams for discrete and continuous data • simple line graphs for time series • simple scatter graphs • stem-and-leaf diagrams What is an appropriate graph / chart for this? Why? -Can the mean = median = mode? -What do the scales mean? -Are scatter diagrams appropriate for these data? -What does the graph tell you? -Why would you choose to use ICT here? -Why is this graph misleading? -Does this piece of data fit the trend. If not, can you think of a reason why it doesn’t? -Give examples of discrete / continuous / primary / secondary data -Give an example of a survey for which your class would make a fair sample -Substitute values into formulae and solve the resulting equations. -Derive algebraic expressions and formulae. -Check by substituting in particular values. -In simple cases change the subject of a formula. -Collect the data using a suitable method such as observation, controlled experiment using ICT, or questionnaire. -Construct, on paper and using ICT, graphs and diagrams to represent data, including barline graphs and pie charts. -Draw and interpret line graphs. -Construct, on paper and using ICT, pie charts for categorical data. -Construct graphs and diagrams (including compound bar charts) to represent data and identify key features. -Identify which diagrams are most useful -Calculate statistics from data, using ICT as appropriate. -Find the mode, median and range of a small set of discrete data. -Collect data using a suitable method, such as observation, controlled experiment or questionnaire. -Construct, on paper and using ICT: -Pie charts for categorical data. -Bar charts and frequency diagrams for discrete data. -Frequency diagrams for continuous data. Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate. -Recognise when it is appropriate to use the range, mean, median & mode. -Construct and use stem-and-leaf diagrams. -Calculate a mean using an assumed mean. -Calculate statistics from a frequency table. -Construct on paper & using ICT scatter graphs. -Have a basic understanding of correlation. -Construct diagrams & graphs. Kangaroo Assessment (level ladders) stage 5 Processing, representing and interpreting data Working with grouped data Comparing distributions Kangaroo Assessment (level ladders) stage 4 Selecting and constructing graphs and charts Kangaroo Assessment (level ladders) stage 3 Averages Graphs and diagrams Kangaroo Assessment (level ladders) stage 2 Frequency diagrams and line graphs Mode and range 29 -Read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Data -Discussing and interpreting data and drawing conclusions -Writing short and Two-way table, mode, frequency, median, mean, range, event, frequency table, distribution, statistics, class interval, modal class, modal group, stem-and leaf, scatter graph, assumed mean, compound barchart, pie chart, trend, discrete, continuous, primary source, secondary source. NRICH Searching for (Mean)ing Litov's Mean Value Theorem M, M and M Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks extended responses -Presenting their findings to an audience TenQQ (Starter & plenaries) Kangaroo worksheets Week 3 and 4 Number Operatio ns and Calculati on Methods Week 4 and 5 Factors, Multiples -Strengthen and extend mental methods of calculation, working with decimals, fractions, percentages, squares and square roots, cubes and cube roots; solve problems mentally -Make and justify estimates and approximations of calculations -Carry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots and fractions; use brackets and the memory -Enter numbers and interpret the display in different contexts (extend to negative numbers, fractions, time) -Select from a range of checking methods, including estimating in context and using inverse operations -Rehearse recognition of primes. - How can you check if your answer makes sense? [Last digits / estimating] -Can division ever make a number larger? -Can multiplication ever make a number smaller? - -Show me an amount and a percentage increase that gives the answer £33 -What is the same/different about: 17/100 × 37 = 629/100 = 6.29 0.17 × 37 = 6.29 1% of 37 = 0.37 so 17% of 37 = 0.37 × 17 = 6.29 -What do the factors of the numbers in this problem tell me about the situation? -Calculate the mean for a small set of discrete data. -Calculate statistics, using ICT as appropriate. -Calculate the mean from a frequency table. -Group data into equal class intervals; Find the modal class of grouped data. -Calculate statistics for small sets of discrete data. -Make and justify estimates and approximation s of calculations -Check a result by considering whether it is of the right order of magnitude. -Understand square, square roots, cube and cube roots using a calculator. Support: -Recognise and use multiples. -Make and justify estimates and approximations of calculations -Know that a positive integer has two square roots, one positive and one negative. -Find square roots by factorising, e.g. √196 = √ (4 x 49) = 2 x 7 = 14 -Use factors to calculate, e.g. √ 576 = √ (3x3x8x8) -Find an upper and lower bound for a cube root. -Use rounding to approximate and judge whether the answer is the right order of magnitude. -Use a calculator to estimate cube roots -Interpret the display on a calculator Use trial and improvement to solve problems. Extension: -Find the prime factor decomposition of Kangaroo Assessment (level ladders) stage 1-5 Mental calculatio ns Kangaroo Assessment (level ladders) stage 3 Known facts, place value and order of operation s Equivalen ce between fractions Kangaroo Assessment (level ladders) stage 4 Percentage increases and decreases -explaining calculation strategies and talking about methods for the solution of problems -reasoning in working towards a solution and justifying results -comparing different mathematical processes for their efficiency and effectiveness -talking about mathematical expressions using mathematical and non-mathematical language http://www.slides hare.net/stanhope kris/multiplesand-factorsquestions -Exploring mathematical concepts -Solve worded problems 30 square number, cube, square root, cube root, inverse, calculation, powers, NRICH The Remainders Game Countdown Remainders Number Daisy Got It The Greedy Algorithm Thousands and Millions Keep it Simple Egyptian Fractions Cinema Problem Kangaroo Assessment (level ladders) stage 2 Mental methods Multiplication facts Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets prime number, factor, factorisation, prime factor, highest common NRICH http://nrich.maths.o rg/public/search.ph p?search=factors% Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core and Primes Week 1 and 2 3D Shapes Week 3 and 4 Construc tion and Loci -Find a prime factor decomposition of a number. -Use factors to simplify calculations. -Rehearse recognition of multiples, and lowest common multiple (LCM) -Rehearse recognition of factors and highest common factor (HCF) -Use prime factors to find the LCM and HCF of a set of numbers. -Visualise 3-D shapes from their nets; use geometric properties of cuboids and shapes made from cuboids; - use simple plans and elevations - Identify all the symmetries of 2-D shapes -Make scale drawings -Find the midpoint of the line segment AB, given the coordinates of points A and B -Use straight edge and compasses to construct: - What do the multiples of the numbers in this problem tell me about the situation? - Will breaking the numbers into factors help me solve this problem? If so, how? - Will listing the multiples of the numbers in this problem help me to solve this problem? If so, how? -Show me a net of a i) cube ii) cuboid iii) prism iv) pyramid -True/Never/Sometimes: 3-D shapes have more than one net -Convince me that: a cube has at least five different nets a cuboid has at least five different nets a triangular prism has at least two different nets -Given 2 elevations (or 1 elevation and a plan) of a 3-D shape, what could the shape be? -Show me: a solid with a plan that is square. a solid with front and side elevations that are all triangles. a solid with front and side elevations that are all triangles and a square plan -Show me an estimate of an angle. -Show how you can construct an angle of 30 / 45 / 75 with just a -Find the lowest common multiple of two numbers. -Find all the pairs of factors of a number. -Find the highest common factor of two numbers. -Recognise prime numbers up to 100. a number (e.g. 6 3 8000 = 2 x 5 ) -Rehearse recognition and use of multiples, common multiple, lowest common multiple. -Rehearse recognition and use of factors (divisors), common factor, HCF. -Use prime factors to find the HCF and LCM of a set of numbers. -Use prime factor decomposition to find the LCM of denominators of fractions in order to add or subtract them. NRICH involving HCF http://nrich.maths. and LCM. org/public/search. php?search=factor s%2C+multiples %2C+primes Support -Use 2-D representation s to visualise 3-D shapes and deduce some of their properties. -Draw 2-D representation s of 3-D shapes -Use ruler and protractor to construct simple nets of cuboids. -Use ruler and protractor to construct simple nets of 3-D shapes, for example regular tetrahedron, square-based Extension -Analyse 3-D shapes through 2D projections, including plans and elevations -Visualise and use 2-D representations of 3-D objects. Including use of isometric paper. -Identify reflection symmetry in 3-D shapes. Kangaroo Assessment (level ladders) stage 2 Making models and drawing shapes Kangaroo Assessment (level ladders) stage 4 2D representations of 3D shapes NRICH Cuboids Support: -Use a ruler and protractor to construct a triangle given two sides and the included angle Extension: -Use and interpret maps and scale drawings. -Given the coordinates of points A and B, find the mid-point factor, lowest common multiple, 2C+multiples%2C+ 2.3Extension primes -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets -Keywords are used and spelt correctly. -Writing the meaning for the keywords -Describing visualisations of shapes, movements and constructions -Discussing which mathematical equipment and materials to use Isometric, plan view, front elevation, side elevation, draw, sides, angles, included angle, included side, sketch, coordinates grid, mean, face, edge, cube, cuboid, tetrahedron, prism, pyramid, isometric, net, volume, crosssection, 2- D, 3D, plane of symmetry. NRICH Square It Cut Nets Egyptian Rope Where Are They? Nine Colours Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo Assessment (level ladders) stage 1-5 Construction, loci Kangaroo Assessment (level ladders) stage 2 31 -Describing visualisations of movements and constructions -Discussing which mathematical construct, sketch, SSS, scale drawing, ratio, scale, coordinates, mid-point, line segment, bearings, clockwise, NRICH Stringy Quads Making Cuboids Rollin’ Rollin’ Rollin’ Kangaroo worksheets Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core 2.3Extension -Level Up Texts Week 5 and 6 Interpret ing Data • the midpoint and perpendicular bisector of a line segment • the bisector of an angle • the perpendicular from a point to a line • the perpendicular from a point on a line • a triangle, given three sides (SSS) -Use ICT to explore these constructions -Find simple loci, both by reasoning and by using ICT, to produce shapes and paths, e.g. an equilateral triangle -Use bearings to specify direction straight edge and compasses. -What regular polygons can you construct just using straight edge and compasses? -Show me an example of: A point equidistant from these two points, and another and another …. A point a metre from this line, and another, and another… A point a metre from this point, and another,… The locus of the path traced out by the centres of circles which have two given lines as tangents -Identify and draw parallel and perpendicular lines. Recognise vertically opposite angles. -Know the sum of angles at a point, on a straight line and in a triangle, and recognise vertically opposite angles. -Identify and use angle, side and symmetry properties of triangles -Use a ruler and protractor to construct a triangle given two sides and the included angle (SAS) or two angles and the included side (ASA). -Use a straight edge and compasses to construct a triangle, given three sides (SSS). -Find coordinates of points determined by geometric information. -Given the coordinates of points A and B, find the mid-point of the line segment AB. of the line segment AB. -Use straight edge and compasses to construct: -the mid-point and perpendicular bisector of a line segment; the bisector of an angle. -Use straight edge and compasses to construct; the perpendicular from a point to a line, the perpendicular from a point on a line. -Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS) -Use bearings to specify direction. -Find simple loci, both by reasoning and by construction methods to solve problems on paper. -Use loci and construction methods to solve problems on paper. -Use ICT to explore constructions. Measuring and drawing angles Kangaroo Assessment (level ladders) stage 4 Standard constructions Kangaroo Assessment (level ladders) stage 5 Locus -Interpret tables, graphs and diagrams for discrete and continuous data, relating summary statistics and findings to - What does average mean? - Why do we have more than one way of working out an average? -Interpret tables, graphs and diagrams. -Compare two distributions -Interpret diagrams & graphs and draw inferences to support or cast Kangaroo Assessment (level ladders) stage 2/3/4 equipment and materials to use - Solve worded problems involving Construction and Loci anticlockwise, locus, path, equidistant, perpendicular bisector, bisector, vertex, vertices, angle bisector, 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets 32 -Read text from a variety of sources, including: Instructions Questions Discrete, continuous, class, modal class, distribution, Collins Maths Frameworking: Pupil Books 2.1Support 2.2Core the questions being explored -Compare two distributions using the range and one or more of the mode, median and mean -Write about and discuss the results of a statistical enquiry using ICT as appropriate; justify the methods used - Can the average be bigger than the largest number? - Can an average be the same as the largest number? - How can we represent a group of numbers, with a single number? - Any possibilities using Averages - Give examples of discrete / continuous / primary / secondary data - What do these words mean: hypothesis, discrete, continuous, sample? - What is an appropriate graph / chart for this? Why? - What do the scales mean? - Is it more efficient to use ICT here? - What does the graph tell you? - What is wrong with this graph/chart? - Why is this graph misleading? - Does this piece of data fit the trend? If not, can you think of a reason why it doesn’t? using the range and one or more of the mode, median and mean. doubt on initial conjectures. -Discuss how data relate to a problem; identify possible sources, including primary & secondary sources. Gather data from specified secondary sources, including printed tables and lists from ICTbased sources. Processin g, representi ng and interpreti ng data Frequenc y diagrams and line graphs Mode and range Averages Graphs and diagrams Working with grouped data Comparing distributions Explanations Tables Diagrams Graphs and Charts Data range, time series, conversion graphs, primary source, secondary source, sample size, data collection sheet, -Discussing and interpreting data interpret, cyclic, and drawing pie chart, bar conclusions chart, bar-line -Writing short and graph, line graph, extended horizontal, vertical, responses proportion, -Presenting their compound bar findings to an chart, statistics, distribution, audience mean, median, mode, frequency diagram, analyse, raw data. Investiga tion Please identify the common, moderated assessment opportunity for this unit in the space below: …………………………………………………………………………………………………................................................................................................................................................... 33 2.3Extension -Level Up Texts 3-5 4-6 5-7 Mathswatch Worksheets 10 ticks TenQQ (Starter & plenaries) Kangaroo worksheets