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YEAR 8: AUTUMN TERM Teaching objectives for the oral and mental activities a. b. c. d. e. Order, add, subtract, multiply and divide integers. Multiply and divide decimals by 10, 100, 1000. Count on and back in steps of 0.4, 0.75, 3/4… Round numbers, including to one or two decimal places. Know and use squares, positive and negative square roots, cubes of numbers 1 to 5 and corresponding roots. f. Convert between fractions, decimals and percentages. g. Find fractions and percentages of quantities. h. Know or derive complements of 0.1, 1, 10, 50, 100, 1000. i. Add and subtract several small numbers or several multiples of 10, e.g. 250 + 120 – 190. j. Use jottings to support addition and subtraction of whole numbers and decimals. k. Calculate using knowledge of multiplication and division facts and place value, e.g. 432 0.01, 37 0.01. l. Recall multiplication and division facts to 10 10. m. Use factors to multiply and divide mentally, e.g. 22 0.02, 420 15. n. Multiply and divide a two-digit number by a one-digit number. o. Use partitioning to multiply, e.g. 13 1.4. p. Use approximations to estimate the answers to calculations, e.g. 39 2.8. q. Solve equations, e.g. 3a – 2 = 31. r. Visualise, describe and sketch 2-D shapes. s. Estimate and order acute, obtuse and reflex angles. t. Use metric units (length, mass, capacity) and units of time for calculations. u. Use metric units for estimation (length, mass, capacity). v. Convert between m, cm and mm, km and m, kg and g, litres and ml, cm2 and mm2. w. Discuss and interpret graphs. x. Apply mental skills to solve simple problems. YEAR 8 AUTUMN TERM Number/algebra 1 Number of lessons: 6 one-hour lessons Integers, powers and roots (48 – 59) Sequences and functions (144 – 157) Teaching objectives:A. Add, subtract, multiply and divide integers. B. Recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes; find the prime factor decomposition of a number (e.g. 8000 = 26 x 53). C. Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers. D. Generate and describe integer sequences. E. Generate terms of a linear sequence using term-to-term and position-to term definitions of the sequence, on paper and using a spreadsheet or graphical calculator. F. Begin to 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. Oral and Mental Objective l, x Arithmegon on page 54 (last bullet point) Main Teaching 1/2 lessons Objective B Notes Key vocab. Plenary multiple, prime, factor, common factor, lowest common multiple, powers Repeat arithmegon idea and recall key words. Recap Highest Common Factor of two numbers. Objective x Group work e.g. Find factors of 36, 60. Write 3 digits on board and What are the common factors? ask pupils to find a What is the Highest Common Factor? multiple of 3 or 4 or 5 etc Could use number cards/whiteboards Continue factors or prime number e.g. 5, 1, etc. with lower 4 attaining groups Recap Lowest Common Multiple. Multiple of 3 is 51 Use multiple cards in small groups. Include talk of Prime Numbers in Recaps. Ask for factor pairs of a number e.g. 200 200 = 25 x 8 200 = 2 x 100 continue factorising until prime factors are found. Discuss more examples if necessary. Worksheets/text for exercises. Why are prime factors useful? What is the difference between a factor and a multiple? Recall key words and investigate problems page 54. Model solutions. Oral and mental Objectives e, l Target Board 4 in ‘10 min starters’. Ask for types of numbers. Extend to questions such as those in framework. (Page 59) Main Teaching 1/2 lessons Objectives C, A Put nos: {1, 2, 3, 4, 5 ………… {1, 4, 9 ………. {1, 3, 6 ………. {1, 8, 27 on board and lead into square numbers, triangular numbers, cubes, square roots, etc. Worksheet/text for exercises Revisit negative numbers – Squaring and cubing Negative mini-white board numbers e.g.: responses to teacher’s questions. What is the value of – 3 2? (-3)2? Can we predict the value of (-1) 99 ‘I like’ from ‘10 minute Inverse: starters’. What are square roots of 64, 9? Conclude: every number has 2 roots Estimate square roots and cube roots Check answers with calculators Worksheet/text for exercises. Notes Key vocab. roots, inverse, square, triangular, cube Plenary Using mini-white boards, find squares and square roots. Differentiate to groups. Support Concentrate on triangular numbers, powers of 10n, 2n etc. What do you think 43 x 42 = ? (law of indices) Oral and mental Objectives c, x Counting stick to generate sequences. Hands up sequences (Additional 10 minute starters). Main Teaching 2/3 lessons Objectives D, E & F Use flowcharts (e.g. page 145) to generate finite, infinite sequences, using multiples, triangular numbers, square numbers or fractions. Worksheet/text for exercises. Introduce 1st term and term to term rule (p149) with 1 or 2 examples. Worksheet/text for exercises Resource sheets or group work devising sequences and rules. Extend to nth term rules. Year 7 growing matchstick problem (p154) can be extended to similar problems. Groups generating their own picture sequences. Resource sheets IT/graph plotting sequences/spreadsheet. Make links to gradient and y intercept. Worksheet/text for exercises. Investigate: Paving stones p157. Notes Key Words Flowchart, sequence, finite, infinite Plenary Find rules from a given sequence. e.g. 5, 10, 15 ………….. 6, 11, 16 ………….. Sequences at bottom of p157. People sitting at a table. What is the link between tables and people if we add more tables. Can we predict how many people can sit at 100 tables etc. Try other arrangementsplot graph- make linksnumber machinesequations etc. YEAR 8 AUTUMN TERM Number 2 Number of lessons: 6 one-hour lessons Fractions, decimals, percentages (60–77) Calculations (82–85, 88–101) Teaching objectives:A. Know 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. B. Add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction. C. Interpret percentage as the operator ‘so many hundredths of’ and express one given number as a percentage of another; use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease. D. Understand addition and subtraction of fractions; use the laws of arithmetic and inverse operations. E. Recall known facts, including fraction to decimal conversions; use known facts to derive unknown facts, including products such as 0.7 and 6, and 0.03 and 8. F. Consolidate and extend mental methods of calculation, working with decimals, fractions and percentages; solve word problems mentally. Oral and mental Main Teaching Notes Plenary Objectives b, c, m, k. Using counting stick or number line count forwards/backwards in decimals/fractions (if counting in eighths pause for simplification when possible). Objectives A,E 1 -2 lessons. Calculators needed. How do you know not all fractions can be expressed as exact decimals? Select 10 students ask 1/10 to stand up. Now ½. Now 3/10. Ask for decimal equivalents. What about ¼? If I had 100 students could ¼ stand up? Discuss. Given 80 x 3 = 240 What else What about 1/3? do I know? Use a web diagram In pairs explore relationship between to record suggestions – these fractions and decimals – produce should include other decimal table ½ = 0.5 1/3 =0.3333 etc. mult. and divisions as well as Discuss recurring/terminating doubling halving etc. decimals. Discuss equivalents we should learn. Mult. and dividing by 10, 100, Which are easiest to compare 1000 etc. moving digits. fractions or decimals – generalize a method for comparing fractions? Tackle some questions – link to percentages. Is 3 ÷ 10 x 4 ÷ 10 the same as 3 x 4 ÷ 10 ÷ 10 Is this not 0.3 x 0.4? Explore and use this method to multiply decimals. Key Vocab. Decimal Fraction Recurring Terminating decimal Which are the important fractions to remember as decimals? What can you tell me about a ÷ 10 x b ÷ 10? Extend to 100, 1000 etc. Ask some mental decimal mult. Why is 0.3 x 0.2 not 0.6? How would you compare ¾ , 2/3, 0.8 and 23%? Oral and mental Objectives b and B Count up in quarters without a counting stick (do not simplify). Draw this on the board (pupils can copy on mini white boards if available). Explain that the first diagram shows ¼ of 1 row which is ¼ , the second shows ¼ of 2 rows which is 2/4 etc. Now count up saying a quarter of 1 is…..a quarter of 2 is…… The penny may begin to drop if not explain. Extent to thirds etc. What fraction/percentages/decimals of 60 could we find? Web diagram. How do we do it? Main Teaching Objectives B, C (2 lessons) Generalize from the starter about finding fractions of integers. Explore a quarter of 6 is six quarters which is one and two quarters which is one and a half etc. In pairs tackle some questionsextent to 2/3 etc. Notes Calculators may be needed. Explore percentage and or Draw me a diagram to show fraction key. 2/3 of 12 etc. Vocab. Unit fraction How does ¼ of and 0.25 of and 25% Value added tax of link? Explore with our remembered special fractions (2/5 = 0.4 = 40% etc. Consolidate with mixed questions – try to use real contexts not just numbers. Extend to 1 ¼ of or times and amount. Link to ¼ more then link to 125%. Extent to percentage increase and decrease. Questions in context. Explore which is cheaper 10% discount then add on V.A.T or add on V.A.T then give a 10% discount. (see page 77 for more ideas). Plenary What is another way of thinking of 2/3 of 12? (12 lots of 2/3). How do you know a fraction is bigger than one? How do we simplify it? Who can explain a link between fractions and decimals? Decimals and percentages? Etc. Which are the easiest fractions to find? What do you think 1/3 is as a percentage. How does V.A.T. work? Which is more 1/3 of £45 or 25% of £64? Why? Oral and mental Main Teaching (1 or 2 lessons) Notes Plenary Objectives v and F Ask questions like – what fraction is a mm of a cm? What percentages. What fraction is an inch of a foot etc? Make a grid with some fractions on. Ask pupils to find equivalents. Ask which are bigger than others and why? Which give recurring decimals? Which one is twice another etc? Use a paper folded grid with various squares coloured or shaded. Fold and ask what fraction or percentages or decimals are shown of rows, columns or the whole grid. Objective D, F, B Explore patterns on page 69 to interpret division by a fraction. Try and generalize but ensure students can make links to multiplication. Use diagrams to help e.g. how many 2/3 in 6? Use the grids from previous lessons. Establish which fractions are easy to add. Why do we not add the denominators? Ask why ½ + ½ can’t be 2/4. Vocab Numerator Denominator Top heavy Improper Proper Mixed number Cancel Simplify Multiples Verify Why is 6 ÷ ½ not 3? What is an equivalent calculation? Recap on cancelling and opposite process. Recap on common multiples. Establish generalization for addition and subtraction of proper fractions extent to answers with mixed numbers. Questions involving fractions in context. If I use 2/3 of a pint of milk to make a milk shake cocktail how many cocktails could I make with 6 pints – what’s the ‘sum’? How would we find 6 ÷ 2/3? Would a picture help. Can we generalize for division by fractions? T ÷ a/b could be written as what? ( b/a x T). What fractions are easy to add? What questions do you ask yourself before trying to add fractions? A pupil when asked to add ¾ and 3/8 did 24/32 add 12/32 is s/he right is there a better way? Who would add fraction? YEAR 8 AUTUMN TERM Shape, space and measures 1 Number of lessons: 6 one-hour lessons Geometrical Reasoning: lines, angles and shapes (178-189) Construction (220-223) Solving Problems (14-17) Teaching objectives:A. Identify alternate angles and corresponding angles; B. Understand a proof that: The sum of the angles of a triangle is 180º and of a quadrilateral is 360º; The exterior angle of a triangle is equal to the sum of the two interior opposite angles. C 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 geometric properties. D. Use straight edge and compasses to construct: a. the mid-point and perpendicular bisector of a line segment; b. the bisector of an angle; c. the perpendicular from a point to a line; d. the perpendicular from a point on a line. E. Investigate a range of contexts; space and shape. Oral and mental Objectives s,t Main Teaching (3/4 lessons) Notes Plenary Objectives A, B, C & E Write “ANGLE” in capitals on the board, identify from the letters types of angles and lines e.g. identify a reflex angle. (Pupils use of correct vocabulary essential). Recap on These lessons could be enhanced using a dynamic geometry software packages. Additional 10-min Starters Booklet “Shape recognition” “Imagining shapes.” Write a capital ‘A’ on the board a b d c e Give the size of angle a, ask pupils to calculate and explain how they got the other angles. Lucky dip bag of vocabulary. Pupil picks out a word and explains what it is using the correct vocabulary. Key Vocab. - angles on a line Parallel - opposite angles Perpendicular - angles at a point Horizontal - angles in a triangle Diagonal - use a shape such as Adjacent Opposite to bring out Point the above Intersect points Intersection Vertex Draw a pair of parallel lines and a transversal on the Vertices board. Ask pupils to indicate those angles that Side appear to be the same. Bring out alternate and Angle corresponding angles from that discussion. Degree Acute Worksheet/text for examples. Obtuse Reflect Additional questions: Base angles Vertically 1. Write a short poem about Opposite angles a) alternate angles Corresponding angles b) corresponding angles Alternate angles 2. Write a rap about what you’ve learnt in the Supplementary lesson. Complementary Interior angle Equidistant Proof Prove Bring the class together, and ask for pupils to read their poem or rap. Imagine an F shape, what angles can you see? Imagine z shape, what angles can you see. What other letters help us with angles (X, L, etc.) and why? How do we label angles (conventions)? What other conventions do we use in geometry? Where do people use the skills we have developed today? Where might you use your geometry skills in, technology, sport/games, science etc.? Using alternate and corresponding angles, prove that the angle sum of a triangle. a ‘a’ alternate ‘b’ alternate a + b + c = 180º straight line QED! b c a b Extend proof to angle sum of a quadrilateral, framework p183. Also proof that the exterior angle of a triangle is equal to the sum of the 2 interior angles p184. Worksheet/text for examples. Discuss- 1. Use 2 way tables with types of properties to place quadrilaterals in the appropriate section. P183 NNS example at bottom of 1st column Pairs of equal angles Classify quadrilaterals by their geometric properties Pairs of equal sides 0 1 P17 NNS bottom of first column put example onto OHT 2 0 1 2 Hypothesise on which spaces would have the most/least shapes. 2. Identify and classify the 16 quadrilaterals using a 3 x 3 pinboard or 3 x 3 dot paper. Worksheet/text for solving problems involving quadrilaterals and triangles. Sheet of quads and triangles included Provide a convincing argument to explain for example, that a square is a rectangle, but a rectangle is not necessarily a square (rhombus/Parallelogram) etc. Objective n Doubling/halving activity e.g. ‘Double, Halve Stick’ in ‘Additional Starters’ or loops. Objective r and E Imagine a quadrilateral , mark the midpoints with a dot. Go around the shape clockwise and join together the midpoint dots. What shape do you get? Now draw it and share it with a partner. I think it is always a parallelogram – why? Draw a rectangle. Draw in one diagonal. If I cut along the diagonal, I get two congruent right angled triangles. By fitting together matching sides of the 2 triangles, make a new shape. What is the name of the new shape? Explain to a partner why you have given the shape its name. How many possible shapes are there? (6) 2/3 lessons Objectives D & E Introduce via review of horizontal, vertical and perpendicular. Consider words starting with the prefix bi- to lead onto bisect and bisector. Mark 2 points on the board (not horizontally opposite). Explain that these are wild animals tied up, and a safe pathway between them is needed. Develop the idea of a safe path, leading onto the construction of the perpendicular bisector. What quadrilateral have we constructed? – Discuss rhombus and its properties. Vocabulary Bisect Bisector Equidistant Straight edge Compasses Locus Loci Look at the maximum number of right angles in quadrilaterals, extend to other polygons. Revisit construction stressing the link to a rhombus – could a kite’s construction be used instead – would this help sometimeswhat have a kite and rhombus got in common? Demonstrate/devise construction to bisect on angle. Pupils could practise with acute, obtuse and reflex angles. Relate to the rhombus construction. Introduce the construction of a perpendicular from a point to a line by an example using the shortest distance to a line e.g. lazy camper to a river for water. Relate to the rhombus construction Pupils could construct perpendiculars within a rhombus/kite and arrowhead. Introduce the construction of a perpendicular from a point on a line by giving examples of who would use the construction e.g. a builder building a wall. Relate to the rhombus construction Link to loci ideas. Pupils could model loci paths according to given instructions. YEAR 8 AUTUMN TERM Algebra 2 Number of lessons: 6 one-hour lessons Equations and Formulae (112-199, 138-143) Teaching objectives: A. Begin to distinguish the different roles played by letter symbols in equations, formulae and functions; know the meanings of the words formulae and function. B. Know that algebraic operations follow the same conventions and order as arithmetic operations; use index notation for small positive integer powers. C. Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket. D. Use formulae from mathematics and other subjects; substitute integers into simple formulae, and positive integers into expressions involving small powers (e.g. 3x² + 4 or 2x³); derive simple formula Oral and mental Objective q Put up 56+37=56+30 =86+7=93 and ask the pupils to tell you about it. Why is it incorrect, what is being done? How could we write it correctly? Use this to bring out the vocab of equality [as page 113]. Main Teaching 1/2 lessons Objectives A, B Equation, Formula, Function make clear the difference. (113) Pupils make up in pairs or groups some equations functions and formulae – class discussion about the results. Go through the written language of algebra. 2 x n = 2n etc. [see page 113]. Go through BODMAS again emphasising that algebra follows the same rules. Stress how brackets inclusion changes priority. Use brackets homework to reinforce. Look at index notation. Yellow Red Red White Notes Vocabulary Equation Formula Function Variable Substitute Term Expression Plenary Give me an example of an equation. Are there any variables? Are there any expressions? Which equations can you solve? What types of equations have lots of solutions? Are these functions or formulae? Discuss observed misconceptions. Write 2+5+7 on the board. What other number sentences can I write using 2, 5 and 7? 7-2=5 7-5=2 5+2=7 If a + e = y what other algebra sentences can I write? Does it work for all numbers? Discuss variables/function etc. Extend to a x b = c If I know the width of yellow and red how do I find white? How do I write an algebraic sentence to express this? What about yellow + white? (page 115). Pupils in groups form their own diagrams and formulae. 2 stage formulae need to be looked at – link to earlier sequence work or growing patterns. Group work producing patterns and formulae perhaps. Discuss patterns/formulae produced. Can we transform a formula? How? Link to number machines. What have we learned today? What do we have to remember? Objective q Use whiteboards and introduce the idea of simplification. Students discuss and hold up whiteboard with simplifications after each question. Equation matching cards. (just simplification) (Resource sheet 4) 3x4+2x4=5x4 Discuss – generalise write using brackets i.e. (3 + 2) x 4 2/3 lessons Objective C Vocabulary Talk about simplifying and distributive law. Note: try not to use ideas like “can’t add apples and bananas” pupils must realise that the letters represent numbers (often measurements). Show distributive law simply 3(a+2)=(a+2)+(a+2)+(a+2) Show examples of how this can help write and simplify expressions. Put diagram on the board. Find the area of the shape Use examples similar to those below. not shaded. 10 12 2 a 5 b b How did you do it, are there any other ways? c d 6 Variable Substitute Term Expression Simplify Simplification Homework Humdingers (Resource sheet 8) What does 3(a + 2) mean? How do you know? What about (a + 2) 3 ? If I have an apple and I label it ‘a’. What could ‘a’ stand for? Mass, cost, width, height, calorific value… What could it not stand for? Apple, colour, variety… If m = 4 are the values of the following the same? 3m² (3m)² Show all Simplify to same expression (7-a) x 5 + (5-b) x 3 + a x 3 etc. Use other diagrams. Number Tricks sheet. Either read out or put on OHP. (Resource sheet 9). 10 b 3a b Find shaded area for each shape. Oral and mental Main Teaching 1/2 lessons Tell a story. Andrew buys 4 Objective D bags of sweets. He doesn’t Exercises needed on forming know how many sweets are in expressions/equations/formulae each bag but he does know that Use whole class teaching on they are all the same. He gave expressions for 1 more than a one bag to his brother and sister variable, 1 less, 3 times a variable, to share equally, how many what about add one then times by 3? does each have? He gives etc. another bag to his friend John Talk about what can change and what who already has 4 sweets, how can’t change– variables and many does John have? Andrew constants. eats 2 sweets, how many does he have left? Use page 143 for ideas of formulae to At each pause, pupils respond derive. with expressions. Perhaps give a value for the number of sweets in the bag originally and then substitute into the expressions formed. Notes Plenary Objective x What happens when you have more than 2 variables? Address observed misconceptions. Model different ways of expressing division. Relate to problem solving in science and the real world. YEAR 8 AUTUMN TERM Shape, Space and Measures 2 Number of lessons: 6 one-hour lessons Measures and mensuration (228 – 231, 234 – 241) Solving Problems (18 – 21) Teaching objectives:A. Use units of measurement to estimate, calculate and solve problems in everyday contexts involving length, area, volume, capacity, mass, time and angle; know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons). B. Deduce and use formulae for the area of a triangle, parallelogram and trapezium; calculate areas of compound shapes made from rectangles and triangles. C. Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids. D. Investigate in a range of contexts: measures. Main Teaching 2/3 lessons Objectives B, A Follow on from length conversion grid to discuss the units of area. Use information grids Revise area of rectangle. (enlarged) to check conversions Demonstrate area of triangle is half that by asking: of rectangle by cutting. Oral and mental Objective v Which are the same? Which are greater than…? Which are less than…? Etc. Consider other triangles by demonstration or use spotty grids (p 237) Notes Reinforce vocabulary: area, square, centimetre, square metre, square millimetre Plenary Why do we use squares to measure area rather than: circles rectangles triangles hexagons? These lessons could be enhanced using a dynamic geometry software package. How would you work out the area of the shaded square given the base and height of each right angle triangle? Worksheet/text for exercise Consider compound areas of rectangles and triangles. Vertical height Worksheet/text for exercise. Demonstrate area of parallelogram by cutting. Emphasise perpendicular height rather than sloping side. Group work – drawing sets of parallelograms with same area. Is the rhombus just a special case of a parallelogram? Altitude Perpendicular Area How do we get a triangle with the same area as a given parallelogram? What about a trapezium. (same base twice height). Given a square how can we produce a parallelogram with the same area? (cut diagonal and reform the two triangles created). What about a rhombus? Worksheet/text for exercise. Pupils to investigate area of a trapezium as introduction. Discuss pupils’ answers bringing out the mean of the two sides multiplied by height. Worksheet/text for exercise. How can we draw sets of triangles with the same area? Mean Trapezium Why is the area of a rhombus – half the product of the diagonals? (Use the 4 right angles triangles). Why do we use the mean in the trapezium formula? Oral and mental Objective l Tables practice using counting stick or verbal loop e.g. start off with 3 x 7 and ask a pupil to answer. That pupil then asks the person next to them a number fact and so on. Lead onto multiplying 3 numbers together. Main Teaching 2/3 lessons Objectives C, A Notes Plenary Reinforce length units and area units. Discuss surface area of a cuboid. Discuss volume and the units. Say cubic metres not metres cubed. Useful equipment: a litre cube filled with 1 cm³ gives the pupils something tangible on which to base the theory. How do we find the volume of a cuboid measuring 7 cm x 5 cm x 0.2m? Review volumes of cuboids and devise a formula. Worksheet/text for exercises. Extend to shapes made up of cuboids. Worksheet/text for exercises. Show how to calculate the surface area of a cuboid using a net or alternative method. Worksheet/text for exercises. How do we find its surface area? If the volume of a cuboid is increased, does its surface area always increase? Oral and mental Objective u Estimate length in classroom (already measured) Estimate volume (bring in various bottles) Cut cone shape top of a plastic bottle to leave a cylinder of the same base radius and height. Compare volumes (estimate ratio). Demonstrate with sand or water by pouring from cone to cylinder. Objective r Ask students to describe the cone and cylinder. Describe a common 3D or 2D shape and ask students to Main Teaching 1/2 lessons Objectives A, D Review volume units (from last lesson). Discuss appropriate units to measure the volume of: A matchbox A telephone The school hall Notes Key Vocabulary: cubic millimetre cubic centimetre cubic metre hectare ounce pound foot mile pint gallon tonne Lead on from volume to mass and capacity and discuss units of weight g, Try and bench mark kg, tonne and units of capacity ml, l. measurements. E.g. coke can holds Consider imperial units of oz, lb, ft, 330ml. mile and then pint and gallon. A ruler is 15 or 30cm etc. Rough equivalent to learn: 1 kg = 2.2 lb 1oz = 30 g 1 mile = 1.6km 1km = 0.6 miles 1 litre is just less than 2 pints. Rhyme (‘A litre of water’s a pint and three quarters’). Plenary Examples such as: Apples are sold at 40p per kg and 24p per pound. Which are the cheapest apples? Explain how you worked it out. Further example framework p21 Check/match conversions. Check units – what would we measure in hectares? Check bench marks – what is about 100metres, a km? etc. Who would use ounces? etc. visualise it as you describe it using key vocab. Ask them to guess what it is (table, stereo earphones, mobile phone, gear stick etc.) See ‘Imagine’ worksheet in the summer term. Invite pairs to develop their own descriptions for the class to draw. Worksheet/text or group activities for conversion exercises. Discuss appropriate units of area to measure the area of: Thumb nail Desk Classroom floor London Playing field Make last one appropriate so that hectare (ha) is introduced as 1 ha = 10 000m² Use problems to illustrate conversions between one unit and another e.g. A rectangular field measures 250m by 200m – what is its area in hectares? Each side of a square tablecloth measures 120cm. Write its area in square metres. Worksheet/text for exercises. Handling Data 2 (6 Hours) Autumn Term See Y8 Mini pack – handling data (note additional calculator work may be needed). Handling data (248–273) Solving problems (28–29) A. Discuss a problem that can be addressed by statistical methods and identify related questions to explore. B. Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources. C. Plan how to collect the data, including sample size; design and use two-way tables for discrete data. D. Collect data using a suitable method, such as observation, controlled experiment using ICT, or questionnaire. E. Calculate statistics, including with a calculator; recognise when it is appropriate to use the range, mean, median and mode; plus Y7 objectives - construct and use stem-and-leaf diagrams. Calculate statistics for small sets of discrete data: Find the mode, median and range: Calculate the mean, including from a simple frequency table, using a calculator for a large number of items. F. Construct, on paper and using ICT: - pie charts for categorical data; - bar charts and frequency diagrams for discrete data; - simple scatter graphs; - identify which are most useful in the context of the problem. G. Interpret tables, graphs and diagrams for discrete data and draw inferences that relate to the problem being discussed; relate summarised data to the questions being explored. H. Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate; justify the choice of what is presented. I. Solve more complex problems by breaking them into smaller steps or tasks, choosing and using resources, including ICT.