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YEAR 8: SPRING TERM Teaching objectives for the oral and mental activities a. Order, add, subtract, multiply and divide integers. b. Round numbers, including to one or two decimal places. c. Know and use squares, positive and negative square roots, cubes of numbers 1 to 5 and corresponding roots. d. Know or derive quickly prime numbers less than 30. e. Convert between improper fractions and mixed numbers. f. Find the outcome of a given percentage increase or decrease. o. Use approximations to estimate the answers to calculations, e.g. 39 2.8. g. Know complements of 0.1, 1, 10, 50, 100, 1000. h. Add and subtract several small numbers or several multiples of 10, e.g. 250 + 120 – 190. i. Calculate using knowledge of multiplication and division facts and place value, e.g. 432 0.01, 37 0.01, 0.04 8, 0.03 5. j. Recall multiplication and division facts to 10 10. k. Use factors to multiply and divide mentally, e.g. 22 0.02, 420 15. l. Multiply and divide a two-digit number by a one-digit number. m. Multiply by near 10s, e.g. 75 29, 8 –19. n. Use partitioning to multiply, e.g. 13 1.4. s. Use metric units (length, area and volume) and units of time for calculations. t. Use metric units for estimation (length, area and volume). u. Recall and use the formula for perimeter of rectangles and calculate areas of rectangles and triangles. v. Calculate volumes of cuboids. p. Solve equations, e.g. n(n – 1) = 56. q. Visualise, describe and sketch 2-D shapes, 3-D shapes and simple loci. r. Estimate and order acute, obtuse and reflex angles. w. Discuss and interpret graphs. x. Apply mental skills to solve simple problems. Handling data 1 (6 hours) Probability (276--283) A. Use the vocabulary of probability when interpreting the results of an experiment; appreciate that random processes are unpredictable. B. Know that if the probability of an event occurring is p, then the probability of it not occurring is 1 – p; find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way, using diagrams and tables. C. Estimate probabilities from experimental data; understand that: if an experiment is repeated there may be, and usually will be, different outcomes; increasing the number of times an experiment is repeated generally leads to better estimates of probability. Unit : Handling Data 1 Year Group Y8 Number of 1 Hour Lessons 6 Oral and mental Obj. f\(Summer term) Counting up and down in fract. dec. & %ages. Divide class into 3 groups each group shouts out their allotted category. 1) 0.1, 0.2, 0.3 2) 1/10, 2/10, 3/10 3) 10%, 20%, 30% Class/Set Core Main Teaching Obj. A ( 1 lesson) Students show and tell using mini-white boards events that they think are certain, evens prob., higher than evens probability etc. Select examples and place them on large probability line at front of class. Discuss positioning. Suggest events e.g. next person to speak will be left handed, and ask where to place the event on the prob. line. Discuss situations where prob. can be given as a fraction (framework 277). Relate to number line placing probability as a fraction. Answer questions relating to rolling dice, picking playing cards etc. If time check if the theory works e.g. how many red cards should I get if I pick 10 from 52 at random? Notes Key Vocab. Event Theory Random Predictable Unpredictable Revisit Y7 vocab. Much of this revisits Y7 work. Plenary Test on key words. Why doesn’t probability guarantee success/failure? Who uses probability? If I toss a coin twice will I get at least one head? What is the probability if it isn’t certain? What events are easy to give a fraction probability to? Why? How do we work it out? How can we cheat at cards/dice? What happens to the probability if we cheat? If I tossed a drawing pin what are the outcomes of the event? Are the outcomes equally likely? Oral and mental Obj. f (summer term) Counting up in fractions until we get a whole one. Counting up in fractions and saying what is needed to make a whole one, e.g, 1/10, 9/10 2/10, 8/10 3/10, 7/10 etc. Obj. a Beat the teacher! One student asks mult. table questions and the class try to beat the teacher to the answer. Hopefully the teacher will win. Discuss the probabilities of the teacher winning and relate back to previous work. Main Teaching Obj. A,B, and C. (1 lesson) Recap on questions about prob. of rolling a six on a dice etc. Extend to prob. of not rolling a six. How does this relate to our starter? Generalise that probabilities sum to one and how we can use this in problem solving. Set group tasks on this theme (see 279). Mini-plenary to check findings/answers/misconceptions. Is probability reliable – does the theory work? Groups roll a dice 60 times – how many sixes should we get? Put the results from two groups together to make 120 rolls – how does this compare? – continue adding results- discuss. Notes Dice needed Try and use probability notation P(six) etc. Plenary Give a sentence about the prob. of an event, happening and not happening. If I toss a coin 120 times tell me what might happen. If 2 pupils each toss a coin what is the chance of at least one getting a head? (This leads into next lesson. It also shows that only 2 tails doesn’t count as a success, with a prob. of 1/4. therefore 1 - 1/4 gives 3/4.) Higher or lower activity. Use A4 cards or mini-white boards with the numbers 1 through to 10. Cards are blue-tacked to board or held by students at front of class. First card is revealed and students have to state the probability of the next card being higher or lower. Highlight the reducing denominator as the game proceeds. Oral and mental Obj. g, c & d. Using large or O.H.T. 100 grid ask questions. e.g. Name a prime number between 20 and 30. Point to a cube number – what is it the cube of etc. Extend to the probabilities of each number or type of number being selected. Relate the numbers to raffle tickets. Ask about chances of winning. If you bought 10 tickets are they best together e.g. 1 to 10 or spread out? Ask questions on complements to 50, 100 25,80 etc. Main Teaching Obj. B (2 lessons) Recap on possible outcomes from single events – rolling a dice, picking a card etc. Recap on ‘equally likely’ and how we express probabilities. Set task to explore the outcomes of two successive events recording results (2 coins, two dice, 1 coin and 1 dice etc). Discuss outcomes of tasks/experiments. Highlight sample spaces and how to tabulate outcomes. Do this for rolling two dice etc. How can we use this to establish probabilities of events? Notes Key Vocab. Sample Sample spaces. Event Biased How many possibilities? List the sample space. Can we safely give a probability to any combination of meal? Why not? Could we sample our preferences to help us decide? Why might our class sample not be representative? Reinforce – equally likely. Which number on a dice is hardest to throw? What sort of events can we assign a probability to easily? What if we can’t? Revisit the drawing pin question from the last plenary. How might probability help a chef with preparing lunch for factory workers? Explore probability of getting a six by adding the scores on two dice. Is there more or less chance than getting a six by rolling a single dice? Explore menu choices e.g. Starter Main Soup fish and chips Melon pasta Salad steak and kidney pie Plenary Question key language. See also probability problems page 23 How do we work out the prob. of throwing a six on a dice and then picking a spade from a pack of cards? How many attempts should guarantee success in the above? Oral and mental Obj.A & B Ask questions about probabilities of single events. Offer a menu choice to the group. Predict choices collect responses on mini-whiteboards, discuss number of outcomes possible etc. Obj x Put students in groups of 6, 8, 10, etc. Ask for ½ or 50% of each group to stand up. Extend to other fractions. Discuss why some groups can/ can’t complete the task. This activity can be done with a line of students at the front of the class and a fraction of the line have to raise their hands. This can be easily related to a number line and probabilities. Main Teaching Obj. C (2 lessons) Further tasks looking at the sample spaces and theoretical probabilities of outcomes. (tossing 2 coins etc.) Tabulate outcomes then set up experiments for groups of students to check how the experimental results compare. Discussion on findings – perhaps group presentations. Notes Key Vocab. Theory Experimental probability Theoretical probability Demonstrate probability activity where students are invited to draw out and replace multi-cubes from a bag. After 10 selections estimate proportion or numbers of each colour in bag, (good opportunity to discuss proportion). Bag with 8 red and 2 white multi-cubes inside. Pupils set up their own experiments using counters, playing cards etc. to make predictions. Discussion. How does the increase in the number of trials affect the reliability of your estimates? Group work deciding how best to answer probability problems (see 285). Plenary A lake contains 8 species of fish. Anglers catch and release fish in the lake every day. Could a record of their catches lead to an estimation of the proportion of the fish in the lake? What about the number of fish in the lake? Discuss. (Note: how are the fish caught; does a particular method /bait only catch certain fish; are some fish only caught in certain area of the lake or a certain times of the year; are some types of fish cleverer and therefore get caught less {carp}?) Groups design and trial their own experiment to solve a problem. Groups write a short report on their findings and share with the class in the plenary Extended plenary sharing results/findings and discussing key issues/misconceptions. Algebra 3 (6 hours) Sequences, functions, graphs(160–177) CORE From the Y8 teaching programme A. Express simple functions in symbols; represent mappings expressed algebraically. B. 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. C. Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations. Unit : Algebra 3 Year Group Y8 Number of 1 Hour Lessons 6 Class/Set Core Oral and mental Obj. a Count up in 2’s, 3’s, squares etc. To illustrate idea of mapping, teacher says each counting number and pupils respond with a function. e.g. 11 2 4 3 9 for squares etc. Obj.B Using mini whiteboards or (resource sheet with x and y axes in plastic sleeves to create miniwhiteboard effect), plot coordinates shouted out by teacher. Find midpoint of two points – can we generalise a rule? (see worksheets). Main Teaching Objective A (2lessons) Revisit Y7 work on number machines. Activities investigating what a machine’s functions are, given input and output tables. Model different ways of describing the function. x 2x + 3 xy y = 2x + 3 Include negative numbers and some non-integer values. Include input and output tables not in numerical order (see 163). Relate to mapping diagrams. Draw mapping diagrams – note features -parallel etc. particularly projecting mapping lines backwards. Relate to enlargement (161). Group work with students drawing mappings and making generalisations about the patterns. Group work investigating properties of functions by combining functions. E.g. Two mult. is same as one single mult. Two mult. followed by a division is the same as one mult or division. (163) Notes Revisit Y7 vocab. Term Expression Variable Integer Evaluate Substitute Introduce Linear function Difference pattern Linear sequence Arithmetic sequence Notation T(n) Some spreadsheet work could be done here using ‘formula function’ to generate output tables from input table. Graphical calculators could be used to generate input output tables and later graphs of linear functions. Plenary Can we generalise on how to discover a function’s rule? What do we mean by the difference method? What is the difference between a term and expression? What is the difference between an equation and expression? What do we mean by a mapping? How is a mapping different from an equation? What types of shapes do mapping lines give – what does each shape tell us? Generalise on what happens when projected mapping lines meet. Explore x x2 Oral and mental Obj. a Number machines/mappings. Split class into two groups. Each group gets one part of a function e.g. x 2 and -3 . Teacher calls out input and groups operate their part of the function. Input output table recorded and discussed. Mapping diagrams predict and confirm. Main Teaching Obj. A & B (2lessons) Using axes grid plot coordinates of mappings e.g x 2x Plot (1, 2), (-2, -4) etc. Discuss implications of joining sets of points together with a straight line. Discuss which points lie above and below the line – possibly link this to inequalities. Discuss labelling the line and the steepness of the line. How do we describe steepness in maths? Explore in groups lines with equations y = mx (initially where m is a positive integer). Notes Key vocab. Linear function Linear relationship Slope Gradient Steepness Discuss – generalise - what about other values of m? Could use graph package or graphical calculators. Extend to y = mx + c Groups of students design their own function. Other groups give inputs and receive outputs. First group to guess function receives points. Discuss – generalise - make conjectures. How does this link to sequences, mappings and rules/number machines? Extent to y = x2 y = 1/x Revisit axes coordinates quadrants Plenary Which would give the steepest graph line y = x y = 2x ? What do we mean by steep? Teacher offers an equation and asks students to respond with an equation that will give a steeper line/less steep line etc. What do all straight line graphs have in common? How do we show a negative gradient? What about a gradient of 1.5. How does 3/2 help? Revisit mixed number/imp. fraction conversion (obj. e) What is an intercept? How do we remember how to plot co-ords? X is a cross (across) Y’s up (wise up) (x, y) is alphabetical. Human graphs. Students stand as in picture. If the origin is where their sternum is now, they have to model equations shouted out by the teacher. (y = 0, y = 2, y = -2, y = 2x, y = 2x + 2 etc.) Oral and mental Obj. B Revisit ‘human graphs’ see what has been remembered. Main Teaching Notes Obj B. (2lessons) Present various graphs of straight lines where gradient and intercept can/cannot be seen. Students have to guess or accurately state the equation of the line. Count up in coordinates of functions e.g. y =2x +1 (0, 1), (1,3), (2,5)etc. Group activity – students have to produce their own graph (could be on OHT acetates for class to see). Group presents their graph or graphs and other groups have to state the equation, predict some points on/not on the line, calc. the gradient, note the main features etc. Display graphs and invite comments. Obj C Students explore situations from real life to give straight line graphs (conversion graphs, cost of using mobile phone per month, car hire £50 + £40 per day etc.) Can we form equations? How do they relate to y = mx + c ? What does the gradient and intercept tell us in real life? Plenary Ask for sentences describing what to look for when first looking at a function graph (may be produce a worded flow chart). Generalise on what we know now – relate back to objectives. Mini-whiteboards in pairs sketch and show graph lines from information given by teacher (e.g. ..with a gradient of 2, ;;;passing through (5, -5) with a negative gradient…with equation y = …. parallel to ……..etc. Questions about real life situations that lead to linear functions. How do graphs help? What must we be careful of, if we compare graphs? How could we cheat? Add data and ask for further comments – suggestions of functions etc. Link sequences mappings functions and real life situations together. Multiplicative Relationships See N.N.S. minipack (6 hours) This is a detailed mini-pack. Note that adjustments to the sample medium term plans have been made to accommodate this important mini-pack. Handling Data 2 was another mini-pack and should have been taught in the autumn term. Handling Data 1 has been placed in the spring term. The objectives of Multiplicative Relationships are from the strand on number so the list of objectives addressed in Number 2, 3 & 4 is reduced. The units Number 3 and Number 4 should be taught after this unit. The objectives for the unit Solving Problems are addressed in the units, Number 2, Multiplicative Relationships (this unit), Number 3 and Number 4 SSM3 moves to summer term. Number 3 (9 hours) Place value (36–47) Calculations, (92–107, 110–111) Calculator methods (108--109) CORE From the Y8 teaching programme A. Read and write positive integer powers of 10; multiply and divide integers and decimals by 0.1, 0.01. B. Order decimals. C. Round positive numbers to any given power of 10; round decimals to the nearest whole number or to one or two decimal places. D. Consolidate and extend mental methods of calculation, working with decimals, squares and square roots, cubes and cube roots; solve word problems mentally. E. Make and justify estimates and approximations of calculations. F. Consolidate standard column procedures for addition and subtraction of integers and decimals with up to two places. G. Use standard column procedures 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. H. Check a result by considering whether it is of the right order of magnitude and by working the problem backwards I. Carry out more difficult calculations effectively and efficiently using the function keys of a calculator for sign change, powers, roots and fractions; use brackets and the memory. J. Enter numbers and interpret the display of a calculator in different contexts (negative numbers, fractions, decimals, percentages, money, metric measures, time). Unit : Number 3 Number of 1 Hour Lessons Oral and mental Obj. b Hold up or shout out numbers – students have to respond with number rounded to nearest 10, 100, tenth etc. In groups come up with a sentence to help explain what to do. Relate to number line not just rules. 9 Year Group Y8 Class/Set Core Main Teaching Obj. C (1 or 2 lessons) Discuss rounding to nearest whole number and one/two decimal places. In pairs use calculators to explore how to write the answers to calculations like: 1 ÷ 3, 1 ÷ 7, £3.23 ÷ 5 £4.27 x 1.63 Pairs then complete some calculation drawn from real life situations involving rounding. Highlight £1.9 and £1.90 and 190p Generalise on the rounding of money, metres kilometres etc. 1 ÷ 3 can be written as 1/3 which is a fraction. How does it look as a decimal? List fractions and their decimal equivalents/approximations using rounding where needed. Notes Highlight the idea of conventions in rounding Note calculator conventions. Link to other conventions in maths. Key Vocab. Recurring decimal Terminating decimal Plenary Discuss generalisations for rounding drawing from ideas/misconceptions in lesson. How do calculators round? Which fractions have exact decimal equivalents? Why? Explore/restate conventions for writing money. Why does the £ sign come first? Do other currencies do this? Present provocative statements or calculations and ask for comments. e.g. I need a piece of wood 2.333333metres long –how did I get this answer? What should I do? Revisit key vocab. Oral and mental Obj A Counting up and down in powers of 10 Perhaps have groups one setting the power another saying the number and another saying the number of zeros. Extent to powers of 100. Main Teaching Obj. I, D, H and E (1 or 2 lessons) Link powers to roots (square and cube) explain notation. Identify squares and cubes on a 100 grid. Estimate the square roots and cube roots of some numbers chosen on a 100 grid – justify answers. Use a calculator to find square roots (without using the square root key). Explain the use of the square root key – extend to cube and cube root if scientific calc. available. Use squaring and square rooting in context. E.g. a square has an area of 90 square units. What must be the length of each side – extend to volume of a cube. Perhaps explore Pythagoras’ theorem in an informal way! Explore square roots and squares of negative numbers – draw conclusions. Evaluate 4 x (6.78)2 using a calc. explore use/non-use brackets etc. review BODMAS. Notes Scientific calculators are needed. Consider difficulties if students have different makes /models of their own calculator. Key Vocab. Justify Billion Index Power Square (root) √ Cube (root) 3 √ Cube number To the power of Plenary How many ways are there of doing 4 x (6.78)2 ? How do we estimate the answer? How do we round a calculator answer? Does a calculator use BODMAS? How do we estimate a root? How can we check our square root makes sense? Work through some calculations on a calculator. Oral and mental Obj.A Obj. b Have operation cards ÷10, x 10, ÷100, x100 etc. to hold up or write these operations on the board. Offer a number and then an operation – ask students to respond with solution. Mix and match the operations – discuss joint effect of combined operations. Obj F What is 0.2 less than……more than….etc. Offer incorrect solutions to addition and subtraction ‘sums’ in column form. Discuss – explore misconceptions. Main Teaching Obj. B (1 or 2 lessons) Explore strategies for ordering decimals. Perhaps use target boards with sets of four decimals. Label them a, b, c, and d, then students have to order them (like fastest finger first in who wants to be a millionaire). This could be an alternative starter. Obj. A Explore multiplication. Establish that other operations have the same effect e.g. x 0.1 is the same as ÷10. Discuss why. Generalise- link to fractions. Discuss making bigger and smaller. Extend to mult. by 0.01 etc. perhaps redo the starter activity using new knowledge. Move on to ÷ 0.1 and 0.01 with a calculator as above. Extend to combinations of operations Obj F Build in a check on, or do a lesson on addition and subtraction of decimals. Work from mental to jotting to column methods. (see pg 37) Apply skills in contexts. Notes Calculators needed. Possible spreadsheet activity entering formulae and filling down to operate the formula on consecutive numbers and generalising on the effect. Key Vocab. Counter example Plenary Revisit generalisations. Revisit oral and mental starter incorporating new skills. Check understanding and links e.g. Why is x 0.1 the same as ÷10 Extend activities to x 0.2 and 0.02 and division. Make provocative statements like multiplying always makes bigger. Multiplying by 0.1 always makes numbers smaller (0.1 x -2 )? Explore counter examples. Explore misconceptions in decimal addition and subtraction. Oral and mental Obj. i and k ‘Larger or smaller?’ Ask the question for problems like 14 x 0.1 14 ÷ 0.1 18 ÷ 0.01 Pupils respond with mini-white boards or left and right hand up for larger and smaller respectively. Make a web diagram. Given the ‘sum’ in the box tell me something else we know. Add new boxes to the end of the arrows. 0.4 x 3 = 1.2 (see worksheets for blank web diag) Main Teaching Obj. G ((2 lessons +) Explore equivalent calculations. Present ideas first and ask for students in pairs to agree on generalisations. E.g. Is 1.4 x 3 the same as 14 ÷ 10 x 3 and the same as 14 x 3 ÷ 10 ? How does the last version help us to do the calculation? Demonstrate ways of doing 1.4 x 3 Notes Calculators needed. Use estimating and inverse operations to check answers. Try grid multiplication method. 3 1 0.4 3 1.2 Plenary Discuss generalisations. Explore ‘difficult’ questions. Explore worded questions and contexts. (area, volume, proportion etc.) Investigate shortcuts and equivalence. e.g 8 x 0.25 8x¼ 25% of 8 = 4.2 Establish methods for mult. of decimals. Extend to 1.4 x 1.3 using 1.4 x 1.3 and then ÷ 10 twice or grid multiplication.(see pg 105). Incorporate estimates (objectives E and H). What about grid mult? May have to explore 0.3 x 0.4. 160 16 = and how this relates to 4 0 .4 the opposite of cancelling fractions. How do we use this to make division easier? Generalise – practise (see page 107). Extend to division by 1.2 etc. (using chunking). Relate to practical contexts. Address misconceptions. Model solutions – explore different methods decide which is more efficient. Explore 16 ÷ 0.4 relate to 0.2 x 0.3 = 0.6 is this true? Chunking or method of division may need revisiting. A student had to do 16 ÷ 0.4 She did 160 16 = 4 0 .4 now 160 ÷ 4 = 40 so the answer is 40 ÷ 10 = 4 What is wrong with her thinking? Oral and mental Questions on all of previous work. Present a selection of ‘sums’ and a selection of answers – invite students to match ‘sums’ to answers and justify their decisions. (see worksheetssums and ans) Main Teaching (1 or 2 lessons) Obj. J Demonstrate the use of a fraction key on a calculator. Explore operations with fractions (four rules). Try squaring and square rooting fractions. Try repeated addition of 1/16 etc. – relate to imperial spanner sizes which increase in increments of 1/16 inches (gap across nut). Ask questions like 3/16” , what size bigger comes next? Explore how to enter 3 hours 15 min. or even 3hours 17min. etc. How would this help with speed calculations – do some. Address misconceptions. Set up group work using a calculator to solve problems incorporating BODMAS and fractions and decimals. Notes Calculators with fraction facilities. Plenary Discuss best ways or alternative tackling calculations on a calculator. Address misconceptions. Add 2 feet 6inches and 3 feet 5 inches using a calculator. Explore other calculations with imperial units. Revisit 6 x (3.2)2 and ways of estimating and doing on a calculator. Explore use of change sign key. When is it useful? Use memory key or constant function to do metric/currency conversions. Explore the use of the reciprocal key perhaps and how it might 4.2 help in the calculation 6.7 2.1 Model the speed of 100miles in 3hours 20min as 100 ÷ 3.2 and discuss. What does 3.2 hours mean really? Algebra 4 (6 hours) Equations and formulae (112–113, 122–125, 138–143) A. Begin to distinguish the different roles played by letter symbols in equations, formulae and functions; know the meanings of the words formula and function. B. 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 the same way). C. Use formulae from mathematics and other subjects; substitute integers into simple formulae, including examples that lead to an equation to solve; derive simple formulae. Unit : Algebra 4 Year Group Y8 Number of 1 Hour Lessons 6 Class/Set Core Oral and mental Main Teaching Obj. a (2 lessons) Ask which is bigger Obj. B Consolidate forming and solving linear equations with one a a, 2a, , or a2 unknown on one side of the equation. 2 Can we order them? Develop to equations with brackets. What do they mean? If 2(x + 3) = 12 is x + 3 = 6 OK? (see page 125) Explore thinking about best method of solving. Relate to What if a = 0.5? Discuss and develop contexts where possible. Relate to worded questions leading to equations. E.g. with other values. An isosceles triangle has a perimeter of 20cm and sides Can we think of a 3x, 3x and 3x + 2. Calculate the lengths of each side. value to make each term the smallest? Try arithmagon activities number walls etc. (page 122 and 123). What function does this graph show? (say y =x + 4). Ask for values of x given y etc. Solve linear equations with the unknown on both sides. Use practical examples to visualise simple situations e.g. Opposite sides of a rectangle are 3x + 12 and 5x + 8 how long is each of the opposite sides? One side of my rectangular garden has 6 fencing panels and a 1metre gap for a gate. The opposite side has 4 fencing panels and a 3metre gap for my car. How long is each panel? Students in groups should be given opportunities to develop and form their own equations. Notes Key Vocab. Expression Equation Expand Simplify Solve Encourage checking by substitution. Plenary Explore misconceptions. Make provocative statements e.g. ‘to solve an equation always multiply out the brackets first’ ‘a2 is always bigger than a’ Generalise on possible strategies for solving equations particularly worded questions. Model solutions. Touch on equations with unknowns on both sides or perhaps with squared terms. What about fractions negatives etc.? Generalise on techniques and checking answers. Discuss solutions. Ask students to demonstrate their solutions. Relate to work/real life problem solving. Encourage use of key vocabulary. Extend to fractions and powers in equations. Oral and mental Obj x and B I think of a number double it and add 6. If my answer is 16 what is the number etc? Extend to n(n-l) = 56 x ÷ 2 + 4 =16 etc. in words After each problem, students model equation and solution. Pupils set their problems to class. Obj A Matching equivalent algebraic expressions. E.g. 2(x + 2) and 2x +4 n x n x n and n3 Discus Main Teaching Obj. A, B and C (2 lessons). Review ideas of collecting like terms simplification and key vocab. Explore ideas of functions (relate to algebra 3) equations and formulae. Revisit restaurant tables’ activity (from last term). Notes Key Vocab Expression Term Equation Formula Function Like terms Solve Simplify Plenary Check key vocab. Model links between practical restaurant tables problem and formulae, equations, data tables, graphs, functions and mappings etc. What have we learned? If we don’t have a T= formula what skills do we need to use the P= formula to calculate T given P? Make a table of values for people and tables. T P 1 6 2 8 3 10 Revisit linear functions, graphs and rules to model this situation and make links. Establish formula. P = 2T + 4 Experiment with substitutions of T. What if we knew P. Could we work out T. Set problems – investigate for other arrangements. Can we create a formula T=? Formulae from every day life and other areas from the curriculum. (Speed, electricity, mobile phone costs, angles in a pie chart, Celsius to Fahrenheit etc.) Substitution into formulae to find subject value. Substitution into formulae to find vale of a non- subject variable given the value other variables in a formula. Model some other formulae from every day life. Explore generalisations and tips for substitutions. How are formulas used in spreadsheets? Model misconceptions/incorrect substitution e.g. 2x2 and (2x)2 x x3 and +3 3 3