SOW Year 8 Higher Target Levels: 6 7 Set 1 only

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1 SOW Year 8 Higher Target Levels: 6 7 Set 1 only Date Module Topic Key skills development & Pre-Requisites & Assessment & Tests as well as Examples of what pupils should know and be able to do at Level 5/6 & Level 5/6 Probing Questions 23 rd Jun 1.1 Properties of Number Prime numbers Factors & multiples Square numbers Prime factor decompiosition Cube numbers & hiher powers Recall x-tables to 12x12, use column method, long division, partitioning, encourage pupils to approximate answers by estimating/rounding to 1s.f. Examples of what pupils should know and be able to do Homework Homework Teachers are to set roughly 30 minutes of homework each week. Alternate with a written piece. Other Resources for use in lessons Inc. Framework Reference (page ref in brackets) 30 th Jun 1.2 Fractions Equivalent fractions +, - and fractions Examples of what pupils should know and be able to do at Level 6 Starter Activity Q: What can you say about these fractions? ; ; ; ; ; Q: Which fraction do you think is the largest? Which is the smallest? Why? Q: Pick two fractions and say which one is larger Q: Tell me another fraction that is equivalent to. And another, and another. Explain how you know they are equal to? And now do the same with. Q: How would you add and without a calculator? Q: The answers to + is a little bit more than 1. Is there any way you could have predicted this without working this out exactly? Main Activity: Q: I want you to add together as many of the six fractions as like to get an answer as near to 1 as possible. You can only use each fraction once (you can t get exactly 1!) Extension & Homework UKMT questions

2 Why are equivalent fractions important when adding or subtracting fractions? What strategies do you use to find a common denominator when adding or subtracting fractions? Is there only one possible common denominator? What happens if you use a different common denominator? Give pupils some examples of addition and subtraction of fractions with common mistakes in them. Ask them to talk you through the mistakes and how they would correct them. How would you justify that = 20? How would you use this to work out 4 2 5? Do you expect the answer to be greater or less than 20? Why? 15 th Jul 1.3 Area & Perimeter Rectangles, triangles, parallelograms & trapeziuums Area & problem solving Charlie has been drawing rectangles: The first rectangle has a perimeter of 30 units and an area of 50 square units. The second rectangle has a perimeter of 24 units and an area of 20 square units. Charlie wondered if he could find a rectangle whose perimeter and area have the same numerical value. Can you find a rectangle that satisfies this condition? Alison says "There must be lots of rectangles whose perimeter and area have the same numerical value." Charlie is not so sure. Can you find more examples of such rectangles? Can you come up with a convincing argument to help Charlie and Alison decide who is right? Why do you have to multiply the base by the perpendicular height to find the area of a parallelogram? The area of a triangle is 12cm2. What are the possible lengths of base and height? Right-angled triangles have half the area of the rectangle with the same base and height. What about non-rightangled triangles? What other formulae for the area of 2-D shapes do you know? Is there a formula for the area of every 2-D shape? How do you go about finding the volume of a cuboid? How do you go about finding the surface area of a cuboid? You can build a solid cuboid using a given number of identical interlocking cubes. Is this statement always,

3 15 th Jul Activities week 23rd Jul 6 th Sept SUMMER HOLODAYS 9 th Sept 1.4 Negative numbers +, - and with negative numbers 16 th Sept 1.5 Sequences Find the next term Fins & use a rule for a sequence Solve problems using differences sometimes or never true? If it is sometimes true, when is it true and when is it false? For what numbers can you only make one cuboid? For what numbers can you make several different cuboids? NB: also called directed numbers Find the nth term in a sequence such as: 7, 12, 17, 22, 27,... 12, 7, 2, 3, 8,... 4, 2, 8, 14, 20,... The term-to-term rule for a sequence is +2. What does that tell you about the position-to-term rule? Do you have enough information to find the rule for the nth term? Why? How would you go about finding the position-to-term (nth term) rule for this information about a sequence? Position Term Starter from UKMT Challenge 2006: The standard Fibonacci sequence 1, 1, 2, 3, 5, 8, 13,? begins with two 1s and each later number in the sequence is the sum of the previous two numbers. Other Fibonacci like sequences can be constructed by starting with any two numbers a and b (not necessarily 1 and 1) and using the same rule for creating the other numbers in the sequence. What is the first term of the Fibonacci-like sequence whose second term is 4 and whose fifth term is 22? NRICH Making sense of positives & negatives Consecutive negative numbers NRICH Odds, Evens and More Evens 23 rd Sept 1.6 Using a calculator Review BODMAS Learn to use buttons on their calculator 30 th Sept Mixed Review 1 7 th Oct 2.1 Written Calculations Review Written methods of calculations Reading a number scale Teach the Gelosia/Grid method of multiplication for integers and decimals it works and is easy to remember. Probing Questions: How would you explain that 0.35 is greater than 0.035? Why do and give the same answer? My calculator display shows Tell me what will happen when I multiply by 100. What will the display show? I divide a number by 10, and then again by 10. The answer is 0.3. What number did I start with? How do you know? How would you explain how to multiply a decimal by 10, and how to divide a decimal by 100? IV has a PDF of the Gelosia method

4 and decimals 14 th Oct 2.2 Estimating & Checking Answers Estimate the value of a decimal Check answers to see if they are about the right size Round numbers to 1.d.p & 2.d.p 21 st Oct 2.3 Geometrical reasoning Examples of what pupils should know and be able to do at Level 5 Discuss questions such as: Will the answer to be smaller or larger than 75? Check by doing the inverse operation, e.g. Use a calculator to check: = with of 320 = 192 with Looking at a range of problems or calculations, ask: Roughly what answer do you expect to get? Do you think your estimate is higher or lower than the real answer? How could you use inverse operations to check that a calculation is correct? Show me some examples. Examples of what pupils should know and be able to do: Finding angles Prove results in geometry 28 th Oct OCTOBER HALF 1 st Nov TERM 4 th Nov 2.4 Using Algebra Rules of algebra in How could you convince me that the sum of the angles of a triangle is 180º? Why are parallel lines important when proving the sum of the angles of a triangle? How does knowing the sum of the interior angles of a triangle help you to find the sum of the interior angles of a quadrilateral? Will this work for all quadrilaterals? Why? Examples of what pupils should know and be able to do at Level 5 Simplify these expressions: Linear equations: (p )

5 expressions Using algebra to solve problems 3a + 2b + 2a b 4x x 3 x 3(x + 5) 12 (n 3) m(n p) 4(a + 2b) 2(2a + b) Substitute integers into simple formulae, e.g.: Find the value of these expressions when a = 4. 3a and 2a 3 Find the value of y when x = 3 y = and y = 11 th Nov 2.5 Applying Mathematics in a Range of contexts 1 18 th Nov 2.6 Circles Circumference of a circle & perimeters of circle-related shapes Area of a circle Give pupils examples of multiplying out a bracket with errors. Ask them to identify and talk through the errors and how they should be corrected, e.g.: 4(b +2) = 4b + 2 3(p 4) = 3p 7 2 (5 b) = -10 2b 12 (n 3) = 9 n Can you write an expression that would simplify to, e.g.: 6m 3n what about 8(3x + 6)? Examples of what pupils should know and be able to do: Plenary: Are there others? 25 th Nov Mixed Review 2 2 nd Dec 3.1 Reflection Draw reflections on squared paper Draw reflections using coordinates Investigate reflections What is the minimum information you need to be able to find the circumference and area of a circle? Give pupils some work with mistakes. Ask them to identify and correct the mistakes. How would you go about finding the area of a circle if you know the circumference? Examples of what pupils should know and be able to do: Starters:

6 9 th Dec 3.2 Describing Data Mean, median, mode & range Comparing sets of data Finding averages from frequency tables Stem & leaf diagrams 16 th Dec 3.3 Mental Calculations Practising + & - and doubling numbers Mental calculation in a range of contexts Mental arithmetic test-style questions What changes and what stays the same when you: Translate, rotate, and reflect a shape? When is the image congruent to the original shape? How do you know? What changes when you enlarge a shape? What stays the same? What information do you need to complete a given enlargement? The mean height of a class is 150cm. What does this tell you about the tallest & shortest pupil? How do you know? Find five numbers that have a mean of 6 and a range of 8. How did you do it? What if the median was 6 and the range 8? What if the mode was 6 and the range 8? Two distributions both have the same range but the first one has a median of 6 and the second has a mode of 6. Explain how these two distributions may differ. The 11+ and 13+ offers a good range of mental arithmetic practice otherwise go to emaths to access level 5-8 mental arithmetic tests with audio files & answer sheets (no need to print anything) 20 th Dec 3 rd Jan CHRISTMAS HOLIDAYS 6 th Jan 3.4 Using formulas & Expressions Substitution Evaluate complex expressions

7 13 th Jan 3.5 Constructions & Loci Construct triangles With rule, compass & protractor Draw & describe the locus of a point Draw construction with rule & compasses only Examples of what pupils should know and be able to do at Level 7: Level 7 Probing Questions: How can you tell for a given locus whether it is the path of points equidistant from another point or a line? What is the same/different about the path traced out by the centre of a circle being rolled along a straight line and the centre of a square being rolled along a straight line? Starter: Hold a large triangle in one hand and an imaginary telephone in the other. Pretend you are talking long distance: I have designed your triangle. Yes, it has one side of 60cm, another of 70cm yes that s right 70 and an angle of 35 degrees and another of hello! Hello?... I seem to have been cut off. Are these 3 pieces of information enough to reproduce the triangle? Mixed Review 3 20 th Jan 4.1 Bearings & Scale Drawings About bearings Make scale drawing to solve problems Using a spread sheet on a Computer 27 th Jan 4.3 Handling Data draw & interpret scatter graphs Bar & pie charts Produce charts using a computer 3 rd Feb 4.4 Fractions, Decimals & Percentages Change from Fractions to Decimals to % Solve problems involving % increase or decrease Examples of what pupils should know and be able to do at Level 5 Why is it important to estimate the size of an angle before measuring it? What important tips would you give to a person about using a protractor? How would you draw a reflex angle with a 180 protractor? Why are 30º and 150º in the same position on a 180º protractor? Q: What is 10% of ¾ as a decimal? Which sets of equivalent fractions, decimals and percentages do you know? From one set that you know (e.g = 0.1 = 10%) which others can you deduce? How would you go about finding the decimal and percentage equivalents of any fraction? Problems available in the shared area: Rich Uncle Trail & improvement Hot air balloon(tougher)

8 How would you find out which of these is closest to 1 3; 10 31; 20 61; 30 91; ? What links have you noticed within equivalent sets of fractions, decimals and percentages? Give me a fraction between 1 / 3 and ½. How did you do it? Which is it closer to? How do you know? 10 th Feb 4.5 Interpreting & Sketching real-life Graphs Interpret a range of graphs Sketch graphs from real-life contexts The graph below shows information about a race between two animals the hare (red) and the tortoise (blue). Who was ahead after two minutes? What happened at three minutes? At what time did the tortoise draw level with the hare? Between what times was the tortoise travelling fastest? By what distance did the tortoise win the race? 17 th 21 st Feb FEBRUARY HALF TERM 24 th Feb 4.6 Rotation & Combined Transformations Rotating shapes Finding the centre of rotation Combined transformations 3 rd Mar 4.7 Brackets & Equations Multiply out brackets Solve linear equations Solve problems by forming equations Mixed Review 4 10 th Mar 5.1 Enlargement Recognise enlargements and their properties Draw enlargements Use the centre of What do the axes represent? In the context of this problem does every point on the line have a meaning? Why? What s the relevance of the intercept in relation to the original problem? Starter: Solve, e.g.: 3c 7 = 13 4(z + 5) = 84 4(b 1) 5(b + 1) = 0 12/(x+4) = 21/(x+4) The length of a rectangle is three times its width. Its perimeter is 24cm. Find its area. 6 = 2p 8. How many solutions does this equation have? Give me other equations with the same solution. Why do they have the same solution? How do you know? What changes when you enlarge a shape? What stays the same? What information do you need to complete a given enlargement?

9 enlargement Solve problems with fractional scale factors 17 th Mar 5.2 Sequences & Formulas Learn about the nth term Use mapping diagrams to find the nth term Solve problems involving the nth term 24 th Mar 5.3 Applying Maths in a range of Contexts 2 31 st Mar 5.4 Pythagoras Theorem Calculating lengths of sides Solving problems using Pythagoras 7 th 22 nd EASTER HOLIDAYS Apr 28 th Apr 5.5 Drawing & Using Graphs Draw straight line graphs Draw graphs using a computer or graphical calculator Find the equation If someone has completed an enlargement how would you find the centre and the scale factor? When doing an enlargement, what strategies do you use to make sure your enlarged shape will fit on the paper? Examples of what pupils should know and be able to do at Level 7: Investigate the standard paper sizes A1, A2, A3, exploring the ratio of the sides of any A-sized paper and the scale factors between different A-sized papers. Level 7 Probing Questions: Given an object and its enlargement what can you say about the scale factor? How would you recognise that the scale factor is a fraction between 0 and 1? How would you go about finding the centre of enlargement and the scale factor for two similar shapes? How does the position of the centre of enlargement (e.g. inside, on a vertex, on a side, or outside the original shape) affect the image? How is this different if the scale factor is between 0 and 1? Q: 1, 2, 4 think of 3 different ways this sequence should continue. What is the rule to find the next term? Level 7 Probing Questions: Can you find the shorter sides of a RA isosceles triangle given a hypotenuse of 10cm? Can you fit a 13cm pencil into a right cylindrical tin of height 12cm and diameter 10cm? You are not allowed to snap the pencil! How can you use Pythagoras theorem to tell whether an angle in a triangle is equal to, greater than or less than 90 degrees? What is the same/different about a right-angled triangle with sides 5cm, 12cm and an unknown hypotenuse, and a right-angled triangle with sides 5cm, 12cm and an unknown shorter side? Plot the graphs of : y = 2x 3 y = 5 4x Without drawing the graphs, compare and contrast features of pairs of graphs such as: y = 3x y = 3x + 4 y = x + 4 y = x 2 y = 3x 2 y = 3x + 4 How do you go about finding a set of coordinates for a straight line graph, e.g. y = 2x + 4?

10 of a straight line Draw curved graphs Use graphs in reallife contexts 5.6 Using ratios Use & simplify ratios Share quantities in a given ratio Ratio in a range of contexts Solve problems using map scales How do you decide on the range of numbers to put on the x and y axes? How do you decide on the scale you are going to use? If you increase/decrease the value of m, what effect does this have on the graph? What about changes to c? What have you noticed about the graphs of functions of the form y = mx + c? What are the similarities and differences? Potting compost is made from loam, peat and sand in the ratio 7:3:2 respectively. A gardener used 1.5 litres of peat to make compost. How much loam did she use? How much sand? The angles in a triangle are in the ratio 6:5:7. Find the sizes of the three angles. If the ratio of boys to girls in a class is 3:1, could there be exactly 30 children in the class? Why? Could there be 25 boys? Why? Q: Imagine a country where all the parents want to have a boy. Every family keeps having children until they have a boy; then they stop. What is the proportion of boys to girls in this country? 5 th May Mixed Review 5 12 th May Revision Week 19 th May END OF YEAR 8 EXAM WEEK 26 th MAY HALF TERM 30 th May Jun-Jun 20 th Go through the End of Year 8 Exams Finish going through the rest of the book 6.1 More Algebra Solve equations involving fractions Solve equations involving brackets Solve word problems by forming equations

11 Use algebra to explain connections 6.2 Volume of Objects How many small boxes 2cm x 3cm x 1cm can you fit in a big box 1m x 3m x 1m? Volume of a cuboid and other prisms Volume of a cylinder 6.3 Percentage 2 Review interchanging between FDP Find a percentage increase Increase & decrease quantities by a percentage 6.4 Probability Probability of events not occurring Expected no of times an event will occur Examples of what pupils should know and be able to do at Level 5 When you spin a coin, the probability of getting a head is 0.5. So if you spin a coin ten times you would get exactly five heads.' Is this statement true or false? Why? You spin a coin 100 times and count the number of times you get a head. A robot is programmed to spin a coin

12 Probability involving two events Experimental probability 6.5 Drawing 3D Objects Draw 3D objects on isometric paper Solve problems with objects 3-views of an object 1000 times. Who is most likely to be closer to getting an equal number of heads and tails? Why? Probing Questions: 6.6 Statistical Methods Discuss a statistical problem, collect relevant data and then present the data in an effective way Examples of what pupils should know and be able to do at Level 5: Which newspaper is easiest to read? In a newspaper survey of the numbers of letters in 100-word samples the mean and the range were compared: Tabloid: mean 4.3 and range 10 Broadsheet: mean 4.4 and range The mean height of a class is 150cm. What does this tell you about the tallest and shortest pupil? Tell me how you know. Find five numbers that have a mean of 6 and a range of 8. How did you do it? What if the median was 6 and the range 8? What if the mode was 6 and the range 8? Two distributions both have the same range but the first one has a median of 6 and the second has a mode of 6. Explain how these two distributions may differ. Jun 23 rd Mixed Review 6 Summer Term Activities week CHANGE OF TIMETABLE NOTES FOR THE TEACHER This is an Active SOW which tells the teacher what to teach and when. This is a working document and personal notes (Inc. dates/tarsia/tests you give) should be made on it made as required to be shared with the rest of the team during meetings. APP assessment criteria embedded into the SOW Examples of what pupils should know and be able to do are provided so teachers have a feel for how difficult the mathematics is intended to be. These are not activities or examples that will enable an accurate assessment of work at this level. To do this, you need a broad range of evidence drawn from day-to-day teaching over a period of time; this is exemplified in the Standards files. Furthermore, some probing questions are also provided for the teacher to use with pupils in lessons to initiate dialogue to help secure their assessment judgement

13 Classwork Teacher Activity: Page numbers refer to Essential Maths 8H Class Text used with Set 1 in Y8. Examples are provided in the boxes to help you direct the lesson. Student Activity: Page numbers refer to Essential Maths 8H Class Text used with Set 1in Y8. Explicit Differentiation - this should now be an integral part of every lesson Homework Teachers should alternate homework between 1 x Written and 1 x Online ( to ease the pressure of marking) Teachers are advised to keep an Electronic homework record see me if you need help setting this up Assessment All Year 8 pupils will sit for their end of year Exams in May