# Talking REAL Maths. A resource to engage children in discussion based on common errors and misconceptions in mathematics.

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1 Talking REAL Maths A resource to engage children in discussion based on common errors and misconceptions in mathematics.

2 ALGEBRA Discussion mat Suggested year group/ks APP link Simple Sequence Lower KS2 L3 Alg 1 Recognise a wider range of sequences Balance Scale 1 Y2/Lower KS2 L3 Alg 2 Begin to understand the role of = (the equals sign) L3 Alg 2 Begin to understand the role of = (the equals sign) Balance Scale 2 Y2/Lower KS2 L3 Calc 5 Use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers Coordinates Upper KS2 L4 Alg 2 Use and interpret coordinates in the first quadrant L4 SSM 3 Reflect simple shapes in a mirror line, translate shapes horizontally or vertically and begin to rotate a simple shape or object about its centre or vertex

3 Two people are correct: I think one of the missing numbers is 23. I don t have enough information to work out the missing numbers. 18 and 33 are both in the 3 times table, so it must be jumping in 3 s. I think the last number will be zero. I think the sequence is about subtraction. Simple Sequence

4 I think we could have 8 on the left so 8 = 2+6. I think we could put two weights on the number 3 to still make = 8. I think this balance shows that 5+3 = 2+6 I think I could take off the 2 and the 6 and just put a weight on the 8 so 5+3=8 Balance Scale 1 Who s is wrong? Sarah says that the equals (=) sign always has to come at the end of the number sentence so = 8. Is she right?

5 Balancing Scales Which answer would you choose to evenly balance these scales? The answer is 100 because I know that = 100. The answer is 111 because I know that = 100 And = 11 Balance Scale 2

6 The coordinates of point A are (6,4) Which two are correct? The coordinates of point B are (6,6) If I reflect the triangle in the mirror line the new coordinates will be (4,1), (6,1) and (6,4) Coordinates If I translate the triangle its new coordinates could be (4,1), (6,1) and (6,4) The mirror line is y=5

7 NUMBERS AND THE NUMBER SYSTEM Discussion mat Suggested year group/ks APP link Cake Fractions 1 KS1 L1 NNS 4 begin to use the fraction one-half L2 NNS 3 Begin to use halves and quarters and relate the concept of half of a small quantity to the concept of half of a shape Playground Balls 1 KS1 L1 NNS 4 begin to use the fraction one-half L2 NNS 3 Begin to use halves and quarters and relate the concept of half of a small quantity to the concept of half of a shape Playground Balls 2 Y2/Lower KS2 L2 NNS 3 Begin to use halves and quarters and relate the concept of half of a small quantity to the concept of half of a shape Place Value Y2/Lower KS2 L3 NNS 1 understand place value in numbers to 1000 Pizza Fractions 1 Lower KS2 L3 NNS 4 Use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. Chocolate Fractions Lower KS2 L3 NNS 4 Use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. Cake Fractions 2 Lower KS2 L3 NNS 4 Use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. Smarties Fractions Lower KS2 L3 NNS 4 Use simple fractions that are several parts of a whole and recognise when two simple fractions are equivalent. Tricky Sequence Upper KS2 L4 NNS 1 recognise and describe number patterns Pizza Fractions 2 Upper KS2 L4 NNS 4 Recognise approximate proportions of a whole and use simple fractions and percentages to describe these

8 Cake Fractions 1 Which of the thought bubbles show the cake being shared in half? When you ve made the cake you can share it between you!

9 Mr Newman has asked us to put 1 of the balls into the skipping circle. 2 I m going to put one ball in the circle because 1 is the top number I don t think I can do this because if I cut a ball in half then the next group can t use it I think he wants 6 balls because if you put the balls into two groups there will be 6 in each group. I will put 3 balls in because ½ means Playground Balls 1

10 Mr Newman has asked us to put ¼ of the balls into the skipping circle for the next group. I m going to put one ball in the circle because 1 is the top number I think he means 5 because ¼ is I think he wants 6 balls because if you put the balls into two groups there will be 6 in each group. I will put 3 balls in because if I put the balls into 4 equal groups there will be 3 balls in each group and 3 lots of 4 is 12 Playground Balls 2

11 Daisy, Kyle and Luke have been learning about adding tens to three-digit numbers When you add 10 to a three-digit number the hundreds digit always stays the same! I m not too sure what do you think? I think when you add 10 the units digit always stays the same. Place Value

12 I ve eaten 2 slices of pizza, that means I ve eaten 1/2 of the pizza! I have eaten 3 slices that means I have eaten more than ¼ of the pizza I have eaten one slice. That means I ve eaten 1/8 of the pizza Pizza Fractions 1 Only one person is wrong who do you think it is? I ve eaten 4 slices of pizza, that means I ve eaten 1/2 of the pizza!

13 CHOCOLATE CHALLENGE How many pieces would half be? Write a fraction for this chocolate bar that is an equivalent to ¼ What fraction of the bar would 2 squares be? Describe a quarter of this bar? Describe a third of this bar? Even harder!! What is the maximum number of people I could share this bar with? Chocolate Fractions

14 2/5 of the cake will get me the biggest slice Would you like to have some of my birthday cake? I ll have ¼ of the cake please, that will be a fair way to share it out. Can I have 1/6 of the cake. That way I ll get more than Mum. Cake Fractions 2 Two people are right? Can you think of a way to prove this to the others?

15 Convince me that this child is wrong: 6 Smarties are blue so that means: 6 15 is the fraction of blue Smarties here. There are 21 Smarties What fraction of the Smarties are green? Draw a diagram to convince me that the fraction of green Smarties is bigger than the fraction of red Smarties. Smarties Fractions What is this child doing wrong? Fraction of red Smarties Explain what you would do to help. 21 4

16 I think 88 will be in the sequence Only one person is correct. I think the missing number after 33 is 25 ½ Tricky Sequence The difference between 33 and 18 is 15 so it must be counting in steps of 7 ½ The first negative number in the sequence will be -3 What do you think the two missing numbers are?

17 I ve eaten 10 slices so I must have eaten 8/10 of a pizza! Only one person is right who do you think it is? I ve eaten 4 pieces of pizza so I must have eaten ¼ of a pizza! I ve eaten ten slices of pizza, that means I ve eaten 1 ¼ pizzas! I ve eaten 6 slices so I guess I ve eaten 60% of the pizza! Pizza Fractions 2 Pete s pizza are always cut into 8 equal slices.

18 CALCULATING Discussion mat Suggested year group/ks APP link Purses Y2/Lower KS2 L2 calc 3 use mental calculation strategies to solve number problems including those involving money and measures Starburst Y2/Lower KS2 L2 calc 3 use mental calculation strategies to solve number problems including those involving money and measures Make 50 Y2/Lower KS2 L3 Calc 2 add and subtract two digit numbers mentally Toy Shop Lower KS2 L3 Calc 5 - Use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers L3 NNS 5 Begin to use decimal notation in contexts such as money World Cup stickers Lower KS2 L3 Calc 5 - Use mental recall of addition and subtraction facts to 20 in solving problems involving larger numbers L3 Calc 6 Solve whole number problems including those involving multiplication or division that may give rise to remainders Chocolate box Upper KS2 L4 Calc 3 use efficient written methods of addition and subtraction and of short multiplication and division Cricket Scores Upper KS2 L4 Calc 3 use efficient written methods of addition and subtraction and of short multiplication and division Calculator Upper KS2 L4 Calc 5 solve problems with or without a calculator (interpret a calculator display) L5 SSM 6 Solve problems involving conversion of units and make sensible estimates of a range of measures in relation to everyday situations DVDs KS2 No specific APP link as a range of mathematical topics are covered.

19 Which purse shows the correct amount? 20p Lucy s purse Peter s purse Purses Susie s purse Shaman s purse

20 Which coins would you use to buy a packet of Starburst costing 38p? Starburst Only two are correct. Which ones are they?

21 What needs to be added to each cylinder to make 50 ml? 34 ml 35 ml 65 ml Make 50 Who is correct?

22 Can you work out if any of these children worked out their answers correctly? If they have made mistakes how could you help them? If I buy one of everything it will cost Toy Shop If I buy two slinky toys it will cost me = = = 2.18 If I buy a robot and pay with I will get 8.46 change. I know this is right because a robot costs 2.64 and I used my number bonds. There is a half price offer on for this week only. I think that for 5.00 I can buy one of each toy.

23 Two friends are collecting World Cup stickers I can fill 6 pages with 8 stickers on each page so I have 48 stickers I have 37 stickers and if I put 12 on each page I will have 3 full pages with one left over. Stickers cost 50p for 6 stickers so it has cost me 4.00 to buy my stickers. If we add our collections together we will have 75 stickers. One of the statements is wrong! World cup stickers

24 There are 36 chocolates in a layer. How many are in the whole box? One person is correct. Who do you agree with? Chocolate Box

25 How many runs did England win by? Which answer is correct? Cricket Scores

26 The calculator shows the answer to a question. What could this mean? 3kg and 8g mm litres 80ml Two are correct. Calculator

27 I have 24 DVDs. Which two of these statements are I have a rack that holds 100 so I need to get 86 more to fill it. correct? Mum said that ¾ of these are made by Disney so that is 3. ¼ of these are too young. 1/3 of them are too old. So I can only watch 10 of them. DVDs

28 SHAPE SPACE AND MEASURES Discussion mat Suggested year group/ks APP link Sorting Shapes KS1/Lower KS2 L2 SSM 1 use mathematical names for common 3-D and 2-D shapes L2 SSM 2 Describe their properties, including number of sides and corners L2 HD 1 Sort objects and classify them using more than one criterion Ruler 1 KS1/Lower KS2 L2 SSM 5 begin to use a wider range of measures including everyday non-standard and stand units to measure length and mass Measuring Cylinders Lower KS2 L3 SSM 5 Use a wider range of measures including non-standard units and standard metric units of length, capacity and mass in a range of contexts L3 Calc 2 add and subtract two digit numbers mentally Flapjacks Lower KS2 L3 SSM 5 Use a wider range of measures including non-standard units and standard metric units of length, capacity and mass in a range of contexts Cake Time KS2 L3 SSM 6 Use standard units of time Ruler 2 Upper KS2 L4 SSM 5 Interpret, with appropriate accuracy, numbers on a range of measuring instruments Temperature Upper KS2 L4 SSM 5 Interpret, with appropriate accuracy, numbers on a range of measuring instruments Playground Measures Upper KS2 L4 SSM 5 Interpret, with appropriate accuracy, numbers on a range of measuring instruments Timetable Upper KS2 No specific link to APP assessment criteria

29 Sorting Shapes Some faces are triangles Can you find these shapes and name them? Shapes with an even number of faces I think shapes with more faces have more corners? 3 shapes have been sorted incorrectly. Can you find them? What do you think? Now that you ve found the incorrect shapes, can you tell me something that is the same and something that is different about them?

30 Has the correct answer been circled? Explain your answer. This side measures: 4.5 cm 4.05cm 3.50 cm 3.5 cm 4 cm How is this child using the ruler incorrectly? What would you do differently? Ruler 1

31 Measuring Cylinders Convince me that this does not measure 71 ml True/ False? All of these measuring cylinders measure the same amount. Measuring Cylinders True/false? I need to add 38ml more to make 100 ml.

32 I only want to make 6 flapjacks I can t do it! Making Flapjacks Here is a recipe for 18 Flapjacks Ingredients 75 g butter 30ml golden syrup 75g light brown sugar 150g porridge oats 50g raisins If I add the amount of butter to the porridge oats I will have ¼ kg Flapjacks If I have 1 kg of raisins I can make two batches of flapjacks because there are 100g in 1kg There is half as much sugar as porridge oats in this recipe.

33 I think twenty to four is 03:40 I wish I d paid attention at school is twenty to 4 04:20 The cake takes an hour to cook so we ll need to put it in at twenty to four so it is ready for tea time. Twenty to four that s when the cooker clock says 20:4 Cake Time What do you think?

34 Two answers are correct. Which two would you choose? Explain your choices. This line measures: 6.5 cm 6.05 cm 65 mm Only one answer is correct. Which would you choose? Explain your choice. To make it 10cm, I need to add: 4.05cm 4 cm 4.5 cm 3.5 cm Ruler 2

35 The first thermometer s temperature is 2.5 C because if you count up from 0 it is 2.5 more. Which statements do you agree with? I think all of these thermometers have the same temperature reading. Temperature The middle thermometer s temperature is only 1 C because it is 1 more above 0 C

36 This is 26,400 cm The perimeter of our playground is m I think this is > 2km I think this is < 1km I need another 51cm to make 265m This number means 264m, 5cm and 9mm 1 person is correct. Who do you agree with? Playground measures

37 I need to get to Worcester Shrub Hill for 4.30pm. I m not sure which is the best train to get from Gloucester! The half past one train from Bristol Temple Meads takes 82 minutes to get to Cheltenham Spa. Timetable I don t think the 2 o clock train from Bristol goes to Birmingham! Can you help? What is the shortest journey time from Bath Spa to Birmingham New Street?

38 HANDLING DATA Discussion mat Suggested year group/ks APP link School Travel Lower KS2 L3 HD 2 Construct bar charts and pictograms, where the symbol represents a group of units Beans Lower KS2 L3 HD 4 Extract and interpret information presented in simple tables, lists, bar charts and pictograms Pictogram Lower KS2 L3 HD 4 Extract and interpret information presented in simple tables, lists, bar charts and pictograms

39 How children in class 3 travel to school Method of travel Number of children Walk 14 Bus 7 Car 10 Bike? I think the scale needs to start at one. Which one is correct? I think the scale should go up in ones I think four more people walk to school than go by bike. School Travel I think the total number of children is 40. I think the horizontal axis should be labelled walk, bus, car, bike

40 Height in cm Names In Class 3 we all grew beans from seeds. After 5 weeks we measured their height and counted the leaves. Here are some ways to show the results. Kim Tom Number of Leaves Leaves Series1 Name Height In cm Leaves Tom Toby 7 19 Toby My bean plant had 7 leaves and was 19cm high Kim How high our beans grew Tom Tom Toby Kim Names Series1 Kim Mine grew 21cm, had 3 flowers and 12 leaves My bean plant was 37 cm tall and had 13 leaves Beans Do you think the data has been presented correctly?

41 Seven apples were eaten on Saturday Only two children are correct. Who are they? Eleven apples were eaten on one day Twenty two apples were eaten during the week Two more apples were eaten on Thursday than on Wednesday On Wednesday 3 apples were eaten Pictogram

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