KS2 Reasoning & Problem Solving Questions Each question now has a YouTube tutorial

Transcription

1 KS Reasoning & Problem Solving Questions 07 Each question now has a YouTube tutorial

2 Reasoning and Problem Solving Questions Information This booklet contains over 40 reasoning and problem solving questions suitable for KS classes. These are the questions that we have been putting out each day in March 07 on Twitter in the run up to SATS. KS The answers are provided with some simple notes at the back of the booklet and for some questions supplementary questions and variation has been provided. We hope to release more questions like this over the course of next year including some open ended problems. Please keep a look out for our work. If you have not seen our schemes and assessments for primary then please take a look at our website As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team Trinity Academy Halifax 07 For information and comments mathshub@trinityacademyhalifax.org

3 Reasoning and Problem Solving Questions Children s Reponses Children s responses will tell you a lot about their depth of understanding of a given topic. For example Bar Modelling Pictorial Methods KS Many of the problem solving questions in this booklet can be solved using a bar modelling method. Encourage children to use diagrams to help them solve the problem. Here is a problem where bar modelling would help. Children who reason verbally or written that 5 is less than 6 and then 4 is being added each time potentially indicate a deeper understanding of number than those who work out both sides of the inequality. Trinity Academy Halifax 07 For information and comments mathshub@trinityacademyhalifax.org If you want to find out more about bar modelling please contact the Hub.

4 KS Problem Solving Questions Wednesday st March 07 Complete Which diagram has 3 shaded? 40, , = 6, = 5, = 5,80 A B 30, = 36,905 C Explain the reason for your choice. Explain why the other diagrams do not have shaded. 3 D

5 KS Problem Solving Questions Thursday nd March 07 A Find the missing values = = 0cm The area of square A is 36cm. Find the area of one of the triangles. 3 Calculate tens minus tenths

6 KS Problem Solving Questions Friday 3 rd March 07 Complete 3 Here is a rectangle. 6 = cm 4cm A bottle is a third full. Mary puts 30ml of juice into the bottle. A new shape is made up of three of these rectangles. The bottle is now full. How much juice does the bottle hold when full? What is the perimeter of the new shape?

7 KS Problem Solving Questions Monday 6 th March 07 Complete Yesterday at a museum = = of the visitors were adults = = children visited the museum. 3 8 of the adults were male. How many male adults visited the museum yesterday? (You may find the bar model diagram below helpful) Adults

8 KS Problem Solving Questions Tuesday 7 th March 07 (a) The area of a square is 64m Maria has three number cards. One of the cards has a value of 35 The other cards have a smaller value. What is the perimeter of the square? When you add the cards you get. (b) A rectangle is cm longer than it is wide. + = 6 + = 38 The perimeter of the rectangle is 44cm. + = 46 Find the area of the rectangle. (You may find it useful to draw a bar model) What is the value of each card?

9 KS Problem Solving Questions Wednesday 8 th March 07 Mr Singh parks his car. A group of 5 friends share a bag of sweets. Here are the charges. White Rose Car Park First hour.50 Every additional 30 minutes (or less).80 They each receive 6 sweets and there are 3 left over. Mr Singh arrives at 0.45am He leaves the car park at.30pm How much did he pay to park? Two more friends arrive. They share the sweets again between all 7 of them. (a) How many do they each receive? (b) How many are left over?

10 KS Problem Solving Questions Thursday 9 th March 07 Anna, Zoe and Carl donated some money to charity. A blue strip of paper is shown above part of a ruler. Carl donated twice as much as Anna Zoe donated more than Anna 6cm 7cm Altogether they donated 88 How much money did Carl donate? What is the length of 6 of these strips of paper? (You may find it useful to draw a bar model)

11 KS Problem Solving Questions Friday 0 th March 07 8 cans of cola cost 4.80 Sally and Leon each have some money. Sally has 80 Sally spends 3 4 of her money cans of cola and 3 cakes cost 3.60 How much does one cake cost? Leon spends of his money 7 They now have the same amount of money left. How much money did Leon have at the start?

12 KS Problem Solving Questions Monday 3 th March 07 A number is made up of the following digits. The pie chart shows how children in Y6 travel to school The digit in the tenths place is the same as the digit in the ones place. The digit in the hundreds place is one more than the digit in the hundredths place. What is the number? Walk Car Bus 35% 35% of children travel by bus. 8 more children travel by bus than by car. (a) How many children are in Y6? (b) How many walk to school?

13 KS Problem Solving Questions Tuesday 4th March 07 Work out 3 A jar contains 30 sweets. 3 seconds + of a minute = seconds 7 hours + 50 minutes = hours Here are some digit cards (a) What is the largest -digit number you can make that is divisible by 4? (b) What is the largest -digit number you can make that is divisible by 8? The weight of the jar and sweets is 60g. David eats sweets. The weight of the jar and sweets is now 440g. How much does the jar weigh?

14 KS Problem Solving Questions Wednesday 5 th March 07 Henry makes a 3-digit number. A shopkeeper sells fruit. At the start of the week she has 50 oranges and 0 apples. My number lies between 09 and 0 On Monday, she sells 0% of the oranges. The digits sum to 9 5 of the apples How many more apples than oranges are now left? What number did Henry make?

15 KS Problem Solving Questions Thursday 6 th March 07 cm Here are number lines. 6cm 6cm A B 0cm What is the area of the shaded triangle? 0 5 C A, B, C and D are points on the lines. Work out D (a) B A = (b) D C =

16 KS Problem Solving Questions Friday 7 th March 07 A toy shops sells these items. Mel, Martina and Pat have the same number of cards. Toy Aeroplane Toy Train 3 Teddy 8 The bar chart shows how many of each item was sold last week Mel and Martina each give Pat a quarter of their cards. Pat now has 4 cards. How many cards do they have altogether? How much money did the toy shop make last week for these items? (You might find it helpful to draw a bar model)

17 KS Problem Solving Questions Monday 0 th March 07 Dev has a 3kg bag of flour. Mina buys 3 pizzas and a bottle of cola. He uses 7 kg of the flour to make a 0 cake and uses 0.65kg to make some bread. A pizza costs 3.0 more than a bottle of cola. The total cost of the items is 9.40 How much does a pizza cost? How much flour has he left? (You might find it helpful to draw a bar model)

18 KS Problem Solving Questions Tuesday st March 07 Gavin has a tin of paint. Here is a rectangle. Some lines have been drawn inside. a The tin is full and weighs 5.8kg. He paints a wall in his house. The tin is now full and weights 4.4kg 3 How much does the empty tin weigh? 35 Work out the size of the angle marked a. Explain your reasoning.

19 KS Problem Solving Questions Wednesday nd March 07 If Find the missing values. Find the value of = 30 = = = = = 3 Freya has some money. She buys a book for 5 She has 3 of her money left. 8 How much did she have at the start?

20 KS Problem Solving Questions Thursday 3 rd March 07 A shape has been drawn on a cm by cm square grid. Sue has some counters. A quarter of the counters are green. cm She gives 5 her friend. of the green counters to She has 4 green counters left. Find the area of the shape. How many red counters does she have?

21 KS Problem Solving Questions Friday 4 th March 07 A square is divided into smaller squares. Sophie has some marbles. The marbles are identical. The mass of an empty jar is 480g The mass of the jar when full with the marbles is.kg What is the mass of the jar when it is What fraction of the shape is shaded? half full with marbles?

22 KS Problem Solving Questions Monday 7 th March 07 Nimesh has 60 boxes of oranges. Each box contains 5 oranges. A loaf of bread costs the same as 3 apples. Nimesh sells 800 oranges. Millie buys 3 loaves of bread and 5 apples for 5.60 He packs the remaining oranges into boxes of 50 How many boxes does he pack? How much does each item cost?

23 KS Problem Solving Questions Tuesday 8 th March 07 The square and rectangle have the same area. 3 Complete 6 40 = 8 4cm 0% of = 0cm Find the perimeter of the rectangle. Calculate 5 of =

24 KS Problem Solving Questions Wednesday 9 th March 07 A box contains 40 cubes. Find the area of the shaded region. 7cm For every one red cube there are four blue cubes. cm 6cm red cubes are removed from the box. Some blue cubes are also removed. There are now 3 times as many blue as red cubes. How many blue cubes were removed? 6cm

25 KS Problem Solving Questions Thursday 30 th March 07 Alex has a bag of sweets. Mr Dexter buys the following. He eats the same number of sweets each day. After days he has 5 of the sweets 6 left. After another 4 days he has 5 left. How many sweets are in the bag? The TV costs 30 more than the bike. The total cost is 40 How much does the TV cost?

26 KS Problem Solving Questions Friday 3 st March 07 Fiona has a box of chocolates. Find the angle marked x The box contains 60 chocolates She eats 5 of the chocolates. x She gives 3 chocolates away. What fraction of the chocolates does she have left? Give your answer in its simplest form.

27 Reasoning and Problem Solving Questions KS Day Question Answer Notes 47,607 6, ,00 Because it is part shaded out of 3 equal parts. Discuss with children why the other three do not show 3 8cm different methods to get the Encourage children to find two answer ml What is 30ml equivalent to? 3 56cm 9 9 Would the perimeter change if the top rectangle moved?

28 Reasoning and Problem Solving Questions KS 5 80 male adults a 3m Encourage children to use a bar model. What is the length of each side? 5 b 0cm a 4 b 5 Carl donated cm 80p a 80 children b 3 children 8 seconds 9.5 hours /9 hours 30 minutes a 84 b g Encourage children to draw a comparison bar model. What is the length of one strip of paper? What would one marking be worth? What does one can of cola cost? How much does Sally have left? It may be useful to draw a bar model. Or equivalent What is the weight of one sweet?

29 Reasoning and Problem Solving Questions KS What is the weight of 30 sweets? 6 4 How many oranges did she sell? How many apples did she sell? How many of each are left? What is the area of the big right 8cm angled triangle? What is the area of the small right angled triangle? a B A = 0.5 Or equivalent b D C = kg kg 57 Toy aeroplane = 0 Toy train = 690 Teddy = 0 How many cards does Pat have? The question says 7 0 kilograms not 7 0 of the bag of flour. How much does a bottle of cola cost? (.45) Subtract fractions to find what 6 of the paint weighs. Encourage children to mark angles on the diagram. What do angles on a straight line add up to? What do angles in a rectangle add up to?

30 Reasoning and Problem Solving Questions KS What is a circle equal to? What is a star equal to? cm g 4 boxes Loaf of bread =.0 Apple = 40p Perimeter of rectangle = 08cm 8 What fraction of her money did the book cost? What is the area of one square? How many squares are in the diagram? How many half squares are in the diagram? What fraction does she keep? How many green counters are there? Or equivalent What is the mass of the marbles? What is the mass of half of the marbles? How many oranges does Nimesh have in total? How many does he have left? How many apples will 3 loaves of bread be equal to? What is the area of the square? What is the length of a side of the rectangle?

31 Reasoning and Problem Solving Questions KS blue cubes were removed 7cm 30 sweets How many red cubes are there? How many blue cubes are there? How many chocolates does she eat? How many chocolates does she have left?