Includes CD-ROM for whiteboard use or printing Primary Problem Solving, Reasoning & Investigating Year 1 MATHEMATICS CURRICULUM
Maths Problem Solving, Reasoning & Investigating Year 1 Lizzie Marsland Susannah Palmer
Acknowledgements: Author: Lizzie Marsland, Susannah Palmer Series Editor: Peter Sumner Cover and Page Design: Kathryn Webster, Jo Sullivan The right of Lizzie Marsland and Susannah Palmer to be identified as the authors of this publication has been asserted by them in accordance with the Copyright, Designs and Patents Act 1998. HeadStart Primary Ltd Elker Lane Clitheroe BB7 9HZ T. 01200 2305 E. info@headstartprimary.com www.headstartprimary.com All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Published by HeadStart Primary Ltd 2018 HeadStart Primary Ltd 2018 A record for this book is available from the British Library - ISBN: 978-1-908767-57-8
CONTENTS Year 1 INTRODUCTION Year 1: NUMBER - Number and place value Page Objectives Page 1 Count to and across 100, forwards Page 2 Count to and across 100, backwards Page 3 Count to and across 100, forwards and backwards Page Count to and across 100, forwards and backwards Page 5 Count in multiples of two Page 6 Count in multiples of five Page 7 Count in multiples of ten Page 8 Count in multiples of two, five and ten Page 9 Count in multiples of two, five and ten Page 10 Compare and order numbers up to 20 Page 11 Compare and order numbers up to 100 Page 12 Identify one more or less than a given number up to 20 Page 13 Identify one more or less than a given number up to 100 Page 1 Identify 10 more or less than a given number up to 100 Page 15 Use the language of equal to, more than and less than (fewer) Page 16 Use the language of equal to, more than, less than, most and least Page 17 Read and write numbers from 1 to 20 in numerals and words Page 18 Read and write numbers from 1 to 20 in numerals and words Page 19 Solve mixed problems involving number and place value Page 20 Solve mixed problems involving number and place value Page 21 Solve mixed problems involving number and place value Pages 22-31 MASTERING - Number and place value Year 1: NUMBER - Addition and subtraction Page 32 Read, write and interpret mathematical statements involving addition (+), subtraction ( ) and equals (=) signs Page 33 Read, write and interpret mathematical statements involving addition (+), subtraction ( ) and equals (=) signs Page 3 Read, write and interpret mathematical statements involving addition (+), subtraction ( ) and equals (=) signs Page 35 Read, write and interpret mathematical statements involving addition (+), subtraction ( ) and equals (=) signs Copyright HeadStart Primary Ltd
CONTENTS Year 1 Page 36 Use number bonds to 10 Page 37 Use number bonds to and within 10 Page 38 Use number bonds to 20 Page 39 Use number bonds to and within 20 Page 0 Add one-digit and two-digit numbers to 20, including zero Page 1 Subtract one-digit and two-digit numbers to 20, including zero Page 2 Add and subtract one-digit and two-digit numbers to 20, including zero Page 3 Solve one-step problems involving addition Page Solve one-step problems involving addition Page 5 Solve one-step problems involving subtraction Page 6 Solve one-step problems involving subtraction Page 7 Solve one-step problems involving addition and subtraction Page 8 Solve one-step problems involving addition and subtraction Page 9 Solve one-step problems involving addition and subtraction Page 50 Solve one-step problems involving addition (money) Page 51 Solve one-step problems involving subtraction (money) Page 52 Solve one-step problems involving addition and subtraction (money) Pages 53-68 MASTERING - Addition and subtraction Year 1: NUMBER - Multiplication and divison Page 69 Page 70 Page 71 Page 72 Page 73 Page 7 Page 75 Page 76 Page 77 Page 78 Page 79 Page 80 Page 81 Double numbers and quantities Double numbers and quantities Double and halve numbers and quantities Use arrays to solve one-step multiplication problems Use arrays to solve one-step multiplication problems Solve problems involving grouping or sharing Solve problems involving grouping or sharing Solve problems involving grouping or sharing (money) Solve problems involving grouping or sharing (money) Make connections between number patterns and counting in twos, fives and tens Make connections between number patterns and counting in twos, fives and tens Solve mixed one-step problems involving multiplication and division Solve mixed one-step problems involving multiplication and division Pages 82-89 MASTERING - Multiplication and division Copyright HeadStart Primary Ltd
CONTENTS Year 1 Year 1: NUMBER - Fractions Page 90 Page 91 Page 92 Page 93 Page 9 Page 95 Page 96 Page 97 Find a half of an object, shape or quantity Find a half of an object, shape or quantity Find a half or a quarter of an amount of money Find a half or a quarter of an amount of money Find a half or a quarter of an object, shape or quantity Find a half or a quarter of an object, shape or quantity Find a quarter of an object, shape or quantity Find a quarter of an object, shape or quantity Pages 98-103 MASTERING - Fractions Year 1: MEASUREMENT Page 10 Compare lengths and heights Page 105 Solve problems involving lengths and heights Page 106 Compare mass or weight Page 107 Solve problems involving mass or weight Page 108 Compare capacity and volume Page 109 Solve problems involving capacity and volume Page 110 Compare time Page 111 Solve problems involving time Page 112 Solve problems involving time Page 113 Choose appropriate measuring tools Page 11 Solve problems involving knowing the value of different denominations of coins and notes Page 115 Solve problems involving knowing the value of different denominations of coins and notes Page 116 Sequence events in chronological order Page 117 Sequence events in chronological order Page 118 Recognise and use language relating to dates Page 119 Recognise and use language relating to days of the week Page 120 Recognise and use language relating to weeks, months and years Page 121 Solve problems involving time to the hour and half past the hour Page 122 Solve problems involving time to the hour and half past the hour Pages 123-130 MASTERING - Measurement Copyright HeadStart Primary Ltd
CONTENTS Year 1 Year 1: GEOMETRY - Properties of shapes / Position and direction Page 131 Recognise common 2D shapes and compare them to everyday objects Page 132 Recognise, name and compare common 2D shapes Page 133 Recognise common 3D shapes and compare them to everyday objects Page 13 Recognise, name and compare common 3D shapes Page 135 Solve problems involving 2D and 3D shapes Page 136 Solve problems involving 2D and 3D shapes Page 137 Describe position, direction and movement Pages 138-15 Pages 155-167 Pages 168-17 MASTERING - Geometry - Properties of shapes / Position and direction INVESTIGATION - Fruit shop ANSWERS Copyright HeadStart Primary Ltd
INTRODUCTION These problems have been written in line with the objectives from the Mathematics Curriculum. Questions have been written to match all appropriate objectives from each content domain of the curriculum. Solving problems and mathematical reasoning in context are difficult skills for children to master; a real-life, written problem is an abstract concept and children need opportunities to practise and consolidate their problem solving techniques. As each content domain is taught, the skills learnt can be applied to the relevant problems. This means that a particular objective can be reinforced and problem solving and reasoning skills further developed. The first section of each content domain is intended to provide opportunities for children to practise and consolidate their problem solving skills. Each page has an identified objective from the National Curriculum; the difficulty level of the questions increases towards the bottom of each page, thus providing built-in differentiation. Mastering a skill involves obtaining a greater level of understanding of the skill, the ability to transfer and apply knowledge in different contexts and explaining understanding to others. The MASTERING and INVESTIGATION sections provide extra challenges as children s problem solving skills and confidence increase. The problems in the MASTERING sections encompass several objectives from the relevant curriculum domain. The INVESTIGATION covers objectives from across the whole curriculum. At HeadStart, we realise that children may need more space to record their answers, working out or explanations. It is recommended, therefore, that teachers use their discretion as to where children complete their work. Since a structured approach to problem solving supports learning, developing a whole-school approach is highly recommended. Copyright HeadStart Primary Ltd
Throughout this book, 6 children are solving problems. Their names are: Olivia Matt Rose Ali Usma Jing Copyright HeadStart Primary Ltd
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. NUMBER Number and place value These are all about number and place value! Copyright HeadStart Primary Ltd
NUMBER - Number and place value Year 1 Count to and across 100, forwards 1 Matt is counting his sweets. He counts 3 and then counts another 5. How many has he counted altogether? 2 Olivia starts at 6 and counts up 7 more. What number does she count to? 3 Mrs Flower asks Class 1 to count on 6 numbers from 30. What number should they say? On a number line, Rose starts at number 62. She counts on 7 more. What number does she count to? 5 Ali counts 91 cars in the car park. Then he counts 10 more. How many has he counted altogether? Copyright HeadStart Primary Ltd 1 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. MASTERING Number and place value These are harder. Are you ready for the challenge? Copyright HeadStart Primary Ltd
MASTERING - Number and place value Year 1 1 Matt, Ali and Rose have the results of their maths test. Matt scored the highest with 10. Rose scored the least with 3. How many could Ali have scored? Can you find six answers? 2 I start from 3 and count in twos until I reach 9. How many even numbers do I say? Explain your answer....... 3 Draw lines to match these statements to the given numbers. You can only use each number once. an even number seven a number smaller than 5 four a number between 8 and 6 three an odd number larger than 8 nine Copyright HeadStart Primary Ltd 22 Name...
MASTERING - Number and place value Year 1 Usma, Rose and Olivia have 15 sweets between them. Usma has the most sweets. Rose has one less sweet than Usma and one more than Olivia. How many sweets does each girl have? Usma Rose Olivia 5 Count the apples. Count the oranges. Complete this sentence using apples and oranges. There are more... than... 6 Here is a number line. Fill in the missing numbers 10 20 30 0 Copyright HeadStart Primary Ltd 23 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. NUMBER Addition and subtraction These are all about addition and subtraction! Copyright HeadStart Primary Ltd
NUMBER - Addition and subtraction Year 1 Read, write and interpret mathematical statements involving addition (+), subtraction ( ) and equals (=) signs 1 Write a number statement that shows the total of 12 and 13. 2 Write a number statement that shows the difference between 9 and 3. 3 Ali has 15 and Jing has 8 more. How much does Jing have? Show your answer as a number statement. Usma runs 100 metres in 25 seconds and Rose runs 100 metres in 18 seconds. How many seconds quicker is Rose than Usma? Show your answer as a number statement. Copyright HeadStart Primary Ltd 32 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. MASTERING Addition and subtraction These are quite difficult. Challenge yourself! Copyright HeadStart Primary Ltd
MASTERING - Addition and subtraction Year 1 1 Ali has these coins. How much money does he have altogether? p 2 I have 15p to spend. I want to buy two items. Sort the items into pairs that can be bought with exactly 15p and those which would need change. 7p 5p 9p 8p 10p 6p One has been done for you. Exactly 15p Change needed cake and sweet Copyright HeadStart Primary Ltd 53 Name...
MASTERING - Addition and subtraction Year 1 3 How many ways can you complete this? One has been done for you. 8 10 10 2 10 10 10 Year 1 are designing new flags for their classroom. Each flag has four small squares. One square needs to be coloured blue and one square needs to be coloured red. Write b or r in the squares to make as many different flags as you can. One has been done for you. b r Copyright HeadStart Primary Ltd 5 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. NUMBER Multiplication and division These are all about multiplication and division! Copyright HeadStart Primary Ltd
NUMBER - Multiplication and division Year 1 Double numbers and quantities 1 What is double 1? 2 Usma says, Double 3 is 6. Is she correct? Explain your answer. Yes / No...... 3 Rose has 2 cupcakes. Olivia has double that amount. How many cupcakes does Olivia have? Mr Davies asks Matt to double 5. What number should he say? 5 Ali says, If you double 6, the answer is 1. Is he correct? Explain your answer. Yes / No...... Copyright HeadStart Primary Ltd 69 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. MASTERING Multiplication and division You will need all your brain power for these! Copyright HeadStart Primary Ltd
MASTERING - Multiplication and division Year 1 1 Olivia buys some pencils. Each pencil costs 10p. She spends 60p. How many pencils did Olivia buy? 2 There are 5 exercise books in each packet. How many exercise books are there in 2 packets? 3 Usma has lots of 5p and 10p coins. How can she make 25p? Can you find three ways to do this? Write the number of coins needed in the boxes. a 5p 10p b 5p 10p c 5p 10p Matt gives the same number of stickers to Ali and Jing. He gives out 1 stickers altogether. How many stickers does he give to each friend? Copyright HeadStart Primary Ltd 82 Name...
MASTERING - Multiplication and division Year 1 5 Matt was counting in fives. He missed out a number. Write the number that Matt missed out in the correct place. 5 10 15 20 30 35 6 At the zoo, lizards are kept in tanks. There are 5 lizards in each tank. How many lizards are there altogether? 7 Fill in the missing gaps Two are done for you Double 8 Half 2 2 6 10 8 8 In Year 1, there are 2 children. Each child brings 2 pencils to school. How many pencils do the children bring to school altogether? Copyright HeadStart Primary Ltd 83 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. NUMBER Fractions These are all about fractions! Copyright HeadStart Primary Ltd
NUMBER - Fractions Year 1 Find a half of an object, shape or quantity 1 Olivia buys a whole pizza. She eats half. How much does she have left? 2 children are split into 2 teams. How many children are in each team? 3 Olivia says, The opposite of doubling is halving. Is she correct? Yes / No Explain your answer....... Ali has 10 conkers. He gives half of them to his sister. How many does Ali have left? 5 How much of this shape is shaded? Copyright HeadStart Primary Ltd 90 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. MASTERING Fractions These are quite hard so go for it! Copyright HeadStart Primary Ltd
MASTERING - Fractions Year 1 1 How many small squares make 1 of each shape? Shade them in to show your answer. 2 Ali has 10p and 2p. He uses 1 of his money to buy a sweet. How much does he have left? p 3 How many small squares make 1 of each shape? Shade them in to show your answer. What comes next? 10 9 1 2 9 5 Count up in halves. 6 6 1 2 8 Copyright HeadStart Primary Ltd Name... 98
MASTERING - Fractions Year 1 6 Usma has these coins. She uses half of her money to buy a lollipop. How much has she spent? p 7 Complete this halving wall. a 10 20 Now complete these walls. b 0 c d 8 e 16 Copyright HeadStart Primary Ltd Name... 99
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. MEASUREMENT These are all about measurement! Copyright HeadStart Primary Ltd
MEASUREMENT Year 1 Compare lengths and heights 1 The blue line is 10 metres long and the red line is 1 metres long. Which is the longer line? 2 Jing's foot is the length of 9 cubes. Olivia's foot is the length of 7 cubes. Whose foot is longer? 3 Usma is 110 cm tall. Rose's height is 111 cm. Who is taller? Ali's sunflower is 123 cm tall. Olivia's flower grows to be 132 cm tall. Whose flower is taller? 5 Rose is 108 cm tall. Rose's dog is 55 cm tall. Is Rose's dog exactly half of Rose's height? Yes / No Explain your answer....... Copyright HeadStart Primary Ltd 10 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. MASTERING Measurement These are tough! Ask for help if you need it. Copyright HeadStart Primary Ltd
MASTERING - Measurement Year 1 1 Rose weighed different fruits using cubes. This table shows the number of cubes she needed to balance each type of fruit. Type of fruit Number of cubes apple 31 orange 26 banana 32 plum 16 peach 21 a Which fruit is the heaviest? b Which fruit is the lightest? c Which two fruits weigh between 20 and 30 cubes each? and d Which fruit is 10 cubes heavier than a plum? e Which fruit is 5 cubes heavier than a peach? f Which fruit is 5 cubes lighter than an apple? Copyright HeadStart Primary Ltd Name... 123
MASTERING - Measurement Year 1 2 Look at these clocks. Write the time next to each clock, then match the time with what Jing was doing. One has been done for you. 12 11 1 10 2 9 3 8 7 5 6 Jing woke up. 12 11 1 10 2 9 3 8 7 5 6 Jing started school. 12 11 1 10 2 9 3 8 7 5 6 Jing had lunch. 12 11 1 10 2 9 3 8 7 5 6 7 o'clock Jing left school. 12 11 1 10 2 9 3 8 7 5 6 Jing went to bed. Copyright HeadStart Primary Ltd Name... 12
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. GEOMETRY Properties of shapes / Position and direction These are all about geometry! Copyright HeadStart Primary Ltd
GEOMETRY - Properties of shapes / Position and direction Year 1 Recognise common 2D shapes and compare them to everyday objects 1 What can you see in the classroom that is in the shape of a square? 2 Is a whole pizza usually in the shape of a circle or a rectangle? 3 Ali says, My maths book is in the shape of triangle. Do you think he is correct? Yes / No Look around the room you are in and write down 3 things that are in the shape of a rectangle. 5 Which has more sides: a triangle or a pentagon? Copyright HeadStart Primary Ltd 131 Name...
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. MASTERING Geometry Properties of shapes / Position and direction You will need to think very carefully to solve these! Copyright HeadStart Primary Ltd
MASTERING - Geometry Year 1 1 Draw lines to match the names to the shapes. cuboid cylinder pyramid sphere 2 Decide how you could sort these shapes into two groups. Write them in the table. Group 1 Group 2 Explain why you sorted the shapes like this....... 3 Find two more objects in the classroom to add to each group. Copyright HeadStart Primary Ltd Name... 138
MASTERING - Geometry Year 1 Ali wants to turn this shape around a quarter of a full turn clockwise. Put a circle around how the shape will look after he has turned it. 5 Usma says that all 2D shapes have at least sides. Is she correct? Yes / No Explain your answer....... 6 Circle the shapes which have no curved sides. Copyright HeadStart Primary Ltd Name... 139
It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations. INVESTIGATION Fruit Shop Copyright HeadStart Primary Ltd
INVESTIGATION - Fruit Shop Year 1 1 Year 1 have planned a visit to a fruit shop as part of their healthy eating project. The children all like apples, oranges, bananas and plums. 5p 7p 6p p Write the names of the fruits from cheapest to most expensive. 2 Olivia has 20p to spend. List the fruits she could buy with exactly 20p. One has been done for you. apple + orange + plum + plum 5p + 7p+ p + p Copyright HeadStart Primary Ltd 155 Name...
INVESTIGATION - Fruit Shop Year 1 12 Look at the boxes of fruit on the shelves. The numbers on the boxes tell you how many there are in each box. How many of each type of fruit are there? The first one has been done for you. a 10 apple 10 apple 10 apple 10 apple 10 + 10 + 10 + 10 = 0 apples b banana 3 banana 3 + = bananas c 5 5 5 orange orange orange + + = oranges d plum plum plum plum + + + = plums Copyright HeadStart Primary Ltd 160 Name...
INVESTIGATION - Fruit Shop Year 1 21 On two other shelves, the shopkeeper arranges the boxes of fruit differently. Draw the boxes in the correct places on the shelves. There are two boxes of apples above the box of plums. There are three boxes of bananas to the right of the apples. There are four boxes of oranges below the bananas. plums Copyright HeadStart Primary Ltd 16 Name...
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Primary Year 1 Problem Solving, Reasoning & Investigating MATHEMATICS CURRICULUM covers all National Curriculum objectives includes Mastering sections to provide additional challenge features a multi-objective, extended investigation incorporates built-in differentiation Primary T. 01200 2305 E. info@headstartprimary.com www.headstartprimary.com HSP-113-KW - Copyright HeadStart Primary