doubling problem solving year 4

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Doubling and Halving

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This simple game has been designed to help your child to practice their doubling and halving with a range of different numbers.

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Doubling and Halving – Reasoning and Problem Solving

Doubling and Halving - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of doubling and halving.

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What's included in the pack?

Doubling and Halving reasoning and problem solving worksheet Answer sheet

National Curriculum Objectives:

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Commutativity (part 2), doubling and halving

Spine 2: Multiplication and Division – Topic 2.5

Introduction

Explore how one multiplication equation can have two different grouping interpretations (e.g., an equation from the two times table can be interpreted in terms of groups of two, or two equal groups); make connections between the two times table, doubling and halving.

Teaching points

• Teaching point 1 : The same multiplication equation can have two different grouping interpretations. Problems about two/five/ten equal groups can be solved using facts from the two/five/ten times table. (commutativity)  
• Teaching point 2 : If two is a factor, knowledge of doubling facts can be used to find the product; problems about doubling can be solved using facts from the two times table.  
• Teaching point 3 : Halving is the inverse of doubling; problems about halving can be solved using facts from the two times table and known doubling facts.  
• Teaching point 4 : Products in the ten times table are double the products in the five times table; products in the five times table are half of the products in the ten times table.

Teacher Guide

Representations, all year 2 files, related pages.

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20 Word Problems For Year 4: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 4 play an important role in Year 4 maths. In Year 4, the main focus is to ensure that pupils are becoming more fluent with whole numbers and the four operations. Students work to develop efficient written methods and to be accurate with their calculations. Pupils in Year 4 are exposed to a wider range of problem-solving questions and progress from one to two-step problems.

It is important that all children are given regular opportunities to access reasoning and word problem style questions. Fluency, reasoning and problem solving should be intertwined through every lesson, with all children having the opportunity to tackle each of these question types. 

All Kinds of Word Problems Multiplication

Strengthen your students' problem solving and multiplication skills with this pack of multiplication word problems

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Addition and subtraction , multiplication and division, fractions, decimals and percentages, measurement, why are word problems important in year 4 maths, how to teach problem solving in year 4, addition word problems for year 4, subtraction word problems for year 4, multiplication word problems for year 4, division word problems for year 4, fraction and decimal word problems in year 4, time word problems in year 4, multi-step word problems in year 4., more primary word problems resources.

There can sometimes be a tendency for reasoning and problem solving questions to be treated as extension activities for only the higher attaining pupils to attempt, but children of all abilities need to be accessing them on a regular basis.

To help you with this, we have put together a collection of 20 word problems aimed at Year 4 pupils. For more Year 4 maths resources, take a look at our collection of Year 4 maths worksheets .

Year 4 Maths Word Problems in the National Curriculum

In Year 4, pupils progress from solving one-step problems, to also being exposed to two-step problems across a range of topics, as set out in the National Curriculum.

Solve word problems involving counting in multiples of 6,7,9, 25 and 100; finding 1000 more or less than a given number; counting backwards through 0 to include negative numbers; ordering and comparing numbers beyond 1000 and rounding numbers to the nearest 10. 100 and 1000

Solve addition and subtraction word problems with up to 4 digits, including two-step word problems, deciding which operations and methods to use and why.

Solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems.

Solve problems involving increasingly harder fractions word problems to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number. Also Solve simple measure and money problems involving fractions and decimals to 2 decimal places.

Solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days.

Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Word problems are increasingly important as pupils move through Key Stage 2. As they become more confident with some of the core concepts pupils need to be applying this knowledge to a range of situations. By the end of Year 4, pupils should have memorised their multiplication tables up to and including the 12 times table and should be showing precision and fluency in their work.

Word problems in Year 4 should be fun and engaging for students. There are many ways to do this, including:

• acting out the problem;
• using manipulatives and visual images to help children understand the maths within the problem;
• use of talk partners to encourage children to discuss the question and share strategies for reaching a solution;
• using relatable problem solving situations.

Children need to be encouraged to read word problem questions carefully, to ensure they have identified the key information needed to be able to solve the problem. Pupils need to think about what they already know and how that information can help them to answer the question. They should also be encouraged to draw pictures and visual images, where appropriate, to help them to understand what the question is asking.

Here is an example:

A shop has an 8m roll of fabric.

The first customer buys 125cm of fabric and the second customer buys 3m from the same roll.

How much fabric is left on the roll, once the two customers have taken theirs?

How to solve:

What do you already know?

• The amount the first customer buys is given in cm, the amount the second customer buys is given in m. These needed to be converted to the same unit.
• Pupils in Year 4 need to be able to convert cm to m and vice versa. In this question, both the cm can be given as m or the m changed to cm to solve it.
• Once the units are the same, the two amounts need to be added together, to work out the total amount bought by the two customers.
• We can see this is a two-step question. To calculate how much fabric is left on the roll, the total amount bought by the two customers needs to be subtracted from the initial amount of fabric on the roll.

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

• To calculate the total amount of fabric bought, we need the units to be the same. We can either calculate in cm (300cm + 125cm = 425cm) or in m (3m + 1.25m = 4.25m)
• The amount of material bought needs to be subtracted from the original amount. This can again be solved in m or cm. Either in m: 8m – 4.25m = 3.75m or in cm: 800cm – 425cm = 375cm
• The total amount of material left is 3.75m or 375cm

In Year 4, addition word problems involve questions up to 4-digit numbers. They can include one and two-step addition and incorporate a range of concepts, such as measures and money word problems  

Addition question 1

It is 4164 miles to travel from London to Doha and 3266 miles to travel from Doha to Bangkok.

How far is it to travel from London to Bangkok, if the flight stops in Doha first?

Answer (1 mark): 7430 miles

Addition question 2

Fill in the missing numbers in this calculation.

Answer (1 mark): 6840

Addition question 3

On Saturday, 5486 fans attended a football game and 3748 fans attended a rugby game.

How many fans watched the two games in total?

Answer (1 mark): 9234

Subtraction word problems in Year 4, also involve numbers up to 4-digits, including both one and two-step problems, covering a range of concepts. By this stage, children should be confident in estimating and using the inverse, to check calculations.

Subtraction question 1

3241 people visited the zoo on Saturday.

On Sunday 2876 people visited.

How many more people visited the lake on Saturday than on Sunday?

Answer (1 mark): 365

 3241 – 2876 = 365

Subtraction question 2

 A teacher prints out 1242 worksheets in a term.

If 435 were maths worksheets, how many did she print out for the other subjects?

Answer (1 mark): 807

Subtraction question 3

The temperature in Toronto dropped to minus 15 degrees celcius in December. 

In July the temperature was 47 degrees celsius warmer than it was in December. What was the temperature in July? 

Answer (1 mark): 32 degrees warmer

47 – 15 degrees = 32 degrees celsius

Counting on 47 degrees from minus 15 degrees  = 32 degrees celsius

In Year 4, multiplication word problems can include recalling facts for times tables up to 12 x 12 and multiplying two and three-digit numbers by a 1-digit number, using formal written layout.  

Multiplication question 1

All the pupils in Year 4 complete a mental maths test.

27 pupils score 9 marks out of 10.

What is the total number of marks scored by the 27 pupils?

Answer (1 mark): 243

27 x 9 = 243

Multiplication question 2

Year 3 and 4 children from a local primary school go on a school trip. 

Six mini buses are used to transport the children.

 There are 17 children on each minibus.

How many children go on the school trip?

Answer (1 mark): 102

17 x 6 = 102 children

Multiplication question 3

Biscuits come in packs of 18.

Mrs Smith buys 8 packs for the parents at the Y4 maths workshop.

How many biscuits does she buy altogether?

Answer (1 mark): 144 biscuits

Division word problems in year 4 require pupils to be able to recall division facts for multiplication tables up to 12 x 12. Formal written method of division isn’t a requirement until Year 5 however, many schools choose to teach the formal method in Year 4. Pupils need to understand the concept of grouping and sharing and to understand the link between multiplication & division.

Division question 1

Sam has 28 friends coming to his birthday party.

Each child will receive a cupcake, which come in packs of 4.

How many packs of cupcakes will Sam need to buy?

Answer (1 mark): 7 packs

28 ÷ 4 = 7 

Division question 2

4 children raised £96 between them on a sponsored walk.

If they split the money evenly between the four of them, how much did each pupil raise?

Answer (1 mark): £24 each

96 ÷ 4 = 24

Division question 3

Ahmed is thinking of a number

He says, ‘when I divide my number by 12, the answer is 108.

What number was Ahmed thinking of?

Answer (1 mark): 9

108 ÷ 12 = 9

In Year 4, decimal and fraction problems involve increasingly harder fractions to calculate quantities and fractions to divide quantities, including non-unit fractions, where the answer is a whole number. Decimal word problems include measure and money problems involving fractions and decimals up to 2 decimal places.

Fraction and decimal question 1

Jamie has 18 sweets. 

He gives \frac{1}{6} of the sweets to his friend and keeps the rest himself.

How many sweets does Jamie have now?

Answer (1 mark): 15 sweets

\frac{1}{6} of 18 = 3

18 – 3 = 15

Fraction and decimal question 2

Jaxon collected 36 conkers. 

\frac{1}{4} of the conkers fell out of a hole in his bag, when he was walking home.

How many conkers did Jaxon have left, when he got home?

\frac{1}{4} of 36 = 9

36 – 9 = 37      or      \frac{3}{4} of 36 = 29 (3 x 9)

Fraction and decimal question 3

Sara ate \frac{3}{12} of a chocolate bar and gave \frac{2}{12} to her friend.

What fraction of the chocolate bar did she have left? 

 Answer (1 mark): \frac{7}{12}

In Year 4, time word problems include: converting from hours to minutes, minutes to seconds, years to months and weeks to days.

Time question 1 

A cake was put in the oven at 4:35pm and taken out at 4:57pm.

How long was the cake in the oven?

Answer (1 mark): 22 minutes

57-35 = 22 minutes

Using an number line: 

Time question 2

It took Evie 25 minutes to complete a page of number problems. 

If she started at 2:45pm. What time did she finish?

Answer (1 mark): 3:10pm

In Year 4, children are introduced to multi-step word problems requiring up to two steps. These problems cover a range of concepts, including the four operations, fractions, decimals and measures.

Third Space Learning’s online one-to-one tutoring frequently incorporates multi-step questions to test students’ knowledge and problem solving skills. Our personalised tutoring programme works to identify gaps in students’ learning, fill those gaps, reinforce students’ knowledge and build confidence.

Multi-step question 1

There are 6 handwriting pens in each pack.

A class has 30 children and each child needs 2 handwriting pens.

How many packs will the teacher need to buy?

Answer (2 marks): 10 packs of handwriting pens.

30 x 2 = 60

Multi-step question 2

 Sophie has £4.50.

She buy 3 books at a carboot sale, costing 50p, 65p and £1.20.

How much money does she have left?

Answer (2 marks): £2.15 left

Multi-step question 3

Abullah is thinking of a number.

He doubles the number and adds 7.

He gets an answer of 25. 

What was his original number?

Answer (2 marks): 9

Third Space Learning offers word problems for all primary year groups. Take a look at our word problems for year 3 , word problems for year 5 and word problems for year 6 . Our word problems span a range of topics such as ratio word problems and percentage word problems .

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Explore all our in-depth problem solving investigations for Year 4 .

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Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

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Differentiated word problems for doubling Y2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

30 May 2014

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brilliant resource

Anon54596968634538510

Looks really good. Looking forward to trying it out. Many thanks for sharing...

Looks good, will try with Y2 tomorrow. I love that you let us share so that we can edit - change names etc, also means I can combine with other Q for lower attainers. Great that the Q can be cut up- I will ask children to stick in their books as rarely does work fit exactly the following year so no need to hang onto the Q. THANKYOU !

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