year 4 multiplication reasoning and problem solving

My Account / Login

Year 4 – Multiplication and Division

Welcome to Year 4 Multiplication and Division at Primary Maths Hub. Here you will find a growing library of outstanding resources and activities to support multiplication and division lessons in Year 4 and at home.  

If there’s a resource you’d like to see here, just visit our ‘Request a Resource’ page and Primary Maths Hub will create the resource and add it to the site.

Do Now Tasks / Starters

Six Times Table Do Now Tasks

Seven Times Table Do Now Tasks

Eight Times Table Do Now Tasks

Nine Times Table Do Now Tasks 

Eleven Times Table Do Now Tasks

Twelve Times Table Do Now Tasks 

Mixed Times Table Do Now Tasks

Differentiated question sets.

Short Multiplication Question Set

Times tables strips.

Strips- 6 Times Table 

Strips- 7 Times Table

Strips- 9 Times Table 

Strips- 11 Times Table 

Strips- 12 Times Table 

Short multiplication.

Faded Scaffolding Strips –  Short Multiplication –  2 Times Table

Faded Scaffolding Strips –  Short Multiplication –  3 Times Table

Faded Scaffolding Strips –  Short Multiplication –  4 Times Table

Faded Scaffolding Strips –  Short Multiplication –  5 Times Table

Faded Scaffolding Strips –  Short Multiplication –  6 Times Table

Faded Scaffolding Strips –  Short Multiplication –  7 Times Table

Faded Scaffolding Strips –  Short Multiplication –  8 Times Table

Faded Scaffolding Strips –  Short Multiplication –  9 Times Table

 Short Multiplication

Faded Scaffolding Strips –  Short Multiplication

Short Multiplication –  3 Digit by 1 Digit

Short Multiplication –  3 Digit by 1 Digit –  2 Times Table

Short Multiplication –  3 Digit by 1 Digit –  3 Times Table

Short Multiplication –  3 Digit by 1 Digit –  4 Times Table

Short Multiplication –  3 Digit by 1 Digit –  5 Times Table

Short Multiplication –  3 Digit by 1 Digit –  6 Times Table

Short Multiplication –  3 Digit by 1 Digit –  7 Times Table

Short Multiplication –  3 Digit by 1 Digit –  8 Times Table

Short Multiplication –  3 Digit by 1 Digit –  9 Times Table

Short division.

Faded Scaffolding Strips –  Short Division

Faded Scaffolding Strips –  Short Division –  2 Times Table

Faded Scaffolding Strips –  Short Division –  3 Times Table

Faded Scaffolding Strips –  Short Division –  4 Times Table

Faded Scaffolding Strips –  Short Division –  5 Times Table

Faded Scaffolding Strips –  Short Division –  6 Times Table

Faded Scaffolding Strips –  Short Division –  7 Times Table

Faded Scaffolding Strips –  Short Division –  8 Times Table

Faded Scaffolding Strips –  Short Division –  9 Times Table

Short Division- 3 Digit by 1 Digit- 2 Times Tables 

Short Division- 3 Digit by 1 Digit- 4 Times Tables

Short Division- 3 Digit by 1 Digit- 3 Times Tables 

Short Division- 3 Digit by 1 Digit- 5 Times Tables 

Short Division- 3 Digit by 1 Digit- 6 Times Tables 

Short Division- 3 Digit by 1 Digit- 7 Times Tables 

Short Division- 3 Digit by 1 Digit- 8 Times Tables 

Short Division- 3 Digit by 1 Digit- 9 Times Tables 

Short Division- 3 Digit by 1 Digit- Mixed Times Tables 

Mixed multiplication and division, multiply and divide using know facts.

Multiply Using Known Facts to 10,000

Faded Scaffolding Strips- Multiply by Known Facts to 10,000

Divide Using Known Facts to 10,000

Faded Scaffolding Strips- Divide by Known Facts to 10,000 

Faded Scaffolding Strips- Multiply and Divide by Known Facts to 10,000 

Equality and inequality statements.

Equality and Inequality Statement Matching- Short Multiplication and Short Division

Equality and Inequality Statement Matching – Multiply 3 numbers

Problem solving.

Problem Solving- Multiplication Facts

Steps to success.

Short Multiplication – Steps to Success 

Short Division- Steps to Success 

Can't find what you are looking for.

Reasoning/Problem Solving Maths Worksheets for Year 4 (age 8-9)

This category is all about children choosing the most appropriate method to achieve a quick and accurate answer and to be able to explain their methods and reasoning.

Problem solving: finding the missing digits in 4-digit numbers. Tricky!

Problem solving: finding the values of missing counters. Logical thinking and careful work needed here!

Reasoning about numbers on a number line and rounding numbers.

More reasoning about number and place value.

Not only do the questions have to be answered, but explanations given. These pages really show how well children understand what they are doing.

More written explanations on which operation to use and whether the question should be done mentally or on paper.

Lots of questions, most of which can be done mentally. The important thing is to explain how they were tackled.

Decide which operation is needed (add, subtract, multiply, divide) and whether a calculator, or pencil and paper are needed, or whether it can be done, 'in your head'.

Solving problems

A selection of problem solving activities and word problems.

Here are some problems written in words. Fairly straightforward as they require just one mathematical step to work out the answer

Some word problems that need at least two steps to find the answer. This makes them much harder, so careful thinking is needed.

5 pages of word problems, all involving money. Some are suitable for calculator work as they are specially written to make the process the most important factor: it is no use having a calculator if you don't know what calculation to carry out!

A range of number and money problems, typical of those found in KS2 test papers.

More number and money problems, typical of those found in KS2 test papers.

Tricky word problems involving time and money.

More word problems; this time on measurement of length, mass and capacity. These really test children's understanding of when to use addition, subtraction, multiplication or division to solve a problem.

Time problems are especially tricky, especially when finding lengths of time that cross the hour boundary. A good knowledge of the number of days in each month is also needed.

Not many problems on a page, but there is an awful lot within each question. Each is a mini investigation, which can be explored in depth.

Number patterns, remainders, number machines and much more in this mixed selection of problems.

Working out the missing value.

More working out missing values.

Using the instructions on the packet what is the maximum number of bulbs that can be grown in the garden?

Using the instructions on the packet what is the maximum number of seeds that can be sown in the garden?

Using the instructions on the packet what is the maximum number of vegetables that can be grown in the garden?

An addition challenge suitable for year 4 on.

The fish are all called numbers. Can you work out their names by solving the clues?

Investigations

More open ended activities where children choose the approach to the task.

Making rules for sequences is an early step towards understanding algebra, and an important part of Year 5 maths. More 'How would you...?' type questions as well.

How many different three course meals can Sam choose?

Investigate patterns made by placing consecutive numbers in a number square.

A great little investigation which has plenty of extension possibilities.

Fun addition investigation using the date: 22.02.2022.

Some thoughts on how important this area of maths is.

Subscribe to our newsletter

The latest news, articles, and resources, sent to your inbox weekly.

© Copyright 2011 - 2024 Route One Network Ltd. - URBrainy.com 5.1

Or search by topic

Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

For younger learners

• Early Years Foundation Stage

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

Resources tagged with: NC Yr 4

There are 51 NRICH Mathematical resources connected to NC Yr 4 , you may find related items under NC .

Satisfying Four Statements

Can you find any two-digit numbers that satisfy all of these statements?

Representing Numbers

Find as many different ways of representing this number of dots as you can.

Ordering Journeys

How would you put these journey lengths in order?

What Distance?

Can you use addition and subtraction to answer these questions about real-life distances?

Count Me In

How do you know whether you will reach these numbers when you count in steps of six from zero?

Dicey Operations in Line

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Seeing Squares

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Reasoned Rounding

Four strategy dice games to consolidate pupils' understanding of rounding.

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Let Us Divide!

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

Discuss and Choose

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Bryony's Triangle

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Sorting Logic Blocks

This activity focuses on similarities and differences between shapes.

Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

A task which depends on members of the group noticing the needs of others and responding.

What Shape?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Counters in the Middle

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Table Patterns Go Wild!

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Times Tables Shifts

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Reflector ! Rotcelfer

Can you place the blocks so that you see the reflection in the picture?

Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Four-digit Targets

You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Venn Diagrams

How will you complete these interactive Venn diagrams?

Eight Hidden Squares

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Shape Times Shape

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Multiplication Square Jigsaw

Can you complete this jigsaw of the multiplication square?

Twice as Big?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Multiples Grid

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Coordinate Challenge

Use the clues about the symmetrical properties of these letters to place them on the grid.

Torn Shapes

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Fractional Wall

Using the picture of the fraction wall, can you find equivalent fractions?

Stringy Quads

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Nine-pin Triangles

How many different triangles can you make on a circular pegboard that has nine pegs?

Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Andy's Marbles

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

How Big Are Classes 5, 6 and 7?

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

Fractional Triangles

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

The Deca Tree

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Symmetry Challenge

How many symmetric designs can you make on this grid? Can you find them all?

Let Us Reflect

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

A Cartesian Puzzle

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Shapes on the Playground

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Efficient Multiplication: Reasoning and Problem Solving

• Home Learning
• Free Resources
• New Resources
• Free resources
• New resources
• Filter resources
• Childrens mental health
• Easter resources

Internet Explorer is out of date!

For greater security and performance, please consider updating to one of the following free browsers

Solve Problems with Multiplication-Reasoning and Problem Solving

Solve Problems with Multiplication - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of Solve Problems with Multiplication.

Not a member? Sign up here.

What's included in the pack?

Solve Problems with Multiplication reasoning and problem solving worksheet Answer sheet

National Curriculum Objectives:

(6C8)  Solve problems involving addition, subtraction, multiplication and division (6C6)  Perform mental calculations, including with mixed operations and large numbers

This resource is available to download with a Premium subscription.

Our Mission

To help our customers achieve a life/work balance and understand their differing needs by providing resources of outstanding quality and choice alongside excellent customer support.​.

Yes, I want that!

Keep up to date by liking our Facebook page:

Membership login, stay in touch.

01422 419608

[email protected]

Interested in getting weekly updates from us? Then sign up to our newsletter here!

Information

• Cookie Policy
• Privacy Policy
• Terms and Conditions

Copyright: Classroom Secrets 2024

Company number: 8401067

VAT number: 248 8245 74

• Terms & Conditions

Designed by Classroom Secrets

share this!

May 5, 2024

This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility:

fact-checked

trusted source

written by researcher(s)

Math degrees are becoming less accessible—and this is a problem for business, government and innovation

by Neil Saunders, The Conversation

There's a strange trend in mathematics education in England. Math is the most popular subject at A-level since overtaking English in 2014. It's taken by around 85,000 and 90,000 students a year.

But many universities—particularly lower-tariff institutions, which accept students with lower A-level grades—are recruiting far fewer students for math degrees. There's been a 50% drop in numbers of math students at the lowest tariff universities over the five years between 2017 and 2021. As a result, some universities are struggling to keep their mathematics departments open.

The total number of students studying math has remained largely static over the last decade. Prestigious Russell Group universities which require top A-level grades have increased their numbers of math students.

This trend in degree-level mathematics education is worrying. It restricts the accessibility of math degrees, especially to students from poorer backgrounds who are most likely to study at universities close to where they live . It perpetuates the myth that only those people who are unusually gifted at mathematics should study it—and that high-level math skills are not necessary for everyone else.

Research carried out in 2019 by King's College London and Ipsos found that half of the working age population had the numeracy skills expected of a child at primary school. Just as worrying was that despite this, 43% of those polled said "they would not like to improve their numeracy skills." Nearly a quarter (23%) stated that "they couldn't see how it would benefit them."

Mathematics has been fundamental in recent technological developments such as quantum computing , information security and artificial intelligence. A pipeline of more mathematics graduates from more diverse backgrounds will be essential if the UK is to remain a science and technology powerhouse into the future.

But math is also vital to a huge range of careers, including in business and government. In March 2024, campaign group Protect Pure Math held a summit to bring together experts from industry, academia and government to discuss concerns about poor math skills and the continuing importance of high-quality mathematics education.

Prior to the summit, the London Mathematical Society commissioned a survey of over 500 businesses to gauge their concerns about the potential lack of future graduates with strong mathematical skills.

They found that 72% of businesses agree they would benefit from more math graduates entering the workforce. And 75% would worry if UK universities shrunk or closed their math departments.

A 2023 report on MPs' staff found that skills in Stem subjects (science, technology, engineering and mathematics) were particularly hard to find among those who worked in Westminster. As many as 90% of those who had taken an undergraduate degree had studied humanities or social sciences. While these subject backgrounds are valuable, the lack of specialized math skills is stark.

Limited options

The mathematics department at Oxford Brookes has closed and other universities have seen recruitment reductions or other cuts. The resulting math deserts will remove the opportunity for students to gain a high-quality mathematics education in their local area. Universities should do their best to keep these departments open.

This might be possible if the way that degrees are set up changes. For many degree courses in countries such as the US and Australia, students are able to take a broad selection of subjects, from science and math subjects through to the humanities. Each are taught in their respective academic departments. This allows students to gain advanced knowledge and see how each field feeds into others.

This is scarcely possible in the UK, where students must choose a specialist and narrow degree program at aged 18.

Another possible solution would be to put core mathematics modules in degree disciplines that rely so heavily on it—such as engineering, economics, chemistry, physics, biology and computer science—and have them taught by specialist mathematicians. This would help keep mathematics departments open, while also ensuring that general mathematical literacy improves in the UK.

The relevance of mathematics and its vast range applications would be abundantly clear, better equipping every student with the necessary mathematical skills the workforce needs.

Provided by The Conversation

Explore further

Feedback to editors

NASA's Chandra notices the galactic center is venting

17 minutes ago

Wildfires in old-growth Amazon forest areas rose 152% in 2023, study shows

41 minutes ago

GoT-ChA: New tool reveals how gene mutations affect cells

Accelerating material characterization: Machine learning meets X-ray absorption spectroscopy

Life expectancy study reveals longest and shortest-lived cats

New research shows microevolution can be used to predict how evolution works on much longer timescales

Stable magnetic bundles achieved at room temperature and zero magnetic field

Is dark matter's main rival theory dead? The Cassini spacecraft and other recent tests may invalidate MOND

High-speed atomic force microscopy helps explain role played by certain biomolecules in DNA wrapping dynamics

Genetic study of cauliflower reveals its evolutionary history

Relevant physicsforums posts, formal definition of multiplication for real and complex numbers.

May 6, 2024

Identity Theorem for power series

Probability - two possible points of view.

May 4, 2024

How to interpret Pascal's Triangle for negative numbers?

May 2, 2024

Tennis Probabilities Challenge

Scissor blade problem.

Apr 29, 2024

More from General Math

Related Stories

How can Australia solve the math teacher shortage? It can start by training more existing teachers to teach math

Apr 2, 2024

Studies recommend increased research into achievement, engagement to raise student math scores

Feb 15, 2024

'Math anxiety' causes students to disengage, says study

Nov 22, 2023

The numbers do not add up for mathematics homework, according to a new study

Mar 12, 2024

Why putting off college math can be a good idea

Jul 10, 2023

Disparities in advanced math and science skills begin by kindergarten

Nov 10, 2022

Recommended for you

Random processes shape science and math: Researchers propose a unified, probabilistic framework

May 9, 2024

Study of new method used to preserve privacy with US census data suggests accuracy has suffered

New study is first to use statistical physics to corroborate 1940s social balance theory

May 3, 2024

Investigation reveals varied impact of preschool programs on long-term school success

Too many vehicles, slow reactions and reckless merging: New math model explains how traffic and bacteria move

Apr 30, 2024

Theoretical biologists test two modes of social reasoning and find surprising truths in simplicity

Let us know if there is a problem with our content.

Use this form if you have come across a typo, inaccuracy or would like to send an edit request for the content on this page. For general inquiries, please use our contact form . For general feedback, use the public comments section below (please adhere to guidelines ).

Please select the most appropriate category to facilitate processing of your request

Thank you for taking time to provide your feedback to the editors.

Your feedback is important to us. However, we do not guarantee individual replies due to the high volume of messages.

E-mail the story

Your email address is used only to let the recipient know who sent the email. Neither your address nor the recipient's address will be used for any other purpose. The information you enter will appear in your e-mail message and is not retained by Phys.org in any form.

Newsletter sign up

Get weekly and/or daily updates delivered to your inbox. You can unsubscribe at any time and we'll never share your details to third parties.

More information Privacy policy

Donate and enjoy an ad-free experience

We keep our content available to everyone. Consider supporting Science X's mission by getting a premium account.

E-mail newsletter