length problem solving year 3

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Length word problems

Measurement word problems: length .

These word problems involve length and height and the addition / subtraction / multiplication or division of lengths measured in customary (inches, feet) and metric (centimeters, meters) units. No conversion of units is required.  

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Measure length Year 3 Length and Perimeter Step 1 Free Resource Pack

Step 1: Measure length Year 3 Length and Perimeter Step 1 Spring Block 4 Resources

Measure length Year 3 Length and Perimeter Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Spring Block 4.

What's included in the pack?

This pack includes:

• Measure length Year 3 Length and Perimeter Step 1 Teaching PowerPoint.
• Measure length Year 3 Length and Perimeter Step 1 Varied Fluency with answers.
• Measure length Year 3 Length and Perimeter Step 1 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 3: (3M2a)  Measure lengths (m/cm/mm)

Differentiation For Year 3 Measure length:

Varied Fluency Developing Questions to support measuring in millimetres (mm) or centimetres (cm) only. Expected Questions to support measuring in millimetres (mm), centimetres (cm) and metres (m) with some mixed units, using increments of 1cm and 1mm. Objects placed at different positions on the ruler. Greater Depth Questions to support measuring in millimetres (mm), centimetres and metres (m) with mixed units, using increments of 1cm and 1mm. Objects placed at different positions on the ruler, with some increments not shown.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Find and measure items in the classroom shorter or longer than a given length in only millimetres (mm) or centimetres (cm). Round to the nearest whole cm. Expected Find and measure items in the classroom shorter or longer than a given length in millimetres (mm), centimetres (cm) or metres (m). Includes use of some mixed units, using increments of 1cm and 1mm. Round to the nearest 5mm. Greater Depth Find and measure items in the classroom shorter or longer than a given length in millimetres (mm), centimetres (cm) and metres (m). Includes use of mixed units, using increments of 1cm and 1mm. Round to the nearest 1mm or 1cm.

Questions 2, 5 and 8 (Reasoning) Developing Explain which measurement is the most suitable for the object stated. Measurements include millimetres (mm) or centimetres (cm) only. Expected Explain which measurement is the most suitable for the object stated. Measurements include some mixed units. Greater Depth Explain which measurement is the most suitable for the object stated. Measurements include use of mixed units, using increments of 1cm and 1mm.

Questions 3, 6 and 9 (Reasoning) Developing Explain if a total measurement is correct or not. Includes measurements of centimetres (cm) only. Expected Explain if a total measurement is correct or not. Includes some mixed measurements with objects placed at different positions on the ruler. Greater Depth Explain if a total measurement is correct or not. Includes use of mixed units using increments of 1cm and 1mm. Objects placed at different positions on the ruler and some increments not shown.

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Measure lengths in cm and m and convert units - Problem-Solving Investigation - Year 3

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

15 April 2024

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Year 3 Measures and Data: Measure lengths in cm and m; convert units.

This in-depth maths investigation will develop maths meta-skills, and enable children to learn to think mathematically and articulate mathematical ideas.

In-depth Investigation: Hands and Fingers Children test a theory finding and using accurate measurements to the nearest half centimetre.

This problem-solving investigation is part of our Year 3 Measures and Data block. Each Hamilton maths block contains a complete set of planning and resources to teach a term’s worth of objectives for one of the National Curriculum for England’s maths areas.

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Resources tagged with: Length/distance

There are 58 NRICH Mathematical resources connected to Length/distance , you may find related items under Measuring and calculating with units .

Car Journey

This practical activity involves measuring length/distance.

Can You Do it Too?

Try some throwing activities and see whether you can throw something as far as the Olympic hammer or discus throwers.

Olympic Measures

These Olympic quantities have been jumbled up! Can you put them back together again?

Now and Then

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

Olympic Starters

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

The Animals' Sports Day

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Place Your Orders

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

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.

Order, Order!

Can you place these quantities in order from smallest to largest?

Speed-time Problems at the Olympics

Have you ever wondered what it would be like to race against Usain Bolt?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

A Question of Scale

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

All in a Jumble

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Sizing Them Up

Can you put these shapes in order of size? Start with the smallest.

Up and Across

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Take Your Dog for a Walk

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

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Rolling Around

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Four on the Road

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Uniform Units

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

Where Am I?

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

Lengthy Journeys

Investigate the different distances of these car journeys and find out how long they take.

Working with Dinosaurs

This article for teachers suggests ways in which dinosaurs can be a great context for discussing measurement.

Swimmers in opposite directions cross at 20m and at 30m from each end of a swimming pool. How long is the pool ?

Triangle Relations

What do these two triangles have in common? How are they related?

A Scale for the Solar System

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Flight Path

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Chippy's Journeys

Chippy the Robot goes on journeys. How far and in what direction must he travel to get back to his base?

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

Measure for Measure

This article, written for students, looks at how some measuring units and devices were developed.

Eclipses of the Sun

Mathematics has allowed us now to measure lots of things about eclipses and so calculate exactly when they will happen, where they can be seen from, and what they will look like.

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

How can the school caretaker be sure that the tree would miss the school buildings if it fell?

N Is a Number

N people visit their friends staying N kilometres along the coast. Some walk along the cliff path at N km an hour, the rest go by car. How long is the road?

The Dodecahedron Explained

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

Do You Measure Up?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

The Hare and the Tortoise

In this version of the story of the hare and the tortoise, the race is 10 kilometres long. Can you work out how long the hare sleeps for using the information given?

A Flying Holiday

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.

Watching the Wheels Go 'round and 'round

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

Nirmala and Riki live 9 kilometres away from the nearest market. They both want to arrive at the market at exactly noon. What time should each of them start riding their bikes?

Practice Run

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

A Rod and a Pole

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

How many centimetres of rope will I need to make another mat just like the one I have here?

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

On the Road

Four vehicles travelled on a road. What can you deduce from the times that they met?

Use your hand span to measure the distance around a tree trunk. If you ask a friend to try the same thing, how do the answers compare?

Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Year 3 Maths Worksheets UK Hub Page

Welcome to our Year 3 Maths Worksheets area. Here you will find links to our Year 3 Math worksheets for your child will enjoy.

Come and take a look at our multiplication pages, or money flashcards. Perhaps you would prefer our telling the time worksheets, maths games or identifying 2d and 3d shapes in the geometry section?

For full functionality of this site it is necessary to enable JavaScript.

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 3 Maths Learning

Here are some of the key learning objectives for the end of Year 3:

• know and use Place value up to 1000
• Compare and order numbers up to 1000
• Counting on and back in 1s, 10s and 100s from different starting points
• Position numbers on a number line up to 1000
• know addition and subtraction facts to 20
• add or subtract 1s, 10s or 100s from a 3-digit number
• subtract 2- and 3-digit numbers in columns
• solve problems using addition and subtraction
• count from 0 in multiplies of 4, 8, 50 and 100
• recall and use multiplication and division facts from the 2, 3, 4, 5, 8 and 10 times tables
• multiply 2-digit numbers by a 1-digit number
• solve problems using multiplication and division
• count up and down in tenths
• understand tenths as decimals
• recognise and use fractions as numbers
• understand and use fractions of objects or shapes
• add and subtract amounts of money
• use £ and p notation correctly
• measure, compare, add and subtract lengths, mass and volume
• measure the perimeter of simple 2D shapes
• tell the time from an analogue clock
• convert between 12- and 24-hour clock
• measure and compare times
• Identify angles including right angles
• identify acute and obtuse angles
• identify horizontal, vertical, parallel and perpendicular lines
• recognise and draw 2D and 3D shapes
• interpret and present data in bar graphs, pictograms and tables
• solve 1-step and 2-step problems using data in tables, pictograms and graphs

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 3 is generally equivalent to 2nd Grade in the US.

On this page you will find link to our range of math worksheets for Year 3.

Quicklinks to Year 3 ...

• Place Value Zone
• Mental Math Zone

Word Problems Zone

Fractions zone.

• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 3 place value charts.

Here you will find a range of Free Printable Number Charts for Years 2 & 3.

These printable charts will help your child learn to read and write numbers.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Number Grid up to 200
• Number Grid up to 300

Place Value & Counting Worksheets

Below are our selection of Place Value, Ordering and Rounding Worksheets

Using these Year 3 Maths worksheets will help your child to:

• learn to count by hundreds, tens, fives, twos and ones;
• learn their place value to Hundreds;
• order numbers to 999.
• Place Value Models and Representations
• Place Value Worksheets 3 Digits
• Math Practice - Counting by 1s 2s 5s 10s 100s

Ordering and Rounding Worksheets (3-digits)

Once your child is confident with their place value to hundreds, they can start learning about ordering and rounding numbers.

The Year 3 Maths worksheets here will help your child learn to compare numbers to 999, and round numbers to the nearest 10.

• Ordering Numbers Worksheets up to 3-Digits

Year 3 Number Line Worksheets

The following webpages involve correctly placing numbers on a number line.

Using these Year 3 maths worksheets will help your child to:

• count by 1s 2s 5s 10s 50s and 100s;
• position numbers on a number line;
• understand place value up to 3 digits.
• Number lines up to 100 (easier)
• Number Line Worksheets 3 Digits

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Year 3 Mental Maths Zone

Here you will find a range of printable mental math sheets for Year 3 to enjoy.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math test or math quiz!

• Year 3 Mental Maths Worksheets Series A
• Year 3 Mental Maths Worksheets Series B

Year 3 Addition Worksheets

• learn their addition facts to 20+20
• learn how to solve addition sums where one of the addends is missing, but the total is given;
• learn to add numbers to 999 in columns.
• Number Bonds to 20
• Math Addition Facts to 20
• 2 Digit Column Addition Without Regrouping
• 2 Digit Column Addition Worksheets With Regrouping
• 3 Digit Column Addition Worksheets

Year 3 Subtraction Worksheets

The following worksheets involve using the skills of subtracting numbers, and solving subtraction problems.

• know their subtraction facts to 20;
• know how addition and subtraction are related to each other;
• learn to do 3 digit column subtraction.
• Subtraction Facts to 20 Worksheets
• Two Digit Subtraction Worksheets Without Regrouping
• 2 Digit Subtraction Worksheets With Regrouping
• 3 Digit Subtraction Worksheets

Addition & Subtraction Worksheets

You can create your own addition and subtraction worksheets with our random generator.

All you need to do is to set your number size and let the generator do the rest!

• Addition Subtraction Fact Worksheets
• Column Addition and Subtraction Worksheets

Year 3 Multiplication Worksheets

The following worksheets involve using the Year 3 Maths skills of multiplying, and solving multiplication problems.

• learn their multiplication tables up to 5 x 5;
• understand multiplication as repeated addition;
• learn how multiplication and division are related to each other.

Online Times Table Practice

• Times Tables Online Practice Zone
• Understanding Multiplication Worksheets
• Printable Times Tables - 2 Times Table sheets
• Printable Times Tables - 3 Times Table sheets
• Times Tables for kids - 4 Times Table sheets
• Times Table Math - 5 Times Table sheets
• Learning Times Tables - 8 Times Table

Multiplication Word Problems

• Year 3 Multiplication Word Problems (2nd Grade)

Randomly Generated Multiplication Worksheets

• Times Tables Worksheets (randomly generated)

2 Digit by 1 Digit Written Multiplication

• Multiplication Worksheets for 3rd Grade 2-digits by 1-digit
• Year 3 Division Worksheets

The following worksheets involve using the skills of dividing, and solving division problems.

Using these Year 3 maths worksheets will help your child learn to:

• understand division as repeated subtraction or sharing;
• understand different models of division;
• Division Facts Worksheets (randomly generated)

Here are a range of problems solving sheets for Year 3 children. Most of the sheets contain 'real-life' problems related to animal facts.

Using the sheets will help your child to:

• apply their addition, subtraction, and multiplication skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems.

These sheets involve solving one or two more challenging longer problems. This link opens in a new tab.

• Year 3 Maths Challenges

These sheets involve solving many 'real-life' problems involving data.

• Year 3 Math Word Problems

These sheets involve solving a range of addition word problems within 100.

• Addition Word Problems 2nd grade

These sheets involve solving a range of subtraction word problems up to 100.

• Subtraction Word Problems 2nd grade
• 2nd Grade Addition and Subtraction Word Problems

These sheets involve solving a range of multiplication problems.

• Multiplication Word Problems Year 3

Year 3 Fraction Worksheets

• understand what a half is;
• shade in half of a shape;
• find different numbers involving 'halves' on a number line;
• find half of different numbers up to 20.
• Fraction Math Worksheets - Understanding a half
• Fraction Riddles for kids (easier)

Year 3 Geometry Worksheets

At a Year 3 level, children are introduced to a wider range of 2d and 3d shapes, and start to learn to reflect, flip and rotate shapes.

They are able to classify and sort two-dimensional shapes using different criteria, and they learn the properties of three-dimensional shapes.

The following worksheets will help your child to:

• Identify and name a range of 2d and 3d shapes;
• Draw 2d shapes;
• Know some of the properties of 2d shapes.
• Year 3 Geometry Worksheets (2nd Grade)

Symmetry Worksheets

• learn how to reflect simple shapes in a horizontal or vertical mirror line;
• learn how to reflect simple shapes in 2 mirror lines.
• Symmetry Worksheets - Block Symmetry

Measurement Zone, including Time & Money

Year 3 measurement worksheets.

These sheets involve reading scales going up in ones, fives, tens and hundreds to find the length, weight or liquid capacity.

Using these sheets will help children to consolidate their counting as well as learning to read a simple scale.

• Year 3 Measurement Worksheets (2nd Grade)

Counting Money Worksheets UK - £2, £1, 50p and 20p coins

Here you will find a selection of Counting Money sheets designed to help your child count different amounts of money using UK coins up to £2.

• count a range of coins up to £5
• compare money amounts
• apply their existing skills to puzzle out clues;
• understand money terminology;
• develop their thinking skills.

The free Year 3 Money worksheets in this section are suitable for children in Years 2 and 3.

• Free Money Worksheets UK Coins up to £1
• Year 3 Money Worksheets to £5
• Money Riddles for Kids (UK coins)
• Year 3 Money Challenges

Time Worksheets

Here are our collection of clock worksheets for Year 3. These sheets cover telling the time for quarter past and quarter to times.

• read times to the nearest 5 minutes;
• convert analogue to digital times;
• adding and subtracting hours from different times.
• Clock Worksheets - Quarter Past and Quarter To
• Telling Time to 5 Minutes Worksheets
• Add and Subtract Time Worksheets

Year 3 Bar Graph Worksheets

These sheets involve reading and interpreting a range of bar graphs and picture graphs with a scale going up in ones or twos.

Draw missing bars on a bar graph to the correct height.

Use the information in a bar graph to add data into a table.

Using the link below will open the 2nd grade Math Salamanders website in a new browser window.

• Year 3 Bar Graphs (2nd Grade)

Fun Zone: Puzzles, Games and Riddles

Year 3 math games.

All children like to play Math games, and you will find a good range of 2nd Grade Math Games here for your child to play and enjoy.

The following games involve different Second Grade Math activities which you and your child can enjoy together.

• Year 3 Math Games (2nd Grade)
• Year 3 Maths Puzzles

The puzzles will help your child practice and apply their addition, subtraction and multiplication facts as well as developing their thinking and reasoning skills in a fun and engaging way.

The Number Square Puzzles page will open a new browser window which will take you to the 2nd grade math salamanders website.

Using these puzzles will help your child to:

• learn their addition facts to 20+20;
• learn and practice subtraction facts to 20;
• pratice multiplying up to 5x5;
• develop thinking and reasoning skills;
• develop perseverance.
• Number Square Puzzles
• Math Puzzles at 2nd Grade Math Salamanders

Math Salamanders Year 3 Maths Games Ebook

Our Year 3 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store, use the link below to find out more!

• Year 3 Maths Games Ebook

Help & Support

Looking for a resource which is not here.

Take a look at our 2nd Grade Math Salamanders website.

On this site you will find a wider selection of Year 3 maths worksheets and free math resources.

• 2nd Grade Math Salamanders

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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The Sunday Read: ‘Why Did This Guy Put a Song About Me on Spotify?’

The answer involves a remarkable — and lucrative, and ridiculous — scheme to game the way we find music today..

By Brett Martin

Read by Eric Jason Martin

Produced by Adrienne Hurst and Aaron Esposito

Narration produced by Tanya Pérez and Krish Seenivasan

Edited by John Woo

Original music by Aaron Esposito

Engineered by Sophia Lanman and Devin Murphy

Listen and follow The Daily Apple Podcasts | Spotify

Have you heard the song “Brett Martin, You a Nice Man, Yes”?

Probably not. On Spotify, “Brett Martin, You a Nice Man, Yes” has not yet accumulated enough streams to even register a tally. Even Brett Martin, a contributing writer for The New York Times Magazine and the titular Nice Man, didn’t hear the 1 minute 14 second song until last summer, a full 11 years after it was uploaded by an artist credited as Papa Razzi and the Photogs.

When Martin stumbled on “Brett Martin, You a Nice Man, Yes,” he naturally assumed it was about a different, more famous Brett Martin: perhaps Brett Martin, the left-handed reliever who until recently played for the Texas Rangers; or Brett Martin, the legendary Australian squash player; or even Clara Brett Martin, the Canadian who in 1897 became the British Empire’s first female lawyer. Only when the singer began referencing details of stories that he made for public radio’s “This American Life” almost 20 years ago did he realize the song was actually about him. The song ended, “I really like you/Will you be my friend?/Will you call me on the phone?” Then it gave a phone number, with a New Hampshire area code.

So, he called.

There are a lot of ways to listen to ‘The Daily.’ Here’s how.

We want to hear from you. Tune in, and tell us what you think. Email us at [email protected] . Follow Michael Barbaro on X: @mikiebarb . And if you’re interested in advertising with The Daily, write to us at [email protected] .

Additional production for The Sunday Read was contributed by Isabella Anderson, Anna Diamond, Sarah Diamond, Elena Hecht, Emma Kehlbeck, Tanya Pérez, Frannie Carr Toth and Krish Seenivasan.

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