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Year 5 Maths Worksheets UK Hub Page

Welcome to our Year 5 Maths Worksheets area.

Here you will find a wide range of free printable Maths Worksheets for pupils in Year 5, and Math activities for your child to enjoy.

Take a look at our decimal place value sheets, our mental math sheets, or maybe some of our equivalent fraction worksheets. Perhaps you would prefer our statistics worksheets, or how to measure angles?

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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 5 Maths Learning

Here are some of the key learning objectives for the end of Year 5:

  • know and use Place value up to 1 million
  • Compare and order numbers up to 1 million
  • Counting on and back in steps of powers of 10 from any number up to 1 million
  • Round numbers to the nearest 10, 100, 1000, 10000 or 100000.
  • Count forwards and backwards through zero with positive and negative numbers.
  • Read Roman numerals to 1000
  • add and subtract with more than 4 digits in columns
  • add or subtract larger numbers mentally
  • solve multi-step problems using addition and subtraction
  • Multiply and divide whole numbers and decimals up to 2dp by 10, 100 or 1000
  • identify multiples and factors including common factors
  • multiply up to 4-digit numbers by a 1-digit number
  • multiply up to 3-digits numbers by 2-digits
  • divide numbers up to 4-digits by a 1-digit number
  • recognise and use squared and cubed numbers
  • solve problems using multiplication and division
  • know what a prime number is and recall prime numbers up to 20
  • compare and order fractions whose denominators are multiples of the same number
  • identify, name and write equivalent fractions
  • convert between mixed numbers and improper fractions
  • add and subtract fractions with the same denominator or whose denominators are multiples of the same number
  • multiply proper fractions and mixed numbers by whole numbers
  • read and write decimal numbers as fractions.
  • Multiply and divide whole numbers and decimals by 10, 100 or 1000
  • read, write, order and compare numbers up to 2dp
  • round decimals with up to 2dp to the nearest whole
  • solve problems with numbers up to 2dp
  • understand and use the percent symbol
  • convert percentages to fractions with a denominator of 100
  • know fraction-percentage equivalence for halves, quarters, fifths and tenths
  • solve problems using simple percentages
  • measure, compare and calculate using different measures
  • find the area and perimeter of a range of rectilinear shapes
  • convert between different units of time
  • convert between different units of metric measure
  • convert between simple imperial and metric units
  • solve more complex money and measure problems
  • draw and measure angles in degrees
  • know the sum of angles at a point (360°rees;) and angles at a point along a line (180°rees;)
  • identify 3D shapes from 2D representations
  • Identify, describe and represent the position of a shape following a reflection or translation
  • find the area and perimeter of composite rectilinear shapes
  • know properties of regular and irregular shapes

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 5 is generally equivalent to 4th Grade in the US.

On this page you will find link to our range of math worksheets for Year 5.

Quicklinks to Year 5 ...

  • Place Value Zone
  • Mental Math Zone

Word Problems Zone

  • Fractions & Percentages 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 5 place value worksheets.

Using these Year 5 maths worksheets will help your child to:

  • Understand decimals;
  • Use place value notation with tenths and hundredths;
  • Know how to read and write numbers to 10 million;
  • Understand place value to 10 million.
  • Decimal Place Value Worksheets
  • Year 5 Place Value up to 6 digits
  • Comparing and Ordering Whole Numbers up to 6 Digits
  • Ordering Decimals Worksheets
  • Roman Numerals worksheets

Year 5 Number Worksheets

Using these Year 5 Maths worksheets will help your child to:

  • learn to estimate and approximate;
  • order numbers, including negative numbers and decimals;
  • learn how to place decimal numbers on a number line;
  • understand and use multiples and factors, and know what a prime number is;
  • complete the missing number to balance a math equation.
  • Factors and Multiples Worksheet
  • Rounding Decimals to the nearest whole
  • Rounding to the nearest tenth
  • Balancing Math Equations

Year 5 Counting Worksheets

Using these sheets will support you child to:

  • count on and back by multiples of 10;
  • fill in the missing numbers in sequences;
  • count on and back into negative numbers.
  • Counting on and back by tens

Year 5 Mental Maths Zone

Here you will find a range of printable Year 5 mental maths sheets for your child to enjoy.

Each quiz tests the children on a range of maths 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 5 Mental Maths Worksheet

Top of Page

Year 5 Addition Worksheets

  • add multiple numbers in columns up to 5 digits;
  • add numbers in columns, including money amounts with up to two decimal places.
  • Decimal Addition Worksheets (mental)
  • Free Addition Worksheets (randomly generated)
  • Addition Worksheets with Multi-Addends
  • Money Addition Worksheets (£ )
  • Money Worksheets (randomly generated)

Year 5 Subtraction Worksheets

  • learn to subtract numbers with up to 5 digits;
  • learn to subtract numbers involving money with decimals with up to two decimal places.
  • Free Subtraction Worksheets (randomly generated)
  • 5 Digit Subtraction Worksheets
  • Money Subtraction Worksheets UK (£ )
  • Subtracting Decimals Worksheets (mental)

Year 5 Multiplication Worksheets

Using these 4th grade math worksheets will help your child to:

  • use their multiplication table knowledge to multiply by 10s and 100s mentally
  • multiply any whole number by a single digit;
  • multiply a two or three digit number by a two digit number.
  • Times Table Worksheets Circles 1 to 12 tables
  • Times Tables Worksheets (randomly generated)
  • Multiplying Decimals by 10 and 100
  • Multiply and Divide by 10 100 (decimals)
  • Multiplying by Multiples of 10 and 100
  • Single Digit Multiplication Graded Sheets
  • Double Digit Multiplication Worksheets (Graded)
  • Single Digit Multiplication Worksheets Generator
  • Multi-Digit Multiplication Generator
  • Multiplication Word Problems

Year 5 Division Worksheets

Using these Year 5 maths worksheets will help your child learn to:

  • apply their division facts up to 10x10 to answer related questions involving 10s and 100s.
  • divide any whole number by a single digit.
  • Divding by Multiples of 10 and 100 Worksheets
  • Year 5 (4th Grade) Long Division Worksheets

These sheets involve solving a range of division problems.

  • Division Worksheets (Grade 4) Word Problems
  • Division Facts Worksheets (randomly generated)

Year 5 Math Problems

  • apply their addition, subtraction and problem solving skills;
  • apply their knowledge of rounding and place value;
  • solve a range of 'real life' problems;
  • attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

These sheets involve solving one or two more challenging longer problems.

  • 4th Grade Math Problems

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

  • 4th Grade Math Word Problems

These sheets involve solving a range of multiplciation problems.

  • Division Worksheets Grade 4 Word Problems

Fractions & Percentage Zone

Quicklinks to ...

  • Year 5 Fractions Worksheets

Year 5 Percentage Worksheets

Year 5 fraction worksheets.

  • position different fractions on a number line;
  • understand equivalent fractions;
  • understand what a mixed number is;
  • compare two or more fractions;
  • begin to convert fractions to decimals and decimals to fractions.
  • Equivalent Fractions Worksheets
  • Comparing Fractions Worksheet page
  • Improper Fraction Worksheets
  • Fractions of Numbers
  • Convert Fractions to Decimal Sheets
  • Convert Decimal to Fraction Sheets
  • Free Printable Fraction Riddles (harder)

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

  • Fractions Decimals Percents Worksheets
  • Percentage Word Problems

Year 5 Geometry Worksheets

Using these sheets will help you to:

  • classify angles - acute, obtuse, right, reflex, straight;
  • classify triangles - acute, obtuse, right;
  • measure angles using a protractor;
  • know that angles in a triangle add up to 180°
  • know the properties of regular and irregular shapes
  • plot and write coordinates in the first quadrant.
  • 4th Grade Geometry Worksheets
  • Symmetry Activities
  • Coordinate Worksheets (1st Quadrant)

Measurement Zone, including Time & Money

Year 5 measurement worksheets.

Using these sheets will help your child understand how to:

  • read scales in both the standard and metric systems;
  • read a scale going up in a range of fractions: halves, quarters and eighths;
  • read a scale going up in tenths, fives, tens, fifties, and hundreds.
  • 4th Grade Measurement Worksheets
  • Converting Customary Units Worksheets
  • Metric Conversion Worksheets

Area and Perimeter Worksheets

  • understand area and perimeter;
  • learn how to find the area and perimeter of rectangles and rectilinear shapes.
  • Area Worksheets
  • Perimeter Worksheets

Year 5 Time Worksheets (4th Grade)

Using the sheets in this section will help your child to:

  • tell the time to the nearest minute;
  • become familiar with both digital and analogue times;
  • add and subtract time intervals.
  • Telling Time Worksheets Grade 4 (1 minute intervals)
  • 24 Hour Clock Conversion Worksheets

On this webpage there is a selection of printable 24 hour (military time) conversion worksheets which will help you learn to convert from 24 hour clock to standard 12 hour time, and from standard time to 24 hour time.

Time Interval Worksheets

These sheets will help you learn to add and subtract hours and minutes from times as well as working out a range of time intervals.

  • Add and Subtract Time Worksheets
  • Elapsed Time Worksheets

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

  • Time Word Problems Worksheets - Riddles (harder)

Using these 4th grade math worksheets will help you to:

  • draw and read bar graphs with increasingly complex numbers;
  • read, interpret and draw line graphs;
  • Year 5 Bar Graph Worksheets (4th grade)
  • Year 5 Line Graph Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 5 maths games.

  • Year 5 Math Games (4th Grade)

Year 5 Maths Puzzles

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

  • Year 5 Maths Puzzles (4th Grade)

Math Salamanders Year 5 Maths Games Ebook

Our Year 5 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 5 Maths Games Ebook

Other UK Maths Worksheet pages

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

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Problem Solving and the New Curriculum   Age 5 to 11

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Developing a Classroom Culture That Supports a Problem-solving Approach to Mathematics   Age 5 to 11

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Developing Excellence in Problem Solving with Young Learners   Age 5 to 11

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Using NRICH Tasks to Develop Key Problem-solving Skills   Age 5 to 11

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Trial and Improvement at KS1   Age 5 to 7

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Trial and Improvement at KS2   Age 7 to 11

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Working Systematically - Primary Teachers   Age 5 to 11

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Number Patterns   Age 5 to 11

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Working Backwards at KS1   Age 5 to 7

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Working Backwards at KS2   Age 7 to 11

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Reasoning   Age 5 to 11

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Visualising at KS1 - Primary Teachers   Age 5 to 7

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Visualising at KS2 - Primary Teachers   Age 7 to 11

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Conjecturing and Generalising at KS1 - Primary Teachers   Age 5 to 7

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Conjecturing and Generalising at KS2 - Primary Teachers   Age 7 to 11

  • Mathematical Problem Solving in the Early Years
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  • Group-worthy Tasks and Their Potential to Support Children to Develop Independent Problem-solving Skills
  • Developing the Classroom Culture: Using the Dotty Six Activity as a Springboard for Investigation

year 5 maths problem solving

Geometry in Year 5 (age 9–10)

In Year 5, children will be expected to be able to solve problems about shapes by reasoning using their knowledge of geometric properties. This includes:

  • drawing and measuring angles in degrees
  • finding missing angles at a point, on a line and in rectangles
  • describing translations and reflections of shapes on a four-quadrant coordinate grid.

Measurement in Year 5 (age 9–10)

In Year 5, children will be expected to be able to convert between metric units of measurement and solve problems involving decimal measurements, money and time. This includes:

  • calculating the perimeter and area of shapes (including those made up of squares and rectangles)
  • estimating volumes of 3D shapes and capacities of containers
  • learning some imperial units, such as inches, pounds and pints.

Statistics in Year 5 (age 9–10)

In Year 5, children will interpret and present data in a range of ways. This includes:

  • solving problems by comparing, adding, and subtracting using data presented in line graphs
  • representing data in time graphs by using the scales on the axes to plot points
  • completing, reading, and interpreting information in tables, including timetables.
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Visual maths worksheets, each maths worksheet is differentiated and visual.

Year 5 Maths Worksheets

Our Year 5 Maths Worksheets are an excellent resource for students (aged 9-10) to practice and strengthen their maths skills. With clear instructions and plenty of examples, these worksheets are suitable for independent learning at home or in the classroom. They help pupils develop their problem-solving abilities while also reinforcing previously learnt concepts. All Year 5 Cazoom Maths PDF worksheets provide a wide range of questions and activities that cover all the critical topics from numbers, algebra, geometry, measurement and statistics. These worksheets are designed to challenge and assess pupils’ understanding and strengthen knowledge of decimals, fractions, rounding numbers, prime numbers, angles, reading from timetables and more.

MATHS WORKSHEETS FOR YEAR 5 STUDENTS

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Try some free sample year 5 maths worksheets

Year 5 Colourful Equivalences Maths Worksheet

Outstanding Year 5 Maths Worksheets

  • Separate answers are included to make marking easy and quick.
  • Over 100 pages of the highest quality year 5 maths worksheets. Each worksheet is differentiated, including a progressive level of difficulty as the worksheet continues.
  • Single user licence for parents or teachers. Separate school licences are also available.
  • Single digital pdf download, with worksheets organised into high level chapters of Number, Measurement and Geometry, and further by subtopics. See below for the extensive range of sheets included.

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FUN and ENgaging Maths Worksheets

Our maths worksheets are thoughtfully designed to make mathematical problems great fun for your year 5 students. 

This range of year 5 maths worksheets PDF are designed with colour and with the space for children to show their working. Our resources are perfect practice material for helping your child learn maths, enhance their reasoning skills, and for pupils to develop their mathematical knowledge.

Some of our most popular resources include those on multiplication word problems, measuring angles, ordering fractions, and even roman numerals!

With over 200 pages of mathematical problems for your students to work through, Cazoom Maths worksheets are the perfect way for your year 5 students to develop their mathematical skills . 

ALL YEAR 5 TOPICS COVERED

Cazoom Maths pdf year 5 maths worksheets cover all topics in the curriculum at this formative stage for young learners.

We have worksheets covering addition and subtraction, place value, missing numbers, and resources requiring students to identify the correct number.  The range also includes lots of different exercises of topics like equivalent fractions, formal written methods, number and place value, negative numbers, and much more.

Our resources include real life problems such as how to interpret different until, and use metric measures. Covering such a comprehensive range of maths topics, Cazoom has everything needed to help children practice their year 5 maths skills. 

List of Topics

See below the list of topics covered. All KS1 and KS2 worksheets can be accessed here.

  • Adding to a Single Digit
  • Adding to a Two Digit Number
  • Adding to a Three Digit Number
  • Adding Three Numbers
  • Number Bonds up to 20
  • Number Bonds over 20

SUBTRACTION

  • Single Digit Subtraction
  • Two Digit Subtraction
  • Three Digit Subtraction
  • Working with the Difference
  • Multiplication and Division worksheets
  • Number and Place Value Worksheets
  • Fractions, Decimals and Percentages

MEASUREMENT

  • Metric Measures
  • Area and Perimeter
  • Properties of Shapes
  • Position and Direction
  • Transformations

ALGEBRA & STATISTICS

📝 NEW NATIONAL NUMERACY DAY WORKSHEETS ADDED - CLICK HERE TO DOWNLOAD NOW ✅

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Math Workbooks for Grade 5

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5th Grade Math Word Problems Worksheets

Math word problem worksheets for grade 5.

These worksheets present students with real world word problems that students can solve with grade 5 math concepts. 

We encourage students to think about the problems carefully by:

  • providing a number of mixed word problem worksheets
  • including irrelevant data  so students need to understand the context before applying a solution

The four operations

Mixed 4 operations

Estimating and rounding word problems

Grade 5 fractions and decimal word problems

Addition and subtraction of fractions

Addition and subtraction of mixed numbers

Division of numbers with fractional answers

Dividing by unit fractions

Multiplying fractions word problems

Mixed operations with fractions

More mixed fraction word problems

Decimals word problems

Measurement word problems

Mass and weight word problems

Volume and capacity word problems

Length word problems

Word problems worksheets with variables

Variables and expressions

Variables and equations

Other grade 5 word problems worksheets

Volume of rectangular prisms

GCF / LCM word problems

Mixed grade 5 word problems  

year 5 maths problem solving

Sample Grade 5 Word Problem Worksheet

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year 5 maths problem solving

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Reasoning/Problem Solving Maths Worksheets for Year 5 (age 9-10)

Real life problem solving.

A collection of problem solving activities based on real life situations.

Preview of worksheet  Solve single step 'real life' problems

Some of the questions are quite long, but they can be answered with a single step operation.

Preview of worksheet Multi step problems using bar models

Using bar models to help understand what to do to solve multi-step problems.

Preview of worksheet  Solve multi step word problems

Much trickier questions as they all need more than one step to reach the right answer.

Preview of worksheet Multi-step problems: shopping

Multi-step problems with shopping.

Preview of worksheet Multi-step problems: hobbies

Tricky multi-step problems on thew theme of hobbies.

Preview of worksheet Multi-step problems: using cards

Multi-step problems: using cards.

Preview of worksheet Multi-step problems: using place value charts

Multi-step problems: using place value charts.

Preview of worksheet Vending machine

Buying snacks and drinks from a vending machine.

Preview of worksheet Work out the price of the plants

Straightforward addition of money which can be done mentally, maybe using jottings to help.

Preview of worksheet Cost of houseplants

Work out the cost of the plants from the information given.

Preview of worksheet Buying three houseplants

Addition of money to really stretch the brain!

Preview of worksheet Meal deal

Choosing sets of meals to save money with the meal deal.

Preview of worksheet Days out (1)

Solving problems involving '3 for 2' voucher offer.

Preview of worksheet Days out (2)

Solving money problems with 3 for 2 offers and percentages.

Preview of worksheet Days out (3)

More percentage problems.

Preview of worksheet  Solve problems involving money

Money, money, money! Lots of money questions which will need a lot of working out!

Preview of worksheet Solving multi step problems

Tricky word problems needing more than one step to solve.

Preview of worksheet  Solve problems involving measurement

Questions all on the theme of measurement, including length, capacity and weight.

Preview of worksheet  Solve problems involving time

Hours, minutes seconds are all found in these questions on time.

Preview of worksheet 5-digit numbers: problem solving

Find the number from the clues given.

Preview of worksheet Problem solving: inverse operations

Solve multi-step problems and check by carrying out inverse operations.

Preview of worksheet Digit cards: largest and smallest numbers

Find the largest and smallest numbers and the difference between them.

Preview of worksheet  Choose the correct strategy

Not so much the correct answer needed; more choosing the method and an explanation of how to solve the problem.

Fractions, decimals and divisibility

Problem solving involving fractions, decimals and tests of divisibility.

Preview of worksheet Bar modelling: facts about decimals

Finding facts about decimal fractions, including bar modelling.

Preview of worksheet Bar modelling facts about decimal (2)

Finding facts about decimal fractions, including using bar modelling to help.

Preview of worksheet Order decimals

Order decimals.

Preview of worksheet Find half way between two decimals

Find half way between two decimals.

Preview of worksheet Word problems with decimals

Word problems with decimals.

Preview of worksheet Ordering fractions

Ordering fractions.

Preview of worksheet  Tests of divisibility

Some tests of divisibility are easy, such as divisible by 2, 5 or 10. Others, such as divisible by 6 or 8 are much harder.

Challenges and investigations

Further challenges, investigations and games requiring sound mathematical thinking and working in a systematic way.

Preview of worksheet  More on odd and even numbers

More on odd and even numbers, plus a little bit on multiples.

Preview of worksheet 12 to 15 square

Place the digits in the rows and columns to make the total shown in the middle.

Preview of worksheet  More problem solving

Some great ideas for children to use as starting points to investigate further.

Preview of worksheet  Make and investigate general statements

Find examples to back up general statements about numbers, shape etc.

Preview of worksheet  Use binary trees to solve problems

Binary trees are often used in science, but here we use them to sort numbers.

Preview of worksheet Challenges and Investigations in Year 5

A look at some of the maths concepts involved with investigations in year 5.

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18 Word Problems For Year 5: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 5 are a great way to assess pupils’ number fluency. By the time primary school children reach Upper Key Stage 2, they will be building on their knowledge and understanding of the number system and place value, working with larger integers. An increased understanding of the connections between the different maths concepts is crucial, as children will be expected to tackle more complex, multi-step problems.

It is important children are regularly provided with the opportunity to solve a range of word problems and Year 5 maths worksheets with reasoning and problem solving incorporated alongside fluency, into all lessons.

To help you with this, we have put together a collection of 18 word problems aimed at Year 5 maths pupils.

Place value 

Addition and subtraction , multiplication and division , fractions, decimals and percentages, measurement , why are word problems important in year 5 maths, how to teach problem solving in year 5, addition word problems for year 5, subtraction word problems for year 5,  multiplication word problems for year 5, division word problems for year 5, fraction and decimal word problems in year 5, mixed four operation word problems, word problem resources.

All Kinds of Word Problems

All Kinds of Word Problems

Download this free pack of multiplication word problems to help your Year 5 class grow their problem solving skills

Year 5 maths word problems in the national curriculum

The National Curriculum states that by Year 5, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. Children also begin to use the language of algebra for solving a range of problems.

By Year 5, pupils should be starting to gain confidence in solving more complex two-step and multi-step word problems, covering topics across the Year 5 curriculum.

Solve number and practical problems involving ordering and comparing numbers to at least 1,00,000; counting forwards or backwards in steps of powers of 10; interpreting negative numbers in context and rounding to the nearest 10,100, 1000, 10,000 and 100,000.

Solve addition and subtraction word problems and a combination of these, including understanding the meaning of the equals sign.

Solve problems involving multiplication and division, including using knowledge of factors, multiples, squares and cubes and scaling by simple fractions.

Solve problems involving numbers up to 3 decimal places and problems which require knowing percentage and decimal equivalents.

Solve time word problems and those involving converting between units of time and problems involving measure (for example, length, mass, volume and money word problems ) using decimal notation and scaling.

Solve comparison, sum and difference problems, using information presented in a line graph.

Word problems are an important element of the Year 5 curriculum. By this stage, children need to be building confidence in approaching a range of one, two and multi-step word problems . They require children to be creative and apply the skills they have learnt to a range of real-life situations. 

Children need to be taught the skills for successfully approaching and tackling word problems. Reading the question carefully and identifying the key information needed to tackle the problem, is the first step, followed by identifying which calculations are required for solving it and deciding whether it will be helpful to draw a picture/ visual representation to understand and answer the question. 

Using mental maths skills to round and estimate an answer is also very helpful for children to establish whether their final answer is realistic. Children need to also be able to calculate the inverse, to be able to check their answer, once the problem has been completed.

See also: Mental maths year 5

Here is an example:

A transport museum has 1243 visitors on Monday morning and another 1387 visitors in the afternoon. On Tuesday 736 fewer visitors go to the museum than who visited on Monday.

How many visitors were there altogether on Tuesday?

How to solve:

What do you already know?

  • The number of visitors on Monday morning and Monday afternoon are given separately. They need to be added together to give the total number of visitors for Monday.
  • ‘Fewer’ means I will need to subtract the number of fewer visitors on Tuesday from the total number of visitors on Monday.
  • Column addition and subtraction will be needed to solve this question.

How can this be drawn/represented pictorially?

We can draw a bar model to represent this problem:

year 5 problem solving

  • To calculate the total number of visitors on Monday, we need to add 1243 and 1387 together. 1243 + 1387 = 2630
  • The number of fewer visitors on Tuesday needs to be subtracted from Monday’s total: 2630 – 736 = 1894.
  • The total number of visitors on Tuesday was 1894.

In Year 5, addition word problems can involve whole numbers with over 4 digits and decimal numbers. Children should be able to round number to check the accuracy and begin to solve two step number problems 

Addition question 1

Gemma picks two cards from the cards below and adds them together.  She is able to make three different totals. What will they be?

2365     6281      9782

Answer (2 marks) : 12,147   16,063  8646

long addition example

Addition question 2

Ahmed adds two of these numbers mentally.

357         280          294          232

In his calculation, he exchanges twice to create one ten and one hundred. Write Ahmed’s calculation and work out the total.

Answer (1 mark) : 357 + 294 = 651

long addition example

Addition question 3

Change one digit in the calculation below, so that the answer is a multiple of 10.

Answer (1 mark) : 723 + 347 = 1070

Subtraction word problems in Year 5 require pupils to be confident subtracting numbers over 4 digits and problems involving decimal numbers. Pupils need to be able to round numbers to check accuracy and to use subtraction when solving mixed word problems. 

Subtraction question 1

A coach is travelling 4924 km across the USA It has 2476 km to go. How many kilometres has the coach already travelled?

Answer (1 mark) : 2448 km

long subtraction example

Subtraction question 2

A primary school printed 7283 maths worksheets in the Summer term. 2156 were for Key Stage 1 pupils. How many were printed for Key Stage 2?

Answer (1 mark): 5127 worksheets

long subtraction example

Subtraction question 3

 A clothing company made £57,605 profit in 2021 and £73,403 in 2022.  How much more profit did the company make in 2022 than in 2021?

Answer (1 mark): £15,798

long subtraction example

In year 5, multiplication word problems include problems involving times tables and multiplying whole numbers up to 4-digits by 1 or 2-digit numbers. Pupils also need to be able to combine multiplication with other operations, in order to solve two-step word problems. 

Multiplication question 1

In this diagram, the numbers in the circles are multiplied together to make the answer in the square between them.

Complete the missing numbers.

complete the missing number

Answer (1 mark)

complete the missing number answer

Multiplication question 2

Mrs Jones was printing the end of year maths test. Each test had 18 pages and 89 pupils were sitting the test. Mrs Jones also needed to print out 12 copies for the teachers and Teaching Assistants who were helping to run the test. 

How many pieces of paper did Mrs Jones need to put in the photocopier, to make sure she had enough for all the tests?

long multiplication

Multiplication question 3

A school is booking a trip to Alton Towers. Tickets cost £22 per pupil. There are 120 children in each year group and all the children from 3 year groups will be going.

What will be the total price for all the tickets?

Answer (2 marks): £7920

long multiplication question

Third Space Learning often ties word problems into our online one-to-one tutoring. Each lesson is personalised to the needs of the individual student, growing maths knowledge and problem solving skills.

multiplication word problem slide

In Year 5, division word problems can involve whole numbers up to 4 digits being divided by 1-digit numbers. Pupils need to understand how to answer word problems, when the answer involves a remainder.

Division question 1

Tom has 96 cubes and makes 12 equal towers. Masie has 63 cubes and makes 9 equal towers. Whose towers are tallest and by how many cubes?

Answer (2 marks): Tom

Tom’s tower has more cubes. His towers have 1 more cube than Maise’s towers.

96 ÷ 12 = 8

Division question 2

A cake factory has made cakes to deliver to a large event. 265 cakes have been baked. How many boxes of 8 cakes can be delivered to the event?

Answer (2 marks) : 33 boxes

long division question

Division question 3

Lily collected 1256 stickers. She shared them between her 8 friends. How many stickers did each friend get

Answer (1 mark): 157 stickers

long division answer

In Year 5, fractions word problems and decimals can include questions involving ordering, addition and subtraction of fractions. They can also involve converting between fractions and decimals. 

Fraction and decimal question 1

Isobel collected 24 conkers. She gave \frac{1}{8} of the conkers to her brother. How many conkers did she have left?

Answer (1 mark): 21 conkers left

\frac{1}{8} of 24 = 3

24 – 4 = 21

Fraction and decimal question 2

Ahmed counted out 32 sweets. He gave \frac{1}{4} of the sweets to his brother and \frac{3}{8} of the sweets to his friend. How many sweets did he have left?

Answer (2 marks): 12 sweets

\frac{1}{4} of 32 = 8

\frac{3}{8} of 32 = 12

He gave away 20 sweets, so had 12 left for himself.

Fraction and decimal question 3

Two friends shared some pizzas, 1 ate 1 \frac{1}{2} pizzas, whilst the other ate \frac{5}{8} of a pizza. How much did they eat altogether?

Answer (1 mark): 2 \frac{1}{8} of pizza

1 \frac{1}{2} = \frac{12}{8}

\frac {12}{8} + \frac{5}{8} = \frac{17}{8} = 2 \frac{1}{8} pizzas

Problems with mixed operations, or ‘multi-step’ word problems, require two or more operations to solve them. A range of concepts can be covered within mixed problems, including the four operations, fractions, decimals and measures. These are worth more marks than some of the more straightforward, one-step problems.

Mixed operation question 1

At the cake sale, Sam buys 6 cookies and a cupcake . He pays £2.85 altogether. Naya buys 2 cookies and pays 90p altogether.

How much does the cupcake cost?

Answer (2 marks): 60p for one cupcake

money word problem

Mixed operation question 2

Large biscuit tin – 48 biscuits (picture of boxes here) Small biscuit tin – 30 biscuits Ben bought 2 large tins of biscuits and 3 small tins.

How many biscuits did he buy altogether?

Answer (2 marks): 186 biscuits

2 x 48 = 96

3 x 30 = 90

96 + 90 = 186 biscuits

Mixed operation question 3

The owner of a bookshop bought a box of 15 books for £150.

He sold the books individually for £12 each. 

How much profit did he make?

Answer (2 marks)

long multiplication money question

Third Space Learning offers a wide array of maths and word problems resources for other year groups such as word problems for year 6 , word problems for year 3 and word problems for year 4 . Our word problem collection covers all four operations and other specific maths topics such as ratio word problems and percentage word problems .

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Teens come up with answer to problem that stumped math world for centuries

A s the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson: So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Ne'Kiya Jackson and Calcea Johnson

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Year 5 mixed operation word problems

Year 5 mixed operation word problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

mjt89

Last updated

12 May 2020

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year 5 maths problem solving

A range of mixed operation Maths word problems that are in line with NC targets for Year 5 but suitable across all of Key Stage Two

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a woman in glasses and a maroon blazer and a woman in a blue dress

Teens who discovered new way to prove Pythagoras’s theorem uncover even more proofs

As high school students, Calcea Johnson and Ne’Kiya Jackson worked to find valid new proof for the 2,000-year-old theorem

Two college freshmen who, during their final year of high school, found a new way to prove Pythagoras’s theorem by using trigonometry – which mathematicians for generations thought was impossible – have since uncovered multiple more such proofs, they revealed in a national interview on Sunday.

“We found five, and then we found a general format that could potentially produce at least five additional proofs,” Calcea Johnson said on CBS’s 60 Minutes, a little more than a year after she and Ne’Kiya Jackson collaborated on an accomplishment that earned them international recognition.

Nonetheless, in comments that stunned their interviewer, Bill Whitaker, the two graduates of St Mary’s Academy in New Orleans denied seeing themselves as math geniuses and dismissed any interest in pursuing careers in mathematics.

“People might expect too much out of me if I become a mathematician,” Jackson said, shaking her head. Johnson, for her part, added: “I may take up a minor in math, but I don’t want that to be my job job.”

Sunday’s conversation on CBS’s popular Sunday evening news magazine were perhaps their most extensive, widely broadcast remarks to date on the new ground that they broke with respect to the Pythagorean theorem.

The 2,000-year-old theorem established that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse – the third, longest side opposite the shape’s right angle. Countless schoolchildren taking geometry have memorized the notation summarizing the theorem: a 2 + b 2 = c 2 .

For 2,000 years, mathematicians maintained that any alleged proof of the Pythagorean theorem that was based in trigonometry would constitute a logical fallacy known as circular reason – in essence, trying to validate an idea with the idea itself.

But the bonus question on a math contest that Johnson and Jackson took home to complete during the Christmas break of their final year at St Mary’s served as the impetus for them to plot out a new way to demonstrate that one could indeed use trigonometry to prove Pythagoras’s theorem.

Their work was so compelling that the pair went to a regional meeting of the American Mathematical Society in Atlanta in March 2023 to outline their findings. At the organization’s recommendation, Jackson and Johnson have submitted their discoveries for final peer review and publication – as well as working on additional proofs while that process is pending, as 60 Minutes noted.

The 60 Minutes interview gave Johnson and Jackson occasion to reflect on the intense reaction caused by initial media reports on their innovative work at St Mary’s, a Catholic high school that has been dedicated to educating Black girls since its founding shortly after the US civil war.

Some of it was negative. Some in the math community smarted at claims in a press release issued by St Mary’s that asserted Jackson and Johnson’s research was “unprecedented”. And they flocked to social media demanding that a 2009 trigonometry-based proof for Pythagoras’s theorem get its due.

Yet a lot of the reaction to Johnson and Jackson was positive, especially as mathematicians who picked apart their work confirmed that – by all indications – they had arrived at a valid new proof, a celebration-worthy accomplishment.

Michelle Obama wrote a post on social media that linked to a story about Johnson and Jackson, adding the text: “I just love this story. … Way to go, Ne’Kiya and Calcea! I’m rooting for you and can’t wait to see what you all do next.”

They also received a commendation from Louisiana’s then governor as well as symbolic keys to the city of New Orleans .

Asked on 60 Minutes why they thought people were so impressed with what they had done, Jackson said she thought the public was surprised young Black women could author such a feat.

“I’d like to be celebrated for what it is,” Jackson said. “Like – it’s a great mathematical achievement.”

Jackson is now attending New Orleans’ Xavier University and enrolled in its pharmacy department. Meanwhile, Johnson – who graduated from St Mary’s as its valedictorian – is now an environmental engineering student at Louisiana State University in Baton Rouge.

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COMMENTS

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    A high school teacher didn't expect a solution when she set a 2,000-year-old Pythagorean Theorem problem in front of her students. Then Calcea Johnson and Ne'Kiya Jackson stepped up to the challenge.

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    A high school teacher didn't expect a solution when she set a 2,000-year-old Pythagorean Theorem problem in front of her students. Then Calcea Johnson and Ne'Kiya Jackson stepped up to the ...

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  27. Stormy Daniels Takes the Stand

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