problem solving year 6 questions

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Year 6 Maths Worksheets UK Hub Page

Welcome to our Year 6 Maths Worksheets area.

Here you will find a wide range of free printable Year 6 Maths Worksheets for your child to enjoy.

Come and take a look at our rounding decimal pages, or maybe some of our adding and subtracting fractions worksheets. Perhaps you are looking for some worksheets about finding angles in a triangle, or need some ratio problem worksheets to help your child learn about ratio?

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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 6 Maths Learning

Here are some of the key learning objectives for the end of Year 6:

know and use Place value up to 10 million
Counting on and back in steps of powers of 10 from any number up to 10 million
Round numbers to any given degree of accuracy.
Count forwards and backwards through zero with positive and negative numbers.
Read Roman numerals to 1000 and recognise years written in Roman numerals
solve multi-step problems using addition and subtraction in a range of contexts
identify multiples and factors including common factors
multiply and divide up to 4-digit numbers by up to 2 digits
Use their knowledge of the order of operations to carry out calculations involving the four operations.
Identify common factors, common multiples and prime numbers.
solve problems involving addition, subtraction, multiplication and division
simplify fractions
compare and order fractions including mixed numbers
add and subtract fractions with different denominators including mixed numbers
multiply simple fractions together and simplify the answer
divide proper fractions by whole numbers
recall and use equivalence between simple fractions, decimals and percentages.
Multiply and divide whole numbers and decimals up to 3dp by 10, 100 or 1000
read, write, order and compare numbers up to 3dp
round decimals with up to 3dp to the nearest whole
solve problems with numbers up to 3dp
work out percentages of different amounts
solve problems using percentages
use simple formulae
express missing number problems using algebra
find pairs of numbers that satisfy equations with two variables
solve problems involving simple ratios
solve problems involving similar shapes where the scale factor is known
use, read, write and convert between standard units of measure
measure, compare and calculate using different measures
know that shapes with the same area can have different perimeters
find the area of parallelograms and right triangles
find the volume of cubes and cuboids
convert between miles and km
name and understand the parts of circles - radius, diameter and circumference
draw 2D shapes accurately using dimensions and angles
compate and classify 2D shapes by a range of properties
find missing angles in triangles, quadrilaterals and regular shapes
use coordinates in all 4 quadrants
draw and translate simple shapes in all 4 quadrants
interpret and construct pie charts and line graphs
calculate the mean as an average

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

On this page you will find link to our range of math worksheets for Year 6.

Quicklinks to Year 6 ...

Place Value Zone
Mental Math Zone

Word Problems Zone

Fractions percents ratio zone.

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 6 number worksheets.

Here you will find a range of Free Printable Year 6 Number Worksheets.

Using these Year 6 maths worksheets will help your child to:

use place value with numbers up to 10 million;
use place value with up to 3 decimal places;
understand how to use exponents (powers) of a number;
understand and use parentheses (brackets);
understand and use multiples and factors;
extend their knowledge of prime and composite (non-prime) numbers up to 100;
know and be able to use the PEMDAS (or PEDMAS) rule.
Place Value Worksheets to 10 million
Place Value to 3dp
Ordering Decimals Worksheets
PEMDAS Rule Support Page
PEMDAS Problems Worksheets
Balancing Math Equations
Roman Numerals worksheets

Ordering Large Numbers and Decimals to 3dp

The sheets in this section involve ordering lists of decimals to 3 decimal places and also large numbers up to 100 million.

There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.

Ordering Large Numbers up to 100 million
Ordering Decimals to 3dp

Rounding Decimals

Rounding to the nearest tenth
Rounding Decimal Places Sheets to 2dp
Rounding Decimals Worksheet Challenges

Year 6 Decimal Counting Worksheets

Using these sheets will support you child to:

count on and back by multiples of 0.1;
fill in the missing numbers in sequences;
count on and back into negative numbers.
Counting By Decimals

Year 6 Mental Maths Zone

Each worksheet 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 quiz!

Year 6 Mental Maths Tests

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Year 6 Addition Worksheets

add decimals including tenths and hundredths mentally;
add a columns of multi-digit numbers, including decimals.
Decimal Addition Fact Worksheets
5th Grade Addition Worksheets BIG Numbers
Decimal Column Addition Worksheets
Money Worksheets (randomly generated)

Year 6 Subtraction Worksheets

Using these sheets will help your child to:

subtract decimals including tenths and hundredths mentally;
subtract multi-digit numbers, including decimals using column subtraction.
Subtracting Decimals Worksheets (mental)
Subtraction Worksheets up to Billions (columns)
Column Subtraction with Decimals

Year 6 Multiplication Worksheets

extend their knowlege of multiplication to decimals;
use their multiplication tables to answer related facts, including decimals;
multiply a range of decimals with up to 2 decimal places (2dp) by a whole number;
multiply different money amounts by a whole number.
Multiplying Decimals by 10 and 100
Multiplication Fact Sheet Decimals
Decimal Multiplication Worksheets to 1dp
Decimal Multiplication Worksheets to 2dp
Free Multiplication Worksheets (randomly generated)
Multiply and Divide by 10 100 (decimals)
Multiplication & Division Worksheets (randomly generated)
Multiplication Word Problems

Division Worksheets 5th Grade

Using these Year 6 maths worksheets will help your child learn to:

divide any whole number up to 10000 by a two digit number;
express any division with a remainder in the form of a mixed number (a number with a fraction part).
Long Division Worksheets (whole numbers)
Long Division of Decimal Numbers
Decimal Division Facts
Division Facts Worksheets (randomly generated)

Year 6 Maths Problems

apply their addition, subtraction, multiplication and division skills;
apply their knowledge of rounding and place value;
solve a range of problems including "real life" problems and ratio problems.

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

Year 6 Math Problems (5th Grade)

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

Year 6 Math Word Problems (5th Grade)

These sheets involve solving a range of ratio problems.

Year 6 Fraction Worksheets

Year 6 percentage worksheets, year 6 ratio worksheets.

compare and order fractions;
add and subtract fractions and mixed numbers;
understand how to multiply fractions by a whole number;
understand how to multiply two fractions together, including mixed fractions;
understand the relationship between fractions and division;
know how to divide fractions and mixed fractions;
convert decimals to fractions.
Comparing Fractions Worksheet page
Adding Fractions Worksheets
Adding Improper Fractions
Subtracting Fractions Worksheets
Adding Subtracting Fractions Worksheets
Improper Fraction Worksheets
Converting Decimals to Fractions Worksheets
Fractions Decimals Percents Worksheets
Multiplying Fractions Worksheets
Dividing Fractions by Whole numbers
Divide Whole numbers by Fractions
Simplifying Fractions Worksheets
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.

Percentage of Numbers Worksheets
Money Percentage Worksheets
Percentage Word Problems

These Year 6 Ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

Ratio Part to Part Worksheets
Ratio and Proportion Worksheets

Year 6 Geometry Worksheets

know how to find missing angles in a range of situations;
learn the number of degrees in a right angle, straight line, around a point and in a triangle;
know how to calculate the area of a triangle;
know how to calculate the area of a range of quadrilaterals.
learn the formulas to calculate the area of triangles and some quadrilaterals;
write and plot coordinates in all 4 quadrants.
(5th Grade) Geometry - Angles
Area of Quadrilaterals
5th Grade Volume Worksheets
Coordinate Worksheets (1st Quadrant)
Coordinate Plane Worksheets (All 4 Quadrants)
Parts of a Circle Worksheets

Measurement Zone, including Time & Money

Year 6 measurement worksheets.

Using these sheets will help your child understand how to:

learn how to read a standard scale going up in different fractions: halves, quarters, eighths and sixteenths;
learn how to read a metric scale going up in 0.1s, 5s, 10s, 25s, 50s & 100s;
learn how to estimate a measurement of length, weight or liquid;
convert temperatures in Celsius and Fahrenheit.
(5th Grade) Measurement Worksheets

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

Time Word Problems Worksheets - Riddles (harder)

Using these sheets will help you to:

find the mean of up to 5 numbers;
find a missing data point when the mean is given.
Mean Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 6 maths games.

Year 6 Math Games (5th Grade)

Year 6 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.

Printable Math Puzzles

Math Salamanders Year 6 Maths Games Ebook

Our Year 6 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 6 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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25 Year 6 Algebra Questions And Answers: KS2 Assessment Preparation

Emma Johnson

Here are 25 Year 6 SATs algebra questions designed to cover the algebraic concepts pupils are likely to encounter in the Key Stage 2 SATs.

In addition to these questions, we look in depth at the key algebraic vocabulary children should be familiar with when tackling algebraic questions ahead of the maths SATs.

Generally, algebra appears in the KS2 reasoning papers and not the Year 6 arithmetic questions . Usually appears less frequently in KS2 maths SATs papers than other national curriculum strands such as the four operations, place value and percentages, decimals and fractions questions .

But, it is still essential that Year 6 pupils are confident in addressing algebraic questions for their KS2 assessments so they can develop their understanding of algebra in KS3 and at GCSE.

Why are Year 6 algebra questions important in Key Stage 2?

Understanding basic algebraic concepts and formulas in Key Stage 2 helps to lay the foundations for more complex algebra in KS3, at GCSE and beyond. It also helps to develop children’s problem solving, critical thinking and logic.

Often, algebra may evoke anxiety in children before they even enter year 6 — they aren’t aware that they have been engaging with basic algebraic concepts since Key Stage 1.

For example, missing number calculations in Year 1, such as 3 + \_ = 10 are the starting blocks for algebraic expressions in Year 6, such as x + 3 = 10 .

As educators, it is important to make pupils aware of this relationship, helping to reduce the anxiety associated with algebra.

Similarly to ratio questions , it helps to link algebraic concepts to real-life situations when teaching algebra in KS2 . This helps to enhance pupils’ understanding.

Demonstrating how to apply algebra in Year 6 can help pupils independently solve problems in everyday scenarios and grasp its practical relevance.

For instance, solving the equation 3x = 24 may initially seem quite abstract. But when asked to calculate the cost of one apple, when the cost of 3 apples is 24p, pupils can contextualise the question and make connections to this algebraic concept.

Providing children with concrete resources, visual representations and real-life situations is vital in the teaching of algebra. This approach helps pupils break down the abstract nature of algebra and develop a conceptual understanding.

Key terminology for Year 6 SATs algebra

Children need to have an understanding of algebra terminology in order to secure their knowledge of algebraic concepts.

Year 6 pupils will need to have an understanding of the following key terms:

Algebra: The use of letters and symbols to represent numbers, when we don’t know the value in an equation. For example, y + 5 = 10
Variable : A symbol (usually a letter), used to represent an unknown or changing quantity. For example, in the number sentence 2x + 5 = 19, \; x is the variable
Term : A single mathematical expression separated by addition or subtraction in an algebraic expression. For example, in 4x + 6, \; 4x and 6 are terms
Unknown: The value you are trying to work out is shown as a letter. For example, in the number sentence 3x + 4 = 13, \; x is the unknown
Expression: A mathematical sentence using numbers and/or variables. For example, 3x + 7 is an expression.
Equation: a mathematical statement or expression that contains two equal sides separated by an equals sign. For example, 2y + 4 = 12 or 2y + 4 = 3x + 3
Formula: Algebra uses formulas, which refer to a mathematical rule or relationship that uses letters to represent amounts which can be changed. For example, 7 + x = 10
One- step equation : An equation which can be solved in only one step. For example, x + 7 = 15
Two- step equation : An algebraic equation that takes you two steps to solve. For example, 3x + 5 = 11
Substitution: Replacing variables in an algebraic expression with their numerical values. For example, x + 3 = 13 is equal to 10 + 3 =13
Pair of unknowns: A number sentence where there are two unknown values. For example, x + y = 12 and x is 3 times greater than y . Both x and y are unknowns.
Enumerate: Finding all possible answers to an algebraic problem and making a complete list of answers. For example, x + y = 5
Balancing equations: Performing operations on both sides of a number sentence to find the missing value. For example, where 3x +12 = 24 start by subtracting 12 from both sides of the equation. 24 - 12 = 3x = 12 12 ÷ 3 = 4 x = 4

200 arithmetic and reasoning questions for Year 6

Download 100 free arithmetic questions and 100 free reasoning questions for Year 6. Includes answers and mark scheme.

How do these Year 6 algebra questions help pupils prepare for the KS2 SATs?

These Year 6 algebra questions cover the breadth of the national curriculum. They have been designed by a math expert to cover the array of algebra SATs questions pupils may encounter in the KS2 SATs.

All problems, including algebra word problems, are contextualised to represent real-life scenarios. This helps pupils take the abstract concept and relate it to a familiar situation.

Practising a variety of algebra questions helps familiarise pupils with the question formats they will encounter in the KS2 SATs and develop confidence in their strategies for solving them.

Each question in the sequence becomes progressively harder, providing children with the opportunity to deepen their understanding of algebra. This also means questions will challenge those pupils who are working at greater depth.

25 Year 6 algebra questions and answers

Year 6 algebra questions: using simple formulae.

According to the national curriculum, pupils must be able to use and apply basic mathematical formulas to solve problems. To do this, they must be familiar with simple formulas and recognise the relationship between variables.

For example, the formula to find the area of a rectangle: Area = length x width

Question 1: using simple formulae

Calculate the value of each letter below: 4a = 12 7b = 63 9c = 27

Answer: a = 3, \; b = 9, \; c = 3

a. 12 ÷ 4 = 3

b. 63 ÷ 7 = 9

c. 27 ÷ 9 = 3

Question 2: using simple formulae

Calculate the value of the letter in the equation below:

Answer: x = 4

Question 3: using simple formulae

The formula for calculating the area of a rectangle is A = ab ( A is the area and ab are adjacent sides).

A rectangle has sides with a length of 7.2cm and a width of 3.8cm. What is the area?

Answer: 27.36 \, cm^2

Question 4: using simple formulae

The formula for converting kilometres (k) to miles (m) is: k = m \times 8÷5

Use this formula to convert 20 miles into kilometres.

Answer: 32 \, km

Question 5: using simple formulae

The formula for calculating the area of a triangle is \cfrac{1}{2} \, (b \times h)

What would be the height of a triangle with an area of 300 \, cm^2 and a base of 15 \, cm ?

Answer: 4 \, cm

More Year 6 algebra questions: Year 6 Forming Expressions Worksheets

Year 6 algebra questions: generate and describe linear number sequences

By the end of Year 6, pupils should be able to create and articulate linear number sequences where there is a constant difference between consecutive terms.

Pupils should also be able to create sequences where they are given the first term and a constant difference to continue expanding the sequence.

Question 6: linear number sequences

What are the next two terms in this sequence?

37, 44, 51, 58, ,

Answer: 65, 72 (+ 7)

Question 7: linear number sequences

Fill in the missing numbers in this sequence:

Answer: 98, 89, 80, 71

Question 8: linear number sequences

The formula 4n + 3 is used to generate a sequence,

Give the first 5 numbers of the sequence.

Answer: 7, 11, 15, 19, 23

Question 9: linear number sequences

Here is a linear sequence:

4, 11, 18, 25

What is the n th term?
What is the 15th term?

Question 10: linear number sequences

Ben has £28 at the start of the month. He spends 30p everyday day in January. How much does he have at the end of the month?

Answer: £18.70

30 x 31 = 930 (£9.30)

£28 – £9.30 = £18.70

Year 6 algebra questions: express missing number problems algebraically

A requirement of the national curriculum is for Year 6 pupils to be able to solve problems involving unknown values using algebraic expressions or algebraic equations.

Children first encounter missing number problems in KS1. For example: 3 + \_ = 10 . By the end of KS2, pupils progress to writing missing expressions and solving equations for a range of real-life problem solving scenarios.

Question 11: express missing number problems

12 more than a number is 33. Write an expression for this, using n to represent the number:

Answer: n + 12 = 33

Question 12: linear number sequences

What needs to be added to 27 to make 59?

Show the expression and the value of n.

Answer: 27 + n = 59 \quad \;

Question 13: linear number sequences

A function machine multiplies by 4 and then adds 5. What would be the expression if x was put into the function machine?

Answer: 4x + 5

Question 14: linear number sequences

An electrician charges £15 per hour and £25 for a call out.

What is the formula to express this calculation? (Use c for the cost and h for hour)

Answer: C = 15h + 25

Question 15: linear number sequences

A painter charges £14 per hour, but in December offers a discount of £8.

Write a formula to express this calculation (use c for cost and h for hour)
How much would it cost to hire the painter for 8 hours in December?

Answer: a. C = 14h - 8

Answer: b. £104

(14 x 8)-8 = 104

Year 6 algebra questions: find pairs of numbers that satisfy an equation with two unknowns

Equations with two unknowns involve two variables which are usually represented by letters such as x and y.

Each equation expresses the relationship between the variables. Pupils should be able to identify and apply pairs of numbers to the two variables in order to solve the equation.

Question 16: pairs of numbers for two unknown values

Find a possible solution for the following equation:

Answer: x = 6 , \; y = 3 (other possible solutions can be given)

Question 17: pairs of numbers for two unknown values

Find a possible solution for this equation:

Answer: a = 3, \; b = 7 (other possible solutions can be given).

Question 18: pairs of numbers for two unknown values

x is 3 times the value of y . What are the values of x and y?

Answer: x = 27, \; y = 9

Question 19: pairs of numbers for two unknown values

If z = 25 give one possible value of x and y?

Answer: x = 6, \; y = 3.5 (other possible answers may be given)

Question 20: pairs of numbers for two unknown values

Mason has some 50p and 20p coins. Altogether he has £2.40.

How many of each coin could he have?

Can you find the 2 possible solutions?

Answer: 2 x 50p and 7 x 20p

Or 4 x 50p and 2 x 20p

More questions: Year 6 Finding Pairs of Values Worksheet

Year 6 algebra questions: Enumerate possibilities of combinations of 2 variables

Enumerate possibility questions involve systematically listing and exploring various combinations of values for two variables.

By the end of KS2, pupils should be able to methodically consider various combinations of values for two variables.

Question 21: enumerate possibilities of combinations

The total of two numbers is 15. Both numbers are between 3 and 12.

Find all possible combinations that the two numbers could be:

Answer: 4 + 11, 5 + 10, 6 + 9, 7 + 8

Question 22: enumerate possibilities of combinations

The difference between two numbers is 7. Both numbers are between 18 and 30.

What could the numbers be?

Find all the possible combinations.

Answer: 30 – 23, 29 – 22, 28 – 21, 27 – 20, 26 – 19

Question 21: enumerate possibilities of combinations

Year 6 has a maths test every week and there are 15 questions on each test.

Mason worked out he scored double in the last week of term compared to the first week of term.

How many correct answers might Mason have scored in the first week?

Give all the possibilities.

Answer: 1, 2, 3, 4, 5, 6 or 7

Find all the possible combinations, where x and y are whole numbers:

x < 17 and y < 27

Answer: 26 + 15, 25 + 16

Question 23: enumerate possibilities of combinations

d is an odd number < 16 and e is a multiple of 3 < 13

What could the values of d and e be?

List all the possibilities.

Answers: 3 x 15 + 2 x 3, 3 x 13 + 2 x 6, 3 x 11 + 2 x 9, 3 x 9 + 2 x 12

More Year 6 algebra worksheets and algebra resources

Year 6 Algebra and Measures Worksheet
Year 6 Forming and Solving One Step Equations Worksheet
Year 6 Forming and Solving Two Step Equations Worksheet
Year 6 Algebra Recap
15 Algebra Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

While algebra does appear in Year 6 SATs questions, there are a lower percentage of algebra questions in the KS2 exams than some of the other content domains from the maths national curriculum. Over the last 5 years, algebra questions have made up between 4\% and 9\% of the Key Stage 2 maths assessments.

Algebra is explicitly taught to children from Year 6 (age 10 and 11 ) onwards. But children are introduced to basic algebra concepts, such as missing number questions, in primary school at a much younger age.

Pupils are introduced to the concept of algebra in Year 6. According to the national curriculum, by the end of Key Stage 2, pupils should be able to: • Use simple formulae • Generate and describe linear number sequences • Express missing number problems algebraically • Find pairs of numbers that satisfy an equation with two unknowns • Find enumerate possibilities of combinations of two variables

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FREE Year 6 Survival Pack

A selection of fun activities to use with your Year 6 class after SATs plus our most downloaded free SATs resources to support next year's cohort.

Includes KS2 maths games and investigations and our most popular resource, Fluent in Five!

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Word problems Year 6 – Mixed 3-mark maths questions & answers

PDF and PowerPoint

This Year 6 maths word problems resource contains lots of real-world scenario questions that require multi-step problem-solving. These tasks are ideal for helping pupils master essential maths skills in a fun and meaningful way.

The resource presents a range of word problems designed specifically to push Year 6 students’ reasoning and mathematical fluency.

Word problems for Year 6

These problems focus on different topics, from calculating averages and unit costs to measuring volumes and areas. They are all wrapped in contexts that are relatable to everyday life.

Each problem is worth three marks. This gives students the opportunity to demonstrate their working process and practise full multi-step problem-solving skills.

This makes the resource perfect for revision sessions, SATs preparation , or as part of your regular maths lessons. You can easily slot these problems into group work, homework tasks or individual assessments.

The problems are easy to read, with enough space for students to show their working, and the answers are provided at the end.

With its focus on key Year 6 maths topics like multiplication, division, fractions and units of measurement, this downloadable Year 6 word problems resource is a valuable tool for reinforcing learning.

Primary Maths Hub was founded in 2022 by Sarah Farrell and Andrew Jennings and offers high-quality maths resources. Follow on X at @PrimaryMathsHub .

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