multiplication problem solving year 6

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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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Problem Solving — Multiplication and Division (Year 6)

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In this PowerPoint, children will recap the methods of long multiplication, short division and long division, before applying their knowledge to some problem solving questions. Each problem shows step-by-step workings, before the PowerPoint concludes with a helpful 'key tips' slide.

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: Multiplication & Division
• Topic Group: Calculations
• Year(s): Year 6
• Media Type: PowerPoint
• Resource Type: Front-of-Class Teaching
• Last Updated: 31/10/2023
• Resource Code: M2PAT144
• Curriculum Point(s): Solve problems involving addition, subtraction, multiplication and division.

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Grade 6 Multiplication & Division Worksheets

Multiplication and division math worksheets.

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Problem-Solving Investigation: Multiples, factors & prime numbers (Year 6 Multiplication & Division)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 October 2019

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Year 6 Multiplication and Division: Multiples, factors and prime numbers.

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: Magic Multiplication Squares Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square.

This problem-solving investigation is part of our Year 6 Multiplication and Division block. Each Hamilton maths block contains a complete set of planning and resources to teach a terms worth of objectives for one of the National Curriculum for England’s maths areas.

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Year 6 Multiplication and Division - Problem-Solving Investigations

These in-depth maths investigations are open-ended problem solving activities for Year 6 children. **In-depth Investigation: Magic Multiplication Squares** Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square. **In-depth Investigation: The Eights Have It** Children multiply numbers starting with 9 by 9 and add single-digit numbers in a decreasing sequence. They identify and describe the patterns and start to explain them. **In-depth Investigation: Awesome Answers** Using a magic square to generate 3-digit numbers, children create divisions with dividends containing specified fractions. **In-depth Investigation: Stunning Squares** Children explore patterns in the squares of numbers with reversed digits to find pairs of ‘stunning squares’. **In-depth Investigation: Geometry Genius** Children use what they know about how to find the areas of triangles and parallelograms to find the areas of rhombi, kites and trapezia. **In-depth Investigation: Get to the Root** Children use their fluency in mental multiplication to explore the patterns of digital roots in multiplication. **In-depth Investigation: Riveting Reversals** Multiply 3-digit numbers with consecutive digits by a 2-digit number; reverse the 3-digit number and repeat. Find the difference between the two answers. **In-depth Investigation: Why is it so?** Children identify a pattern in the division of a total of six numbers created using the same 3 digits. They then use algebra to explain why it is so. These investigations will develop maths meta-skills, support open-ended questioning and logical reasoning, and enable children to learn to think mathematically and articulate mathematical ideas. These problem-solving investigations come from our [Year 6 Maths Blocks](https://www.hamilton-trust.org.uk/maths/year-6-maths/). 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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Years 5 and 6: Multiplication and Division

This list consists of activities, games and videos designed to support the new curriculum programme of study in Years 5 and 6. Containing tips on using the resources and suggestions for further use it covers:

Year 5 : identifying factors and multiples, prime numbers and composite numbers, use formal methods for multiplication and division of up to 4 digits by 1 or 2 digit numbers, recognise and use square and cube numbers and solving problems involving one or more of the four operations.

Year 6 : formal written method of long multiplication/long division for numbers up to 4 digits by 2 digits, mental calculations, identify common factors, multiples and prime numbers, solving problems and estimating to check answers to calculations.  

Visit the primary mathematics webpage to access all lists:.

NRICH: Factors and Multiples Game

This game could be used to practise knowledge of factors and multiples. Children choose a number and then challenge a partner to find a factor or multiple of the number from their grid. Play it on sheets or interactively in pairs at the end of a lesson.

Multiplication and Division

Quality Assured Category: Mathematics Publisher: Department for Education

Interactive activities which show different methods of multiplication and division. Multiplication and division using partitioning allows teachers to demonstrate these methods to children on the interactive whiteboard.

Go Further with Games

Quality Assured Category: Mathematics Publisher: Unwin Hyman Ltd

40 games sheets related to many mathematical areas. Laminate and keep in a box for when they are needed.Sheet 2 looks at division with remainders.

The Multiplication card games help children consolidate multiplication facts.  

Multiple games using simple apparatus provides practice on specific multiples.

Factor games encourages students to think which numbers are factors of grid column and row headings.

Multiplication dice games practice mental single digit multiplication and keeping a running total.

Primary Progression in Multiplication Videos

Quality Assured Collection Category: Mathematics Publisher: NCETM

This series of short video clips look at elements of progression in multiplication across the primary school. Starting with various concrete representations using physical apparatus, children are guided into transferring to the calculations they represent. Children in years 5 and 6 may be at different stages in their mathematical learning, so may need to approach multiplication in a different way. The NCETM provides similar videos which show progression in other calculation strategies.

Models and images materials

This set of images and models, from the national strategies, give examples of key pictorial representations and abstracts which can enhance the teaching of mental calculation strategies through years one to three. In addition, the materials offer a list of potential difficulties and examples to illustrate progression through to years four, five and six.

Multiplication Makes Sense

Quality Assured Category: Mathematics Publisher: SMILE

15 activities focusing on multiplication

Page 24 is a children's worksheet which asks children to explain why the grid method of multiplication works for multiplying two 2-digit numbers. The grid method will have been used by most children at upper Key stage Two and for some it will be an efficient and understandable method. It also is a step along the way to developing a more formal written method, including long multiplication. See the models and images resource which shows example representations of multiplication and progression of learning.

Page 26 shows how long multiplication may be carried out using Gelosia, providing questions to calculate. The NRICH website contains an investigation which challenges children to use this method.

35 year 6 maths questions

Practise 35 year 6 maths questions that will help your child stay on track!

Author Amber Watkins

Published February 2024

• Key takeaways
• Year 6 maths word problems help students apply mathematical concepts to real-world scenarios.
• In year 6 maths, it’s important to master fractions, decimals, and order of operations.
• Hard problems  can be simplified by drawing a picture or using a method that makes them easier to solve.

Table of contents

• Word problems

Numbers & place value

Multiplication.

If this maths page has 5 sections of maths questions  with an average of 7 questions in each section, can you guess how many problems there will be in all? That’s right, there will be a total of 35 year 6 maths questions for us to practise. Without realising it, you just solved one of our first year 6 word problems . Excellent work! Together we will review year 6 maths problems with decimals, fractions, order of operations, and rounding. We will even consider hard maths problems, like multiplying using square models and number lines. Don’t worry about getting the answers right the first time, each section includes answers if you need a sneak peek. So grab a pad and pencil and let’s begin.

Year 6 maths word problems

Let’s begin by covering maths word problems.

Mia’s water bottle can hold 300 millilitres of water. She drinks two and a half water bottles each day. How many total millilitres of water does Mia drink each day? 

The playground is made up of four rectangular lots that are each 10 metres by 7 metres. What is the total area of the playground?

 Josh lives 2.5 kilometres away from the park. Josh rides his bike to the park and back home four days a week. How many kilometres does Josh ride his bike each week?

Since we are solving word problems, a word should always be in our answer.

In this section, we will cover maths questions that use place values, word form to standard form, standard form to word form, and expanded form.

Place value

Which digit in the number 245 is in the hundreds place?

Which digit in the number 4,602 is in the tens place?

Which digit in the number 752 is in the ones place?

Word form to standard form

Standard form to expanded form.

4,000 + 300 + 2 = 4,302

600 + 50 + 4 = 654

20,000 + 2,000 + 300 + 60 + 5 = 22,365

In this section, we will cover year six maths questions that include comparing decimals and rounding decimals to the nearest tenth, hundredth, and thousandths place. Let’s get started.

8.9 and 8.900 are the same.

Remember if the number to the right is 5 or larger, you can borrow and become one digit larger. If the number to the right is between 0 and 4, you can’t borrow and the number remains the same.

In this section, we will review maths questionss for year six that cover the topics of adding and subtracting two and three-digit numbers using transformation, division using area models, and the order of operations.

Adding and subtracting whole numbers by transformation

A large portion of year 6 maths problems can be made easier to solve by transformation or changing numbers to make the problem simpler. Let’s practise adding and subtracting two and three-digit numbers by transformation.

How to add numbers using transformation?

When adding or subtracting numbers, look for ways to round to make the problem simpler. Don’t forget what you do to one number, you have to do the opposite to the other. This makes sure the problem stays balanced. Let’s see how this is done. What is 48 + 52? 48 + 2 = 50

52 – 2 = 50 

50 + 50 = 100.

It may be difficult to add 48 + 52 in your head, so we round 48 to 50 by adding 2. Since we added 2 to the first number, we have to make sure to subtract 2 from the second number. So now the problem is 50 plus 50, which is much easier to calculate! 

32 – 2 = 30 68 + 2 = 70 30 + 70 = 100 The answer is 100.

208 – 8 = 200 432 + 8 = 440 200 + 440 = 640 The answer is 640.

321- 1 = 320 199 + 1 = 200 320- 200 = 120 The answer is 120

Division using area models

Don’t know what an area model is? See our area model guide to help with these problems.

Using an area model find the quotient of 365 ፥ 5 =

Using an area model find the quotient of 504 ፥ 6 =

Using the area model below, find the quotient of 872 ፥ 2 =

Order of operations

Many people remember the Order of Operations with the acronym PEMDAS- “Please Excuse My Dear Aunt Sally”, with each letter representing an operation: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Solve the following equations using the order of operations.

Remember that the steps Multiply or Divide can be done in any order. Also, the steps Add or Subtract can be done in any order, do the operation that comes first.

Some of the hardest maths questions involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines. Let’s practise a few of each!

Multiplying using square models

Multiplying using square models is a method to help students “see” multiplication problems in a simpler way.

Multiply 42 x 35 using the square model below.

Multiply 55 x 76 using the square model below.

Multiply 98 x 42 using the square model below.

Multiplying fractions and whole numbers using expanded form

Multiply ½ x 5 using expanded form.

Multiply ⅔ x 6 using expanded form.

Multiply ⅙ x 7 using expanded form.

Multiplying fractions using a number line

For more maths practice for year 6 , our app for maths help provides year 6 maths help in a way that makes maths fun, rewards effort over being correct, and scaffolds learning. Plus, you’ll get access to a dashboard that displays your child’s participation and progression on maths topics they struggle with. Check it out today !

Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!

Word problem answer sheet

Mia drinks 750 millilitres  of water each day.

Explanation: 300 x 2 = 600. 300 / 2 = 150. 600 + 150 = 750.

280 square metres.

Explanation: The area of one lot is 10 x 7 = 70 metres. Take that area and times it by four, so 70 x 4 = 280 metres.

Josh rides 20 kilometres on his bike each week.

Explanation: Each day Josh rides 5 total kilometres: 2.5 kilometres to the park and 2.5 kilometres back home. If we multiply that number by 4 days a week, it equals 20 kilometres in all.

Writing numbers answer sheet

2 is in the hundreds place.

0 is in the tens place.

2 is in the ones place.

Division using area models answer sheet

Multiplying using square models answer sheet

Multiplying fractions and whole numbers using expanded form answer sheet

Multiplying fractions using a number line answer sheet

Explanation – First divide the number line into 6 equal parts and draw up a line up to 4/6. Then find the ½ way mark of that line you drew up to 4/6. You will now see the line is divided into three parts. So the answer would be ⅓. 

Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring students in maths. "Knowing that my work in maths education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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Free Printable Multi-Step Word Problems Worksheets for 6th Year

Multi-Step Word Problems: Discover a collection of free printable math worksheets for Year 6 students, designed to help them master solving complex problems through a series of smaller, manageable steps. Empower your teaching with Quizizz!

Explore Multi-Step Word Problems Worksheets by Grades

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Explore printable Multi-Step Word Problems worksheets for 6th Year

Multi-Step Word Problems worksheets for Year 6 are an essential resource for teachers looking to enhance their students' math skills and problem-solving abilities. These worksheets provide a variety of challenging and engaging math word problems that require students to use multiple steps and operations to find the solution. By incorporating these worksheets into their lesson plans, teachers can help their Year 6 students develop a deeper understanding of mathematical concepts, improve their critical thinking skills, and build confidence in their ability to tackle complex problems. With a wide range of topics covered, from fractions and decimals to geometry and algebra, these Multi-Step Word Problems worksheets for Year 6 are a valuable tool for any math teacher looking to challenge and inspire their students.

In addition to Multi-Step Word Problems worksheets for Year 6, teachers can also utilize Quizizz, an interactive platform that offers a variety of engaging and customizable quizzes, games, and activities to supplement their math curriculum. Quizizz allows teachers to create their own quizzes or choose from a vast library of pre-made quizzes, covering a wide range of topics and difficulty levels. This platform not only provides a fun and interactive way for students to practice their math skills but also offers valuable insights and analytics for teachers to track their students' progress and identify areas for improvement. By incorporating Quizizz into their lesson plans, teachers can provide a well-rounded and engaging learning experience for their Year 6 students, helping them excel in math and build a strong foundation for future success.