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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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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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Welcome to the Year 6 Mini-Maths homepage. Daily maths questions for Year 6 are available for every week of the year, providing free help for teachers, pupils and parents. 1000s of free tasks and activities are available to support children in their learning both in the classroom and at home. Use the search and filter box below to easily find the outcomes you require.
It is recommended that a topic is selected per week and daily maths tasks accessed using the links provided below. Use each day’s answers to help identify and guide the required support in preparation for the following day’s task. Watch your understanding, application and confidence grow throughout the week. New resources are always being added, so keep checking for updates.
More about Year 6 Maths Questions …
The Year 6 curriculum completes the Key Stage 2 maths programme of learning bringing understanding and confidence together from Year 3 through to the end of Year 6. This journey culminates in the KS2 SATs assessments where learners are able to demonstrate their progress and development in the subject.
Year 6 NUMBER …
The four operations reach a natural conclusion in Year 6 – addition, subtraction, multiplication and division involve more complex examples before introducing decimals values . Learners are looking to extend their understanding of units, tens, hundreds, thousands, etc, with the Place value of digits in decimal places, supporting the wider curriculum such as calculating decimal remainders using short division.
Year 6 SHAPE …
Learners have been developing a sound understanding of 2D shape and 3D shape allowing them to sort and classify by their properties. Being able to identify and use these properties also improves an awareness of a shape’s area and perimeter or volume .
Year 6 DATA …
Year 5 offers further coverage of tables, charts and graphs, where learners are expected to both read and interpret information in all types of graphs and charts including pie charts . Drawing graphs and charts from given data is also introduced in Year 6 maths.
All learning objectives are supported by a Home Learning pack and iQ mastery questions challenge learners’ understanding, application and confidence. The Home Learning packs provide first class opportunities for effective intervention and an ever growing library of help videos for Year 6 maths is available on the MyMiniMaths YouTube channel in support of quality learning.
Year 6 SATs …
MyMiniMaths also offers specialised support for Year 6 SATs with a programme of practice KS2 SATs papers for the arithmetic paper . Easy identification of key skills in need of further support to maximise attainment is available through the Arithmetic Target Questions .
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35 SATs Maths Questions And Answers With Worked Examples: Essential Maths Reasoning Practice For Year 6 [FREE]
Anantha Anilkumar
For Year 6, the toughest of their SATs maths questions are the reasoning questions.
No matter how good pupils’ subject knowledge is or how effective your SATs revision lessons are, the examiners always manage to come up with maths questions that can baffle and flummox even the hardiest year 6 pupil.
To mitigate against this for SATs 2024 your pupils need plenty of exam practice and more specifically exam question practice to be familiar with both the types of SATs reasoning questions that can come up and the skills needed to answer them.
So to make life easy for you we’ve put together here a comprehensive collection of 35 SATs maths questions, organised by the sorts of question that pupils can expect to encounter.
All these practice SATs questions have been based on a mix of questions from past SATs papers , our own free year 6 maths SATs papers , and our collections of year 6 reasoning questions from the Rapid Reasoning resource collection. The answers are all taken from the answer sheets we provide for each test paper.
Other useful SATs revision resources
Before we get into the year 6 maths questions you might find it helpful to know that we have hundreds of other free KS2 SATs revision resources, including free SATs papers , and SATs intervention packs for those wanting to use the Year 6 SATs revision lessons we use in one to one tutoring in their own boosters.
You should also make sure you’re up to date with the latest analysis on the 20 most ‘valuable’ topics to study for SATs this year and also this analysis of the KS2 SATs Maths Papers Question Breakdown in 2023 .
You may also wish to read this guide to SATs first to give you some background information about the tests.
Why the focus on maths reasoning questions for SATs?
Ever since the new national curriculum Key Stage 2 SATs in 2016, the emphasis in the all SATs papers has been very much on SATs reasoning questions. While there is one arithmetic paper, there are two reasoning papers; and the variety, breadth and level of challenge in the reasoning paper continues to impress us.
Most Year 6 pupils find the reasoning SATs maths questions the hardest part of these maths papers. Unsurprisingly! We teach thousands of pupils every week in the run up to SATs, and teaching them maths reasoning skills at KS2 is a big part of what we do.
We even recently took the decision to restructure our SATs lessons to introduce maths reasoning questions earlier in the learning journey as the level of challenge just at the end of the lesson was too high. So we feel the Year 6 teacher’s pain!
Whatever level pupils go on to perform at in maths, maths reasoning questions and numerical reasoning tests (such as those used by grammar and private schools) are likely to be a part of the practice they require.
If you find you have children in your class with much further to catch-up than the others then we we would be happy to support them with some personalised online one to one maths tuition .
35 SATs maths questions for KS2 year 6 SATs
For the KS2 SATs tests, there are 7 types of maths reasoning question that are likely to come up:
- Single step worded problems
- Multiple step worded problems
- Problems involving measures
- Problems involving drawing
- Explanation questions
- Sequence questions
- Ordering questions
For each of these types we’ll examine an example SATs maths question from a previous SATs paper, looking at the question, the correct answer, and how to go about answering this question.
We’ll also look at further examples of each type of maths reasoning questions and answers from Third Space’s Rapid Reasoning resource, again with worked examples and an explanation of how to answer each.
Finally, at the end of this article we provide links to further Year 6 maths questions, assessments and other SATs papers that you may find useful including plenty of arithmetic practice too.
Our aim is to provide you as part of your SATs practice with a sample of the types of KS2 SATs questions pupils can expect in the reasoning papers and how to teach the reasoning and problem solving skills they’ll need to answer them.
For more word problems like this, check out our collection of 2-step and multi-step word problems for you as well as tips on how to use the bar model to answer Year 6 word problems . For advice on how to teach children to solve problems like this, check out these maths problem solving strategies.
SATs Maths Question Type 1: Single step worded problems
The simplest type of reasoning question pupils are likely to encounter in the reasoning papers, single step problems are exactly that: pupils are asked to interpret a written question and carry out a single mathematical step to solve it.
Have a look at the question below:
Reasoning Question 1
Answer: 65p
A relatively easy question to interpret and solve – the first step is to recognise £2 and £1.35 as equivalent to 200 and 135. From here the simple mathematical step is subtraction i.e. 200-135=65.
The most crucial skill for primary school pupils in this question is a solid understanding of money as relating to place value. If this understanding is present, the mathematical step itself is quite easy.
Below are several more examples, taken from Third Space Learning’s Rapid Reasoning resources:
Reasoning Question 2
Answer : 7 hours 24 minutes
Pupils need to understand that one hour is equal to 60 minutes. From here the single mathematical step is short division: 444/60, with a remainder.
Reasoning Question 3
Answer : 48 cm 3
Pupils must calculate length by breadth by height, using the figures provided by the question.
Reasoning Question 4
Answer : 124 cm
A simple enough calculation (doubling) if pupils are aware that the diameter is twice the radius.
Reasoning Question 5
Answer : 7,590
A single, relatively simple rounding problem – pupils should recognise that ’94’ is the operative part of this figure.
SATs Maths Question Type 2: Multiple step worded problems
A more complex version of the single step worded problem, multi-step problems require pupils to interpret a written problem, but solving it then requires the use of two or three maths skills,
For example, consider this question from the 2019 KS2 maths SATs:
Reasoning Question 6
Answer: £1.85
This question encompasses three different maths skills: multiplying (and dividing) mixed numbers, addition and subtraction. Pupils can choose to work out the multiplication or division first, but must complete both before moving on.
Once these values have been worked out the next steps are relatively simple – adding the two values together, and subtracting the total from £5.
Multi-step problems are particularly valuable to include in practice tests because they require children to apply their knowledge of maths language and their reasoning skills several times across the course of a single question, usually in slightly different contexts.
More examples:
Reasoning Question 7
Answer : £5,520
There are two steps to this problem, but both are multiplications. The first is to work out how much money is made per day – 92 x £15. This sum is then multiplied by 4 – the number of days – to get to the solution.
Reasoning Question 8
Answer : 2,160 km
Another two step problem. The first step is to work out 10% of 5400 km. Then multiply this by 4 to solve 40%.
Reasoning Question 9
Answer : £43.50
There are three steps involved in solving this problem: multiplication (doubling £51 and £36 to find the cost of two adult and two child tickets), addition (putting the two costs together) and division (dividing the total by four to obtain the mean cost).
Given the number of steps involved it can be easy for pupils to make arithmetic mistakes, and the mark scheme accounts for this by allowing for one mistake – but no more.
Read more: Mean median mode
Reasoning question 10.
Answer : 11.45 kg
A two-step problem again: multiplying 3.45 kg by 4, then subtracting 2.35 kg from the total. As with the previous problem, the mark scheme again allows for at most one arithmetic error, assuming the method is correct.
Year 6 Rapid Reasoning (Weeks 1-6)
Download 6 weeks of Rapid Reasoning slides for your Year 6 pupils and help them get a head start on preparing for the SATs reasoning papers.
SATs Maths Question Type 3: Problems involving measures
As their name suggests, these questions ask pupils to solve a problem that includes one or more units of measurement.
Take a look at this question from 2018’s Reasoning Paper 3:
Reasoning Question 1 1
Answer: 40 washes
This is a two step problem; pupils must first be able to read and convert kilograms to grams (and therefore know the relationship between the two units), then divide 2600 by 65 to work out the number of washes possible.
Questions involving measures tend to be few in number in the KS2 exam papers, but they often provide an excellent way to couch key maths skills such as the four operations.
Further examples:
Reasoning Question 12
Answer : 50g
A relatively simple division problem, relying on pupils having knowledge that 200g is one fifth of a kilogram.
Reasoning Question 13
Answer : 1.1kg
Another three step problem – multiplying 500 by 4 to get the total mass of the four melons, multiplying 300 by 3 to get the total mass of the remaining three melons, and then subtracting 2000 from 900 to obtain the mass of the fourth melon.
It’s worth noting that the mark scheme allows either 1.1kg or 1,100g as acceptable answers – the units of measurement are not as important as obtaining the current figure.
Reasoning Question 14
Answer : 216cm
Interesting to note that in this problem (unlike the previous example), the units for the answer are specified – an answer given in metres will be marked as wrong, since cm is specified in the answer box. This is why we encourage pupils to keep an eye on whether units are provided in the answer box.
Reasoning Question 15
Answer : 170g
As with the melon question there are three steps involved to solve this problem: working out the mass of the four cars (4 x 80), working out the mass of the remaining three cars (3 x 50) and subtracting 150 from 320 to get the mass of the fourth car.
SATs Maths Question Type 4: Problems involving drawing
Problems involving drawing require pupils to construct an accurate drawing by following a set of instructions, or through reflection, translation, or scaling.
This type of question is quite rare, but there are some notable exceptions, such as the infamous Question 21 in Paper 2 of the 2019 Reasoning SATs:
Reasoning Question 1 6
Answer: Any pair of lines that make a square of 4 units, a rectangle of 6 units, and a square of 25 units.
This question is considerably more complex than it appears, and incorporates aspects of multiplication as well as spatial awareness. One potential solution is to work out the area of the card (35), then work out the possible square numbers that will fit in (understanding that square numbers produce a square when drawn out as on a grid), and which then leave a single rectangle behind.
A lot of work for a single mark!
Some further examples:
Reasoning Question 17
Answer : Any quadrilateral made by joining the dots that has 3 acute angles e.g. an arrowhead shape.
Reasoning Question 18
Answer : An accurately drawn angle.
The mark scheme here allows some room for error – “between 34 and 36 degrees” is acceptable .
Reasoning Question 19
As with the question above, a small amount of room for error is given – “between 139 and 141 degrees”.
Reasoning Question 20
Answer : a new triangle drawn with points at (2,1), (5,1) and (2,4).
Translation can be tricky for pupils. Encourage them to look at the triangle as three points, and to translate each point separately rather than trying to move ‘the whole triangle’.
SATs Maths Question Type 5: Explanation questions
An early form of the ‘Prove X’ questions that come up in GCSEs, these problems ask children to explain a mathematical statement or error.
As an example:
Reasoning Question 21
Answer: If the distance from P to R is 800m and the distance from P to Q is (Q -> R x 4), it must be 4/5 of 800 = 640m. Therefore Olivia is wrong.
More than most problems, this type requires pupils to actively demonstrate their reasoning skills as well as their mathematical ones. Here pupils must articulate either in words or (where possible) numerically that they understand that Q to R is 1/5 of the total, that therefore P to Q is 4/5 of the total distance, and then calculate what this is via division and multiplication.
Further examples from TSL’s Rapid Reasoning resources:
Reasoning Question 22
Answer : No; 20/100 is the same as 20 divided by 100, which equals 0.2.
Reasoning Question 23
Answer : No; multiplication and division have the same priority, so in a problem like 40 x 6 ÷2, you would carry out the multiplication first as it occurs first.
The mark scheme notes that vague answers or any answers with a mathematical error are unacceptable.
Reasoning Question 24
Answer : No
Any explanation that provides a counter-example is acceptable e.g. “Not if the number is 1”, “Not for 0” etc.
Reasoning Question 25
Answer : Any answer that refers to the fact that there is a 5 in the hundreds place, AND a 9 in the thousands place, so that the number has to be rounded up as far as the ten-thousands place.
SATs Maths Question Type 6: Sequence questions
Another relatively simple kind of reasoning question, sequence problems involve pupils completing mathematical sequences.
Consider this example:
Reasoning Question 26
Answer: 35 , 42, 49, 56 , 63, 70
Number sequence questions, particularly those that involve linear sequences or (as in this case) times tables, come up relatively frequently in the SATs maths tests. The question’s instructions point clearly to the solution: work out what the increase between numbers is, then apply this via addition or subtraction to find the missing numbers.
Higher attaining pupils might quickly pick up that this is in fact the 7 times table and rely on their knowledge of multiplication facts to obtain the answer – this should be encouraged so long as they then check their answer in the normal method to ensure they haven’t made a mistake.
Reasoning Question 2 7
Answer(s) : 5/8 and 2 1/8 (OR 17/8)
Both answers must be correct to receive the mark. Pupils must recognise that 3/4 is the same as 6/8, so the following number must be three eighths higher.
Reasoning Question 28
Answer(s) : -19 and 9
Reasoning Question 29
Answer(s) : 128, 135 and 156.
Reasoning Question 30
Answer(s) : -10 and 22
This question can be a little tricky; pupils need to work out that the marks on the line represent increments of 4, and count backwards and forwards in 4s to obtain the missing numbers.
SATs Maths Question Type 7: Ordering questions
A slightly more complex variation of the sequence question, ordering problems require pupils to put a set of numbers, fractions or measures in the correct order.
A good example is this question from Paper 2 of the 2018 SATs:
Reasoning Question 31
Answer: 3/5, 3/4, 6/5
This question throws a stick in the wheels by including an improper fraction, but this is hardly unusual. These sorts of questions are just the place to find other ‘curveballs’ such as equivalent fractions, mixed numbers and decimals and fractions combined.
A good knowledge of the fundamentals of fractions is essential here: pupils must understand what a larger denominator means, and the significance of a fraction with a numerator greater than its denominator.
Reasoning Question 32
Answer : D,C,A,B
Encourage pupils to convert all the fractions to one denominator value to make ordering easier.
Reasoning Question 33
Answer : (descending down the ‘Place’ column) 3rd, 5th, 2nd, 4th
As with the example above, pupils should be encouraged to convert the fractions to make it easier to order them.
Reasoning Question 34
Answer : C, B, D, A
Reasoning Question 35
Answer : D, A, C, B
7 top tips for answering SATs questions
Now that we’ve covered how to answer some specific types of reasoning questions, here are some more generic tips for success in the reasoning papers. They may not all be applicable to every single question type, but will apply to at least two, usually more.
- Get pupils in the habit for any practice paper of identifying what information they’re given in a question, and what they need to know to solve the problem. This helps them start to form the steps needed to find the solution.
- Ask pupils to ‘spot the maths’ in a question – which calculations or skills do they actually need to use to solve the problem? This is useful even for arithmetic questions – it’s no surprise how often children can misread a question.
- Check the units! Especially in questions involving multiple measures, it can be easy to give the answer in the wrong one. The answer box might give a specific unit of measurement, so pupils should work to give their answer in that unit.
- In a similar vein, remind pupils to convert different units of measurement in a question into the same unit to make calculations easier e.g. kg to g.
- Encourage numerical answers where possible. Even in explanation questions demonstrating the mathematical calculation is a better explanation than trying to write it out.
- The bar model can be a useful way of visualising many different types of questions, and might make it easier to spot the ‘steps’ needed for the solution.
- Check your working out! Even if the working is ultimately irrelevant to the question, you can lose marks if it is wrong.
More free SATs questions (all with answers)
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Resources tagged with: NC Yr 6
There are 50 NRICH Mathematical resources connected to NC Yr 6 , you may find related items under NC .
4 by 4 Mathdokus
Can you use the clues to complete these 4 by 4 Mathematical Sudokus?
Different Deductions
There are lots of different methods to find out what the shapes are worth - how many can you find?
Name That Triangle!
Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?
Number Lines in Disguise
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
Price Match
Can you find pairs of differently sized windows that cost the same?
Finding 3D Stacks
Can you find a way of counting the spheres in these arrangements?
Extending Fraction Bars
Can you compare these bars with each other and express their lengths as fractions of the black bar?
More Fraction Bars
What fraction of the black bar are the other bars? Have a go at this challenging task!
Always, Sometimes or Never? Shape
Are these statements always true, sometimes true or never true?
Always, Sometimes or Never? Number
Round the Three Dice
What happens when you round these three-digit numbers to the nearest 100?
Round the Four Dice
This activity involves rounding four-digit numbers to the nearest thousand.
Use the information on these cards to draw the shape that is being described.
Dicey Perimeter, Dicey Area
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Domino Sets
How do you know if your set of dominoes is complete?
Making Spirals
Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.
Round a Hexagon
This problem shows that the external angles of an irregular hexagon add to a circle.
Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?
So It's Times!
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Button-up Some More
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Counting Cogs
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Doughnut Percents
A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.
Next Size Up
The challenge for you is to make a string of six (or more!) graded cubes.
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
What can you see? What do you notice? What questions can you ask?
Treasure Hunt
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
First Connect Three
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
Factor-multiple Chains
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Fraction Fascination
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
Triangles All Around
Can you find all the different triangles on these peg boards, and find their angles?
Diagonal Sums
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Ten Hidden Squares
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
Orange Drink
A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?
Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?
Sponge Sections
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Factor Lines
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Would You Rather?
Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?
Plenty of Pens
Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?
Mystery Matrix
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The Moons of Vuvv
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Where Are They?
Use the isometric grid paper to find the different polygons.
Rectangle Tangle
The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?
Pumpkin Pie Problem
Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?
Quadrilaterals
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
Two and Two
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Making Cuboids
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Round and Round the Circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Doplication
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
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{{item.title}}, my essentials, ask for help, contact edconnect, directory a to z, how to guides, maths trains brains, five resources to build positive maths mindsets in years 5 and 6.
Keep your child’s curiosity in maths flourishing with these resources, videos and tips. Packed with profound lessons and real-life stories about resilience, problem solving and perspective, these resources can help you continue to support your child build a positive mindset towards learning.
What Do You Do With A Problem?
Written by Kobi Yamada.
This picture book is about a persistent problem that follows a child around. The longer the problem is avoided, the larger it seems to get – isn’t that always the way? When the child finally musters up the courage to face the problem, it turns out to be something quite different all together. This profound story might just help your child uncover how brave they can be and how important it is to embrace challenges, no matter what format they come in.
Salt In His Shoes: Michael Jordan In Pursuit Of A Dream
Written by Deloris Jordan and Roslyn M. Jordan and illustrated by Kadir Nelson.
When Michael Jordan was a child, he almost gave up on being a basketball player because he feared he would never be tall enough. Then his parents taught him about patience, determination and hard work. This inspirational illustrated story is about how a family can work together to help a child achieve their dreams - true for almost all things when you want to feel more confident.
Confidence-Boosting Maths Messages
Developed By Youcubed at Stanford . Speaker: Professor Jo Boaler.
In this insightful video, Professor Jo Boaler from Stanford University and her students explain why everyone can master maths. They use the latest brain research as well as examples and stories of mathematicians in history who’ve encountered setbacks and spent years working on problems. This video can help us realise that maths isn’t about speed – it’s about growing our brains, creativity, and finding and solving problems.
Mistakes That Worked: The World’s Familiar Inventions And How They Came To Be
Written by Charlotte Jones and illustrated by John O'Brien.
Did you know many of the things we use in daily life were invented completely by accident? How’s that for an upside to making a mistake? This book shares 40 tales of the unlikely origins of foods, clothing, toys and devices we use in our daily lives. Perfect for any upcoming entrepreneurs in your family!
The Boy Who Dreamed Of Infinity: A Tale Of The Genius Ramanujan
Written by Amy Alznauer and illustrated by Daniel Miyares.
This is a real-life story of Ramanujan, who managed to change modern mathematics and science forever. The beautifully illustrated book will make your child think twice about numbers, and inspire them to dare to dream as big as Ramanujan did.
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Euro 2024 Maths Resources
Subject: Mathematics
Age range: 11-14
Resource type: Game/puzzle/quiz
Last updated
30 May 2024
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A selection of maths resources linked to football and specifically Euro 2024. I use for pupils in years 5 through to year 8.
Euro Maths Challenge is a new effort so we shall see how it goes in the classroom, hopefully fun competitive ish Maths!
Euro Mascots is a data handling exercise based on ranking the past Euro mascots, a firm favourite every couple of years.
16 questions - football related - a number of tricky questions involved.
Football dice simulation - I normally get pupils in a group to play a group and then enter the knock out stages, it ensures more are involved into the latter stages.
The flags are simply a method of assigning a country to each member of my form group, they pick out a team randomly and that gets put up next to a large Euro 2024 fixtures poster.
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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);
Find out how the order of operations shows you which bit of a calculation to do first. Year 6 KS2 Maths Problem solving learning resources for adults, children, parents and teachers.
Our collection of year 6 maths worksheets are is a great place to start. To help child practice their problem solving skills, we have put together a collection of 20 word problems, organised by topic. This collection encompasses the types of questions children may encounter in the two reasoning papers.
These maths problems year 6 Cards are a fun activity and require children to use a variety of different calculations to solve each one. Maths problems also help develop children's reasoning skills, as they have to think logically and identify the important information within a problem in order to solve it.
Problem Solving. This feature is somewhat larger than our usual features, but that is because it is packed with resources to help you develop a problem-solving approach to the teaching and learning of mathematics. Read Lynne's article which discusses the place of problem solving in the new curriculum and sets the scene.
Examples of Year 6 Maths Problem-Solving Resources: The following are examples of resources on this page that you can use to help plan your year 6 maths lessons: Year 6 Diving into Mastery: Draw Nets of 3D Shapes Teaching Pack - help your children to consolidate and deepen their understanding of nets in preparation for year 6 SATs.
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 ...
A set of 20 problem-solving questions suited to year 6 students. This set of problem-solving questions has been designed to support teachers when teaching students about problem-solving in mathematics.. It provides students with the opportunity to work through 20 maths word problems, identifying the important information and how they can work it out using a variety of methods.
By year 6 children should be able to: Solve maths problems involving addition, subtraction, multiplication and division. Solve calculations involving fractions, decimals and percentages. Solve problems involving multiple operations, in the correct order.
6. Add three or more fractions with the same denominator: word problems. 7. Add and subtract mixed numbers with the same denominator. 8. Add and subtract mixed numbers with the same denominator: word problems. 9. Add up to 4 fractions with denominators of 10 and 100. 10.
Full Week. ANS. Welcome to the Year 6 Mini-Maths homepage. Daily maths questions for Year 6 are available for every week of the year, providing free help for teachers, pupils and parents. 1000s of free tasks and activities are available to support children in their learning both in the classroom and at home. Use the search and filter box below ...
Different activity sheets that give children questions that look at their fluency, reasoning or problem solving skills for that area of Maths with the answers included. Example questions from the sample reasoning papers and 2016 reasoning papers are also being included for mini practise. ... Year 6 Maths Scheme of Work (based on White Rose ...
Year 6 Maths Mastery Resources: a comprehensive set of teaching materials, perfect for developing your pupils' fluency, reasoning and problem-solving skills. KS2 Maths Investigations: a huge range of worksheets and games, which are perfect for developing your pupils' maths knowledge and skills. KS2 Mystery Games: fun and engaging, these maths ...
Year 6 Maths Worksheets for problem solving and reasoning: Rapid Reasoning. Children often struggle with maths reasoning at KS2, e specially in lower Key Stage 2. This set of more than 120 maths reasoning questions includes modelled answers and step by step guidance to support pupils through solving them. Each Year 6 reasoning worksheet has ...
These open-ended Year 6 maths investigations are a really fun and creative way to get children learning and engaging with different problems from a mathematical perspective. These activities will not only expand children's maths knowledge, but they will also help them improve their problem-solving skills and logical thinking. Twinkl Key Stage 2 ...
Challenge children to choose the correct operations to answer these real-life multi-step maths word problems with these problem-solving year 6 maths worksheets. ... This example of a multi-step math word problem for year 6 requires children to use division and subtraction. "Six pencils cost $1.92. Three pencils and one rubber cost $1.21.
For more word problems like this, check out our collection of 2-step and multi-step word problems for you as well as tips on how to use the bar model to answer Year 6 word problems. For advice on how to teach children to solve problems like this, check out these maths problem solving strategies. SATs Maths Question Type 1: Single step worded ...
Test Your Class with These Maths Word Problems for Year 6. Challenge your key stage 2 children to choose the correct operations and solve these real-life puzzles with these problem-solving year 6 maths worksheets. Complete with eight tricky multistep word problems, this teacher-made worksheet is a quick and easy way of reinforcing your teaching ...
By Nick Barwick - 7 Aug 2018. Hamilton provide an extensive suite of problem-solving maths investigations for Year 6 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor - high ceiling' activities for all. Explore all our in-depth problem solving investigations for Year 6.
IXL offers hundreds of year 6 maths skills to explore and learn! Not sure where to start? ... N. Problem solving and estimation. 1. Estimate to solve word problems 2. Multi-step word problems 3. Word problems with extra or missing information 4. Guess-and-check word problems ...
We have found 50 NRICH Mathematical resources connected to NC Yr 6, you may find related items under NC
Keep your child's curiosity in maths flourishing with these resources, videos and tips. Packed with profound lessons and real-life stories about resilience, problem solving and perspective, these resources can help you continue to support your child build a positive mindset towards learning.
Use this set of 5 challenge cards to reinforce your teaching on Year 6 calculation maths mastery and test your students' knowledge. Great as an opening or finishing activity. You can find specific addition and subtraction word puzzles for Year 6 here . Show more. year 6 problem solving problem solving year 6 multiplication word problems money ...
A selection of maths resources linked to football and specifically Euro 2024. I use for pupils in years 5 through to year 8. Euro Maths Challenge is a new effort so . ... I use for pupils in years 5 through to year 8. Euro Maths Challenge is a new effort so we shall see how it goes in the classroom, hopefully fun competitive ish Maths! ...