Online Investigations

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Welcome to hours of mathematical enjoyment!

(Ages 4-7): Subtract 1 (FREE!)

Explore what happens when you subtract 1 from numbers up to 10.

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(Ages 4-7): Add 1 (FREE!)

Explore what happens when you add 1 to numbers up to 10.

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(Ages 4-7): Numbers that Add to Make Ten (FREE!)

Put ten counters in two rows. Split them in different ways and explore the patterns that you get (eg 6 + 4 = 10 so 4 + 6 = 10, 8 + 2 = 10 so 2 + 8 = 10).

Write and speak. 4 add 6 makes 10 etc.

Use the Tap Say Turn game (printable activity) to memorise the number pairs.

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(Ages 5-8): Teen Facts (FREE!)

Understanding how the teens numbers work is really important.

In this first of three activities, we use counters arranged in blocks of two rows to explore the teens facts with 10 placed first: eg 10 + 6 = 16, 10 + 3 = 13 etc.

Discuss the patterns in the numbers.

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(Ages 5-8): Teen Number Names (FREE!)

In this second teens activity, we again use counters to explore the teens facts with the ten in the second place.

We introduce silly number names to help with understanding. 6 + 10 is SIX-TEEN, so 2 + 10 could be called TWO-TEEN, eleven would be ONE-TEEN, etc!

Then explore how to solve problems like:
3 + 10 = ?
? + 10 = 17 etc

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(Ages 5-8): Teen Subtractions (FREE!)

The idea that subtraction is the opposite to addition is a really important one to establish early on. Addition triangles and their associated fact families are an excellent way of showing this link.

The two numbers at the bottom of the triangle add together to make the top number, so if you subtract one of the bottom numbers from the top number you get the other number at the bottom.

Seeing the connections between the facts should make mastering the teens subtraction facts much easier.

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(Ages 5-8): Doubles, Teens and Pairs that make Ten (FREE!)

If you have learned your doubles, your teens facts and your pairs that make ten, it is good to do some mixed practice where you have different calculations jumbled up.

Look at a list of mixed facts. Can you spot which are teens facts, which are doubles and which are pairs?

Can you work out the answers, without counting, using the facts that you know?

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(Ages 5-8): Doubles, Teens and Ten Pairs Subtractions (FREE!)

If you can do mixed addition examples with doubles, teens facts and pairs that make ten, then challenge yourself with some subtraction examples.

Look at this list of mixed facts and discuss how you can work them out without counting back. Can you spot which are teens facts, which are doubles and which are pairs?

Can you work out the answers, without counting, using the facts that you know?

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(Ages 5-8): Adding Odds and Evens (FREE!)

Using counters in two rows, investigate what happens when you add and subtract other odd and even numbers.

For example:
Even + even always gives even (two numbers with even ends stick together exactly).
Odd + odd always gives odd (the two sticky-out-bits pair up with each other).
Odd + even, or even + odd gives odd.

What happens with subtraction?

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(Ages 5-8): Addition Triangles (FREE!)

Addition triangles and their fact families are really powerful for understanding the link between addition and subtraction.

The two numbers at the bottom of the triangle add to make the number at the top. So if you subtract one of the bottom numbers from the top number you get the other bottom number.

You can use addition triangles to consolidate the linked addition and subtraction facts within 20. Take twenty counters and investigate pairs of numbers that make 20. Draw each addition triangle and write out its fact family. Practise speaking the sums out loud using so and because: 12 + 8 = 10 and 8 + 12 = 20 so 20 - 8 = 12 and 20 - 12 = 8, etc.

Extend to exploring other numbers!

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(Ages 5-8): Doubles and Teens (FREE!)

Once you have learned your doubles facts and your teens facts, then you can get to know the teens numbers better by exploring the different ways of partitioning teens doubles like 12: 6 + 6 = 12, and 10 + 2 = 12, etc.

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(Ages 5-8): Near Doubles (FREE!)

If you know your doubles facts, then you can use them to work out other facts WITHOUT COUNTING. Example: 6 + 6 = 12, so 6 + 7 will be one more and 6 + 8 will be one more than that (ie two more than the original double). You can use the same approach for near doubles subtractions.

Do some oral practice of doubling and then work on near doubles that are 1 apart. When this is secure try with facts where the numbers are 2 apart. Once you are secure with both you can try mixing up questions with 1 apart and 2 apart together!

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(Ages 5-8): Doubles Patterns (FREE!)

Gather the children round a table and explore how to build two equal rows of counters to work out simple doubles. (You could do each row in a different colour.) Practise counting in twos to get the total.

Introduce the children to the online activity. Explore the pattern you get when you put doubles in order.(pp3ff) Then discuss the pattern, 1+1, 6+6, 11+11 etc (p7).

Set the children to work in pairs to explore further doubles patterns.(pp3-15)

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(Ages 5-8): Numbers that Add to Make Twenty (FREE!)

A really important idea in the early stages of learning number is that if you know some facts then you can work out other facts WITHOUT COUNTING.

If you know by heart the number pairs that make ten and also know your teens facts, then you can work out the pairs for twenty like this.

Arrange ten counters of one colour and ten of another as shown in the first diagram. Play "point and speak" like this:
2 + 8 = 10 sooo 12 + 8 = 20, drawing with your finger round the different groups of counters.

Then move the group of ten counters to the other side as shown in the second diagram and "point and speak" again:
2 + 8 = 10 sooo 2 + 18 = 20.

Explore other pairs that make ten and twenty in the same way.

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(Ages 5-8): Odd Add What Equals Even? (FREE!)

Arrange counters in pairs to explore the idea that odd numbers always have an odd one out.

Investigate what you need to add to various odd numbers to make an even number. What do you notice? In each case, the number you add also has to be odd because, when you put two odds together, the odd ones pair up and you get an even number.

Investigate various pairs of odd numbers and see what patterns you can find.

Take the investigation further by adding together two even numbers, or by adding an odd and an even. What happens?

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(Ages 5-8): Add Ten (FREE!)

Use a metre stick and base-10 material along with your tablet or laptop to investigate what happens when you add ten to two digit numbers!

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(Ages 5-8): Subtract Ten (FREE!)

Use a metre stick and base-10 rods along with a tablet computer or laptop, to investigate what happens when you subtract ten from two digit numbers.

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(Ages 5-8): Tens Pairs for 100 (FREE!)

Complements are the missing parts of things. We have already been introduced to these with Bod, when we looked at the number pairs that added to make ten.

With two metre sticks and tens rods you can easily extend this idea to explore the tens pairs that make 100.

Put the two metre sticks back to back and explore the idea that one measures from one end of the metre and the other measures from the other end.



Place 5 tens rods along one side of the two sticks from the zero at one end, and 5 rods along the other side from the zero at the other end. The two lines of tens meet in the middle because 5 tens + 5 tens = 10 tens = 100.

Investigate what happens if you only have 4 rods on one side - you get 6 on the other. So 40 + 60 = 100 etc.

Relate these facts to the pairs that make ten: 5 + 5 = 10 so 50 + 50 = 100, 4 + 6 = 10, so 40 + 60 = 100 etc.

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(Ages 5-8): Add 1, 2 or 3 (FREE!)

Most addition and subtraction calculations can be worked out if you know your key facts and are also able to add or subtract 1, 2 or 3 from larger numbers.

Adding 2 or 3 gives us the opportunity to explore what happens when we add across a multiple of ten. eg: 38 + 3 = 41. You can have lots of fun here exploring patterns and discovering that 38 + 3 = 41, 48 + 3 = 51 etc.

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(Ages 5-8): Subtract 1, 2 or 3 (FREE!)

Most addition and subtraction calculations can be worked out if you know your key facts and are also able to add or subtract 1, 2 or 3 from larger numbers.

Subtracting 2 or 3 gives us the opportunity to explore what happens when we subtract across a multiple of ten. eg: 41 - 3 = 38. You can have lots of fun here exploring patterns and discovering that 41 - 3 = 38, 51 - 3 = 48 etc.

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(Ages 5-8): Adding 5 to Zeroes and Fives (FREE!)

Explore the patterns that you get when you add 5 to numbers ending in 0 or 5.

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(Ages 5-8): Adding 5 to Ones and Sixes (FREE!)

Explore what happens when you add 5 to numbers ending in 1 or 6.

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(Ages 5-8): Adding 5 to Twos and Sevens (FREE!)

Explore what happens when you add 5 to numbers ending in 2 or 7.

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(Ages 5-8): Subtracting 5 from Zeroes and Fives (FREE!)

Explore what happens when you subtract 5 from numbers that end in 0 or 5.

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(Ages 5-8): Subtracting 5 from Ones and Sixes (FREE!)

Explore what happens when you subtract 5 from numbers that end in 1 or 6.

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(Ages 5-8): Tens and Units (FREE!)

Explore how two digit numbers are created using tens and units.

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(Ages 6-9): Playing with Tens and Numbers near 100 (FREE!)

Investigate how tens work when you try to add, subtract or double them.

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(Ages 6-9): Odds and Evens Puzzle (FREE!)

A puzzle with odd and even numbers to consolidate facts for addition and subtraction.

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(Ages 6-9): Add Fives Pairs to make Tens (FREE!)

Add together different two digit numbers to make multiples of 10.

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(Ages 6-9): Getting to the Next Ten (FREE!)

Use tens pairs to help work out how many you need to add to get to the next ten.

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(Ages 6-9): Patterns Adding 5 (FREE!)

Investigate what happens when you add 5 to 2-digit numbers. Explore the patterns that you get when you keep added 5 repeatedly. (2, 7, 12, 17 etc.)

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(Ages 6-9): Double Multiples of 5 (FREE!)

Investigate the patterns for doubling multiples of 10 and then explore the in-between numbers to establish patterns for multiples of 5.

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(Ages 6-9): Using Doubles Facts: 6 + 6 (FREE!)

Explore how knowledge of 6+6 can be used to build patterns like 16+6, 26+6 etc and solve problems like 60+60 and near doubles questions like 6+7 etc.

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(Ages 6-9): Add Multiples of Ten (FREE!)

Got to grips with adding ten? Investigate what happens when you add multiples of 10 to any 2-digit number. A metre stick and base-10 rods make this a breeze!

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(Ages 6-9): Subtract Multiples of Ten (FREE!)

An investigation using both practical materials (metre stick and base-10 material) and a tablet or laptop, to investigate what happens when you subtract multiples of ten from two digit numbers.

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(Ages 6-9): Add and Subtract Multiples of 10 (FREE!)

Practise adding and subtracting 20, 30, 40 etc.

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(Ages 6-9): Tens and Fives Pairs for 100 (FREE!)

Explore the multiples of ten and multiples of 5 that add to make 100 and discover that 65 + 45 doesn't make 100, but 65 + 35 does!

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(Ages 6-9): 2-digit Differences with Tens (FREE!)

Explore the concept of finding the difference (the distance between two numbers on the number line) by counting on or counting back using multiples of ten.

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(Ages 6-9): Quick Ways of Adding 9 (and 8) (FREE!)

Practise adding 9 by adding 10 and then taking 1 off. Extend this idea to add 8 by adding 10 and then taking off 2.

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(Ages 6-9): Quick Ways of Subtracting 9 (and 8) (FREE!)

Practise subtracting 9 by taking off 10 and then adding 1 on again. Extend this idea to subtract 8 by subtracting 10 and then adding 2.

Experiment with subtracting 9 and 8 first from tens numbers, then from fives numbers and then from the in-between numbers.

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(Ages 6-9): Add 8 to Even Numbers (FREE!)

Investigate what happens when you add 8 to even numbers.

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(Ages 6-9): Subtract 8 from Even Numbers (FREE!)

Investigate what happens when you subtract 8 from even numbers.

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(Ages 6-9): Number Pairs for 100 (FREE!)

Explore the links between the story of 10 and the number pairs that add to make 100. Build up from easier (30+70) to harder (32+68) pairs and look at patterns of odds and evens.

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(Ages 6-9): Inverse arrows - Add and Subtract (FREE!)

Explore how inverse arrows can be used to help solve subtraction problems.

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(Ages 6-9): Missing Numbers on the Number Line (FREE!)

Explore the patterns that you get on the numbers line when you divide a section of the line into smaller pieces. Investigate counting in 5s, 10s, 20s, 25s and 50s.

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(Ages 6-9): Subtract Multiples of 2 (FREE!)

Investigate the patterns that you get when you subtract 2, 4, 6 and 8 from 2-digit numbers. Explore the idea that you can subtract 6 or 8 by taking away 2 and 2 and 2 (and 2).

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(Ages 6-9): Add Multiples of 2 (FREE!)

Investigate the patterns that you get when you add 2, 4, 6 and 8 to 2-digit numbers. Explore the idea that you can add 6 and 8 by adding 2 and 2 and 2 (and 2).

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(Ages 7-10): Add and Subtract 10, 100, 1000 (FREE!)

Consolidates place value by exploring what happens to numbers when 1 is added to or subtracted from different columns.

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(Ages 7-10): Getting to the Next Hundred (FREE!)

Explore what you need to add to get to the next hundred.

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(Ages 7-10): Adding Tens to 3-digit Numbers (FREE!)

Revise adding tens to 2-digit numbers. Then build up to adding to 3-digit numbers within and across the hundreds.

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(Ages 7-10): Subtracting Tens from 3-digit Numbers (FREE!)

Revise subtracting tens from 2-digit numbers and then build to 3-digit numbers first within and then across the hundreds.

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(Ages 7-10): Take Away 2-digit Numbers from Tens (FREE!)

Investigate how to subtract 2-digit numbers from multiples of ten using the mental take-away strategy of first subtracting the tens and then subtracting the units. Begin by taking away multiples of 10 (eg 90-30)(p3). Then use a metre stick and tens and units to take away numbers with different units digits.

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(Ages 7-10): Adding by Partitioning (FREE!)

Using the fact that 8 + 3 = 11, explore the patterns that you get when you start with a number ending in 8 and add a 2-digit number ending in 3.

Establish the idea that you can add two 2-digit numbers together by first adding the tens and units separately and then adding them together. Extend this idea to other additions.

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(Ages 7-10): Add and Subtract 0.5 (FREE!)

Explore what happens when you add or subtract 0.5 to and from other numbers.

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(Ages 7-10): Add and Subtract 0.1 (FREE!)

Explore what happens when you add or subtract 0.1 to and from whole numbers and other unit decimals.

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(Ages 7-10): Add and Subtract Near Tens (FREE!)

Discuss how to add 9 by adding 10 and subtracting 1. Then develop the idea to include adding 19, 29, 39 etc.

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(Ages 7-10): 2-Digit Difference Patterns (FREE!)

Investigate what happens when you find differences between numbers with different units digits.

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(Ages 8-11): How Many More? (FREE!)

Work out how many more things there are in one group compared with another. Practise finding the difference mentally by subtracting using small numbers and then apply this idea to larger numbers using the standard written method or a calculator.

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(Ages 8-11): Standard Written Methods - Add & Subtract Whole Numbers (FREE!)

Aimed at pupils who have learned the standard (vertical) methods of addition and subtraction and require consolidation to ensure 100% accuracy. Encourages discussion as to whether to do mental or written calculations, introduces self-checking loops and challenges pupils to solve missing number problems.

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(Ages 8-11): Decimal Fifths and Twentieths (FREE!)

Explore how fifths and twentieths work with decimals.

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(Ages 9-12): Add and Subtract with Negative Numbers - Part 1 (FREE!)

Explore how addition and subtraction works with negative numbers. Part 1 investigates what happens when you start on a positive or negative number and add or subtract a postive number.

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(Ages 10-13): Add and Subtract with Negative Numbers - Part 2 (FREE!)

Explore how addition and subtraction works with negative numbers. Part 2 investigates what happens when you start on a positive or negative number and add or subtract a negative number.

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