Online Investigations

Scroll down to browse the listor use the filter on the left to select a topic.

Welcome to hours of mathematical enjoyment!

(Ages 3-6): Interior Angles of Polygons (FREE!)

Explore the patterns in the interior angles of polygons. Investigate the links between the total and single angles and the number of sides.

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(Ages 3-6): OLD Multiply by 5 (FREE!)

Investigate what happens when you multiply by 5. Start from the 5x table and investigate the link with the 10x table. Then explore the idea multiplying by 10 and then halving the answer.

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(Ages 4-7): Counting in 1s to 10 (FREE!)

Counting is the foundation of all number work. This first activity secures counting to 10.

First count aloud from 1-10. Then take turns counting saying alternate numbers. Can you count and clap alternate numbers? (1 clap 3 clap 5 etc.)

Make cards with the numbers from 1 to 10 and lay them in order, face down. Turn one card face up and discuss which number comes before and which comes after.

Practice counting starting on one of the in-between numbers (eg 6, 7, 8 etc).

Play I say you say to a clapping rythmn: I say 3, you say 4; I say 7 you say 8, etc. Extend to work out numbers two or three away from the starting number.

Give your child a number of objects to count. Show how to arrange the objects in a row and count at a steady speed without rushing. Give lots of practice with different objects.

Practise counting by repeatedly adding one more object to a group.

Ask and answer: What is one more than 6? etc

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(Ages 4-7): Counting down in 1s within 10. (FREE!)

Counting backwards is just as important as counting forwards.

Start with ten objects and count back as you keep taking one away. (10, 9, 8, 7...)

Take turns counting saying alternate numbers. Can you count and clap alternate numbers? (10 clap 8 clap 6 etc.)

Practice counting down starting on one of the in-between numbers (eg 6, 5, 4 etc).

Play I say you say to a clapping rythmn: I say 6, you say 5; I say 9 you say 8, etc.

Put cards with the numbers from 10 to 0 in a vertical row, face down. Turn one card face up and discuss which number comes above it and which comes below.Extend to work out numbers two or three away from the starting number.

Ask and answer: What is one less than 6? etc

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(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): Counting in 1s Beyond 10 (FREE!)

Give your child a number of objects to count. Show how to arrange the objects in a row and count at a steady speed without rushing. Give lots of practice with different objects.

Count aloud from 1. How far can you get?

Practise counting by repeatedly adding one more object to a group. Make sure you can count starting on one of the in-between numbers (eg 16, 17, 18 etc).

Investigate a metre stick that shows the numbers for the tens (and also, if possible, the fives) but only has the divisions for the in-between numbers, not the numbers themselves.



Play the show me game, first looking for the tens numbers, then the multiples of five, and then any number.

Discuss the numbers that come before and after the numbers marked on the stick. How do you know what they are?

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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): Count on in 2s (FREE!)

Exploring Odds and Evens:

Try arranging different numbers of counters in pairs. Some work, some do not. Discuss why. Identify odd numbers having the sticky out bits. Talk about being the odd one out. Get your child to make drawings of the different numbers and practise identifying and sorting them into odd and even.

Mastering the Even Numbers:

Arrange an even number of counters in pairs (this is called an array). Count in twos (2, 4, 6 etc) to see what it is. Now make a set of separate arrays to show 2, 4, 6, 8, 10. Get your child to point and speak the name of each one until the pattern for each number is memorised.

Practise counting finger pairs - hold up one finger on each hand and say '2', two fingers on each hand and say '4' etc. Make the number of fingers change up and down the way and get your child to say how many there are. Discuss doubles. Say aloud 'double three is six' etc.

Get your child to practise counting in twos by repeatedly adding two more objects to a group.

Finally, make sure your child can count in 2s fluently without looking at the objects.

Mastering the Odd Numbers:

Once your child recognises the even arrays then make arrays for the odd numbers. Show your child how to work out which is which by noticing that they are just an even array with one more added.

Practise and then memorise saying the odd numbers in order (1, 3, 5 etc).

More about Odds & Evens

Explore repeatedly adding 2 to different numbers. Start on 0 and keep adding 2 - you get the even numbers. Start on 1 and keep adding 2 - you get the odd numbers.

Getting used to different words

Say aloud 'one more than', '2 more than' etc. Practise using different words for adding - plus, add, and.

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(Ages 4-7): Count back in 2s (FREE!)

Start with ten objects and count back as you keep taking one or two away. (10, 9, 8, 7...) (10, 8, 6...)

Explore what happens when you subtract 2. Start with 10 and you get the even numbers. Start on 9 and you get the odd numbers.

Practise using different words for subtracting - take away, subtract, minus.

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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 4-7): Odds and Evens That Make Ten (FREE!)

Try splitting up ten counters in different ways. How many ways can you make 10?

What happens if you start with an even number? (The number pair is also even.)

What happens if you start with an odd number? (The number pair is also odd.)

What are the linked subtraction facts?

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(Ages 4-7): Subtracting from Ten (FREE!)

As well as learning the addition facts for ten, you need to learn the corresponding subtractions. Use ten counters again and try taking some away. How many do you have left?

Explore the facts you get (eg 10 - 3 = 7) and link with the addition facts (eg 7 + 3 = 10).

Each time you make a new pattern, play the "point and chorus" speaking game: "7 add 3 equals 10 sooo 10 take away 3 equals 7", etc.

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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): Finding Half of Even Numbers (FREE!)

Explore how to find half of 8 by splitting 8 counters into two groups (p2). Explore the two different ways of writing this: 8 ÷ 2 = 4 (p3) and ½ of 8 = 4 (p4). Discuss 12 counters in the same way (pp7/8/9) and then investigate patterns with missing numbers (p12).

Set the children to find half of some other numbers (p5,6,10,11,13) and investigate examples and patterns of their own (pp14/15).

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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): Multiplying with Rectangles and Squares (FREE!)

The best way to understand multiplying is to arrange counters in a rectangle.

Start with 6 arranged in 2 rows of 3. Ask the questions: 'How many rows?' (2), 'How many in each row?' (3), 'How many altogether?' (6). Say together '2 rows of 3 is 6. 2 x 3 = 6.

Try now with 4 counters arranged in a 2 by 2 square. 'How many rows?' (2), 'How many in each row?' (2), 'How many altogether?' (4). Say together '2 rows of 2 is 4. 2 x 2 = 4.

Repeat with different numbers of counters! Keep asking and answering the 3 questions and writing down the sums you get.

Investigate rectangles with 3 rows. 3 rows of 1 = 3, 3 rows of 2 = 6, etc. Build number patterns: 3 x 1 = 3; 3 x 2 = 6; 3 x 3 = 9, etc.

Investigate rectangles with 4 rows in the same way. What about other numbers of rows?

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(Ages 5-8): Counting in 2s (FREE!)

Make sure you can count in 2s to 20. Use the Counting Caterpillar to help you learn - see printable activity!

Practise counting aloud in 2s beyond 20. How far can you get. If you get stuck, get out a metre stick that shows the tens numbers (and possibly the fives) but only the divisions for the other numbers, not the numbers themselves.



Can you count along this in 2s? Does this help you to get any further? Why?

Write the numbers out in a vertical column. What patterns are there in the numbers?

Can you go backwards?

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(Ages 5-8): Multiplication Rectangle Pairs (FREE!)

If you have used rectangles to introduce the idea of multiplying, then it is an easy step to explore the idea that multiplication facts comes in pairs.

Arrange 6 counters in 2 rows of 3. Ask the questions: 'How many rows?' (2), 'How many in each row?' (3), 'How many altogether?' (6). Say together '2 rows of 3 is 6. 2 x 3 = 6.

Now turn the rectangle round the other way. Ask the questions: 'How many rows?' (3), 'How many in each row?' (2), 'How many altogether?' (6). Say together '2 rows of 3 is 6, so 3 rows of 2 is 6!

Write down the paired facts: 2 x 3 = 6, 3 x 2 = 6.

Explore other rectangles in the same way.

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(Ages 5-8): Playing with Tens (FREE!)

Our number system is all based around tens. So it is really important to understand how tens work.

First start by counting tens - tens rods from base ten material are really good for this. Or you can use 10p pieces.

Explore the names: forty is 4T which is 4 tens; sixty is 6T which is 6 tens.

Have some fun with silly number names for the ones that don't work: twenty should really be two-ty, thirty should be three-ty etc.

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

The number names in English can cause confusion. Seventeen sounds like seventy, for example.

So if you know how to count 16, 17, 18, 19, 20, it can be tempting to count 60, 70, 80, 90, 20 as well, instead of going to 100!

To correct this problem, use tens and units to explore the difference between (eg) 7 + 10 = 17 = seventeen and 7 lots of 10 = 7T = 70 = seventy.

Then use a metre stick to reinforce the difference between counting in teens and counting in tens.

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

If you can do mixed examples with doubles, teens facts and pairs that make ten, then you are ready for this next challenge.

Look at a list of mixed facts and discuss how you can work them out without counting on. Can you spot which are near teens facts, which are near doubles and which are near 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): Near Double, Teen & Ten Pair Subtractions (FREE!)

If you can do mixed subtraction examples with doubles, teens facts and pairs that make ten, then there is a final challenge to do.

Look at a list of mixed subtraction facts and discuss whether you could work out the answers, without counting, using key facts that you know? Are any of them near to teens subtraction facts, or doubles or ten pairs?

Look at a random list of subtractions within 20. How many can you work out using known facts? Are there examples where counting back is still the quickest strategy.

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(Ages 5-8): 10x Table (FREE!)

Knowing your tables is REALLY important. But before you learn them, you have to understand where they come from.

Arrange 20 counters in a 2 by 10 rectangle. Say together: 2 rows of 10 is 20; 2 x 10 = 20. Do the same with 3 rows of 10: 3 rows of 10 is 30; 3 x 10 = 30.

Write out the pattern that you get when you count rows of 10 like this: Start with no rows: 0 x 10 = 0; then 1 row: 1 x 10 = 10; then 2 rows etc.

Once you have explored the pattern, the next thing is to try to work out the facts jumbled up. Use counters again to work out the ones you cannot remember.

The next step is to try working backwards. For example, if you have 30 cubes altogether and put them in rows of 10, how many rows would you get? ? x 10 = 30. What is the missing number?

Repeat with other numbers of cubes.

Finally, once you understand how it all works, you need to memorise the tables facts. to do this, play the Tap Say Turn game.

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(Ages 5-8): 2x table (FREE!)

Knowing your tables is REALLY important. But before you learn them, you have to understand where they come from.

Arrange four counters in a square. Say together: 2 rows of 2 is 4; 2 x 2 = 4. Do the same with 3 rows of 2: 3 rows of 2 is 6; 3 x 2 = 6.

Write out the pattern that you get when you count rows of 2 like this: Start with no rows: 0 x 2 = 0; then 1 row: 1 x 2 = 2; then 2 rows etc.

Once you have explored the pattern, the next thing is to try to work out the facts jumbled up. Use counters again to work out the ones you cannot remember.

The next step is to try working backwards. For example, if you have 6 cubes altogether and put them in rows of 2, how many rows would you get? ? x 2 = 6. What is the missing number?

Repeat with other numbers of cubes.

Finally, once you understand how it all works, you need to memorise the tables facts. to do this, play the Tap Say Turn game.

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(Ages 5-8): 5x table (FREE!)

Once you have learned the 2x and 10x tables, the next one to work on is the 5x table.

Arrange 10 counters in a 2 by 5 rectangle. Say together: 2 rows of 5 is 10; 2 x 5 = 10. Do the same with 3 rows of 5: 3 rows of 5 is 15; 3 x 5 = 15.

Write out the pattern that you get when you count rows of 5 like this: Start with no rows: 0 x 5 = 0; then 1 row: 1 x 5= 5; then 2 rows etc.

Notice that the numbers alternate with 0 and 5: 0, 5, 10, 15, 20, 25, 30 etc.

Once you have explored the pattern, try to work out the facts jumbled up. Use counters again to work out the ones you cannot remember.

Next try working backwards. For example, if you have 15 cubes altogether and put them in rows of 5, how many rows would you get? ? x 5 = 15. What is the missing number?

Repeat with other numbers of cubes.

Finally, once you understand how it all works, you need to memorise the tables facts. to do this, play the Tap Say Turn game.

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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 (FREE!)

The doubles facts, like the tens pairs are really important since, once you know these, then you can work out all sorts of other facts.

Explore them first with the tablet activity using counters.

Then use the Tap, Say, Turn game to memorise them.

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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): Doubles Subtraction Facts (FREE!)

Children are sometimes less secure with subtraction than with addition because they do not practise it enough!

So once your children have learned the doubles addition facts, make sure you explore the subtraction facts too!

Build the numbers with counters and then play the "point and chorus" speaking game: "7 + 7 = 14 sooo 14 - 7 = 7" 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): Near Tens (FREE!)

If you know your ten pairs, then you can use them to work out other facts WITHOUT COUNTING. Example: 4 + 6 = 10, so 4 + 7 will be one more and 4 + 8 will be one more than that (ie two more than the original ten pair). You can use the same approach for near ten pair subtractions.

Do some oral practice of ten pairs and then work on pairs that add to 11. When this is secure try with pairs that add to 12. Once you are secure with both you can try mixing up questions adding to 10, 11 and 12 together!

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

If you know your teens facts, then you can use them to work out other facts WITHOUT COUNTING. Example: 3 + 10 = 13, so 3 + 9 will be one less and 3 + 8 will be one less than that (ie two less than the teens number). You can use the same approach for subtracting 9 or 8.

Do some oral practice of adding and subtracting 9 and then when this is secure try the same with 8. Once you are secure with both you can try mixing up questions with 9s and 8s 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): Double and Half Small Numbers (FREE!)

Explore doubling first by looking at the idea of 2 lots of (p2), at then at multiplying by 2 (p6). Next look at halving (p10) and how this is the same as dividing by 2 (p14). Along the way, practise each of the four skills using numbers within 20, including missing number problems.

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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): Subtracting from Twenty (FREE!)

Use counters to explore the link between the addition facts for ten and twenty and the corresponding subtraction facts.

eg 2 + 8 = 10 so 12 + 8 = 20 so 20 - 8 = 12, etc.

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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): Factors of 10 and 20 (FREE!)

Factor rainbows are a lovely way of exploring the different multiplication facts you can make with a particular number of counters.

Start with 10 counters and investigate how to arrange them in different rectangles = 2 rows of 5, 5 rows of 2, 1 row of 10, 10 rows of 1. Write down the corresponding multiplication facts: 2 x 5 = 10, 5 x 2 = 10, 1 x 10 = 10, 10 x 1 = 10.

Then draw the factor rainbow. Put the four numbers 1, 2, 5, 10 in order and join together the numbers that multiply to make 10. Discuss how this links with the rectangles you have made and the facts that you have written.

Repeat with 20 counters.

Further investigation: Which other numbers make good factor rainbows?

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(Ages 6-9): 4x table (FREE!)

Once you have learned the 2x, 10x and 5x tables, you can work on the 3s and 4s.

For the 4x table, arrange 8 counters in a 2 by 4 rectangle. Say together: 2 rows of 4 is 8; 2 x 4 = 8. Do the same with 3 rows of 4: 3 rows of 4 is 12; 3 x 4 = 12.

Write out the pattern that you get when you count rows of 4 like this: Start with no rows: 0 x 4 = 0; then 1 row: 1 x 4 = 4; then 2 rows etc.

Notice the repeating pattern in the ending digits: 0, 4, 8, 2, 6, 0, 4, 8, 2, 6, 0. Then use the Counting Caterpillar game to learn to count forwards and backwards in 4s by heart.

Once you have explored the pattern, try to work out the facts jumbled up. Use counters again to work out the ones you cannot remember.

Next try working backwards. For example, if you have 20 cubes altogether and put them in rows of 4, how many rows would you get? ? x 4 = 20. What is the missing number?

Repeat with other numbers of cubes.

Finally, once you understand how it all works, you need to memorise the tables facts. to do this, play the Tap Say Turn game.

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(Ages 6-9): 3x table (FREE!)

Once you have learned the 2x, 10x and 5x tables, you can work on the 3s and 4s.

For the 3x table, arrange 6 counters in a 2 by 3 rectangle. Say together: 2 rows of 3 is 6; 2 x 3 = 6. Do the same with 3 rows of 3: 3 rows of 3 is 9; 3 x 3 = 9.

Write out the pattern that you get when you count rows of 3 like this: Start with no rows: 0 x 3 = 0; then 1 row: 1 x 3= 3; then 2 rows etc. Then use the Counting Caterpillar game to learn to count forwards and backwards in 3s.

Once you have explored the pattern, try to work out the facts jumbled up. Use counters again to work out the ones you cannot remember.

Next try working backwards. For example, if you have 15 cubes altogether and put them in rows of 3, how many rows would you get? ? x 3 = 15. What is the missing number?

Repeat with other numbers of cubes.

Finally, once you understand how it all works, you need to memorise the tables facts. to do this, play the Tap Say Turn game.

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(Ages 6-9): Counting in 1s into the hundreds (FREE!)

Counting into large numbers is easy if you understand that it is all based on repeating patterns.

Start by making sure you can count correctly up to 100. Going immediately beyond 100 is usually OK. Some children may encounter difficulty when they try counting beyond 110 and also count over the join from 199 to 200, 299 to 300 etc. There may also be problems with numbers where digits are repeated.

When errors occur, you can investigate these by building various vertical lists of numbers and comparing how the patterns work.

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(Ages 6-9): Counting down in 1s (FREE!)

As well as being able to count forwards, you need to be able to count backwards, starting on different numbers. As with counting forwards, the difficulties are likely to be encountered when you count past the hundred marks: 403, 402, 401, 400, 399, 398 etc. Again, the best way to understand any errors is to build lists of both larger and smaller numbers and compare the patterns.

It is also interesting to investigate what happens when you count down below zero. Negative numbers can easily be explored using two metre sticks joined end to end with the zeroes together in the middle. Temperature scales can provide a good way in to discussing these.

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(Ages 6-9): Metres and Centimetres (FREE!)

Investigate how to change whole numbers of metres to centimetres and then explore combinations of metres and centimetres. How many centimetres altogether?

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(Ages 6-9): Tens Chains (FREE!)

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

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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): Playing with Hundreds and Tens (FREE!)

Investigate how hundreds work.

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(Ages 6-9): Counting in 10s (FREE!)

See how far you can get counting in tens. Explore what happens when you oount over 100, 200, 300, 1000.

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(Ages 6-9): Metres and Centimetres with Simple Halves (FREE!)

Investigate half metres and their equivalences with centimetres using a metre stick.

Turn the stick over and put blu-tac on the back to show where half a metre is. Discuss what numbers of centimetres will match with no halves, one half and two halves.

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(Ages 6-9): Double and Half with Multiples of Ten (FREE!)

Explore how to double multiples of ten building on knowledge of simple doubles facts. Extend to halving where the answer is a multiple of ten.

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(Ages 6-9): Counting down in 10s (FREE!)

Practise counting down in tens. Make sure you can count down over 100, 200, 300 etc. Explore what happens when you count down below zero!

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(Ages 6-9): Counting in 25s (FREE!)

Explore what happens when you chop a metre stick into four pieces. Learn that 4 25s make a 100 and investigate other multiples of 25 by counting.

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(Ages 6-9): Counting in 20s (FREE!)

Investigate how to divide a metre stick into 5 equal pieces. Count in 20s beyond 100 and explore multiples of 20.

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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): Metres and Centimetres with Mixed Number Halves (FREE!)

Use a metre stick to discuss the meaning of one half and how it is written.

Explore the meaning of 1½m and 2½m etc.

Explore their equivalences in centimetres.

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(Ages 6-9): Multiply and Divide by 10 (FREE!)

Revise the ideas introduced in the Counting section that (eg) 8 tens = 80 (p2) and recap on the 10x table (p3).

Revise the inverse link between division and multiplication (p6) and explore the 10x table division facts (p7).

Recap on the idea that 10 tens (100) + 3 tens (30) = 13 tens (130) (p9) and use this to explore beyond the table - 10 x 13 = 130 etc (p11). Investigate the corresponding division facts (p13).

Extend to facts such as 36 tens = 360 etc (p17).

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(Ages 6-9): Finding Halves of Numbers to 100 (FREE!)

Explore how to find halves of simple numbers using doubles facts in reverse.

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(Ages 6-9): Quartering Numbers in the 4x Table (FREE!)

Make sure you are confident with the 4x table before you try this one!

Explore how to find a quarter of 12 by splitting 12 counters into four groups (p2). Explore the two different ways of writing this: 12 ÷ 4 = 3 (p3) and ¼ of 12 = 3 (p4).

Build a pattern dividing numbers by 4 and note the link with the 4x table (p5). Discuss the two different ways of quartering mentally: either halving and halving again or dividing by 4 (p6).

Set the children to find a quarter of some other numbers (pp7/8/9), explore patterns and problems with missing numbers (pp10/11/12) and investigate examples and patterns of their own (pp13/14).

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

Revise halving multiples of twenty and then explore what happens when you try to halve a multiple of ten like 50. Extend to halving numbers like 170.

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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): Fractions of Twelve (FREE!)

Work with 12 counters to explore what happens when you divide them into two groups (halves) (p2) and then four groups (quarters) (p4). Discuss the idea of one quarter, two quarters three quarters and four quarters of twelve (p6). Practise with mixed examples. Investigate thirds (p9) and then sixths (p14) of twelve in the same way.

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(Ages 6-9): Fractions of Twenty (FREE!)

Work with 20 counters to explore what happens when you divide them into two groups (halves) (p2) and then four groups (quarters) (p4). Discuss the idea of one quarter, two quarters three quarters and four quarters of twenty(p6). Practise with mixed examples. Investigate fifths (p9) and then tenths (p14) of twenty in the same way.

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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): Finding Half of Odd Numbers (FREE!)

Use counters to revise halving some even numbers (p1).

Next get 7 counters and discuss what happens if you try divide them into two equal groups (p2). Agree that there will be a problem because 7 will not divide exactly.

Discuss what could be done with the one left over. Either you can leave it out (this is called a remainder) or you could cut it in half and share it between the two groups. Discuss alternative ways of writing the answer - 3r1 (p3) or 3½ (p4). Repeat with 9 counters (p5) and recap also how to write the answer as a decimal (p6). (See How do decimals work? for a simple introduction to decimals.)

Set the children to investigate other numbers of counters (p7) and then explore patterns (p8ff).

Gather the children together again and explore the link between half of 50 (25) and half of 5 (2.5) (p13). Set them to investigate other pairs of numbers like this (pp13/14).

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(Ages 6-9): Tens Doubles (FREE!)

Investigate doubles of multiples of ten.

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(Ages 6-9): Multiplication Triangles (FREE!)

Investigate multiplication triangles and the linked multiplication and division facts.

Investigate what happens if you try to divide by zero!

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(Ages 6-9): Add a Single Digit by Jumping On (FREE!)

Explore how to add on a single digit to another number by jumping to the next ten and adding on the rest (eg 38 + 2 + 2 = 42).

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(Ages 6-9): Add a Single Digit using Number Bonds (FREE!)

Explore how to add on a single digit to another number by using number bonds (eg 8 + 7 = 15 so 38 + 7 = 45).

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(Ages 6-9): Subtract a Single Digit by Jumping Back (FREE!)

Explore how to subtract a single digit from another number by jumping back to the previous ten and then subtracting the rest (eg 42 - 2 - 2 = 38).

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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): Multiplying and Dividing with Rectangles (FREE!)

See how many different ways you can divide up 12 objects. Explore the use of the division sign and how division relates to rows and columns in a rectangle.

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(Ages 6-9): Metres and Centimetres with Quarters (FREE!)

Investigate quarter metres and their equivalences with centimetres within one metre using a metre stick. Turn the stick over and put blu-tac on the back to mark the quarters. Discuss what numbers of centimetres will match with each piece of blu tac. Check. Agree that ¼m=25cm and ¾m=75cm. Discuss zero quarters, two quarters and four quarters.

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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): Subtract any Single Digit by Adding (FREE!)

Consolidate the different methods of adding a single digit to a 2-digit number. Then explore how to subtract a single digit by using the related addition fact.

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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): 2-digit Differences with Fives (FREE!)

Explore the differences that you get on a metre stick when you start and end on a multiple of five.

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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): The Link between Difference and Subtraction (FREE!)

Explore the idea that you can find the difference between eg 60 and 40 (60 - ? = 40) by starting with 60cm and chopping the 40cm off the beginning. This gives the same answer as when you subtract 40 from 60 (60 – 40 = ?) by chopping 40cm off the end.

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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 6-9): Inverse Arrows - Multiply and Divide (FREE!)

Learn the links between multiplication and division.

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(Ages 7-10): 9x Table Patterns (FREE!)

Explore the amazing patterns in the 9x table and then investigate digital roots.

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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): Millimetres and millilitres (FREE!)

Change between metres and millimetres, litres and millilitres.

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(Ages 7-10): Kilometres and Kilograms (FREE!)

Change kilometres to metres and kilograms to grams.

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(Ages 7-10): Double Tens and Hundreds (FREE!)

Discover how, knowing the 2x table facts, you can use these to double numbers like 20, 300 etc.

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(Ages 7-10): Counting in 1s and 10s Beyond 1000 (FREE!)

Explore what happens when you count (forwards and backwards) in 1s and 10s with numbers up to 10,000. Discover patterns that help you count starting on any number.

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(Ages 7-10): Counting in 10s and 100s Beyond 1000 (FREE!)

Count in 10s and 100s (forwards and backwards) from different starting numbers. Discover patterns that help you count starting on any number.

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(Ages 7-10): Something out of Twelve as a Fraction (FREE!)

Explore how to find what fraction has been selected when you select a number of objects from a larger group. Investigate the link with finding fractions of things.

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(Ages 7-10): Finding Quarters with Remainders (FREE!)

Builds on Finding Quarters, looking first at quartering larger numbers and then at quartering numbers that do not quarter!

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(Ages 7-10): Counting with Halves (FREE!)

Get a metre stick, turn it over to the blank side and discuss where the half metre point is. Mark it with blu-tac. Discuss the fact that two halves make one whole. Explore how to write one half (½), two halves, zero halves.

Can you get three halves? What about four halves? Introduce a second metre stick and put them end to end. Explore! Then get bits of paper and write on the numbers 0, ½, 1, 1½, 2, 2½ etc.

Draw a line on the board. Mark 0 at one end and 4 at the other. Ask the children if there are any numbers in between. (See Numbers between Numbers for a full development of this idea.) Through discussion, mark on ½, 1, 1½, 2, 2½ etc and explore the equivalences with 3/2, 4/2, 5/2 etc.

Consider what happens if you start at 0 and keep adding ½. Then try counting backwards. Discuss how you could show how many halves you would need to make different numbers using the multiplication sign (se pp12/13).

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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): Metres and Centimetres with Halves and Quarters (FREE!)

Investigate half and quarter metres and their equivalences with centimetres within one metre using a metre stick.

Turn the stick over and put blu-tac on the back to show where half a metre is, then mark the quarters. Discuss what numbers of centimetres will match with each. Check. Agree that ¼m=25cm and ¾m=75cm. Establish the equivalence of two quarters with one half and four quarters with one whole.

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(Ages 7-10): Easy Percentages of Easy Numbers (FREE!)

Explore how to find 50%, 25% and 75% of numbers in the four times table.

First introduce the idea of 100% being all of something, 50% being a half, so 25% and 75% are one quarter and three quarters(p1). Then use halving to find 50% of various numbers (p4) then halve 50% to find 25% (p8). Finally explore alternative ways of finding 75% (p12).

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(Ages 7-10): 9x table (FREE!)

Get secure with 9x table facts by exploring patterns. Includes missing number problems.

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(Ages 7-10): Multiply Teens Numbers by 5 (FREE!)

Use rectangles to discover that, for example, 14 rows of 5 is the same as ten rows plus four rows. Use this to work out 14 x 5 mentally etc.

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(Ages 7-10): Multiply and Divide with Tens by 5 (FREE!)

Explore the patterns in multiplying tens by 5.

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(Ages 7-10): 6x table (FREE!)

Get secure with 6x table facts by exploring patterns. Includes missing number problems.

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(Ages 7-10): 8x table (FREE!)

Get secure with 8x table facts by exploring patterns. Includes missing number problems.

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(Ages 7-10): 7x table (FREE!)

Get secure with 7x table facts by exploring patterns. Includes missing number problems.

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(Ages 7-10): Multiply Teens Numbers by 4 (FREE!)

Use rectangles to discover that, for example, 16 rows of 4 is the same as ten rows plus six rows. Use this to work out 16 x 4 mentally etc.

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(Ages 7-10): Multiply and Divide with Tens by 4 (FREE!)

Explore the patterns in multiplying tens by 4.

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(Ages 7-10): Adding to Make Tens (FREE!)

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

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(Ages 7-10): Playing with Hundreds and Numbers near 1000 (FREE!)

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

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(Ages 7-10): Multiply Teens Numbers by 3 (FREE!)

Use rectangles to discover that, for example, 14 rows of 3 is the same as ten rows plus four rows. Use this to work out 14 x 3 mentally etc.

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(Ages 7-10): Multiply and Divide with Tens by 3 (FREE!)

Explore the patterns in multiplying tens by 3.

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(Ages 7-10): Something out of 10 or 20 as a Fraction (FREE!)

Explore how to find what fraction has been selected when you select a number of objects from a larger group. Investigate the link with finding fractions of things.

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(Ages 7-10): Counting in Decimal Tenths, Halves and Fifths (FREE!)

Learn how to count forwards and backwards in single, double or five tenth intervals within 10. (Eg 4, 4.2, 4.4, 4.6 etc) Explore 14 tenths = 1.4 etc.

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(Ages 7-10): Metres and Centimetres with Two Kinds of Halves (FREE!)

Investigate half metres and their equivalences with centimetres using a metre stick.

Turn the stick over and put blu-tac on the back to show where half a metre is. Discuss what numbers of centimetres will match with this. Check. Can you get three halves? What about four? Use a second metre stick to investigate. Discuss different ways of expressing fractions (three halves = one and a half etc.)

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(Ages 7-10): Metres and Centimetres with Many Quarters (FREE!)

This activity builds on Metres and Centimetres with Halves and Quarters.

Recap on quarters within one metre.

Then ask the question: Can you get five quarters? What about six? Seven? Eight? More? Use a second metre stick to investigate. Explore the idea of improper fractions and mixed numbers. (5 quarter = 1 and a quarter etc.)

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(Ages 7-10): Metres and Centimetres with Halves and Tenths (FREE!)

Investigate what happens if you chop a metre stick into ten equal pieces. Each piece is called one tenth. Investigate their equivalences with centimetres.

Agree that 1/10m=10cm and 2/10m=20cm etc. Establish the equivalence of five tenths with one half and ten tenths with one whole.

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(Ages 7-10): Double Two-digit Numbers (FREE!)

Investigate how doubling questions are easiest when both digits are less than 5, harder when one digit is greater than 5 and trickiest when both digits are greater than 5.

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(Ages 7-10): How Decimals Work - Tenths (FREE!)

Explore the key ideas behind how decimals work using a counting stick.

Explore that idea that each whole metre is divided into ten bits. Each bit is one tenth of a metre. A tenth of a metre is also called a decimetre. (dec = 10 - decade, decimal etc) Introduce the idea that a measurement can be written as a whole number of metres, followed by a decimal followed by the number of bits (tenths). Explore the different ways of writing one tenth (1/10 and 0.1), two tenths etc. Explore mixed numbers with tenths. (12 tenths = 1 & 2 tenths = 1.2 etc.)

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(Ages 7-10): Decimal Halves (FREE!)

Recap that a 1 metre counting stick is divided 10 tenths (p1) and that this can be written as 0.5 (p2).

Use multiple sticks to establish what happens when you count in 0.5s (p5), by adding half a stick each time. Explore the equivalences of these decimals with mixed numbers (2.5 = 2½ etc)(p7) and with improper fractions (3 halves = 1.5 etc)(p9).

Investigate what happens when you multiply 0.5 by 2, 3, 4, 5 etc (p15).

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(Ages 7-10): Decimal Tenths and Halves (FREE!)

Draw a line on the board from zero to 1 and ask if there are numbers in between. Discuss ½, 0.5 etc as appropriate.

Discuss where you would cut to chop a metre stick in into tenths and what these would be as decimals (0.1m, 0.2m etc). Count in 0.1s and explore equivalences between decimal tneths of metres and centimetres (eg 1.9m = 190cm etc).

Recap on where you would cut to chop a metre stick in half, and that ½m = 50cm.

Use two metre sticks to explore that 1½m = 150cm. Recap that ½ = 0.5 and explore 1½ = 1.5. Then explore equivalences between decimal half metres and centimetres (eg 1.5m = 150cm etc).

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(Ages 7-10): Metres and Centimetres with Many Tenths (FREE!)

Explore the link between metres, centimetres and tenths beyond one whole metre.

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(Ages 7-10): Find Unit Fractions using Multiplication Facts (FREE!)

Consolidate the link between finding ½ and dividing by 2, and between finding ¼ and dividing by 4. Then explore how to find one third, one fifth and other unit fractions.

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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): Multiply and Divide beyond the 5x Table (FREE!)

Explore multiplication and division within the 5x table and use this knowledge to tackle problems with bigger numbers.

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(Ages 7-10): Half Two-digit Even Numbers (FREE!)

Investigate how to half two digit even numbers by halving the tens, halving the units and combining the answers.

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(Ages 7-10): Divide within the 5x Table (FREE!)

Explore how division works within the 5x table, first by sharing and then by building patterns and using tables facts.

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(Ages 7-10): Divide within the 4x Table (FREE!)

Explore how division works within the 4x table, first by sharing and then by building patterns and using tables facts.

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(Ages 7-10): Divide within the 3x Table (FREE!)

Explore how division works within the 3x table, first by sharing and then by building patterns and using tables facts.

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(Ages 7-10): Multiply and Divide beyond the 3x Table (FREE!)

Explore multiplication and division using the 3x table. Begin with multiplying single digits and then investigate multiplying multiples of ten by 3.

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(Ages 7-10): Multiply and Divide beyond the 4x Table (FREE!)

Explore multiplication and division within the 4x table and use this knowledge to tackle problems with bigger numbers.

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(Ages 7-10): Multiply and Divide by 10 and 100 (FREE!)

Investigate how to multiply and divide different numbers by 100.

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(Ages 7-10): Factors of 100 (FREE!)

Discuss where you would cut a metre stick to chop it into two equal pieces (p3). Make the link with halves (p4) and factor pairs (p5).

Next work out where to cut if you want to chop a metre stick into four equal pieces (p8). Again, make the link with quarters (p7) and factor pairs (p8). Repeat for five equal pieces (p9) and then ten (p12).

Finally, draw the factor rainbow for 100 (p15) and then build the factor pair pattern (p16).

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(Ages 7-10): 20x table (FREE!)

Discover how easy the 20x table is when you see the link with the 2x table.

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(Ages 7-10): Multiply Single Digits by Tens (FREE!)

Learn how to multiply by a multiple of 10.

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(Ages 7-10): Multiply Tens by Tens (FREE!)

Learn how to multiply a multiple of 10 by another multiple of 10.

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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): Subtracting from Tens using Differences (FREE!)

Explore how to subtract a two digit number from a tens number by using the difference method and counting on.

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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): Subtract 2-digit Numbers by Taking Away (FREE!)

Investigate how to subtract 2-digit numbers using the mental take-away strategy of first subtracting the tens and then subtracting the units.

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(Ages 7-10): Metres and Centimetres with Tenths and Fifths (FREE!)

Investigate where you would have to cut to chop a metre stick into 2 equal pieces (halves), ten equal pieces (tenths) and five equal pieces (fiths).

Through discussion/investigation establish the fact one tenth is smaller than one half; one fifth is bigger than one tenth.

Discuss how you can use the centimetre equivalents for different fractions to compare their sizes and then investigate equivalences between halves, fifths and tenths of 1 metre.

This investigation builds nicely on Counting in 20s. (see Counting section)

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(Ages 7-10): Find Fifths and Tenths Using Tables (FREE!)

Explore how to find one fifth of a number by dividing counters into five groups. Make the link with the 5x table and then extend to finding two fifths, three fifths etc.

Repeat for finding tenths and then explore the links between fifths of and tenths of.

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(Ages 7-10): Decimal Tenths and Fifths (FREE!)

Explore the links between tenths, fifths and decimals on a metre stick.

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(Ages 7-10): Hundreds and Tens Doubles (FREE!)

Investigate doubles of multiples of a hundred.

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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): Getting to the Next Whole (FREE!)

Use tens pairs to help work out how many you need to add to get to the next whole when working with single place decimals.

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(Ages 7-10): 2-digit Subtracting Using Differences (FREE!)

Recap on the link between difference and subtraction. Then experiment with using the difference method to subtract one two digit number from another.

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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): Equivalent Fractions for Halves and Quarters: Part 1 (FREE!)

Use fractions strips to explore families of fractions that are equivalent to one half and one quarter.

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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): Areas of Squares (FREE!)

Discuss the meaning of the area of a square as the flat space inside it. Establish the idea that you can find the area of a square by counting the 1cm squares that would fit into it.

Investigate the areas of different squares and, in the process, revise how to find simple squares and square roots.

Consider what might happen to the area if you double the size of a square. Investigate and discover that if you double the width, the area is multiplied by 4. (This idea is explored further in the section How similar shapes work.)

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(Ages 8-11): Perimeters of Squares (FREE!)

Discuss the meaning of perimeter. Establish how to find the perimeter of a square if you know the width. Set the children the challenge of finding different perimeters and notice the link with the 4x table.

Consider how to find the width if you know the perimeter. Set the challenge of finding widths of different squares, including those where the perimeter is not a multiple of 4. Through investigating this, revise how to quarter a number and express remainders in different ways. (Links are given to earlier investigations to help with this.)

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(Ages 8-11): Factors of 12, 24 and 60 (FREE!)

Discuss the fact that the numbers 12, 24 and 60 are used a lot when measuring time (p1).

Investigate the factors of 12 (p3), draw the factor rainbow (p5) and build the factor pair pattern (p6). Explore the link with months (p7).

Repeat for 24 (p8), exploring the link with hours (p12). Then repeat with 60 (p13), exploring the link with minutes (p17).

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(Ages 8-11): Multiply and Divide beyond the 6x Table (FREE!)

Investigate how to multiply and divide different numbers by 6 and use this knowledge to tackle problems with bigger numbers.

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(Ages 8-11): Patterns Multiplying by 5 (FREE!)

Explore the link between multiplying by 10, dividing by 2 and multiplying by 5 and establish key facts and quick methods for tackling questions like ? x 5 = 80 and 170 x 5 = ?

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(Ages 8-11): Patterns Dividing by 5 (FREE!)

Investigate the link between dividing by 10, multiplying by 2 and dividing by 5 and explore how this can be used to tackle problems like 120 ÷ 5 = ?

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(Ages 8-11): How Decimals Work - Hundredths (FREE!)

Explore the second place of decimals using a counting stick.

Recap the idea that each whole metre is divided into ten bits. Note that each bit (tenth) can be divided into ten little pieces. These are called hundredths and are also called centimetres. (cent = 100 - century, centipede etc) Explore the different ways of writing one hundredth (1/100 and 0.01), two hundredths etc. Explore how measurements can be written as a whole number of metres, followed by a decimal followed by the number of bits (tenths) and then the number of little pieces (hundredths).

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(Ages 8-11): Equivalent Fractions for Halves and Quarters: Part 2 (FREE!)

Use fractions strips to explore families of fractions that are equivalent to two quarters and three quarters and discover rules for converting equivalent fractions.

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(Ages 8-11): Divide and Multiply by 10 with Decimals - Part 1 (FREE!)

Explore what happens if you try to divide a number by 10. Learn the rule for moving numbers relative to the decimal point.

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(Ages 8-11): Divide and Multiply by 10 with Decimals - Part 2 (FREE!)

Explore more about what happens if you try to divide a number by 10. Learn more about the rule for moving numbers relative to the decimal point.

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(Ages 8-11): Hours and Minutes with Halves and Quarters (FREE!)

Use a clock to establish the number of minutes in an hour and then investigate how many there are in 2, 3, 4 or more hours (p4).

How many minutes in half an hour (p5)? What about 1½ etc? How do you write these times in hours and minutes (p8)? Can you work backwards?

Investigate times involving quarter hours (p10). Explore how to change them between the different formats.

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(Ages 8-11): How do Percentages Work? (FREE!)

Use a metre stick to recap on what tenths (p2) and hundredths (p4) of a metre are as decimals. Explain the equivalence between one hundredth and 1% (p7) and extend the pattern to other hundredths such as 0.04 = 4% (p9).

Recap on the location of 0.1m on the metre stick and extablish the equivalence with 10% (p12). Explore other equivalences such as 0.3m = 30% (p14).

Recap on the decimal equivalences for quarters of a metre (p17) and investigate the percentage equivalences (p19).

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(Ages 8-11): Change between Easy Decimals and Percentages (FREE!)

Explore how to convert 1 or 2 place decimals to percentages and convert whole number percentages back to decimals.

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(Ages 8-11): Decimal Pairs for One Whole (FREE!)

Use the knowledge of number pairs to 100 to explore the pairs of 2-digit decimals that make up one whole.

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(Ages 8-11): Something out of 12 or 20 as an Easy Percentage (FREE!)

Explore how to find what percentage (25%, 50%, 75%, 100%) has been selected when you select a number of objects from a larger group. Investigate the link with finding percentages and fractions of things.

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(Ages 8-11): Find Quarters and Eighths Using Tables (FREE!)

Recap on how to find one quarter of a number by dividing counters into four groups. Make the link with the 4x table and then extend to finding two quarters, three quarters etc. Repeat for finding eighths and then explore the links between quarters of and eighths of.

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(Ages 8-11): Counting in Hundredths (FREE!)

Learn how to count forwards and backwards in single, double or five hundredth intervals within 1. (Eg 0.4, 0.42, 0.44, etc) Explore 14 hundredths= 0.14 etc.

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(Ages 8-11): Double 3-digit Multiples of 10 (FREE!)

Explore how to use your knowledge of doubling 2-digit numbers such as 74 to double 3-digit numbers like 740 etc.

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(Ages 8-11): Half 3-digit multiples of 10 (FREE!)

Explore how to use the skill of halving 2-digit numbers such as 74 to halve 3 digit numbers such as 740.

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(Ages 8-11): Multiply and Divide beyond the 8x Table (FREE!)

Explore multiplication and division within the 8x table and use this knowledge to tackle problems with bigger numbers.

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(Ages 8-11): Areas of Rectangles (FREE!)

Discuss the meaning of the area of a rectangle as the flat space inside it. Establish the idea that you can find the area of a rectangle by counting the 1cm squares that would fit into it (p1).

Investigate the areas of different rectangles, exploring what happens if you fix either the length or the width and change the other one (p3). Note note the link with multiplication. Establish that to find the length or width when you know the area you have to divide (p6). Practise this.

Explore to find rectangles that have an area of 30 (p10), and then an area of 100 (p13). Note the link with factors and factor rainbows.

Note: This investigation suggests that the children draw rectangles and tables to record their findings.

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(Ages 8-11): Perimeters of Rectangles (FREE!)

Discuss the meaning of perimeter for a rectangle (p1). Speculate on what will happen to the perimeter if you fix the width and made the length go up in ones (p3). What will happen if you fix the width and increase the length by a different amount (pp7/8). Investigate!

Next, consider what will happen if you increase the width and the length at the same time (p10). Suppose you make the width and length increase at different rates. What then (p14)? Investigate!

Next, discuss what happens if you work backwards. Can you find the length if you know the width and the perimeter (p17)? What happens if the perimeter is an odd number (p18)?

What happens if you fix the perimeter and make the width increase (p21)? etc, etc.

Loads to investigate here! Once the pupils have worked through the investigation given, they may have their own ideas for further exploration.

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(Ages 8-11): A Quick Way to Multiply by 9 (FREE!)

Learn the quick method for multiplying by 9 (find ten lots and take away one lot) and then practise on numbers of your own choice. Self-checking and self-marking.

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(Ages 8-11): Multiply and Divide beyond the 7x Table (FREE!)

Investigate how to use the 7x table to multiply and divide all sorts of numbers by 7.

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(Ages 8-11): Multiply Big Numbers by 7 (FREE!)

If you think you know your tables then apply your knowledge to multiplying larger numbers by a single digit. Use the 7x table because this one is the hardest!

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(Ages 8-11): Tenths, Hundredths and Decimals Bigger than 1 (FREE!)

Use a metre stick to explore where 1 tenth, 3 tenths and 5 tenths would be and what these would be as decimals (p2). Consider whether you could get 12 tenths. What would this be as a decimal (p4)? Investigate other numbers of tenths (p6).

Consider where 1 hundredth, 3 hundredths and 8 hundredths would be and what these would be as decimals (p7). What would 16 hundredths be (p9)? Consider whether you could get 16 hundredths. What about other numbers of hundredths (p11)?

Consider whether you could get 120 hundredths. What would this be as a decimal (p12)?

Investigate other numbers of tenths (p15) and hundredths (p16).

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(Ages 8-11): Multiply 2 Digits by Multiples of 10 (FREE!)

Explores how to multiply by numbers like 30, 40, 60 etc

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(Ages 8-11): Decimal Tenths, Hundredths and Quarters (FREE!)

Use a metre stick to consolidate learning about tenths and hundredths and use this to explore decimal equivalences for halves and quarters.

Use a metre stick to recap on tenths and hundredths. Establish the position of 0.1, 0.2 etc and 0.05, 0.15, 0.25 etc. Turn the stick over and put blu-tac on the back to show where the halves and quarters would be. Recap that ¼m= 25cm etc. Establish that this would be 0.25m using decimals. What about ¾?

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(Ages 8-11): How do Square Numbers Work? (FREE!)

Learn about square numbers.

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(Ages 8-11): Find a Fraction of a Whole Number (without remainders) (FREE!)

Investigate how to find any fraction of a number. Start by exploring quarters and fifths. Then move on to tenths and eighths. Use the open-ended pages to explore fractions with other denominators.

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(Ages 8-11): Decimals for Many Halves and Quarters (FREE!)

Revise basic facts (½ = 0.5, ¼ = 0.25 etc). Then build on these to explore decimal equivalences for larger numbers of halves and quarters.

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(Ages 8-11): How do Square Roots Work? (FREE!)

Find square roots.

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(Ages 8-11): Easy Percentages of Harder Numbers (FREE!)

Explore how to find 50%, 25% and 75% of 2-digit numbers and then three digit multiples of 10 using doubling and halving skills.

First recap on the meaning of 100%, 50%, 25% and 75% (p1). Then use halving to find 50% of various numbers (p4) then halve 50% to find 25% (p8). Finally explore alternative ways of finding 75% (p12).

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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 8-11): Find Percentages that are Multiples of Ten (FREE!)

Recap on what percentages are. Establish the equivalence of 10% with one tenth and explore how to find 10% of a number. From this work out how to find 20%. Then explore other percentages such as 70%, 30% etc.

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(Ages 8-11): Change Fifths and Twentieths to Decimals (FREE!)

Use a metre stick to consider how 1 fifth compares with 1 tenth. What would the decimal equivalents be for 1 fifth, two fifths and three fifths? (p4). Consider whether you could get 6 fifths. What would this be as a decimal (p6)? Investigate other numbers of fifths (p8).

Consider how 1 twentieth compares with 1 tenth. What would the decimal equivalents be for 1 twentieth, two twentieths and three twentieths? (p11). What about larger numbers of twentieths (p13)? Consider whether you could get 21 twentieths or 24 twentieths (p14). What about other numbers of twentieths (p16)?

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(Ages 9-12): Fractions, Decimals, Percentages and Factors of 100 (FREE!)

Recap on factors of 100 (p2), and create the factor rainbow for 100 (p4). Using a metre stick, discuss unit fractions and consider which can be changed easily to decimals or percentages (p5).

Explore the decimal and percentage equivalents for 1/2, 1/4 and 1/10 (p6). Then consider how 1/5 (p9) and 1/20 (p10) compare with 1/10 and what the equivalences will be. Link these facts to the factor rainbow (p13). Next explore 1/100, 1/50 and 1/25 (p14).

Discuss paired number facts such as 20%=1/5 and 5%=1/20 (p15). Finally consolidate all the facts explored (p20).

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(Ages 9-12): Equivalent Fractions for Fifths (FREE!)

Use fraction strips to explore the different fractions that are equivalent to one fifth, two fifths, three fifths etc.

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(Ages 9-12): Find Single Digit Percentages of Things (FREE!)

Revise how to divide numbers by 10 and 100 to give decimal answers. Recap also on what percentages are.

Establish the equivalence of 1% with one hundredth and explore how to find 1% of a number. From this work out how to find 2%. Then explore other percentages such as 7%, 3% etc.

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(Ages 9-12): Change between Tricky Decimals and Percentages (FREE!)

Explore how to convert 2, 3 or 4 place decimals to percentages, and what happens with percentages beyond 100%.

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(Ages 9-12): Fractions to Decimals Using Factors of 100 (FREE!)

This activity builds on Fractions, Decimals, Percentages and Factors of 100 (above). It uses a metre stick to explore fraction-decimal equivalences where the denominator is a factor of 100.

Use the stick to first recap on the decimal equivalvents for ¼ and ¾ (p4). Explore different numbers of tenths in the same way (p6), next explore fifths (p10) and then look at the equivalences between tenths and fifths and decimals (p13).

Continuing to use the metre stick as a visual aid, move on to investigate different numbers of twentieths (p14), then twenty-fifths (p17) and finally fiftieths (p20).

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(Ages 9-12): Halves, Fifths and Tenths on a Number Line (FREE!)

Investigate the sequence of fifths and tenths between zero and one and then continue into improper fractions.

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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 9-12): Multiply and Divide Negative Numbers (FREE!)

Explore how multiplication and division work with negative numbers. Explore patterns in number facts to deduce well known relationships and explain why they work.

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(Ages 9-12): Metres, Centimetres, Millimetres with Decimals (FREE!)

Use a metre stick and explore patterns to help with decimal metric conversions within 1 metre.

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(Ages 9-12): Multiply and Divide Decimals by 10, 100, 1000 (FREE!)

Build understanding step by step from simple examples (6 x 10) to more complicated ones (0.22 x 1000).

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(Ages 9-12): Factors of 360 (FREE!)

Discuss the fact that for thousands of years people have measured angles in a circle by dividing the circle into 360 equal degrees (p1). Speculate as to why the number 360 might have been chosen (365 days in a year, but 365 does not divide up nicely - 360 is close to 365 and does divide up nicely).

Explore the idea that if there are 360 degrees in a full revolution, there will be 180 degress in half a revolution (p2) and 90 in a right angle (p4).

Consider a compass rose with 8 points, work out the angle between the points (p6) and investigate the link with factor pairs (p7).

Next consider hours on a clock (p8), angles in the six equilateral triangles in a hexagon (p10), a three armed windmill (p12) and then minutes on a clock (p14), investigating the angles each time and relating them to factor pairs.

See how many other factors you can find for 360 (p16) and then build the factor pairs pattern (p17). Finally draw the factor rainbow (p19).

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(Ages 9-12): How do Powers Work? (FREE!)

Build number patterns to explore how powers work.

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(Ages 9-12): How do Roots Work? (FREE!)

Explore roots as the inverses of powers.

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(Ages 9-12): How Many Times Bigger? (FREE!)

Learn how to solve problems such as 'How many times bigger is London than Edinburgh?' by exploring the inverse relationship between multiplication and division.

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(Ages 9-12): Fractions to Percentages Using Factors of 100 (FREE!)

This activity closely parallels Change Straightforward Fractions to Decimals (above). It uses a metre stick to explore fraction-percentage equivalences where the denominator is a factor of 100.

Use the stick to first recap on the percentage equivalvents for ¼ and ¾ (p4). Explore different numbers of tenths in the same way (p6), next explore fifths (p10) and then look at the equivalences between tenths and fifths and percentages (p13).

Continuing to use the metre stick as a visual aid, move on to investigate different numbers of twentieths (p14), then twenty-fifths (p17) and finally fiftieths (p20).

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(Ages 9-12): Getting Division the Right Way Round (FREE!)

Which is which, '8 divided by 5' or '5 divided by 8'?

Sort out this confusion once and for all!

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(Ages 10-13): Find Any Percentage of a Number (FREE!)

Investigate different ways of finding a percentage of a number. Explore how to use simple percentages like 10% and 1% to find 20%, 5%, 2% and 0.5%, and then move on to finding general percentages.

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(Ages 10-13): Percentage Increase and Decrease (FREE!)

Investigate how to calculate percentage increases and decreases both mentally and using a calculator.

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(Ages 10-13): Heights of Buildings Using Shadows (FREE!)

Investigate how to use the lengths of shadows to find the heights of buildings and learn all about how ratio works.

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(Ages 10-13): Fractions, Division and Decimal Equivalents (FREE!)

Discover the amazing fact that ½ = 1 ÷ 2 = 0.5, ¾ = 3 ÷ 4 = 0.75 and go on to explore what happens with other fractions.

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(Ages 10-13): Mixed Metric Equivalences with Decimals (FREE!)

Establish that milli-metres/litres/grams are 1000 times smaller than metres/litres/grams and kilm-oetres/grams are 1000 times larger. Consolidate the understanding that since millimetres are smaller you will need more of them, km are larger so you will need fewer. Explore the idea that changing between these measurements is then just a matter of multipiying or dividing by 1000, by moving numbers relative to the position of the decimal point.

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(Ages 10-13): Perimeters and Areas of Polygons (FREE!)

Establish the meaning of polygon(p1) and regular polygon (p2).

Recap on how to find the perimeter of a square and a rectangle. Then consider how you could find the area of a regular hexagon if you know its width (p6). Consider if this would work for other regular polygons (p9).

Recap on how to find the area of a rectangle and a triangle. Then consider a rhombus (p13) and a kite (p17). Investigate areas of these and other quadrilaterals by drawing them on cm squared paper.

Extend these ideas to find the area of a regular hexagon (p20).

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(Ages 10-13): The Connection between Of and Times (FREE!)

Explore the idea that multiplying by (eg) ¼ is the same as finding ¼ of something which, in turn, is the same as dividing by 4. This investigation introduces the fraction triangle, a powerful little tool for exploring this idea.

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(Ages 10-13): Interior Angles of Regular Polygons (FREE!)

Investigate the interior angles around the inside edge of a square, equilateral triangle and regular hexagon (p2). What are their totals?

What about the angles at the centre (p7)? Is there a link?

Could you use what you have discovered to find the angles in a regular pentagon (p9)?

Consider the factor rainbow for 360 (p16). What does this have to do with the angles at the centre of different polygons?

Investigate polygons with more sides. What are their angles?

Establish and test formulas for the interior and centre angles (p21).

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(Ages 10-13): Train Journey (FREE!)

Use self-checking tools to work out the time taken, distance travelled, and average speed on various sections of a train journey.

Supports the paper-based investigation with the same name.

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(Ages 10-13): Expressing Things as a Fraction or Percentage: Part 1 (FREE!)

Discuss the mark 17 out of 20 in a test. Agree that this would be 17 twentieths of the total mark (p2).

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(Ages 10-13): Powers with Negative Numbers (FREE!)

Explore what happens if you square, cube and find other powers of negative numbers.

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(Ages 10-13): Expressing Things as a Fraction or Percentage: Part 2 (FREE!)

Explore how to express something out of something as a percentage if the numbers do not divide exactly.

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(Ages 10-13): Circle Circumference (FREE!)

A new take on PI.

Explore the relationship between the circumference of a circle and its diameter by investigating the perimeter of the circumscribed square (round the outside of the circle) and the inscribed hexagon (on the inside)!

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(Ages 10-13): Change Percentages to Fractions (FREE!)

Change percentages to fractions.

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(Ages 10-13): Change Decimals to Fractions (FREE!)

Change decimals to fractions.

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(Ages 10-13): Circle Area (FREE!)

Investigate how the area of a circle is connected to the square of the radius.

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(Ages 10-13): Roots with Negative Numbers (FREE!)

Explore what happens when you try to find the square root, cube root and fourth root of -1. Discover that it is possible to find odd roots of negative numbers but not even roots.

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(Ages 10-13): Twentieths, Twenty-fifths and Fiftieths on a Number Line (FREE!)

Challenge pupils to sequence fractions on a number line. Revise tenths and fifths and then move on to twentieths, fiftieths and twenty-fifths.

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(Ages 10-13): Tricky Fractions to Decimals or Percentages - Part 1 (FREE!)

Recap on how to convert easy fractions. Investigate eighths, based on them being half of quarters. Then consider fortieths and eightieths as being ten times smaller.

Next explore examples with other denominators where you first have to simplify the fraction to create a denominator that you can handle.

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(Ages 10-13): Fraction, Decimal, Percentage Triangle Magic (FREE!)

Explore the link between finding a % of something and expressing something AS a percentage.

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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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(Ages 10-13): Multiply a Fraction by a Whole Number (FREE!)

Investigate how to multiply fractions by whole numbers.

Get pupils exploring 1 x ¼, 2 x ¼, 3 x ¼ etc and they will quickly discover the rules that for multiplication you multiply the numerator and for division you multiply the denominator.

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(Ages 10-13): Divide a Fraction by a Whole Number (FREE!)

Investigate how to divide fractions by whole numbers.

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(Ages 10-13): Negative Number Reflections (FREE!)

Explore how multiplying and dividing by different positive and negative numbers moves things around on the number line. Start by investigating reflections and then find out how to make numbers move closer to or further away from zero.

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(Ages 10-13): How Can Multiplication Make Things Smaller? (FREE!)

Investigate how multiplying by certain numbers (eg 0.5, 0.1, 0.2, a half, a tenth, a fifth etc) makes a number smaller.

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(Ages 10-13): How Can Division Make Things Bigger? (FREE!)

Investigate why some divisions give answers that are larger than the starting number.

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(Ages 10-13): Multiply and Divide by a Decimal (FREE!)

Weird things start to happen when you multiply and divide by decimals. Things that should get bigger get smaller!

Investigate how to multiply and divide by 0.1 and by 0.01. Then go on to investigate multiplying and dividing by other easy decimals such as 0.2, 0.02, 0.4, 0.04, 0.5, 0.05

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(Ages 11-14): Perimeters of Similar Shapes (FREE!)

Explore how, when you double the size of a shape, the perimeter also doubles. Then look at what happens when the shape is made 3x or 4x larger. Does the same thing work?

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(Ages 11-14): Areas of Simliar Shapes (FREE!)

What happens to the area of a shape when you double its size? It doesn't just double...

And what happens when the shape is made 3x or 4x larger?

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(Ages 11-14): Recurring Decimals and Fractions (FREE!)

Investigate the patterns of digits in recurring decimals arising through division and how this links to fractions decimal equivalences.

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(Ages 11-14): Percentage Increase & Decrease Using Scale Factors (FREE!)

Investigate quick methods for working out percentage increases and decreases using a calculator.

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(Ages 11-14): Fraction, Decimal, Percentage Equivalences (FREE!)

A summary of all the skills you need to switch between fractions, decimals and percentages, with links to the other investigations that teach each skill.

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(Ages 11-14): Zero and Negative Powers (FREE!)

2³ means 2x2x2. 2² means 2x2. 2¹ means 2. But what about 2⁰ or 2^-1 or 2^-2. Explore what happens when you follow patterns past zero and discover how negative powers work.

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(Ages 11-14): Pythagorean Triple Hunt (FREE!)

Find out how to make a spreadsheet to hunt for Pythagorean triples.

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(Ages 11-14): Pythagorean Triple Patterns (FREE!)

Pythagorean triples are groups of whole numbers that fit Pythagoras Theorem. 3, 4, 5 is one. 5, 12, 13 is another. Are there any more? Are there any connections between them?

Use a spreadsheet and the online pattern builder to venture deep into unknown territory!

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(Ages 11-14): Percentage Increase & Decrease Backwards! (FREE!)

Investigate how to solve percentage increase and decrease problems that ask you to work backwards to find the starting number.

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(Ages 11-14): Multiply by a Fraction (FREE!)

Investigate how to multiply a whole number or a fraction by a unit fraction (such as one quarter or one fifth). Then investigate multiplying by other fractions.

Multiplying by a fraction is where things get interesting. Pupils are used to thinking that multiplying a number by something will make it bigger. But when fractions are around, all that changes!

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(Ages 11-14): Divide by a Unit Fraction (FREE!)

Investigate how to divide a whole number or a fraction by a unit fraction (such as one quarter or one fifth).

Dividing anything (whole number or fraction) by a fraction is the same as multiplying by the reciprocal of the fraction.

Dividing by ¼ is the same as multiplying by 4!

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(Ages 11-14): Divide by Any Fraction (FREE!)

Explore how to divide a whole number or fraction by any fraction using the idea of reciprocals.

Discover how dividing by 5 eighths is the same as multiplying by 8 fifths and vice versa.

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(Ages 11-14): Tricky Fractions to Decimals or Percentages - Part 2 (FREE!)

Recap on how to divide 8 by 5 and 5 by 8. Explore how changing thirds to decimals by dividing gives a recurring answer. Repeat with sixths and ninths.

Next explore 30ths, 60ths, 15ths, 90ths and 18ths.

Finally look at fractions like 29ths using a calculator!

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More than 100 quizzes

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