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Welcome to hours of mathematical enjoyment! 
(Ages 47): 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 110. 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 inbetween 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 47): 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 inbetween 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 47): 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 inbetween 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 inbetween 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 47): 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 47): 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 47): 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 47): 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 47): 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 58): 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 58): 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 SIXTEEN, so 2 + 10 could be called TWOTEEN, eleven would be ONETEEN, etc!
Then explore how to solve problems like:
3 + 10 = ?
? + 10 = 17 etc
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(Ages 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 twoty, thirty should be threety etc.
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(Ages 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 stickyoutbits pair up with each other).
Odd + even, or even + odd gives odd.
What happens with subtraction?
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(Ages 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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.(pp315)
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(Ages 58): 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 58): 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 58): 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 58): 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 58): 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 58): 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 69): 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 69): 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 69): 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 69): 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 69): 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 69): 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 69): 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 69): 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 69): 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 69): 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 69): 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 blutac 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 710): 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 blutac.
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 710): 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 blutac 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 710): 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 710): 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 blutac 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 710): 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 710): 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 710): 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 710): 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 710): 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 710): Take Away 2digit Numbers from Tens (FREE!)   Investigate how to subtract 2digit numbers from multiples of ten using the mental takeaway strategy of first subtracting the tens and then subtracting the units.
Begin by taking away multiples of 10 (eg 9030)(p3).
Then use a metre stick and tens and units to take away numbers with different units digits.
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(Ages 710): 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 2digit number ending in 3.
Establish the idea that you can add two 2digit 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 710): 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 811): 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 811): 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 811): 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 811): 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 811): 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 811): 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 811): 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 811): 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 811): 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 811): 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 811): 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 blutac 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 811): 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 912): 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 912): 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 912): 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 fractiondecimal 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 twentyfifths (p17) and finally fiftieths (p20).
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(Ages 912): 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 912): 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 fractionpercentage 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 twentyfifths (p17) and finally fiftieths (p20).
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(Ages 1013): Mixed Metric Equivalences with Decimals (FREE!)   Establish that millimetres/litres/grams are 1000 times smaller than metres/litres/grams and kilmoetres/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 1013): 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 1013): Train Journey (FREE!)   Use selfchecking tools to work out the time taken, distance travelled, and average speed on various sections of a train journey.
Supports the paperbased investigation with the same name.
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(Ages 1013): 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 1013): 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 1114): 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 1114): 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 1114): 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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