Helping you help your child

Transcription

1 Helping you help your child ACTIVITY BOOK / MATHEMATICS DfES: Crown copyright 2004 Open Doors

2 Introduction to maths activities Goal There are key skills that your child needs to practise that will really help them to improve their maths. They include: learning number facts by heart knowing how to use what they already know to work out new facts making jottings on paper so they don t lose track of what they re doing (it doesn t matter how rough or scribbly these are) using images, or pictures, in their head to help them see the maths more clearly. These images can include seeing numbers along a number line, up or down a number staircase, seeing patterns in numbers, imagining the units, tens and hundreds in different colours, or any other image that helps them Below are some examples of the sorts of activities that you can practise with your child. Little and often is the best way to do it. Just 10 minutes every day of this kind of mental maths will help your child develop real mental maths fitness! You will need: pencil and paper for making jottings if needed What you need to do 1. Learning facts by heart - what your child needs to know: Number facts up to 10. Ask your child to tell you as many facts as they can in one minute, e.g. 4+6, 10-3, , etc. Number facts up to 20. Ask your child to tell you as many facts as they can in one minute, e.g , 18 6 etc.

3 Pairs of numbers that total 100. Ask your child to tell you as many pairs as they can in half a minute, e.g , etc. Pairs of numbers that total Ask your child to tell you as many pairs as they can in half a minute, e.g , etc. Number facts to 1. Ask your child to tell you as many facts as they can in half a minute, e.g =1, = 1 etc. Doubling. Ask your child to double as many numbers as they can in a minute, e.g. double 36, double 3.8, double 480 Multiplying and dividing by 10, by 100, by Give your child a number e.g. 30 and ask them to multiply it by 10, then by 100, then by Now give them a larger number, such as 6000 and ask them to divide it by 10, by 100, by 1000 Multiplication and division facts (times tables) up to 10x10 Square numbers: 1x1 =1; 2x2 =4; 3x3 =9; 4x4 =16 etc. You can play a quick-fire challenge with these 2. If your child forgets some number facts, they need to know some strategies they can use to find the answer: Partitioning numbers (splitting them into easier chunks) when adding. For instance, when calculating , each number can be partitioned (split) into chunks. There are different ways your child might do it. They might find it easiest to partition each number 53 is and 26 is They could add the 50 and the 20 to get 70, then add the 3 and the 6 to get 9, and add the 70 and the 9 together for the answer Drawing a number line for the numbers you are adding or subtracting may help your child see how to work out the answer. So another way to calculate would be to partition the 26, but not the 53: Drawing a number line can also be helpful when adding numbers where one of them is close to a tens number. For instance, if asked to add , your child might notice that 29 is close to 30, which as a tens number is easy to add on. So they could do this:

4 If your child forgets how to double, they can use partitioning to work it out. For instance, to double 34 they could: Partition (split) 34 into 30 and 4 Add the two 30s together = 60 Add the two 4s together = 8 Add the two totals together = 68 So double 34 is 68 If your child forgets their times tables facts, they can use facts they can remember to work out the answer. For example, if they forget 7 x 9, they could use the fact that 9 is the same as Then they can use 7 x 6 and 7 x 3, and add the answers together to get 7 x 9, like this: 7 x 6 = 42 7 x 3 = = 63, so 7 x 9 = 63 Or they could decide to use the fact that 9 is also the same as 5 + 4, and work out 7 x 5 and 7 x 4, and add the answers together. It will give the same answer, 63. If they forget what 8 x 6 is, they may be able to use doubling and facts that they can remember to help work it out. So if they already know that 8 x 3 = 24, they may be able to double that to get the answer: 2 x 24 = 48, which is the same as 8 x 6 If your child is asked to double 39, they could use the fact that 39 is very close to 40, a tens number, to calculate the answer more quickly and easily. They could use the fact that = 80, remembering to then take away the 1s that they added onto the 39s. So double 39 is = 80 2 = 78 Your child should practise drawing number lines (just a rough one will do when they are making jottings) for calculations using different sets of numbers, whether small, large or decimal. For example:

5 Remind your child that if they know one number fact, they also know some other facts about those numbers. For example, if they know that = 100, they also know that = 100 and = 32 and = 68. You could think of pairs of numbers that total 100, and ask your child to tell you the other facts about those three numbers. Remind your child that when they are practising their times tables, if they know the 2 times table, then double it to get the 4 times table, and double the 4 times table to get the 8 times table. Similarly, if they know the 3 times table, then double it to get the 6 times table.

6 Reminders Encourage your child to make jottings as they are working out, and to use the facts they do know to work out ones they don t. Check points As you practise with your child, see if you can gradually increase the pace so that they are thinking quickly and confidently. If your child wants to, they could decide which facts they need to learn by heart, and practise them with you. Think about which strategies they find most helpful, and practise those too.

7 Activity 1 Ordering fractions and converting them to decimals Goal This activity will help your child to: put fractions (such as 7/8, 3/4 etc.) in order according to their value change them into decimals use a calculator to check the answers You will need: Pencil, paper and ruler. Some of the paper needs to be cut into squares big enough to write on calculator What you need to do Ask your child to choose three digits (numbers) from a phone display, such as e.g. 2, 4 and 6. Talk together and work out how many different fractions you can make if you use two digits for each fraction. So, for example with the digits 2 and 4 you could make 2/4 and 4/2, and with the digits 4 and 6 you could make 4/6 and 6/4. You can use each digit twice for fractions like 4/4. Write each fraction on one of the squares of paper, and then together decide which is the smallest fraction and which is the largest. Now ask your child to draw a blank number line and mark it from 0 to 3 (see example below). Working together, spread out all the fractions you have written on slips of paper and see if you can put them in order along the number line like this:

8 You should have a lot more than these three fractions! Talk about how you can tell that you ve made all the fractions that are possible with your three numbers. Once you ve agreed that you ve got them all, look at each fraction in turn, then turn over the slip of paper and convert the fraction (change it) into a decimal that s worth the same as the fraction. This is known as the decimal equivalent. You can take turns in using a calculator to check that you have written the right decimal equivalent. For example: Reminders If your child forgets that 2/2 = 1, 4/4 = 1 etc., remind them. N.B. In fractions, the number above/in front of the line is known as the numerator, the number below/after the line is known as the denominator. Check points Did you have any fractions that belong on the same place on the number line? Look at their decimal equivalents. What do you notice? [ Answer: The decimal figures are the same]. That s because the fractions they correspond to are equivalent fractions that are worth the same as each other.] Can your child explain to you what the difference is between fractions that have a smaller numerator than denominator, e.g. 3/6, 17/25 and fractions that have a larger denominator than numerator, e.g. 6/3, 25/17? If your child wants to, they could make another set of fractions and their decimal equivalents using 2, 4 and 8.

9 Activity 2 Finding equivalent fractions Goal This activity will help your child to find fractions that are equivalent ; that is, worth the same as each other even though they are written differently. It s like having several ways of saying the same thing, just like when we tell someone the time we can say 3.15 or we can say quarter past 3. The time is still the same, we just express it in a different way. You will need: pencil and paper calculator What you need to do Start with a straightforward fraction such as 1/2. Ask your child to tell you how they would write 1/2 as a decimal. They should say 0.5. Ask them to check this on the calculator as follows: Now ask them to try this one on the calculator:

10 If you want to get the answer 0.5 in the display again, what would you have to key into the calculator if you started like this? Can you see a pattern beginning? Together write down the three fractions you ve used so far (1/2, 2/4, 3/6,) and talk about what the pattern could be. There should be one pattern for the numerators (the numbers above the line) and one for the denominators (the numbers below the line). You can check some or all of them on the calculator to make sure that they all are worth the same, that is, 0.5. If so, they are equivalent. Now you know the pattern, you could play a challenge game. One of you says a number, which will be the numerator. The other person has to say what the denominator needs to be if the fraction is to be worth 0.5. Take turns to challenge each other, checking with the calculator if you disagree. Reminders You and your child should be able to spot a link between the patterns of the numerators and denominators, and the times tables. Check points You should find that your child becomes quicker at noticing which fractions are equivalent to 0.5. This is probably because they are realising that the numerator will always be half the denominator if the decimal equivalent is 0.5. If your child wants to, they could use a different fraction as a starting point, such as 1/4, which is equivalent to Can they find a list of fractions equivalent to 1/4 just as they did for 1/2?

11 Activity 3 Working out fractions of a given amount Goal This activity will help your child to work out fractions of a given number, or a given amount of money. You will need: a pencil and paper a ruler for drawing number lines What you need to do To work out these problems, you and your child will need to imagine two people who have different amounts of money. Ask your child to choose them they could be friends, or characters from a book or film, or just A and B. One of the people, A, has 10. The first challenge is to work out how much money B has, if half of B s money is the same as a quarter of A s money. Ask your child to start by drawing 2 number lines, one for A and one for B. Because you are going to be finding out half of B s money, B s number line needs to have the halfway point marked on it, and A s needs quarters marked on, like this:

12 You know that A has 10, so ask your child to work out what a quarter of 10 is, and mark the amount on A s number line. Next, remind your child that half of B s money is the same amount as A s quarter, so ask them to mark the same amount on B s halfway point. Now can they work out what B s full amount is? Once you have worked it out, try a different version. A quarter of A s money will still be the same as half of B s money, but can you work out another amount that they could each have, instead of 10 and 5? Get your child to start by drawing two blank number lines and marking them off in quarters and halves as you did before. Reminders It might help your child to see that half of one amount can be the same as a quarter of another amount if you use real objects to share out. You need about 20 or so. Anything small that can be torn or cut in half works well, such as strips of paper, sweets or raisins. Check points Your child may have worked out in their head that if A had 10, half of A s money would be 5. Even so, it is always worth making a jotting of things like this, as it may help later on in the problem to have a record of their earlier thinking. Always encourage them to make jottings. If your child wants to, they could work out how much money A and B would have if 1/2 of A s money was the same as 1/3 of B s.

13 Activity 4 Fractions of given amounts using number lines Goal This activity will help your child to work out a fraction of any given amount, using a number line to help them. You will need: a pencil and paper Some card or paper cut into squares big enough to write numbers on a ruler for drawing a number line What you need to do Together with your child make a set of seven cards, each one numbered 1 to 7, to be the cards for the numerators (the numbers above the line). Then make a set of five cards numbered 4, 6, 8, 10 and 12 to be the cards for the denominators (the numbers below the lines). It might help to number these in a different colour. Ask your child to draw a number line to represent 24cm. It doesn t have to be 24cm long, just long enough to fit several cards along it with spaces in between: you will be working out fractions of 24. To see how to use the cards, choose the numerator card 2 and the denominator card 8, and make the fraction 2/8. Ask your child to work out whereabouts on the 24 number line they think 1/8 and 2/8 would be.

14 They first need to work out that 1/8 of 24 is 3, because 24 8 = 3. Ask them to show this as a jump of 3 on the number line, like this: It might help to write the fraction 1/8 underneath the 3 as a reminder. Now together work out where on the line 2/8 will be. You should easily be able to work out where 3/8, 4/8, 5/8, 6/8 and 7/8 will be. Ask your child to use the number line to work out 5/8 of a piece of string measuring 24 cms Next choose the numerator card 5 and the denominator card 6 and make the fraction 5/6. Ask your child to tell you where they think 5/6 of 24 will be. What will they need to work out first? Together make up some problems like the piece of string one. Reminders When you are working out fractions of given amounts, you need to work out first of all what 1/8, or 1/6 or 1/4 is before you start working out 2/8 or 5/6 or 3/4. If you and your child want to try this with different numbers on the cards, it will only work if you use numbers for the denominator cards (the numbers below the line in a fraction) which divide exactly into the given amount e.g. in the above example, numbers such as 6, 4 and 8, divide exactly into 24. Check points When your child has made a new fraction with the cards, ask them whether this fraction is less than half or more than half. Get them to guess whereabouts roughly it will go on the number line before they work it out exactly. It s always a good idea to estimate first. If your child wants to, they could find a recipe that is intended for two or four people, and work out how to alter the quantities of each ingredient to make it enough for just one person, or for three people. For example, if the recipe says you need four eggs for two people, how many would you need for three people? Or if you need 200g sugar for four people, how much is needed for one person?

15 Activity 5 Percentages without using a calculator Goal This activity will help your child to work out different percentages of a given amount, without using a calculator. You will need: a pencil and paper. You and your child may be able to work the percentages out in your heads, but it can help to make some jottings on a piece of paper What you need to do Talk to your child about what 100% means. It means the total or the maximum, so that when people say that a sports star has given 100%, they mean that he or she could not have tried any harder: they gave the maximum effort. Your child might have scored 100% in a spelling or mental maths test! Another way to help your child see how percentages work is to talk about a pizza next time you have one. The whole pizza is 100%. If you said they could have 50% of your pizza, how much would you be letting them have? What if it was 25%? What percentage would be left for you if you gave them 25%? Where would you cut it to give 5 people an equal slice each, and what percentage of the whole pizza would each person get? Now try working out some percentages of money. Write down an amount of money, such as 80, and tell your child that this amount is the total that you will be working with first it is 100%. Check that they know that 50% is the same as a half,

16 then ask them to estimate (guess) what 50% of 80 will be ( 40). What about 25% (a quarter)? Because 25% is half of 50%, they should be able to work out 25% of 80 by halving 40. See if they can work out 10% of 80 they should know to divide by 10. To find 5% of 80, suggest they halve the 10% figure. Choose another amount of money, and work out together what 50%, 25%, 10%, 5%, 30% and 200% of the amount will be. Reminders As you are not using a calculator, you both need to use what you already know to work things out. For instance, to work out 30% of an amount, work out 10% first, then use three lots of 10%. Check points To help your child become more confident at using percentages in their heads, try some quick questions such as: If 50% of my money is 30, how much would 100% be? If 25% of my money is 20, how much would 50% be? What about 100%? If 100% of my money is 3, how much would 50% be? If your child wants to, they could work out the prices of items in a sale. For instance, if a television usually costs 260, but the shop is taking 35% off in the sale, how much will it cost? A good starting point is to work out 10% and jot it down.

17 Activity 6 Working out percentages using a calculator Goal This activity will help your child to work out percentages of given amounts, using a calculator. You will need: a pencil and paper, in case you want to make jottings a calculator What you need to do Remind your child what they already know about percentages from Activity 5. For instance, they know that 50% is the same as a half, 25% is the same as a quarter, 10% is the same as a tenth and so on. This will be handy even when using a calculator, as it means you and your child can check whether the answer is roughly right or not. Suppose you want to work out the percentage of an amount of money using a calculator, such as What is 10% of 350? Step 1: convert 10% to a decimal that you can key into the calculator. 10% = 1/10 = 0.1 (look back at Activity 1 if unsure of this). Step 2: key the following calculation into the calculator:

18 Step 3: check that the answer you have looks roughly right does it look like one tenth of the whole amount you started with ( 350)? Now you and your child can work out different percentages of the same amount, 350, using the same steps:. What would 25% of 350 be? What about 125% of 350? Then try this together. (You are still working with 350 as the whole amount: it is still100%: it is still the whole amount.) Can you match the percentages to the correct amounts? Reminders Don t forget that if you are working out percentages of an amount of money, your answer will be in or pence. If you are working out percentages of a weight or a length, your answer will be in kg and g or cm or and m. Check points Your child might need to practise the sequence they used on the calculator in order to remember it easily. They should become quicker as they practise with converting different percentages to decimals. If your child wants to, they could work out percentages using real examples from the television or newspaper. For example, if the Lotto rollover jackpot was 8.5 million, and five people had the winning numbers, what percentage would each one receive and how much would that be?

19 Activity 7 Converting fractions to decimals and percentages Goal This activity will build on work you have done together in Activities 1, 2, 5 and 6. It will reinforce your child s understanding of how amounts can be represented in different ways; that is, written as either fractions or decimals or percentages. It will help them remember that 50%, 1/2 and 0.5 are just different ways of saying the same thing. You will need: a pencil and paper a ruler to draw lines a calculator a set of 24 blank cards, big enough to write numbers on clearly, made of paper or card What you need to do Ask your child to draw a line about 30 cm long (the length of a ruler) and mark it as shown. Together make a set of 8 cards for this family of quarters: 1/4, 5/4, 3/4, 7/4, 2/4, 8/4, 6/4, 4/4 Arrange the fractions cards in order along the fraction line.

20 Now take another 8 blank cards and make a new set by converting each fraction into a decimal. You can use the calculator. For example, to convert 1/4 to a decimal: 1/4 is 1 4, so key in Make the decimal cards for the other 7 fractions. Ask your child to draw another line about 30 cm long and mark it as shown. Now you can both arrange the decimal cards in order along the decimal line. Finally, make a percentage line as shown, then make a new set of 8 percentage cards. To convert decimals to percentages, multiply each decimal by 100. Check that you have the right figures on the cards before starting to play the game. Decimals: 0.25, 0.50, 2.0, 1.75, 1.00, 1.25, 0.75, 1.50 Percentages: 125%, 50%, 100%, 25%, 175%, 200%, 75%, 150% To play the quarters game (for 2 or more players): 1. Shuffle all 24 cards and place them face down in a pile 2. Have the three number lines spread out so everyone can see them and reach them 3. One person picks a card and turns it over. The person sitting on their right tells them which number line to put it on but not its own! 4. This means that : a fraction card must be placed on the decimal or % line; a decimal card must be placed on the fraction or % line; a % card must be placed on the decimal or fraction line 4. Carry on until all 24 cards are correctly placed

21 Reminders Each card will have two equivalents. So you can find out the decimal and fraction equivalents of 25%, or the % and fraction equivalents of Check points As further practise for recognising equivalents, at the end of the game, you and your child could shuffle the cards then sort them into rows of equivalents like this: 1/ % 2/ % and so on. You can remove one set of cards, shuffle them, and see how quickly your child can replace them correctly next to their equivalents. If your child wants to, they could make sets of cards for the 1/5 family. There will be ten cards in each set can you work out why?

22 Activity 8 Adding decimals mentally Goal This activity will help your child to add decimals in their head, using an image (a mental picture) to see how the added numbers create larger numbers. The image used here is a number pyramid. You will need: pencil and paper for jottings a blank pyramid block a calculator What you need to do Together with your child, look at the number pyramid (figure1), especially the decimal numbers in the four base blocks. (figure1)

23 You will see that when two adjacent numbers (numbers next to each other) are added together, the total is the number in the block above. So = = = 5.7 When adding decimals in your head, it helps if you try to see the numbers on an imaginary line. Start with the larger of the two numbers you are adding. If you were adding 3.4 and 4.6 in the second row of the pyramid, you would start by seeing 4.6 at the beginning of a number line, then jumping along 3.4. It s easier if you partition (split) the 3.4 into 3.0 and 0.4 and make two jumps like this: Now you can make your own number pyramid. Choose four decimal numbers for the four base blocks. Mentally work out what the decimals will be in the other blocks (you may want to make jottings to help you) and check each answer on your calculator. Reminders Don t forget to start with the larger number first when you add any two numbers together. Use a number line in your mind to see the jumps along it. Check points Ask your child to explain how they partitioned (split) their decimals before they added them on, e.g. I had to add on 7.9 so I split it into 7 and 0.9. If your child wants to, they could choose a decimal number for the top block on the pyramid, and work downwards.

24 Activity 9 Using informal written methods to support, record or explain multiplication Goal This activity will help your child to use number facts they already know to work out other multiplication calculations. It is very important that children find ways of calculating that suit them best. There is not one right way to multiply numbers together. This particular way uses what children already know about the 10 times table. You will need: paper and pencil to make jottings What you need to do Together choose a simple multiplication such as 4 x 7 = 28 Talk about the other calculations you could work out, using this known fact : Changing the 7 to 70 or 700 or 7000 For example, if you know that 4 x 7 = 28, you can work out that 4 x 70 = 280 because 70 is 10 times bigger than 7, so the answer will be 10 times bigger than 28 (10 x 28) which is 280.

25 You can also work out that 4 x 700 = 2800 because 700 is 100 times bigger than 7, so the answer will be 100 times bigger than 28 (100 x 28) which is See if you can work out and tell each other why 4 x 7000 =??? because Changing the 4 to 40 or 400 or 4000 If you know that 4 x 7 = 28, you can work out that 40 X 7 = 280 because 40 is 10 times bigger than 4, so the answer will be 10 times bigger than 28 (10 x 28) which is 280. You can also work out that 400 x 7 = 2800 because 400 is 100 times bigger than 4, so the answer will be 100 times bigger than 28 (100 x 28) which is See if together you can work out and tell each other why 4000 x 7 =??? because All the changes you have been making to 4 x 7 = 28 so far have been to make the numbers bigger and bigger. What about making the numbers smaller and smaller? If you know that 4 x 7 = 28, you can work out that 4 x 0.7 = 2.8 because 0.7 is the same as 7 divided by 10, so the answer will be 28 divided by 10, which is 2.8. You can also work out that 4 x 0.07 = 0.28 because 0.07 is the same as 7 divided by 100, so the answer will be 28 divided by 100, which is 0.28 See if together you can work out and tell each other why 4 x =??? because

26 Reminders Working out calculations in this way means using the factors of the numbers. So 7 is a factor of 700, because you can divide 700 by 7 and there is no remainder. 100 is also a factor of 700, as is 70. Check points Your child should be able to multiply by 10 very quickly in their head. Give them extra practise, starting with single digit numbers such as 3, 6, or 8, and moving on to two digit numbers (12, 27, 49) and three digit numbers (156, 410, 713). See how quickly they can multiply each number correctly: they may enjoy trying to do it against a timer such as the second hand on a watch, but this is optional. If your child wants to, they could choose two numbers from 2 to 9, (not 4 and 7), multiply them together and use this calculation as the starting point instead of 4 x 7 = 28. Make each factor bigger, by 10, by 100, by 1000 then make each one smaller by 10, by 100, by 1000.

27 Activity 10 Using the chunking method for division Goal This activity will help your child to try out a way of dividing one number into another by chunking the larger number. You will need: paper and pencil for making jottings What you need to do Suppose you and your child have been asked to work out 192 6, or how many 6s there are in 192. It s always a good idea to start with an estimate (guess) of what the answer will be, roughly speaking. That way, you will know if the answer you finally come up with is probably correct or not. This can be very important when you are working with larger numbers or with decimals. It s also useful to make jottings of any number facts about 6 that might be handy, such as: 6 x 10 = 60 By doubling you can work out that 6 x 20 = 120 Using the 10 times table you can also work out that 6 x 30 = 180 and that 6 x 40 = 240 So because 192 is somewhere between 180 and 240, you know that the answer to will be between 30 and 40. This is your estimate.

28 Here s how you could use the chunking method: (take away 6 x 10) (take away another 6 x 10) (can take away another 6 x 10) 12 (12 is 6 x 2, so you can take away 6 x 2) 0 Altogether you have taken away 6 x 32 from 192. So = 32. A shorter way would be to start with one of your number facts: 6 x 30 = 180, because 180 is quite close to (6 x 30) (6 x 2) 0 So = = 32. Now together try using the chunking method to work out Reminders Don t forget to check the answer against your estimate. Check points When working out 296 8, ask your child to jot down some number facts about 8 and tell you how they could use them. If your child wants to, they could work out some calculations for you to use the chunking method on. They need to have no remainders or they won t work!

29 Activity 11 Understanding place value 1 Goal This activity will help your child to understand the value of digits in numbers (what each digit is worth), and what happens when you multiply and divide by 10, by 100 and by You will need: pencil and paper for making jottings What you need to do Together, look at the number 3067 and say it aloud: Three thousand and sixty seven. Can your child explain to you what the value is of each of the digits in the number (what each one is worth)? The thousands column has 3, the tens column has 6 and the units column has 7. The hundreds column is empty there aren t any hundreds in 3067 so a zero is used as a place holder. If the zero wasn t there, the number would become 367. The value of a digit (how much it is worth) depends on which column it is in. If you swap the digits around so that 3067 changes to 6703, what is each digit worth now? Ask your child to tell you. They should be able to explain that in 6703, the 6 is worth 6000 because it s in the thousands column, the 7 is worth 700 because it s in the hundreds column, the 3 is worth 3 ones and the tens column is empty so the zero is used as a place holder. If you swap the digits around again so that 3067 changes to 7630, what is each digit worth now? This time, it s your turn to explain to your child!

30 Together work out what is the largest number you can make with the four digits 3, 0, 6 and 7 and what the smallest number is. You may need to make some jottings. Ask your child to close their eyes and imagine the number eighty three thousand, four hundred and twelve. What is the digit between the 4 and the 2? What is the value of this digit (what is it worth)? What is the value of the digit in the middle of the number? When you are working with decimals, you have to remember that the value of a digit (what it s worth) gets smaller after the decimal point, but it s still helpful to think of the digits in terms of columns. So for the decimal 0.7 the 7 is worth 7 tenths, for the decimal 0.07 the 7 is worth 7 hundredths and for the 7 is only worth 7 thousandths. To see how the value of a digit can change, depending on which column it is in, you can write a list of numbers from largest to smallest, using the digit 7. Remembering this will help your child when they are multiplying and dividing by 10, 100 or For example, 7 x 10 = 70. That means that the digit 7 shifts one place to the left when it is multiplied by x 100 = 700 so the digit 7 shifts two places to the left when it is multiplied by 100. Ask your child to tell you what happens to the digit 7 when it is multiplied by Because division is the inverse (the opposite) of multiplication, you shift the digits in the opposite direction to the right - when you divide. So to divide 7000 by 10 you shift the 7 digit one place to the right and get 700. To divide 7000 by 100, you shift the 7 digit two places to the right and get 70. Ask your child to tell you what happens to the 7 digit if you divide 7000 by 1000.

31 This works with decimals, too. To divide 0.03 by 10, which will make it even smaller, shift the 3 digit one place to the right to get To multiply 0.03 by 10, which will make it bigger, shift the 3 digit one place to the left to get Can you and your child divide 0.03 by 100? Reminders You can multiply or divide a number by 10, by 100 or by 1000 simply by shifting the places of the digits. Check first whether you are making the number bigger or smaller so you remember which way to shift them. Check points Encourage your child to say aloud Multiplying makes my answer bigger, division makes it smaller. Suggest they try to visualise the biggest to smallest list in their head. If your child wants to, they could play a Beat the Clock game with you, where you give them a number and challenge them to multiply it by 10 (or 100 or 1000) and then divide it by 10 (or 100 or 1000) as quickly as possible. Encourage them to make jottings to help themselves. Start with whole numbers before you move on to decimals.

32 Activity 12 Place value 2 Goal This activity will help your child to put decimal numbers in order of size, and also to say which digit in a number is the most significant (important) when they are sorting numbers in order of size. You will need: pencil and paper for making jottings What you need to do Together with your child, write down the numbers 3.06 and 3.60, and say them aloud: three point zero six and three point six zero. These two numbers use the same digits (3, 6, 0) and sound quite similar, so how can you check which is bigger and worth more? You can see that both numbers contain units, tenths and hundredths. To compare numbers, start with the most important digit, which in this case is the units, the 3s. They are equal, so to find out which number is bigger you need to move on to compare the next most important digits, the tenths. Ask your child to tell you how many tenths there are in 3.60 (the answer is 6 tenths) and how many tenths are in 3.06 (none: the tenths place has a zero in it). This means that 3.60 is bigger than 3.06 because it has more tenths. You can also compare a number that has two decimal places (two numbers after the decimal point) with a number that has three decimal places (three numbers after the decimal point).

33 Ask your child to write down and say aloud and 0.28 nought point two four nine and nought point two eight. Can they remember what to do first to compare these two numbers? Begin by comparing the most important digit. There are no units in either number, so your child should move on to comparing the tenths. Ask them to say how many tenths there are in (two tenths) and how many in 0.28 (two tenths). Because both numbers have the same number of tenths in them, your child should move on to compare the next most important digit, the hundredths. Ask them to say how many hundredths there are in (four hundredths) and how many in 0.28 (eight hundredths). So 0.28 is bigger than Together make a decimal number line that shows hundredths, like this: Ask your child to mark where 0.28 is on this line and then discuss with them where would be. In between 0.24 and 0.25 are thousandths, and that is where you would find Together make a decimal number line that shows thousandths, like this: Together with your child, put these sets of numbers in order, starting with the largest. Draw a number line if it helps. (i) (ii) Reminders When comparing numbers, what really matters is the place value of the most significant digit (most important digit), not how many digits there are after the decimal point. Check points Can your child tell you how many units, tenths and hundredths there are in any number? Practising doing this aloud, especially with decimal numbers, might help them to be clearer about the value of the digits. If your child wants to, they could put more sets of numbers in order, or think up some sets of numbers for you to sort.