Monday 18th May - Ellesmere College, Leicester

Monday 18th May This week we are going to be working on multiplying by 10, 100 and 1000

Place Values First, let’s try some quick mental calculations!

Hopefully you found this quite easy. Up until now we’ve talked about replacing zeros when we multiply by 10, 100 and 1000. However, it’s important that you realise mathematically what we are doing and why so we will be looking to secure that understanding for the first few lessons before we move onto multiplying decimals be 10, 100 and 1000.

First things first then we need to know about place values.

Thousands Hundreds Tens Units

5 4 2 1

The number above then has 5 thousands, 4 hundreds, 2 tens and 1 unit.

1 x 10 23 x 10 45 x 10

2 x 100 545 x 100 5 x 100

33 x 1000 345 x 1000 341 x 1000

To make sure you know that please complete the activity below.

This skill is really important because it will help with multiplication, division and addition so it is useful to review this skill. The activities today are different ways of practising this skill.

This is quite a straight forward way to revise place value:

This is a different way of revising the place values and will challenge you to think a bit more:

Grid Method for Multiplication

This final worksheet takes it considerably further as you will need to think of thousands and millions.

Tuesday 19th May Once again, some simple questions to start and ensure you are confident with how to x by 10, 100, 1000

3 x 10 7 x 100 8 x 1000 23 x 10 766 x 100 765 x 1000 4563 x 10 656001 x 100 90119000 x 1000 Now we will look at why we are calculating these in the way we are.

Multiplying by 10, 100, 1000

When we multiply a number by 10, 100, or 1000, we move the digits of the number to the left: one place for 10; two places for 100; and three places for 1000. Notice that the number of places we move the digits is the same as the number of zeroes? For example, multiplying by 100 means moving the figures two places to the left.

Now have a go with the calculations above. Check your answers at the bottom of this page and then try the tasks for today.

Remember when we multiply by ten units become tens, tens become hundreds and hundreds become thousands. See below


5 6 1

561 x 10 = 5610


5 6 1 0

300 70 9000 340 890 3200

Worksheet one goes up to 10,000

X 10 X 100 X1000 X10000

4

6 3

45

34

56

345

346

874 876

9032

9430

3461

3461

65780

54246 245490

46586359

Worksheet 2 Goes up to 1000000

X1000 X10000 X100000 X1000000

43

33

8389

324

23

234 543

7879

644

24

67

568

3567 24

568

5768

25802

687000

340

560

Worksheet 3 Mixes between questions

453426 X10

355 X100

4767 X10 754 X100

90 X10

53686 X1000

6776 X10

553 X100

6568 X1000

35 X10000 56704 X100

670 X1

Wednesday 20th May Good morning or afternoon depending on when you read this. I’m hoping you now feel secure in x 10, x 100, x 1000 and further. I also hope you can see how these calculations work. To make sure you do, try the starter below.

Starter I used the example below to show how the numbers move when we multiply by 10, 100, 1000


5 6 1

561 x 10 = 5610


5 6 1 0 Now complete the examples below using the same style

74 x 10 = ?


7 4

X 10 = …………. (show your answer below)


401X 100


6 1

X 100 = ………..(show your answer below)


Today we are looking at decimals. So first you need to consider the place value of decimals. I think by now you are confident with the place values below

Place Vale Thousands Hundreds Tens Units

Number

But have you considered what happens when we add a decimal point?

Place Value

Hundreds Tens Units Tenths Hundreds Thousandths

Ten units make one ten and ten tens make one hundred. Numbers get bigger

Numbers get smaller Moving right of the decimal point the value reduces (gets smaller) So 0.1 is one tenth of one unit. It means we have taken one unit and divided (split) it into ten equal pieces and we have one of those pieces. If we had 0.3 it would mean we had taken one unit and divided (shared) it into ten equal pieces and have kept three. How many tenths is 0.6? So moving to the second decimal place we have hundredths. One hundredth is when we have taken one unit and divided (shared/split) it into one hundred pieces. Imagine how small that would be? If you took ten of those pieces it would be the same size as one tenth. So one tenth is 1/10 or 0.1 One hundredth is 1/100 or 0.01 Guess what a thousandth is? Absolutely right it is one unit divided into a thousand pieces and keeping one. It’s very small.

Worksheet one is to practise place values beyond the decimal. Write the numbers in the place value charts below.

hundreds tens Unit tenths hundredths thousandths







0.853

1.78

43.098

431.089

0.801

70.985

0.0978

Worksheet two Rewrite the place value charts as a number

Work sheet 3


5 4 0 0 9


7 1 3 5 1


5 0 6 7


3 5 4 0 9


4 0 0 5


3 4 5 5 5


3 5 6 0 3

This one will check you understand all that has been taught so far.

1.) How many tenths in 34.945

2.) How many hundredths in 34.902

3.) How many hundredths in 3 tenths?

4.) Which is bigger 34.903 or 34.09945 The last question is similar to questions we have practised in class. These unusually say which is largest and why? 456 or 478? Your answer would be 478 is largest as they both have 4 hundreds but 478 has two more tens than 456. So when looking at decimal numbers 7.121 is larger than 7.0994 because 7.121 has one tenth and 7.0994 has no tenths. For the following questions explain which is larger and why.

5.) 0.873 or 0.945

6.) 0.3881 or 0.19

7.) 0.1 or 0.0911

8.) 0.67 or 0.64

9.) 0.45 or 0.49

Thursday 21st May So, you’ve mastered place values for decimal points. Now you are going to use that knowledge to multiply decimal points by ten, hundred and a thousand. To confirm that knowledge complete the starter below.

Starter 1. How many tenths in 3.981? 2. How many hundredths in 45.9421? 3. How many tenths in 0.802? 4. How many thousandths in 0.1094? 5. How many hundredths in 301.5913?

Just like when we multiply whole numbers by 10, 100 and a 1000 when you multiply a decimal you are going to move the numbers left. See the examples below

hu

nd

red

s

ten

s

un

its

. ten

ths

hu

nd

red

ths

Tho

usa

nd

ths

h

un

dre

ds

ten

s

un

its

. ten

ths

hu

nd

red

ths

Tho

usa

nd

ths

4 . 5 1 X10 4 5 . 1

5 6 . 0 9 1 X10 5 6 0 . 9 1

7 . 2 0 3 X100 7 2 0 . 3

0 . 3 1 X100 3 1 .

Take your time to look at the table above. You will see that the numbers all remain in the same order they just move left. Using this method work out the following: 24.89 x 10 6.901 x 100 67.091 x 10 The worksheets today will practise the skills learnt today.

hu

nd

red

s

ten

s

un

its

. ten

ths

hu

nd

red

ths

Tho

usa

nd

ths

hu

nd

red

s

ten

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un

its

. ten

ths

hu

nd

red

ths

Tho

usa

nd

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. X .

. X .

. x .

Worksheet one has the place value tables to help.











24.967 x 10

45.902 x 100

4.891 x 100

30.901 x 10

40.043 x 10

Worksheet 2 This time I’ve not included the place value charts so that you can work it out without them. I have grouped them though so that you are practising each skill in turn.

1. 45.90 x 10 2. 356.896 x10 3. 350.86 x 10 4. 402.089 x 10 5. 34.0923 x 10 6. 40.095 x 100 7. 345.097 x 100 8. 569.092 x 100 9. 34.094 x 100 10. 23.0974 x 100 11. 2.098 x 1000 12. 44.095 x 1000 13. 678.093 x 1000 14. 309.097 x 1000 15. 23.098 x 1000

Worksheet 3 This time they are muddled up and there is no place value chart

1. 45.09 x 10

2. 40.09 x 100

3. 329.07 x 10

4. 783.9034 x 100

5. 45.0965 x 10

6. 45.096 x 1000

7. 904.0976 x 10

8. 457x 23.986 x 10

9. 56.097 x 1000

10. 764.9864 x 10

11. 87.096 x 10000

12. 65.90 x 1000

13. 56.09 x 100

14. 5.097 x 1000

Friday 22nd May The starter is a speedy re-cap of all you have completed so far.

Starter 456 x 100 67.095 x 100 673 x 1000 984.02 x 10 457.0342 x 1000 56.9823 x 10 80.053 x 100 45.98 x 1000 456x 1000 654 x 10 8.043 x 100 Well another week over and another skill secured. We are going to do something different today using the skills you have learnt. We use decimals in every day life when calculating money. Consider the prices of eggs below.

Instead of thinking of hundreds, tens and units we think of pounds, tens and pennies. Also when multiplying by 10 we could be multiplying by a quantity. If I needed ten packs of eggs costing £2.25 it would cost me £22.50 So using your multiplying decimals knowledge answer the following questions.

How much would ten of each of the above cost?

How much would 100 of each of the above packets cost?

How much would a thousand of each of these cost?

Finally, we like to finish with a game so here is the one for this week. I found this one on GamesforGains so we will thank Brittany for this one.

Playing the game:

Number of players: 2-4 1. Shuffle the deck of cards. Be sure that all face cards and Jokers have been removed. Place the deck of cards in a pile facedown in the center of the table.

2. Each player takes a turn taking one card from the top of the pile. Players place the card face-up directly in front of them so that all players can see each card that has been drawn.

3. Each player looks at the number on the card that he/she drew from the pile. Then, each player looks at "Round 1" on their score sheet to decide which place value to assign the number. The player can only write that number under one place value column (hundreds, tens, ones, tenths, hundredths, or thousandths). Players should not show their opponents where they wrote the number on their score sheet. Once each player has written down the number in a place value column, it cannot be changed at any point during the game.

• In this game, drawing the 10 card does not represent 10, but represents the number 0.

. Players repeats steps 1-3 until all 6 place value columns have been filled in (which means that 6 cards should have been drawn by each player).

5. Players show their final number to their opponents to determine who has written the highest number.

6. The player with the highest number must read his/her decimal aloud correctly (i.e. one hundred and seven thousandths, not one hundred point zero zero seven) in order to score the points.

• If the player with the highest number reads his/her decimal aloud correctly, he/she gets 1 point for the round. The other players do not get any points.

• If the player with the highest number does not read his/her decimal aloud correctly, he/she does not get any points. Every other player gets 1 point for the round.

Materials needed:

1. Score sheet - 1 per player - copy from here

2. Deck of regular playing cards (remove all Jacks, Queens, Kings, and Jokers)

3. Pencil for each player

7. Place all of the used cards back into the pile of cards and shuffle the entire pile again. Begin the next round by repeating the same steps. Play ends after 10 rounds have been played.

Monday 18th May - Ellesmere College, Leicester

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