L.O.1 To be able to recall multiplication and division facts involving the 2,3,4,6,7 and 8 times tables.

Write answers to these questions in your books: 1. What is the product of 7 and 8? 2. Which factors of 60 are shown on the sheet? 3. Which numbers are multiples of 6? 4. Which numbers are square numbers? 5. What is 21 divided by 3? 6. Which numbers are in the 7x table? 7. Which numbers are divisible by 3? 8. Which numbers have no other factors?

L.O.2 To be able to relate fractions to division and to use division to find simple fractions, including tenths and hundredths, of numbers and quantities.

32 40 24 36 56 44 140 84 Copy these numbers into your book as they are here. Underneath each write what half of that number is. Under that write what a quarter of each of these numbers is.

32 16 8 8 8 8 8 This diagram represents 32 divided by 4. 32 16 8 This diagram represents 32 divided by 4. Q. How can we use this grid to find ¾ of 32? 8 8 8 8

We can add 8 + 8 + 8 = 24 This is the same as finding: ¼ + ¼ + ¼ or ¼ x 3 Find ¾ of each of the other 2 numbers by the same method.

9 21 36 60 330 150 99 270 Copy these numbers into your book as they are here. Underneath each write what one third of that number is. Q. How can we use these answers to find two thirds of the number?

2/3 = 1/3+1/3 or 1/3 x 2

4/5 Q. How can we find 4/5 of 30?

30 6 6 6 6 6 1/5 of 30 is 6 4/5 of 30 = 1/5 x 4 4/5 of 30 = 6 x 4 = 24

Q. How can we find 3/5 of 35? Q. How can we find 2/5 of 40?

Discuss these problems with two other people in your group and on the paper provided write down how you solve them. Be prepared to tell the rest of the class how you did it.

To find 3/5 of 35 we divide 35 by the denominator 5 and multiply the answer by the numerator 3. LOOK…… 35 / 5 = 7 7 x 3 = 21 3/5 of 35 = 21

To find 2/5 of 45 we divide 45 by the denominator 5 and multiply the answer by the numerator 2. LOOK…... 45 / 5 = 9 9 x 2 = 18 2/5 of 45 = 18

1/3 ______ 36 2/3 ______ Q. What is 1/3 of 36? What is 2/3 of 36?

2/3 _______ 24 36 3/3 _______ 4/3 _______ 1/3 _______ 12 1/3 _______ 12 2/3 _______ 24 36 3/3 _______ 4/3 _______ Q. What is 3/3 of 36 (i.e. all of it) ? Q. What is 4/3 of 36 (i.e. more than all of it) ?

21 (sevenths) ; 56 ( eighths). 45 ( fifths) ; 48 ( sixths) ; 21 (sevenths) ; 56 ( eighths). With the other two people in your group find fifths of 45 i.e. 1/5; 2/5; 3/5; 4/5; 5/5; 6/5 sixths of 48; sevenths of 21: eighths of 56. Q. What is 6/7 of 21?

Find answers to these sums: Tetrahedra: 2/3 of 30; ¾ of 32; 2/5 of 45 Spheres: ¾ of 36; 2/3 of 24; 4/5 of 60 Prisms: 2/5 of 65; 3/8 of 72; 2/7 of 63; 5/6 of 42; 2/9 of 27; 4/11 of 121. 6 minutes

£ 520 32m. 28 kg. Q. What is 3/10 of $ 520? Q. If 3/8 of 32m. is 12m., what is 6/8 of 32m? What is ¾ of 32m? Q. What is 1/7 of 28kg? What is 3/7; 6/7; 9/7 of 28kg? Be prepared to explain how you worked out the answers!

By the end of the lesson children should be able to: Relate fractions to division. Find fractions to numbers and quantities.

L.O.1 To be able to multiply or divide whole numbers up to 10 000 by 10 or 100

Answer the questions neatly in your books. Put 1 to 10. 10 minutes

L.O.2 To be able to relate fractions to division and to use division to find simple fractions, including tenths and hundredths of numbers and quantities.

Remember….. 3/10 of £520 = (£520 / 10)x 3 = £52 x 3 = £156 (The brackets show which calculation to do first) Let’s try this: 4/5 of 35m. = Copy this calculation into your book as a guide.

£120 was shared out in this way. A had 1/6 B had 2/5 C had 3/10 How much did D have? You have three minutes to work out the answer with your group.

How did you do it? Look: A had 1/6 of £120 = £120 / 6 = £20 B had 2/5 of £120 = (£120 /5)x2 = £24x2 = £48 C had 3/10 of £120 =(£120/10)x3 = £12x3 = £36 £20 + £48 + £36 = £104 D gets £120 - £104 = £16

20 minutes

It is school activity day for the 160 pupils at Lovemaths Junior School. Q. 3/10 of the children play table tennis. How many children is that? Q. 2/5 of the children play football. How many is that? Q. ¼ of the pupils choose a cookery activity. How many are in the kitchen? Q. What number of the pupils can’t decide what to do?

By the end of the lesson children should be able to: Relate fractions to division. Find fractions of numbers and quantities.

To be able to count steps of a quarter, a third, a half and a fifth. L.O.1 To be able to count steps of a quarter, a third, a half and a fifth.

We are going to count in quarters. 0 ¼ 2/4 ¾ 4/4 5/4 6/4 7/4 8/4 9/4 10/4

We are going to count in quarters. 0 ¼ 2/4 ¾ 4/4 5/4 6/4 7/4 8/4 9/4 10/4 1 11/4 12/4 13/4 2 21/4 22/4

We are going to count in thirds. 0 1/3 2/3 3/3 4/3 5/3 6/3 7/3 8/3 9/3 10/3 1 11/3 12/3 2 21/3 22/3 3 31/3

We are going to count in halves. 0 ½ 2/2 3/2 4/2 5/2 6/2 7/2 8/2 9/2 10/2 1 1½ 2 2½ 3 3½ 4 4½ 5

We are going to count in fifths. 0 1/5 2/5 3/5 4/5 5/5 6/5 7/5 8/5 9/5 10/5 1 11/5 12/5 13/5 14/5 2

L.O.2 To be able to order a set of fractions including mixed numbers and position them on a number line.

4/4 = 1; 3/3 = 1; 2/2 = 1; 5/5 = 1 Q. What other fractions are equivalent to 1. Q. If a fraction is equivalent to 1 what can we say about the numerator and the denominator?

4 5 8/4; 6/3; 4/2; 10/5 Q. How else can we represent these fractions? 8/4; 6/3; 4/2; 10/5 Q. How else can we represent these fractions? Q. What fractions would be equivalent to: 3 4 5 Q. How do we decide if a fraction is equivalent to a whole number? [Hint: Is it something to do with the relationship between the numerator and the denominator?]

6 10 3 4 Q. What must the numerators be to make these fractions equivalent to 5 ? Why?

36 40 120 Q. What must the denominators be to make these fractions equivalent to 4 ? Why?

16/5 > 15/5 (= 3) ; 16/5 < 20/5 (= 4) 16 / 5 Q. Which whole numbers does this fraction lie between? Remember these signs? > < Look…. 16/5 > 15/5 (= 3) ; 16/5 < 20/5 (= 4)

31/5 is called a MIXED NUMBER 16/5 = 31/5 31/5 is called a MIXED NUMBER because it’s a mixture of a whole number ( 3 )and a fraction (1/5)

16/5 = 31/5 31/5 0 1 2 3 4 5 This is where our mixed number will go on a number line.

Copy carefully into your book: 9/4 > 8/4 = (2) ; 9/4 < 12/4 =(3) 9/4 = 21/4 11/3 > 9/3 = (3); 11/3 < 12/3 = (4) 11/3=32/3 29/6 >24/6 = (4); 29/6 < 30/6 = (5) 29/6= 45/6 11/10>10/10 = (1); 11/10< 20/10 = (2) 11/10=11/10

9/4 11/3 29/6 11/10 11/10 21/4 31/5 32/3 45/6 0 1 2 3 4 5 This is where our mixed numbers will go on a number line.

Copy these fractions into your books then write underneath each one its value as a mixed number. 9/4 7/4 5/2 15/8 23/8 19/8 Put the mixed number values on a number line.

REMEMBER: ¼ = 2/8 ½ = 4/8 ¾ = 6/8

Do worksheet.

We are going to convert these to mixed fractions and put them on the number line. 22/3 7/3 13/4 3/2 5/4 0 1 2 3 Q. Which is larger 22/3 or 21/4 ?

By the end of the lesson children should be able to : Convert improper fractions to mixed numbers; Place fractions in order.

L.O.1 To be able to round numbers with one decimal place to the nearest integer

Positive and Negative whole numbers are called integers.

Q. How do we round these numbers to the nearest integer? 9.1 9.3 9.5 9.6 9.9 Q. How do we round these numbers to the nearest integer?

9.1 9.3 9.5 9.6 9.9 9 10

Round these numbers to the nearest integer: 10.7 3.2 1.1 0.9 0.1

4 Q. Which numbers with 1 decimal place round to 4?

The numbers from 3.5 to 4.4 round to 4. 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4

In your book write which numbers with one decimal point will round to each of these: 1. 7 2. 1 3. 0

L.O.2 To be able to round a number with one or two decimal places to the nearest integer.

3 4 I need volunteers to draw these numbers on the number line. (but only if you can say the number correctly.) 3.32 3.68 3.94 3.17 3 4 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90

3 4 Would 3.32 be rounded down to 3 or up to 4? 3.32 3.68 3.94 3.17 What about the other numbers? 3.32 3.68 3.94 3.17 3 4 3.17 3.32 3.68 3.94 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90

Q. Which digit is most important when we are deciding how to round numbers to the nearest integer? Q. How does the number 5 as the first decimal digit affect whether we round a number up or down?

In your book draw a number line from 7 to 8. Put these numbers on it. 7.13 7.74 7.57 7.28 7.83 7.46

7 8 You should have a line that looks like this: 7.13 7.28 7.46 7.57 7.74 7.83

In your book round these lengths to the nearest metre: 5.73 m 2.97 m 12.03 m 8.48 m 9.25 m 18.52 m

I start with a number which has two decimal places I start with a number which has two decimal places. I round it to the nearest integer. The answer is 3. Q. What could my number be? Q. What is the largest / smallest number I could have? In your books round each amount on the next slide to the nearest £.

Write some numbers which have 2 decimal points and ask your partner to round them to the nearest integer.

£3.49 Q. Will this round to £3 or £4?

By the end of the lesson children should be able to: Round decimals with one or two decimal places to the nearest whole number.