Welcome to the Maths Department at Ballakermeen … a triangle PQR with lines PQ = 8cm, QR = 5cm and...

Welcome to the Maths Department at

Ballakermeen High School

Aim of this evening…

ContactsHead of Maths – Mrs J Murphy

[email protected] in Faculty – Mr D Crawford

[email protected] KS4 Coordinator – Mr D Godwin

[email protected] KS3 Coordinator – Miss J Wallace

[email protected]

Activity 1

Long multiplication

All 3 methods are accepted.

Activity 2

The Bar Model

What Are Bar Models?

9 7

16

9

716

0 1 2 3 4 5 6 7 8

A Consistent Picture

2 of 20 = ?5Share 20 in the ratio 2:3

20

:4 4 4 4 4

5 x 4 = ?4 + 11 = ?

0 4 ?

11

A Consistent Picture4 + 11 = ?

4 11

?15 - 4 = ?

4

15

?

5 x 4 = ?

4

?

4 4 4 4

20 ÷ 5 = ?

?

20

? ? ? ?

2 of 20 = ?5 20

?

Share 20 in the ratio 2:3

20

? ?

The importance of bar modelling

“Instead of relying on superficial and unreliable clueslike key words, the simple visual diagrams help children

understand why the appropriate operations make sense.”

Beckmann 2014

“Although bar models will not always help children carry out required calculations, they are

clearly designed to help children decide which operations to use.”

Beckmann 2014

“Model drawing trains children to think analytically, providing an important transition

between the concrete and the abstract.”Forsten 2014

“When children have experience and

exposure to many concrete materials, they

are able to develop the ability to visualise”

Ban Har 2016

“Bar models are a tool to help children

visualise stories”

Ban Har 2016

Bar Modelling

Bar Modelling

Model Calculations

Solve… Matthew has a 300g block of cheese. He eats 2

5of the cheese

and puts the rest back in the fridge.

How much cheese did Matthew put back in the fridge?

300g60300 ÷ 5 =

Eats?180

Put back

3 x 60 = 180 60 60 60 60 60

Bar Modelling

Model Calculations

3a + 4 = a + 8

a 4a a

8

3a + 4 a + 8=

2a + 4 = 8

2a = 4

-a

-4 -4

-a

a 4

÷2 ÷2a = 2

Bar Modelling

Solve 2a + 3 = a + 7

a a 3

a 7

2a + 3 = a + 7-a -a

a + 3 = 7-3 -3

4a = 4

Activity 3

Add/Subtract Negative Numbers

Please encourage students to draw a number line.

Number Line

Negative Numbers on the Number Line

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

Negative numbers are useful for representing quantities that can have values below zero. Examples include temperature, debt and heights below sea level. The part of the number line that consists of the positive and negative whole numbers, together with zero, are called the integers.

To add numbers on a number line simply count to the right.

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

ADD +

Subtract -

To subtract numbers on a number line simply count to the left.

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

Adding +2 + 5 = 7

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

0 + 6 = 6

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

-3 + 7 = 4

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

-5 + 5 = 0

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

- 4 + 7 = 3


0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

Subtracting - 7 - 5 = 2

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

6 - 6 = 0

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

4 - 7 = -3

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

0 - 5 = -5

0 1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

- 2 – 7 = -9


Activity 4

COORDINATE BINGO!!!

(Resources/Equipment: Worksheet and Pencil)

Activity 5

Triangle constructions(Equipment: Pencil, Ruler, Compass, Protractor

and Squared paper)

A B

C

Construct a triangle ABC with side lengths AB = 9cm, AC = 5cm and BC = 7cm.

• Draw a 9cm line and label the ends A and B. This is the line AB.

• Set your compass to 5cm and with the point on A draw an arc.

• Set your compass to 7cm and with the point on B draw an arc.

• Label this point C and join A to C then B to C to get the lines AC and BC.

9cm

5cm 7cm

Construct a triangle PQR with lines PQ = 8cm, QR = 5cm and PQR = 40°

• Draw an 8cm line and label the ends P and Q. This is the line PQ.

• Place the centre of the protractor on Q with the 0° line pointing to P.

• Measure a 40° angle clockwise from 0°. Mark it with a dot.

• Draw a 5cm line from Q through the dot. Label the end of this line R.

• Join up P and R to complete the triangle.

P Q

.

R

40

°8cm

5c

m

P Q

Construct a triangle PQR with lines PQ = 8cm, PQR = 40° and RPQ = 30°

• Draw an 8cm line and label the ends P and Q. This is the line PQ.

• Place the centre of the protractor on Q with the 0° line pointing to P.

• Measure a 40° angle clockwise from 0°. Mark it with a dot.

• Draw a line from Q through the dot.

• Place the centre of the protractor on P with the 0° line pointing to Q.

• Measure a 30° angle anticlockwise from 0°. Complete as with other angle.

• Point R is where the two lines meet.

.

R

40

°8cm

.30

°

Activity 6

MyMaths and Its Learning Quick Introduction

Year 7, 9 and 11 Homework/Catch up ClubWednesday 12.02 in D6

Friday 12.02 in D4

Activity 7

Adding and subtracting fractions

Activity 8

Doubling and Halving

(Mini whiteboards)

Double and Halve

Double and halve the numbers given when you are asked to.

Year 7

24 Double itHalve it 4812

15 Double itHalve it 307.5

37 Double itHalve it 7418.5

Activity 9

Percentages of Amounts

(Mini whiteboards)

PERCENTAGES

£1.80

100%

25%15%

5%

30%20%

10%

75%

50%

54p

9p

27p90p 45p

£1.35

18p36p

PERCENTAGES

£1.20

100%

25%15%

5%

30%20%

10%

75%

50%

36p

6p

18p60p 30p

90p

12p24p

PERCENTAGES

£68

100%

25%15%

5%

30%20%

10%

75%

50%

£20.40

£3.40

£10.20£34 £17

£51

£6.80£13.60

Activity 10

What answer do you get for this question?….

Do you agree with the person next to you?...

2 + 3 x 6

20

5 + 4 x 2

13

6 + 8 ÷ 2

10

5 + 10 ÷ 2

10

16 - 6 ÷ 2

13

18 – 6 x 2

6

13 – 2 x 4

5

26 + 14 ÷ 7

28

7 x 3 + 5

26

8 x 9 - 9

63

(4 + 3) x 8

56

(9 – 6) x 12

36

(7 + 5) x 4

48

20 ÷ (10 – 5)

4

16 x (3 – 2)

16

40 ÷ (16 – 8)

5

2 x 4 + 5 x 3

23

8 x 6 + 2 x 7

62

9 x 3 – 4 x 2

19

8 x 5 – 6 x 3

22

Thank you very much for your time and we hope you

leave this evening with a little more love for Maths!!

Welcome to the Maths Department at Ballakermeen … a triangle PQR with lines PQ = 8cm, QR = 5cm and...

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Transcript of Welcome to the Maths Department at Ballakermeen … a triangle PQR with lines PQ = 8cm, QR = 5cm and...