welcome to the maths department at ballakermeen … a triangle pqr with lines pq = 8cm, qr = 5cm and...
TRANSCRIPT
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
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
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
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
Negative Numbers on the Number Line
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
32 Double itHalve it 6416
40 Double itHalve it 8020
48 Double itHalve it 9624
15 Double itHalve it 307.5
28 Double itHalve it 5614
16 Double itHalve it 328
44 Double itHalve it 8822
37 Double itHalve it 7418.5
14 Double itHalve it 287
42 Double itHalve it 8421
18 Double itHalve it 369
52 Double itHalve it 10426
64 Double itHalve it 12832
86 Double itHalve it 17243
74 Double itHalve it 14837
58 Double itHalve it 11629
68 Double itHalve it 13634
86 Double itHalve it 17243
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!!