Welcome to the Maths Department at Ballakermeen … a triangle PQR with lines PQ = 8cm, QR = 5cm and...
Transcript of Welcome to the Maths Department at Ballakermeen … a triangle PQR with lines PQ = 8cm, QR = 5cm and...
![Page 1: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/1.jpg)
Welcome to the Maths Department at
Ballakermeen High School
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Aim of this evening…
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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
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Activity 1
Long multiplication
All 3 methods are accepted.
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Activity 2
The Bar Model
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What Are Bar Models?
9 7
16
9
716
0 1 2 3 4 5 6 7 8
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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
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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
? ?
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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
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Bar Modelling
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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
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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
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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
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Activity 3
Add/Subtract Negative Numbers
Please encourage students to draw a number line.
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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.
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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
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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
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Activity 4
COORDINATE BINGO!!!
(Resources/Equipment: Worksheet and Pencil)
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Activity 5
Triangle constructions(Equipment: Pencil, Ruler, Compass, Protractor
and Squared paper)
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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
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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
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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
°
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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
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Activity 7
Adding and subtracting fractions
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Activity 8
Doubling and Halving
(Mini whiteboards)
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Double and Halve
Double and halve the numbers given when you are asked to.
Year 7
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24 Double itHalve it 4812
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32 Double itHalve it 6416
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40 Double itHalve it 8020
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48 Double itHalve it 9624
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15 Double itHalve it 307.5
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28 Double itHalve it 5614
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16 Double itHalve it 328
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44 Double itHalve it 8822
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37 Double itHalve it 7418.5
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14 Double itHalve it 287
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42 Double itHalve it 8421
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18 Double itHalve it 369
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52 Double itHalve it 10426
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64 Double itHalve it 12832
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86 Double itHalve it 17243
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74 Double itHalve it 14837
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58 Double itHalve it 11629
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68 Double itHalve it 13634
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86 Double itHalve it 17243
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Activity 9
Percentages of Amounts
(Mini whiteboards)
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PERCENTAGES
£1.80
100%
25%15%
5%
30%20%
10%
75%
50%
54p
9p
27p90p 45p
£1.35
18p36p
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PERCENTAGES
£1.20
100%
25%15%
5%
30%20%
10%
75%
50%
36p
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18p60p 30p
90p
12p24p
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PERCENTAGES
£68
100%
25%15%
5%
30%20%
10%
75%
50%
£20.40
£3.40
£10.20£34 £17
£51
£6.80£13.60
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Activity 10
What answer do you get for this question?….
Do you agree with the person next to you?...
![Page 53: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/53.jpg)
2 + 3 x 6
20
![Page 54: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/54.jpg)
5 + 4 x 2
13
![Page 55: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/55.jpg)
6 + 8 ÷ 2
10
![Page 56: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/56.jpg)
5 + 10 ÷ 2
10
![Page 57: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/57.jpg)
16 - 6 ÷ 2
13
![Page 58: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/58.jpg)
18 – 6 x 2
6
![Page 59: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/59.jpg)
13 – 2 x 4
5
![Page 60: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/60.jpg)
26 + 14 ÷ 7
28
![Page 61: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/61.jpg)
7 x 3 + 5
26
![Page 62: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/62.jpg)
8 x 9 - 9
63
![Page 63: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/63.jpg)
(4 + 3) x 8
56
![Page 64: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/64.jpg)
(9 – 6) x 12
36
![Page 65: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/65.jpg)
(7 + 5) x 4
48
![Page 66: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/66.jpg)
20 ÷ (10 – 5)
4
![Page 67: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/67.jpg)
16 x (3 – 2)
16
![Page 68: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/68.jpg)
40 ÷ (16 – 8)
5
![Page 69: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/69.jpg)
2 x 4 + 5 x 3
23
![Page 70: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/70.jpg)
8 x 6 + 2 x 7
62
![Page 71: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/71.jpg)
9 x 3 – 4 x 2
19
![Page 72: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/72.jpg)
8 x 5 – 6 x 3
22
![Page 73: Welcome to the Maths Department at Ballakermeen … 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](https://reader036.fdocuments.net/reader036/viewer/2022081800/5b1ec4617f8b9a8a3a8bf718/html5/thumbnails/73.jpg)
Thank you very much for your time and we hope you
leave this evening with a little more love for Maths!!