Lesson 1: Similar Shapes Learning intention (LI): Linear (edges only) · 2019. 5. 29. · 5 Similar Shapes.notebook 1 May 29, 2019 Sep 2213:40 Learning intention (LI): Linear (edges

5 Similar Shapes.notebook

1

May 29, 2019

Sep 2213:40

Learning intention (LI): Linear (edges only)

Success Criteria (Today we will..)• Understand the term 'congruent' means the same but in a different position. • Be able to find a scale factor and apply this to find a missing length

Lesson 1: Similar Shapes

I can solve problems involving similar figures.


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May 29, 2019

Sep 2213:40

Shapes are similar if they have corresponding angles and edge lengths in the same ratio

Similar490 230

3cm230

108012cm

• Angles are corresponding (same and in same places)• 3 multiplied by 4 is 12. '4' is called the scale factor

490

1080

• Circle two corresponding edges• If going bigger the scale factor is >1, if going smaller the scale factor is 1, if going smaller the scale factor is


3

May 29, 2019

Sep 2213:40

Shapes are similar if they have corresponding angles and edge lengths in the same ratio

Similar490 230

3cm230

108012cm

• Angles are corresponding (same and in same places)• 3 multiplied by 4 is 12. '4' is called the scale factor

490

1080

• Circle two corresponding edges• If going bigger the scale factor is >1, if going smaller the scale factor is


4

May 29, 2019

Sep 2213:40

Learning intention (LI): Linear (edges only)


Plenary Slide: Lesson 1: Similar Shapes

I can solve problems involving similar figures.

25cm7cm

16cmy cm


5

May 29, 2019

Sep 2213:40

Learning intention (LI): Linear (simple)Lesson 2: Similar Shapes



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May 29, 2019

Sep 2213:40

Task: (Int2 bk 2)Page 50 Ex 5.2Q3, Q4, Q6(a)(b), Q7, Q8(a)(b)

Example

Going smaller........smaller bigger

Going bigger........bigger smaller

• These are similar because

280 1140

18cm

y cm

280

380

18cm

14cm


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Sep 2213:40

Learning intention (LI): Linear (simple)Plenary Slide: Lesson 2: Similar Shapes



8

May 29, 2019

Sep 2213:40

Learning intention (LI): Area Lesson 3: Similar Shapes

Success Criteria (Today we will..)• Understand the term 'congruent' means the same but in a different position. • Be able to find a scale factor and apply this to find a missing length• When finding missing area we simply square the scale factor


9

May 29, 2019

Sep 2213:40

5cm

2cm

Area = 10cm2

x cm

15cm

Area = 90cm2

40cm

60cm

Area = 1200cm2

6cm

4cm

Area = 12cm2


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May 29, 2019

Sep 2213:40

For area: 1) Find the scale factor and square it. 2) Multiply by the original area

Examples

6cm

2cm

Area = 12cm2

24cm

8cmArea = ? cm2

Area = 35cm2

18cm

Area = ? cm2

5cm

Task: (Int2 bk 2)Page 54 Ex 5.4Q3, Q4, Q5, Q6, Q8


11

May 29, 2019

Sep 2213:40

Learning intention (LI): Area Plenary Slide: Lesson 3: Similar Shapes

Success Criteria (Today we will..)• Understand the term 'congruent' means the same but in a different position. • Be able to find a scale factor and apply this to find a missing length• When finding missing area we simply square the scale factor


12

May 29, 2019

Sep 2213:40

Learning intention (LI): Triangles Lesson 4: Similar Shapes

Success Criteria (Today we will..)• Understand the term 'congruent' means the same but in a different position. • Be able to find a scale factor and apply this to find a missing length• Know when diagrams are combined we need to begin by sketching and labelling

two separate diagrams first.


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Sep 2213:40

ImportantIf given one diagram that combines shapes first draw and label two different shapes.

Examplex

6

15

5

x

15

65


Examplex

6

15

5

x

15

65


Examplex

6

15

5

x

15

65


14

May 29, 2019

Sep 2213:40


Examplex

6

15

5

x

15

65

Task: (Teachers ref: Int2 bk 2)Page 52 Ex 5.3 Q1(a)(b)(c)(d), Q3, Q6(a)(b)(c)(d)


15

May 29, 2019

Sep 2213:40

Learning intention (LI): Triangles Plenary Slide Lesson 4: Similar Shapes

Success Criteria (Today we will..)• Understand the term 'congruent' means the same but in a different position. • Be able to find a scale factor and apply this to find a missing length• Know when diagrams are combined we need to begin by sketching and labelling

two separate diagrams first.

17

4y

8

17

8

4y


16

May 29, 2019

Sep 2213:40

Learning intention (LI): VolumeLesson 5: Similar Shapes

Success Criteria (Today we will..)• Understand the term 'congruent' means the same but in a different position. • Be able to find a scale factor and apply this to find a missing volume by cubing

the scale factor


17

May 29, 2019

Sep 2213:40

5cm

2cm 2cm

15cm

6cm6cmVolume = 2 x 2 x 5

= 20cm3Volume = 6 x 6 x 15 = 540cm3


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May 29, 2019

Sep 2213:40

For volume: 1) Find the scale factor and cube it. 2) Multiply by the original volume

12cm

Volume = ? mlVolume = 540ml

25cm

Note: 1cm = 1ml3Example


12cm


25cm



12cm


25cm



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May 29, 2019

Sep 2213:40

Task: (Teachers ref: Int2 bk 2)Page 56 Ex 5.5 Q5, Q6, Q7, Q9, Q10


12cm


25cm


Learning intention (LI): VolumeLesson 5: Similar Shapes


20

May 29, 2019

Sep 2213:40

Learning intention (LI): VolumePlenary Slide: Lesson 5: Similar Shapes

Success Criteria (Today we will..)• Understand the term 'congruent' means the same but in a different position. • Be able to find a scale factor and apply this to find a missing volume by cubing

the scale factor

2014 Paper 2 (Calc allowed)


21

May 29, 2019

Sep 2213:40

2014 Paper 2

(Calc allowed)

2014 Paper 2

(Calc allowed)

2014 Paper 2

(Calc allowed)

Attachments

Significant Figures.doc

Rounding rules.docx

rounding off to dp.doc

Rounding to 1 and 2 dp.docx

Multiply by 10, 100 and 1000.docx

Circles State radius or diameter.ppt

Parts of a circle worksheet to glue in.doc

Circumference of a circle.doc

TriangularPrism9.pdf

1 Probabillity matching words to statements.docx

0 Sig fig starters ﴾1 sig fig﴿.docx

4a Patterns y = mx.docx

4b Patterns y = mx +c.docx

0 Sig fig starters ﴾2 sig fig﴿.docx

5 Gradient 7 diagrams, count sqaures, can glue into jotters Yellow sheet.pdf

5 Staright Line, table of values.docx

Establish a relationship between x and y Flashcard.docx

5 Straight Line, Ex 8.4.docx

6 Parts of a circle.doc

3 Similar to N5 06 Pythag 3D without 3D coordinates.docx

3 Pythags based on N5 06.docx

4 Angles mix.docx

Significant Figures

‘Significant figure’ is an extension on rounding.

Section A Round to one significant figure:

a) 36 820 b) 28 328

c) 82 178

d) 6 776

e) 2 056

f) 9 043

g) 1 746

h) 6 728

i) 768

j) 921

k) 651

L) 209

Section B

Round each number to one significant figure and then use this to estimate the answer, the first have been started for you:

a) 38 x 82 ≈ 40 x 80

b) 73 x 47 ≈ 70 x 50

=

=

c) 86 x 28 ≈

d) 41 x 29 ≈

=

=

e) 283 ÷ 42 ≈

f) 324 ÷ 82 ≈

=

=

g) 35 x 21 ≈

h) 352 ÷ 74 ≈

=

=

i) 67 x 44 ≈

j) 87 x 28 ≈

=

=

Section B Round to two significant figures:

a) 36 820 b) 28 328

c) 82 178

d) 6 776

e) 2 056

f) 9 043

g) 1 746

h) 6 728

i) 768

j) 921

k) 651

L) 209

Section C Round to the number of significant figures shown in brackets:

a) 7 845 (1 sf)

b) 78 312 (2 sf)

c) 89 (1 sf)

d) 9 321 (2 sf)

e) 12 897 (1 sf)

f) 891 (1 sf)

g) 89 123 (2 sf)

h) 9 245 (2 sf)

i) 67 (2 sf)

j) 2 189 (1 sf)

k) 789 234 (2 sf)

L) 102 673 (2 sf)

�

SMART Notebook

Rounding ....

......1 dp means one number after decimal point

......2dp means two numbers after decimal point

Rule: 5 or more increase otherwise leave alone!

Rounding ....




Rounding ....




Rounding ....




Rounding ....




Rounding ....




SMART Notebook

Copy each question and use the approximate sign (i.e ≈ )

1) Round these correct to nearest whole number:

a) 12.8 b) 24.689 c) 3.98 d) 1 487.2999

2) Round these correct to one decimal place:

a) 56.02 b) 3.48

c) 20.74 d) 4.07

3) Round the answers to one decimal place first and then do the sum:

a) 3.2 (( 1.8 b) 49.9 ( 21 c) 58 ( 4.2 d) 480 ( 2.8 e) 5.6 ( 21

f) 589.9 ( 56 g) 39.8 ( 18 h) 5.28 ( 1.2 i) 192.8 ( 44 j) 10.8 ( 5

4) Round each of these numbers to the given number of decimal places.

a) 14.827 (1 d.p.) b) 108.932 (1 d.p.) c) 2.0789 (2 d.p.)

d) 66.3328 (3 d.p.) e) 21.682 (2 d.p.) f) 24.308 (2 d.p.)

5) Round each of these numbers to the given number of decimal places.

a) 8.28792 (4 d.p.) b) 50.2351 (3 d.p.) c) 21.805 674 (3 d.p.)

d) 52.316 (4 d.p.) e) 23.3328 (3 d.p.) f) 0.008 026 (3 d.p.)

6) Arrange these in order of size, largest first:

12.01 12.14 12.5 12.8 12.09 12.07

Rounding

� EMBED Word.Picture.8 ��

_1013721863.doc

SMART Notebook

(Name: )

Rounding

1) Round the following to 1dp

a) 15.36 b) 45.86c) 19.42

d) 58.98e) 456.283 f) 1 254.397

g) 78.928h) 25.12547

2) Round the following to 2 dp

a) 23.546b) 48.475c) 125.367

d) 478.1256e) 14.7852f) 45.4598

g) 301.48756h) 1.458714

3) Use your calculator to answer the following sums and round to the the d.p as shown in brackets

a) 145 ÷ 23 (2 d.p)b) 856 ÷ 47 (1 d.p)

c) 783 ÷ 28 (2 d.p)d) 478 ÷ 192 (1 d.p)

e) 6582 ÷ 247 (2 d.p)f) 256 ÷ 48 (2d.p)

SMART Notebook

Multiplying by 10, 100, 1000

Copy and complete the following:

When you multiply a whole number by

· 10 means ___________

· 100 means ___________

· 1000 means ___________

Now do the following:

Section A

a) 53 x 10 b) 91 x 100 c) 32 x 1000 d) 87 x 10

e) 17 x 100 f) 2 x 1000 g) 76 x 100 h) 3 x 10

i) 10 x 87 j) 100 x 201 k) 801 x 10 L) 1000 x 5

m) 17 x 10 n) 100 x 32 o) 1000 x 32 p) 71 x 100

q) 109 x 100 r) 65 x 1 s) 87 x 10 t) 100 x 67

Example:

34

2 x

68

34 x 20 is the same as 32 x 2 x 10

68 x 10 = 680

Section B

a) 32 x 20 b) 81 x 20c) 63 x 20

d) 23 x 40 e) 47 x 30f) 72 x 60

g) 82 x 70 h) 13 x 90i) 59 x 30

Example:

34

2 x

68

34 x 200 is the same as 32 x 2 x 100

68 x 100 = 6 800

Section C

a) 21 x 200 b) 53 x 200c) 82 x 300

d) 92 x 300 e) 76 x 400f) 87 x 600

g) 43 x 900 h) 18 x 600i) 71 x 800

SMART Notebook

14cm

Radius?

3m

Diameter?

27cm

Radius?

8cm

Diameter?

9cm

Radius?

3cm

Diameter?

9cm

Radius?

12cm

Radius?

12cm

Diameter?

12cm

Radius?

12cm

Diameter?

2.8cm

Radius?

4.5m

Diameter?

7.1m

Diameter?

7.2mm

Radius?

8.1mm

Diameter?

17.2m

Radius?

SMART Notebook

Circles

The circumference is all the

The diameter cuts the circle in half all the way around………

The radius is from the centre to the edge……..

Name the parts of these circles marked by heavy bold lines.

Choose from radius, circumference, diameter.

a)

b)

c)

d)

e)

f)

g)

h)

Circles - Complete the following:

Circle Radius

Diameter

�

�

�

35cm

24cm

8cm

32cm

4cm

12cm

SMART Notebook

Calculate the circumference of the following:

1.

2.

3.

4.

5.


1.

2.

3.

4.

5.


1.

2.

3.

4.

5.


1.

2.

3.

4.

5.

18m

12cm

5cm

20cm

28cm

18m

12cm

5cm

20cm

28cm

18m

12cm

5cm

20cm

28cm

18m

12cm

5cm

20cm

28cm

SMART Notebook

http:/worksheetplace.com Score: /6

Name:_________________________________

Calculate the Volume

1.

10in

8 in

12.8 in

8 in

2.

11in

13 in

11.4

in 14.9 in

8 in

3.

9in

8 in

9.8

in 9.8in

9 in

4.

11in

14 in

11.7

in 14.9 in

11 in

5.

11in

16 in

19.4

in

12 in

6.

14in

9 in

14.6

in 14.9in

14 in

http:/worksheetplace.com Score: /6

Name:_________________________________

Calculate the Volume

1.

10in

8 in

12.8 in

8 in

V = 320 in³

2.

11in

13 in

11.4

in 14.9 in

8 in

V = 572 in³

3.

9in

8 in

9.8

in 9.8in

9 in

V = 324 in³

4.

11in

14 in

11.7

in 14.9 in

11 in

V = 847 in³

5.

11in

16 in

19.4

in

12 in

V = 1,056 in³

6.

14in

9 in

14.6

in 14.9in

14 in

V = 882 in³

Triangular-Prism-9

Triangular-Prism-9a

SMART Notebook

BROUGHTON HIGH SCHOOL

Mathematics Faculty

Probability

0 0.5 1

Impossible Even chance Dead cert

Less than likely More than likely

What word would you use for:

Chose a card from a fair pack and it is red

It will be sunny everyday in January

If I roll a fair six sided die

I will get a number greater than 6

The next person I say hello to will be female

I will have chips for my dinner tonight!

Think of an example for the following:

Evens

Fairly certain


Mathematics Faculty

Probability

0 0.5 1

Impossible Even chance Dead cert

Less than likely More than likely

What word would you use for:

Chose a card from a fair pack and it is red

It will be sunny everyday in January

If I roll a fair six sided die

I will get a number greater than 6

The next person I say hello to will be female

I will have chips for my dinner tonight!

Think of an example for the following:

Evens

Fairly certain

SMART Notebook

Round to 1 significant figure (1 s.f):

45 368

587 412

0.004758

368.145

=

=

=

=

26 123

639 741

0.00145

4.12541

=

=

=

=

3 874

108 999

0.00415

1.4758

=

=

=

=

6 410

703 965

0.001247

98.4125

=

=

=

=


45 368

587 412

0.004758

368.145

=

=

=

=

26 123

639 741

0.00145

4.12541

=

=

=

=

3 874

108 999

0.00415

1.4758

=

=

=

=

6 410

703 965

0.001247

98.4125

=

=

=

=


45 368

587 412

0.004758

368.145

=

=

=

=

26 123

639 741

0.00145

4.12541

=

=

=

=

3 874

108 999

0.00415

1.4758

=

=

=

=

6 410

703 965

0.001247

98.4125

=

=

=

=


45 368

587 412

0.004758

368.145

=

=

=

=

26 123

639 741

0.00145

4.12541

=

=

=

=

3 874

108 999

0.00415

1.4758

=

=

=

=

6 410

703 965

0.001247

98.4125

=

=

=

=


45 368

587 412

0.004758

368.145

=

=

=

=

26 123

639 741

0.00145

4.12541

=

=

=

=

3 874

108 999

0.00415

1.4758

=

=

=

=

6 410

703 965

0.001247

98.4125

=

=

=

=


45 368

587 412

0.004758

368.145

=

=

=

=

26 123

639 741

0.00145

4.12541

=

=

=

=

3 874

108 999

0.00415

1.4758

=

=

=

=

6 410

703 965

0.001247

98.4125

=

=

=

=

SMART Notebook

Number Patterns 1

1) a) Joseph is laying out tables, draw the next pattern:

1 Table 2 Tables3 Tables

2 Chairs 4 Chairs 6 Chairs

b) Complete the table below:

Number of Tables (T)

0

1

2

3

4

5

6

15

Number of Chairs (C)

2

4

6

c) Write a formula to find the number of chairs when you know the number of tables.

d) Use your formula to find the number of:

i) chairs needed for 20 tables.

ii) tables needed for 74 chairs.

Number Patterns 1

2) a) Brian is laying out tables, draw the next pattern:



b) Complete the table below:


0

1

2

3

4

5

6

15


3

6

9





SMART Notebook

Number Patterns

1) a) Joseph is laying out tables, draw the next pattern:



b) Copy and complete the table including zero number of tables:


0

1

2

3

4

5

6

15


3

5

7





2) a) Billy is laying out tables, draw the next pattern:



b) Copy and complete the table including zero number of tables:


0

1

2

3

4

5

6

15


5

7

9





3) Sophie is laying out tables:

a) Copy and complete the table including zero number of tables:


0

1

2

3

4

5

6

15


7

13

19

b) Write a formula to find the number of chairs when you know the number of tables.

c) Use your formula to find the number of:



4) Look at this pattern for fences:

a) Copy and complete the table including zero and one number of Posts:

Number of Posts (P)

0

1

2

3

4

5

6

15

Number of Slats (S)

4

8

12

b) Write a formula to find the number of slats when you know the number of posts.


i) slats needed for 21 posts.

ii) posts needed for 88 slats.

5) Look at this pattern for squares and triangles:

a) Copy and complete the table including zero and one number of Posts:

Number of Squares (S)

0

1

2

3

4

5

6

15

Number of Triangles (T)

3

5

7

b) Write a formula to find the number of triangles when you know

the number of squares.


i) triangles needed for 32 squares.

ii) squares needed for 71 triangles.

6) The table shows the cost (C) of hiring a scooter for several days (D).

Number of Days (D)

1

2

3

4

Total Cost (C)

20

25

30

35

a) Write a formula to find calculate how much the scooter would cost to hire when

b) Use your formula to find:

i) the cost for 12 days.

ii) the maximum numbers of days to hire the scooter with £95

7) Sarah makes and sells necklaces. She charges £4.50 per necklace plus a one off payment of £3.50 for postage and packing.

She stipulates the postage remains the same giving an example that 2 necklaces would cost £12.50 and 20 necklaces would cost £93.50.

What is the maximum number of necklaces she can buy for £40?

SMART Notebook


5 418

47 563

0.0012547

74.583

=

=

=

=

19 099

0.014785

50

3.475214

=

=

=

=

√478.63

4.53

74 + 84

95 + (-3)8

= (PRA)

= (PRA)

= (PRA)

= (PRA)

=

SMART Notebook

SMART Notebook

SMART Notebook

Establish a relationship between x and y:

a) x 1 2 3 4 5

y 3 6 9 12 15

b) x 0 1 3 4 5

y -3 -1 1 3 5

Establish a relationship between x and y:

a) x 1 2 3 4 5

y 3 6 9 12 15

b) x 0 1 3 4 5

y -3 -1 1 3 5

SMART Notebook

SMART Notebook

Circles




1) Name the parts of these circles marked by heavy bold lines.


a)

b)

c)

d)

e)

f)

g)

h)

Circles




2) Name the parts of these circles marked by heavy bold lines.


a)

b)

c)

d)

e)

f)

g)

h)

�

�

SMART Notebook


Mathematics Faculty Measure

Name:

mm = millimetres, cm = centimetre, m = metre, km = kilometre

1cm = mm 1 metre = cm 1km = m

To change cm into mm multiply by 10:

5cm = mm 8cm = mm6.3cm = mm

2.7cm = mm 9.3cm = mm13.9cm = mm

To change mm into cm divide by 10:

80mm = cm 60mm = cm95mm = cm

78mm = cm 87mm = cm765cm = mm

To change metres into cm multiply by 100

3m = cm 5m = cm6.3m = cm

2.7m = cm 9.7m = cm0.4m = cm

To change cm into metres divide by 100

400cm = m 700cm = m 890cm= m

430cm = m 3400cm = m 2350cm = m

To change metres to kilometres divide by 1000

6000m = km 8000m = km 7500 m = km

2500m = km 5060m = km 52 803m = km

To change kilometres to metres multiply by 1000

9km = m 7km = m 3.6 km = m

8.25km= m 15.89km = m 76.32km = m

SMART Notebook


Mathematics Faculty

Pythagoras (3D)

1) The shape in the diagram is a cube

with each edge length measuring 7cm.

a) Find the length AH

b) Hence determine the length AG



a) Find the length MN

b) Hence determine the length PM

3) The shape in the diagram is a cuboid

with measurements given.

a) Find the length AH

b) Hence determine the length BH



Determine the length SU


Mathematics Faculty

Pythagoras (3D)



c) Find the length AH

d) Hence determine the length AG



a) Find the length MN

b) Hence determine the length PM



c) Find the length AH

d) Hence determine the length BH



Determine the length SU

C

=

/

*

7

8

9

–

4

5

6

+

1

2

3

0

.

=

C

=

/

*

7

8

9

–

4

5

6

+

1

2

3

0

.

=

SMART Notebook


Mathematics Faculty – Angles

SMART Notebook

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Documents

Lesson 1: Similar Shapes Learning intention (LI): Linear (edges only) · 2019. 5. 29. · 5 Similar Shapes.notebook 1 May 29, 2019 Sep 2213:40 Learning intention (LI): Linear (edges