Appendix A

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Appendix A

Appendixes

Appendix A

A:01 The four operations

Appendix B

B:01 Addition

B:02 Subtraction

B:03 Multiplication

B:04 Division

B:05 Equivalent fractions

B:06 Comparing fractions

B:07 Improper fractions and mixed numbers

B:08 Adding and subtracting fractions

B:09 Multiplying a whole number by a fraction

B:10 Finding a fraction of a number

B:11 Conversions: Fractions and decimals

B:12 Comparing decimals

B:13 Adding decimals

B:14 Subtracting decimals

B:15 Multiplying a decimal by a whole number

B:16 Dividing a decimal by a whole number

B:17 Multiplying and dividing decimals by 10

B:18 Decimal currency

B:19 Changing percentages to fractions

B:20 Changing percentages to whole and mixed

numbers

B:21 Changing fractions and mixed numbers to

percentages

B:22 Changing percentages to decimals

B:23 Changing decimals to percentages

Working Mathematically

Appendix C

C:01 HCF and LCM by prime factors (extension)

Appendix D

D:01 Finite differences (finding the rule)

Appendix E

E:01 Changing repeating decimals to fractions

Appendix F

F:01 Investigation of plane shapes

Fun Spot: Hidden shapes

F:02 Plane shapes and patterns

F:03 Transformations: Reflections, translations and

rotations

F:04 Using plane shapes

F:05 Building solids using blocks

Fun Spot: Making a pop-up dodecahedron

Appendix G

G:01 Investigation: Measurement extension

G:02 Distance, speed and time

Appendix H

H:01 Operations with indices (extension)

Appendix I

I:01 Mass

Investigation: Mass

1


APPENDIX A

A:01 | The Four Operations

The combinations in the following exercises need to be practised until known.

Exercise A:01

1 Have someone time you, as you do each line four times.

Record the times in a table like the one on the right,

and graph the results.

a

b

2 +

10 +

3 1 0 4 7 2 8 5 9 6

0 2 1 9 3 5 7 8 6 4

Use scrap paper

like this until you

can break the

20 second barrier

for each line

c

3 +

3 4 0 2 8 1 7 5 9 6

Time for each trial

Table 1 2 3 4

d

4 +

1 4 2 6 0 3 7 8 5 9

2 + 20 s 18 s 16 s 15 s

10 +

e

5 +

5 2 0 6 4 1 5 3 9 8

3 +

4 +

5 +

f

6 +

2 4 0 1 6 3 7 9 5 8

6 +

7 +

g

7 +

0 1 4 3 7 2 8 6 5 9

8 +

9 +

h

i

8 +

9 +

2 3 8 1 0 7 5 9 4 6

4 0 2 6 5 8 3 1 9 7

Time (in seconds)

20

15

10

5

0

Graph for table 2+

1 2 3 4

Trial number

2 NEW SIGNPOST MATHEMATICS 7


2 Try to do each of these in 2 minutes.

a + 1 9 0 5 8 2 6 4 7 3

1

9 + 1 9 6 3

0 2

5 7 13

8 5

Add the number on

the top to the

number on the left

b + 1 9 0 5 8 2 6 4 7 3

2

6

4

7

3

3 Try to do each line in 20 seconds.

a

18 − 10 8 9 b 17 − 9 10 8 7

The answer to

17 — 7

goes here.

6 + 9 = 9 + 6

4 + 7 = 7 + 4

5 + 8 = 8 + 5

c

16 − 7 9 6 10 8 d 15 − 8 5 10 6 9 7

e

14 − 10 6 8 4 5 9 7 f 13 − 5 10 4 7 9 3 6 8

g

12 − 5 2 9 4 8 3 6 10 7

h

i

11 − 2 8 5 1 9 6 3 10 7 4

10 − 1 10 2 5 7 3 9 4 0 8 6

■ If 10 + 9 = 19,

then

19 − 10 = 9

and

19 − 9 = 10

4 Each box should be completed in 10 seconds.

a 5 − 3 b 6 − 6 c 6 − 5 d 9 − 9 e 9 − 8

8 − 2 3 − 1 7 − 4 6 − 4 7 − 5

6 − 3 9 − 7 4 − 2 7 − 3 9 − 6

9 − 2 8 − 5 8 − 3 9 − 4 8 − 4

8 − 7 7 − 6 9 − 3 8 − 6 9 − 5

APPENDIX A 3


5 Have someone time you as you do each part four times. Record the times in a table like the one

on the right, and graph the results.

a

b

c

d

e

2 ×

3 ×

10 ×

5 ×

4 ×

2 1 5 0 3 10 4 9 6 8 7 11

1 0 3 2 5 10 6 4 9 8 7 11

4 2 0 3 1 7 6 8 10 9 5 11

0 8 2 5 10 4 3 1 6 7 9 11

2 1 5 0 3 10 4 9 6 8 7 11

Time for each trial

Table 1 2 3 4

2 × 24 s 21 s 15 s 13 s

3 ×

10 ×

5 ×

4 ×

6 ×

7 ×

8 ×

9 ×

11 ×

f

g

h

6 ×

7 ×

8 ×

1 0 3 2 5 10 6 4 9 8 7 11

0 2 1 5 10 3 7 4 8 6 9 11

2 1 5 0 3 10 4 9 6 8 7 11

Time (in seconds)

25

20

15

10

5

Graph for table 2 ×

i

9 ×

1 0 3 2 5 10 6 4 9 8 7 11

0

1 2 3 4

Trial number

j

11 ×

0 2 1 5 10 3 7 4 8 6 9 11

■ 7 × 4 = 4 × 7

6 Try to do this in 3 minutes.

× 0 2 1 5 10 3 7 4 8 6 11 9

3

7

5

9

8

6

4 NEW SIGNPOST MATHEMATICS 7

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