Sequence of lessons / ideas
Topic:
Integers
Suggested Time: 2 – 3 weeks
Outcome(s): NS4.2 Syllabus page 58
Outcome Statement: Compares, orders and calculates with integers
Lesson Content
Assessment for Learning
Student discussion on where they have
encountered numbers like -8
Suggested No.
of Lessons
1-2
Activities / Resources
in addition to text
worksheets – illustrating number
stories / puzzles / language
Worksheets A, B, C
Concept of size and direction in real
world contexts eg temperature, banking,
Language and using number sentences
Modelling journeys on the number line
Addition and subtraction of integers
Eg 7 – 10, -3 + 6, -7 – 2, …
1-2
Using the double negative sign
Eg 7 - -5, -4 - -3,
1
Size, order of integers, placing integers
on the number line
1
Mixed questions using addition and
subtraction of integers
Multiplication of integers
Division of integers
Mixed operations with integers
Assessment of Learning Activity
Pen and paper test covering all learning
experiences
Pendle Hill High School Programming Project
1-2
1
1
1-2
1
Number line on card for each
student
Worksheets / puzzles
Worksheets D, E
worksheets /puzzles
Worksheet G
Worksheets E, H
Worksheets F, L
Directed number game with
playing cards (Refer to 12.4
Directed number game, New
Century Maths BLM)
Worksheet J
Worksheet (not included)
Worksheet K
Text for extension activities
Integer bingo game (Refer Integer
Bingo, p52 Reflections 27(2) May
2002.
Assessment A (not included)
Assessment B
1
Planning A Unit of Work on Integers
Integers NS4.2 page 58 (see attached page)
Outcome Statement: Compares, orders and calculates with integers
 Assessment for Learning
Students discuss in small groups where they have seen numbers like –8
before.
Teacher observes and listens to discussion. This discussion will be a basis of
future discussion
 Teacher led discussion on real world contexts for directed numbers eg
thermometers, banking,..
Worksheet
 Looking at the directed number line – on board – on wall in classroom
Teacher led discussion and examples on size, direction of numbers.
Literacy skills here include writing number sentences, words and their
opposites
Worksheet
 Investigating journeys on the number line
Each student to get a number line on card
Graded examples eg 9 – 3, 8 + 4, 3 – 7, -2 + 5, -4 – 2, -6 - -3, …
Worksheets
 Card Game using directed numbers
This will reinforce mental arithmetic skills as well as skills using directed
numbers
 Multiplication Using directed numbers
Worksheet
 Division of directed numbers
Worksheet (not included)
 Mixed Operations using directed numbers
Pendle Hill High School Programming Project
Worksheet
2
 Teacher to consider text exercises to cover questions using order of
operations, fractions and integers, grouping symbols and integers,..
 Integer bingo game
 Assessment of learning
Pen and paper test covering all work and activities taught
Student achievement recorded as beginning, developing, sound on the
outcome.
 Considerations for the teacher
Using calculator with integers
Importance of literacy skills in early activities
Many opportunities to build upon mental arithmetic skills
Review sheets from booklet an extra resource
Researching the topic
We looked at:
The topic in the syllabus – including what came before and what came after
ie NS3.2, NS5.2
Available texts including BLM
Available worksheets
Available activities
Teacher discussion and previous experience
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Worksheet A
Temperature
The Celsius ( C) scale is used on a thermometer.
The freezing point of water = 0oC
o
 A temperature 2o above freezing point is called 2oC
 A temperature 3o below freezing point is called –3oC

Example
The temperature at a ski resort is 5oC.
Later in the day the temperature drops 7oC.
What is the new temperature?
5–7=-2
Use the thermometer to help you answer these questions
Exercise
1. The temperature at 9pm was 7oC.
It dropped 10oC in the next three hours.
What will the temperature be then?
2. The temperature was –2oC early in the morning.
What will be the new temperature if it rises by 6oC?
3. The temperature was 12oC. It then dropped by 16oC.
What is the temperature now?
4. The minimum temperature was 4oC below zero.
The maximum temperature was 12oC higher.
What was the maximum temperature?
5. The temperature in a freezer was 17oC below zero. Someone
left the door open all day. The temperature rose 30oC. What
was the temperature?
6. State the change in temperature if it changes from
i) 8oC to 13oC
ii) –4oC to 4oC
iii) –7oC to –2oC
iv) 16oC to 13oC
v) –2oC to -4oC
vi) 5oC to –2oC
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Worksheet B
At the Bank
Sasha has an account at the local bank. When he deposits money he adds money to
his account. When he makes a withdrawal he takes money out of his account.
Sasha made a deposit of $35 and then a withdrawal of $17.
He wrote this down as
$35 - $17
Sasha made a withdrawal of $20 and then a deposit of $12
He wrote this down as - $20 + $12
Write a number sentence for:
i) A deposit of $5 and a deposit of $6
ii) A deposit of $6 and a withdrawal of $3
iii) A withdrawal of $11 and a deposit of $5
iv) A deposit of $7 and a withdrawal of $13
v) A withdrawal of $4 and a withdrawal of $2
In a Building
Floors in a building can be named many ways. Here the builders have called the
ground level carpark level C.
i)
Starting at C, how many levels do you travel
to get to level +3?
ii)
Starting at C, how many levels do you go down
to get to –1?
iii)
How many levels is it from C to +4 level?
iv)
How many levels is it from –3 level to +5 level?
v)
How many levels are there in Easy-Park?
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Worksheet C
Using Directed Numbers
Complete this table of opposites
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
up
inside
exterior
right
gain
south
below
ascend
decrease
winning
same
minimum
vertical
plus
Write an expression to show the size and direction of each statement.
1. Andrew went 5km east
2. Tim withdrew $35 from his bank account
3. Sandy drove 400km north
4. The temperature was 15o below zero
5. The town was 750m above sea level
6. When I sold my car I lost $950
7. Shares in a company rose by $4.10
8. The lift went up 6 floors and then down 5 floors
9. At a space launch the expression “zero minus one” means one second before
ignition. Write an expression for seven seconds before ignition?
10.A plumber makes a profit of $370
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Worksheet D
Pendle Hill High School Programming Project
Number Lines
7
Worksheet E
The Directed Number Line
Numbers get smaller
-6
-5
-4
-3
-2
Numbers get larger
-1
0
1
2
3
4
5
6
A. Use the number line to complete these journeys
1. 2 + 5
2. –1 + 3
3. –5 + 3
4. –2 + 3
5. 6 – 2
6. 3 – 3
7. 1 – 2
8. 4 – 7
9. –6 + 8
10. –4 + 3
11. –3 + 2
12. –7 +8
13. 0 + 6
14. 6 – 10
15. 9 – 12
16. –5 + 10
17. 6 – 11
18. –3 + 6
19. –2 + 10
20. –3 - 5
B. Write the next three numbers in these patterns
1. 2, 4, 6, 8, __, __, __
2. 3, 2, 1, 0, -1, __, __, __
3. 4, 2, 0, -2, __, __, __
4. 10, 5, 0, __, __, __
5. 3, 6, 9, 12, __, __, __
6. –6, -8, -10, __, __, __
7. –1, -3, -5, __, __, __
8. 30, 20, 10, __, __, __
9. 12, 4, -4, __, __, __
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C. Put these numbers in ascending order (from lowest to highest)
1. 3, -1, 4, 0
2. 3, 9, -2, 7
3. –4, 2, -2, -1
4. 10. –20, 0, 5
5. –1, 10, 1, 0, -10
6. 100, 0, -10, 10, -100
D. Use the number line to find the number halfway between
1. 0 and 10
2. 8 and 10
3. 5 and 9
4. –5 and –1
5. 7 and –5
6. 0 and –2
7. –2 and 4
8. 1 and - 7
E. Write True or False
1. 5 is bigger than 0
2. 8 is less than 10
3. 0 is less than –3
4. –5 is bigger than 1
5. 0 is bigger than –1
6. –2 is less than 2
F. This table shows temperatures recorded in 5 cities in one day
City
Temperature (oC)
Which city had the highest temperature?
Paris
2
Which city had the lowest temperature
Chicago
-4
What is the difference in temperature between
Brisbane
26
a) Moscow and Paris?
Moscow
-13
b) Auckland and Chicago?
Auckland
18
c) Paris and Brisbane?
G. In a card game you win if you reach 500 points and lose if you reach –500
points.
If Greg scores 230 points, how many points does he need to
a) win the game?
b) lose the game?
Pendle Hill High School Programming Project
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Use your number line to make these journeys
Worksheet F
1. 7 – 3 =
2. 10 – 4 =
3. 3 – 2 =
4. 4 – 5 =
5. 7 - 9 =
6. 10 – 14 =
7. 5 – 8 =
8. 8 – 19 =
9. 6 – 12 =
10. 13- 16 =
11. 15 – 18 =
12. 23 – 16 =
13. 25 – 30 =
14. 14 – 23 =
15. 30 – 20 =
16. 23 – 25 =
17. 14 – 20 =
18. 16 – 30 =
19. 17 – 9 =
20. 15 – 26 =
21. 30 – 27 =
22. 16 – 24 =
23. 34 – 17 =
24. 25 – 26 =
25. 12 – 12 =
26. 17 – 20 =
27. 13 – 34 =
28. 18 – 23 =
29. 14 – 14 =
30. 24 – 34 =
31. 8 – 14 =
32. 13 – 14 =
33. 16 – 26 =
34. 16 – 19 =
35. 2 – 1 + 3 =
36. 14 – 9 + 5 =
37. 3 + 5 – 10 =
38. 6 – 10 + 7 =
39. 18 – 20 + 4 =
40. 3 – 5 – 2 =
41. 16 – 20 – 3 =
42. 13 – 14 + 5 =
43. 34 + 6 – 50 =
44. 12 – 4 + 3 =
45. 10 – 6 +8 =
46. 7 + 7 – 10 =
47. 9 – 8 + 12 =
48. 5 + 3 – 8 =
49. 12 – 7 + 4 =
50. 2 – 4 + 5 =
51. 4 – 8 + 2 =
52. 6 – 7 + 3 =
53. 8 – 12 + 5 =
54. 8 – 9 + 1 =
55. 8 – 3 + 1 =
56. 9 – 5 + 4 =
57. 10 – 5 + 8 =
58. 5 – 4 + 6 =
59. 2 – 7 + 6 =
60. 12 – 6 + 8 =
61. 7 + 7 – 15 =
62. 23 – 20 + 2 =
63. 15 – 6 – 9 =
64. 4 – 2 – 2 =
65. 12 – 9 – 3 =
66. 5 – 9 + 4 =
67. 23 – 25 =
68. 30 – 40 =
69. 12 – 20 + 10 =
70. 3 – 17 + 5 =
71. 5 – 12 – 4 =
72. 65 – 30 + 15 =
Pendle Hill High School Programming Project
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Use your number line to make these journeys
Worksheet L
1. - 7 – 3 =
2. - 10 – 4 =
3. - 3 + 2 =
4. - 4 – 5 =
5. - 7 + 9 =
6. - 10 – 14 =
7. - 5 – 8 =
8. - 8 + 19 =
9. - 6 – 12 =
10. – 13+ 16 =
11. - 15 – 18 =
12. - 23 + 16 =
13. - 14 – 23 =
14. - 30 + 20 =
15. - 23 + 25 =
16. - 14 – 20 =
17. - 16 + 30 =
18. - 17 + 9 =
19. - 16 – 24 =
20. - 34 + 17 =
21. - 25 + 26 =
23. - 12 – 12 =
23. - 17 – 20 =
24. - 13 + 34 =
25. - 18 – 23 =
26. - 14 – 14 =
27. - 24 + 34 =
28. - 8 + 14 =
29. - 13 – 14 =
30. - 16 + 26 =
31. - 16 – 19 =
32. - 2 – 1 + 3 =
33. - 14 – 9 + 5 =
34. - 3 + 5 – 10 =
35. - 6 – 10 + 7 =
36. - 18 – 20 + 4 =
37. - 3 – 5 + 2 =
38. - 16 – 20 + 3 =
39. -13 – 14 + 5 =
40. - 34 + 6 – 50 =
41. - 12 – 4 + 3 =
42. - 10 – 6 +8 =
………………………………………………………………………………………………………………………………………………………………………………
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Use your number line to make these journeys
Worksheet G
1. - 7 – - 3 =
2. 10 - - 4 =
3. - 3 + 2 =
4. 4 – - 5 =
5. - 7 - 9 =
6. - 10 - - 14 =
7. 5 – - 8 =
8. - 8 - 19 =
9. - 6 – - 12 =
10. – 13- - 16 =
11. 15 – - 18 =
12. 23 - - 16 =
13. - 25 – - 30 =
14. - 14 – - 23 =
15. 30 - - 20 =
16. - 14 – - 20 =
17. - 46 + 30 =
18. - 17 - - 9 =
19. - 15 – -26 =
20. 18 – -27 =
21. - 16 – - 2 =
22. 34 - - 7 =
23. - 25 - - 26 =
24. - 7 - - 12 =
25. 1 - – 20 =
26. - 13 - - 3 =
27. 8 – - 6 =
28. - 14 – -14 =
29. – 1 - - 7=
30. - 8 - -7 =
31. - 13 – -14 =
32. - 16 - -26 =
33. - 16 – - 9 =
34. - 2 + 1 - - 3 =
35. - 14 + 9 -- 4 =
36. - 3 + 5 – - 3 =
37. 6 – - 10 + 7 =
38. - 8 – - 3 + 4 =
39. - 3 – - 5 - 2 =
40. - 6 – -30 + 3 =
41. -13 – 4 - - 5 =
42. 24 + 6 – - 50 =
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Worksheet H
Placing Numbers on the Directed Number Line
Place these numbers on the number line:
a)
2, -5, 7, 0, -1
b)
–3, 7, 4, -1, 2
c)
–7, 5, 3, 0, -4
d)
–5, -3, -10, 2, 1
e)
6, -1, 4, 2, -3
f)
0.5, 1, 3, 4.5, -1
g)
–0.5, 2, 3.5, 1, 0
h)
–4.5, 2.5, -2, 0, 1.5
i)
½, 0, -3, 2, -1 ½
j)
- 4.2, 3, -1.5, 2 ¼
Placing Numbers on the Directed Number Line
Place these numbers on the number line:
a) 2, -5, 7, 0, -1
b) –3, 7, 4, -1, 2
c) –7, 5, 3, 0, -4
d) –5, -3, -10, 2, 1
e) 6, -1, 4, 2, -3
f) 0.5, 1, 3, 4.5, -1
g) –0.5, 2, 3.5, 1, 0
h) –4.5, 2.5, -2, 0, 1.5
i) ½, 0, -3, 2, -1 ½
j) - 4.2, 3, -1.5, 2 ¼
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Worksheet J
Multiplication Of Integers
1. 4 x 6 =
2. 4 x – 6 =
3. –4 x 6 =
4. –4 x –6 =
5. –6 x 3 =
6. –5 x –5 =
7. 1 x –3 =
8. 7 x –4 =
9. –8 x –2 =
10. 4 x 9 =
11. –8 x –4 =
12. –2 x 2 =
13. 0 x 7 =
14. –4 x –9 =
15. –8 x 1 =
16. –9 x –1 =
17. –1 x –1 =
18. –6 x –6 =
19. 5 x –9 =
20. –8 x –3 =
21. 3 x 5 =
22. 7 x 8 =
23. 2 x 6 =
24. 9 x 7 =
25. –6 x –2 =
26. –9 x –1 =
27. –8 x –4 =
28. – 7 x –3 =
29. 7 x –2 =
30. –8 x 6 =
31. –4 x 6 =
32. –8 x 9 =
33. –11 x 10 =
34. 6 x –7 =
35. –2 x –9 =
36. 1 x 10 =
37. –6 x 5 =
38. –7 x 3 =
39. 8 x –4 =
40. 12 x 8 =
41. –7 x –12 =
42. 3 x –8 =
43. 6 x –4 =
44. – 2 x 6 =
45. 4 x –12 =
46. –5 x –5 =
47. –7 x –12 =
48. 8 x –10 =
49. –12 x 6 =
50. 10 x –10 =
51. 7 x –7 =
52. 3 x 8 =
53. –8 x 8 =
54. 6 x 10 =
55. –7 x 5 =
56. –11 x –4 =
57. 6 x 4 =
58. –15 x 3 =
59. –4 x 2 =
60. 3 x 3 =
61. –5 x 4 =
62. –7 x 4 =
63. 6 x 5 =
64. 4 x 5 =
65. –10 x 6 =
66. 3 x 4 =
67. 3 x –4 =
68. –4 x 3 =
69. –3 x 4 =
70. 8 x –9 =
71. –3 x –8 =
72. 10 x 5 =
73. –3 x –9 =
74. –2 x –5 =
75. 7 x5 =
76. 4 x –2 =
77. –2 x 9 =
78. –7 x –6 =
79. –8 x –4 =
80. –1 x 1 =
81. 3 x –9 =
82. 4 x 8 =
83. –2 x –1 =
84. 7 x –8 =
85. 5 x –3 =
86. 6 x –9 =
87. –9 x –1 =
88. 8 x 8 =\
89. 2 x 8 =
90. –7 x –7 =
91. –3 x –7 =
92. –34 x 0 =
93. –17 x 2 =
94. 2 x 3 =
95. –3 x 18 =
96. –18 x 2 =
97. –5 x –12 =
98. –2 x –8 =
99. 5 x –6 =
100. –3 x –3 =
101. 1 x 7 =
102. 0 x 4 =
103. 5 x –8 =
104. 7 x 0 =
105. 3 x –4 =
106. 7 x –2 =
107. –8 x 6 =
108. –4 x 9 =
109. –7 x –12 =
110. 6 x –9 x 1 =
111. 8 x 8 x 2 =
112. –17 x 2 x 1 =
113. 6 x 7 x –2 =
114. –3 x 2 x –1 =
115. 7 x –2 x –3 =
116. 8 x –1 x 2 =
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Worksheet K
Writing about Integers
Imagine you need to explain operations with integers to someone who doesn’t know
about them. Explain how you would answer these questions in your own words,
using diagrams if necessary.
1.
5-8
2.
–5 – 8
3. –5 + 8
4. 5 + (-8)
5. 5 – (-8)
6. 5 x (-8)
Source: Reflections Volume 27 No.4 November 2002
Pendle Hill High School Programming Project
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Year 7 Integers Assessment B
Name:___________________
1.
7–5=
28. 56 + 5 – 10 =
53. 70 ÷ 10 =
2.
8+4=
29. 12 - - 4 + 5 =
54.
3.
–3 + 7 =
30. 67 + 4 – 34 =
55. –6 ÷ -6 =
4.
7–7=
31. 7 x 3 =
56. 14 ÷ -2 =
5.
–6 –1 =
32. –2 x 5 =
57. 24 ÷ -3 =
6.
8 – 10 =
33. 5 x 7 =
58.
9.
4–7=
34. 2 x – 3 =
59. –12 ÷ -3 =
10. – 3 + 3 =
35. 4 x – 8 =
60. 56 ÷ -7 =
11.
7 - -3 =
36. –3 x 7 =
61. 6 + 7 – 3 =
12.
–5 + 2 =
37. 4 x 5 =
62.
13.
5–5=
38. –4 x 5 =
63. 2 x – 3 =
14.
6--3=
39. 4 x – 5 =
64. 15 ÷ - 5 =
15. –7 - - 2 =
40. –4 x –5 =
65. 45 – 40 =
16.
41.
66. –1 + 1 =
6–6=
2x5x1=
21 ÷ -7 =
–8 ÷ -4 =
15 - - 4 =
17. 12 – 8 =
42. 3 x –1 x 2 =
67. 6 - - 3 =
18.
43. 5 x –2 x 4 =
68. 12 x –2 =
19. – 2 + 2 =
44. –3 x 6 x –2 =
69. 7 ÷ - 7 =
20. –2 - - 6 =
45. –2 x –4 x –5 =
70. –4 x –2 =
21. 2 – 3 + 5 =
46. 12 ÷ 6 =
71. 34 + 6 – 10 =
22. 5 – 7 + 4 =
47. 18 ÷ 3 =
72. 12 - - 10 + 3 =
23. 7 - - 2 + 1 =
48. 20 ÷ -2 =
73. 5 x –2 x 7 =
24 76 – 32 =
49. 3 ÷ -3 =
74. 60 ÷ -10 =
25. 100 – 4 =
50. –10 ÷ 5 =
75. 4 + 6 - 10 =
26. 67 – 70 =
51. –12 ÷ -4 =
76. –3 - - 9 =
27. 12 – 19 + 5 =
52. 16 ÷ -8 =
77. 23 x –1 + 7 =
6–4=
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Pendle Hill High School Mathematics Programming Project
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