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Ministry of Education
Guyana
Activities Booklet
Transitional Guide .
for Mathematics
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Grade 6-7
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ASSISTANT CHIEF EDUCATION OffiCER
(SECONDARY)
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Produced by Ministry of Education (NCERD)
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August, 2009
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Table of Contents
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Unit 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
Pages
2
3-4
5-7
8-9
10-11
12-14
15-17
18-19
20-23
24
25-26
27-29
Unit2
1.1
1.2
30-33
34-39
Unit 3
3.1
3.2
3.3
3.4
•
40
41
42-44
45-49
Unit4
4.1
4.2
50
51
Unit 5
5.1
5.2
5.3
52-53
53-55
56-57-
Unit 1: Numbers, Numeration and Operations.
1.3
Two-, three-, four-, and five digit numbers.
Objectives include:
i.
Recognition of two-, three-, four- and five-digit numbers
ii.
Recognition of digits and number of digits.
Activity 1
Digital Sums
I. Teacher, please copy the table below on the chalkboard.
Numbers
D igits
5
34
203
6789
56 407
0
45
568
3578
40 789
8900
6703
4
23
999
5
3,4
2, 0, 3
Number of Digits
1
2
3
Digital Sums
5
3 +4(7)
2 + 0+3 (5)
2. Invite students to say how the entries in the second, third and fourth columns were
arrived at ( Second column: write the digits; third column: count the number of
digits; fourth column: add the digits)
3. Ask the students to complete the columns of the table:
Answers:
Numbers
Digits
Number of Digits
Digital Sums
0
0
4,5
5,6,8
3,5,7,8
4,0,7,8,9
8,9,0,0
6,7,0,3
4
2,3
"9,9,9
1
0
9
19
23
45
568
3578
40 789
8900
6703
4
23
999
2
3
4
5
4
4
1
2
1
2
.
28
17
16
4
5
27
,t~ctivity
1:
Numb«::r Puz!le
Divide students into groups of three. Give each group a copy of the grid below.
Write the clues on 1lte chalkboard and explain to the children how to do the: puzzle.
Let each group do t:he puzzle.
~--
-
---
~--
5
6
8
12
II
14
13
16
17
15
--
' - - - - ~·--
Ac1·oss
1. . twenty
•
2.
ninety nine 1J1ousand seven hundred
four
6.
ninety nine
7.
six hundi·ed forty four
8.
thirty three
10.
twdve thous1U1d six hundre:d seve:nty eight
12.
nine rnmdred sixty one
14.
thre'e hll!lld.red eighty three
16.
nine thous~md six hundred twenty
17.
three thousc:md three
Answers: (1) 20 (2) 99 704 (6) 99 (7) 644 (8) 33 (10) 12 678 (12) 961
(14) 383 (16) 9620 (17) 3003.
3
9
Objectives include identifying the place value of any digit in a two-, three-, four or fivedigit number.
Ji'un with Place~ Value
l . Divide studentS into groups of three.
2. Give each group 10 cards, each with a number from 0 to 9.
3. Ask each group to use the number cards to :
show a number with 1 as the ones digit, 3 as the tens digit, and 6 as the hundreds
digit (63 1)
- ask them to rearrange the number cards to show 1 ru: the hundreds digit and 6 as
the ones digit (1.36)
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4.
•
('
J.
let them plac:e the numbet card 8 after 6 in the number 136 and say what is the
thousands digit ( 1), what is the hundreds digit( 3), what is the tens digit (6) and
what is the ones digit (8).
Ask them to use the cards to show a number with 7 as the ten thousands digit.
· Ask each group to sho'\V a five digit number. \\'rite the digits on the chalkboard.
6.
Ask the children to order the numbers from least to greatest and then fl·om
greatest to least.
7.
Have tv•o groups come together and use their number ca.rds to show a f1ve digit
number in whlch 9 is the ten thousands digit and also the~ ones digit.
4
Activity 2
Game: Think of a Number
1.
This is a game for two players. Player A and Player B.
2.
Player A thinks of a four -digit number with digits from 0 to 3. He/she writes it
on a piece of paper and ensures the. other player does not see it.
3.
Player A tells player B that the number he has is made up
of four digits, 0, 1, 2, 3.
4.
Player B asks Player A questions about the place value of the digits to find out
what is the number, for example
Is the ones digit 3?
Is the tens digit less than 2?
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Player A can only answer" Yes" or "No".
Activity 3:
Sum of 14
1.
Tell the students that you are thinking of a number and you want each of them
to find out what number you are thinking of.
2.
Give this clue:
the tens digit is the number that comes before 1.
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3.
Let them write the number that comes before 1. Tell them to listen carefully and
write the other digits of the number.
4.
Give this clue:
the hundreds digit is equal to 1 + 0 and the ones digit is 0 + 4.
5. Continue. The thousands digit is 10 - 8.
6. Continue. The tens of thousands digit is 4 + 3.
7. The sum of the digit should be 14. Ask students to check their answer.
8. Ask students to say what number you were thinking of. (72 104)
5
1.5 Types of Numbers
Objectives inClude:
(i) Recognising even , odd, prime and composite numbers
(ii) Definition of even , odd, prime and composite numbers.
Activity 1
Odd and even numbers
1 Dictate the following numbers to the students:
0
2344
33
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5
9
673
3331
23
18
100
6
7
56
60
92
159
1600
495
2 56
45
2
Ask them to circle all of the numbers that are odd. (5, 9, 23, 7, 495, 673, 45, 33,
3331, 159)
3.
Dictate the numbers again.
4.
Ask them to circle the numbers that are even. ( 0, 56, 2344, 18, 6, 60, 92, 256, 100,
1600)
5.
Tell the students to add an:
- even number to an even number.
Is the answer even or odd? (even)
- odd number to an odd number.
Is the answer even or odd? (even)
- even number to an odd number.
Is the answer even or odd? (odd)
6.
Let them say how they decided what numbers to select as even.
7.
Let them say how they decided what numbers to select as odd.
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6
J.&riine Numbers
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•
100
110
120
130
140
150
160
170
180
190
101
111
121
131
141
151
161
171
181
191
102
112
122
132
142
152
162
172
182
192
103
113
123
133
143
153
163
173
183
193
104
114
124
134
144
154
164
174
184
194
105
115
125
135
145
155
165
175
185
195
106
116
126
136
146
156
166
176
186
196
107
117
127
137
147
157
167
~77
187
197
108
118
128
138
148
158
168
178
188
198
109
119
129
139
149
159
169
179
189
199
200
1.
Mount a chart with the grid above on the chalkboard or copy it on the chalkboard.
2.
Divide the students into groups of five.
3. Ask each student to copy the grid above with numbers from 100 to 200.
4.
Remind them that prime numbers from 1 to 100 are 25 in number:
2~3, 5, 7, 11.13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79 83, 89, 97 .
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5.
Ask them to say what is a prime number? (A number greater than 1 that can be
divided by 1 and itself only; it has two factors)
6.
Tell them to list all prime numbers in the grid .and to say how many prime
numbers are there from 100 to 200. (21)
7.
List the prime numbers so the students can verify and list all of the prime numbers.
(101, 103, 107, 109, 113, 127,131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
181, 191, 193, 197, 199)
7
Activity 3
Composite Numbers
No Primes, please!
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100
110
120
130
140
150
160
170
180
190
101
111
121
131
141
151
161
171
181
191
102
112
122
132
142
152
162
172
182
192
103
113
123
133
143
153
163
173
183
193
104
114
124
134
144
154
164
174
184
194
105
115
125
135
145
155
165
175
185
195
106
116
126
136
146
156
166
176
186
196
107
117
127
137
147
157
167
177
187
197
108
118
128
138
148
158
168
178
188
198
109
119
129
139
149
159
169
179
189
199
200
1.
Mount a chart with the grid above on the chalkboard or copy it on the chalkboard.
2.
Divide the students into groups of five.
3.
Ensure that they have the list of prime numbers given below.
(101, 103,107,109, 113,127,131,137,139,149, 151,157, 163, 167, 173,179,
181, 191, 193, 19~ 199)
4.
Ask them to say what is a composite number. (A composite number is greater than
I and has more than two factors).
5.
Explain that a number greater than I that is not a prime number is a composite
number.
6.
Have the students place an X on all prime numbers on the grid.
Let them select the remaining numbers as composite numbers.
(100, 102,104,105, 106,108,110,111,112,114,115,116,117,118,119,120,121,
122, 123, 124, I25, 126, 128, 129,130, 132, 133, 134, 15, 136, 138,140, 141, 142, 143,
144, 145, 146, 147, 148, 150, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 164, 165,
166, 168, 169, 170, 171,172, 174, 175,176, 177, 178, 180, 182, 183, 184,185, 186, 187,
188, 189, 190, 192, 19~, 195, 196, 198, 200)
7.
8
1.4 Rounding numbers
Objectives include rounding numbers to nearest ten and hundred
Activity 1
Round 67 867:
1.
to the nearest 10
(67 870)
2.
to the nearest I 00
3.
to the nearest 1000 (68 000)
4.
to the nearest 10 000 (70 000)
( 67 900)
Answers:
(1) 67 870 (2) 67 900 (3) 68 000 (4) 70 000
Now write > or < .
5.
67870
67867
6.
67 867 ----
7.
68 000
67867
8.
70 000
Answers:
(5) > (6) < (7) > (8) >
Activity 2
Roun~ the
following to the nearest 10.
(9). 25 (1 0). 35 (11 ). 45
(12). 55
(13). 65
Answers:
(9) 30 (10) 40 (11) 50 (12) 60 (13) 70
9
67 900
67867
Activity 3
Round to the nearest 100.
1. 180
2. 230
3.
350
4.
450
5.
Answers:
(1) 200 (2) 300 (3) 400 (4) 500 (5) 600 (6) 700
10
550
6.
650
1.5
Add and Subtract V\1.bole Numbers
Obje<:tives include.:
(i) Adding and subtracting whole numbers up 1o four digits with carrying
. (ii) Adding and subtracting whole numbers up to four digits without carrying.
Activity 1
A palindromic number re~dsthe same forwards and baekwards e.g 121 and 15651.
The students can change a number into a pa1i:ndrome.
1.
Let 1hem take any number, say 168.
2.
Reverse its digits
3.
Add the number formed after its digits are reversed to the number 168.
( 861)
1
4.
168
:!- 86L
10 29
Reverse 10 29 and add it to 1029.
1
168
.:!" 861
5.
1029
+9201
10230
Reverse 10 2.30 and add it to 10 230.
1
168.
+ 861
1029
+9201
10230
+ 03 201.
13431
..
13 431 is a palindrome:!
6.
Now change 472 to a palindrome. ( 9559)
I1
Activity 2
Subtraction Pynllmid
Below is a pyramid that is not complete. Numbers are missing.
[~------------------- ]
----·----]
[
,_]
H
27
G-=_~
•
~---------~--- J
D
[A 100
1.
200
When you subtract. B fi·om A., the answer is E. What is B?
Write your answer on the line inside the box where B h
(5963)
2.
When you subtraet C fi·om D, the answer is G. What is C?
Write your answer on the line inside the box where C is.
( 8027)
.
3. When you subu·act E from F, the answer is H. What is F?
Write your answer on the line inside the box where F is.
( 25 000)
4. When you subtract I from H, the answer is J. \Vbat is 1?
Write your answer on the line inside the box where J is.
12
I
1.6 Multiply Whole Numbers and Decimals
Objectives include:
(i) Multiplying whole numbers without carrying
(ii) Multiplying whole numbers with carrying.
Activity 1
Boxed In
Here is a game the students can play in small groups.
1. Let them solve the 9 muitiplication exercises below and write the product in any
of the 9 boxes that are below the exercises.
2.
When the students have finished filling in the boxes, they have to add across
each row and write the sum in the blank to the right of that row.
3.
Add that column of sums you wrote in the blank.
4.
The winner is the player whose final sum is the greatest.
(1} 11
(6) 66
X
X
J (2) 22
6 (7) 77
X
X
2 (3) 33
7 (8) 88
X
3 (4) 44
X
13
X
8 (9) 99
4 (5) 55
X
9
X
5
Activity 3
Multiplication: Greatest product; least product. 1
1.
Let students look at the following exercises.
(1) 123
(5) 567
2.
X
X
9
5
(2) 234
(6) 678
X
X
8 (3) 345
4 (7) 789
X
X
7
3
(4) 456
(8) 890
X
X
6
2
Ask each student to select one of the exercises that she/he thinks will have the
greatest product.
3.
Ask each student to select one of the exercises that she/he thinks will have the
least product.
4.
Let them put the exercises they select in the appropriate column in the boxes
below.
Exercise I think will have the greatest
product
Exercise I think will have the least product
5.
Guide students in doing the exercises.
(1) 1737 (2) 1872 (3) 2415 (4) 2736 (5) 2835 (6) 2712 (7) 2367 (8) 1780
6.
Let them put the exercises in the appropriate colunu1 in the boxes.
My exercise with the greatest product
My exercise with the least product
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(Correct: 123 x 9 = 1737)
(Correct: 567 x 5= 2835)
14
Activity 4
Multiplication: Greatest product; least product. 2
1.
Let students look at the foll_owing exercises.
(1) 12.3 X 9 (2) 2. 34 X S (3) 3.45 X 12 (4) 45.6 X 1 6
(5) 0. 567 X 5 (6) 6.78 X 14 (7) 7.89 X 1.1 (8) 890 X 2. 2
2.
Ask each student to select one of the exercises that she/he thinks will have the
greatest product.
3. Ask each student to select one of the exercises that she/he thinks will have the
least product.
4.
Let them put the exercises they select in the appropriate column in the boxes
below.
Exercise I think will have the greatest
product
5.
6.
Exercise I think will have the least product
Guide students in doing the exercises.
(1) 110.7 (2) 18.72 (3) 41.4 (4) 729.6 (5) 2.835 (6) 94.92 (7) 8.679 (8) 1958
Let them put the exercises in the appropriate column in the boxes .
My exercise with the greatest product
My exercise with the least product
(Correct: 0.567 x 5= 2.835)
(Correct: 890 x 2.2 = 1958)
15
1.7
Division
Objectives include:
(i) Dividingwhole numbers with and without remainders
(ii) Dividing decimals.
Activity 1: Joke Numbers
Teacher will copy the following exercises on the chalkboard for students to solve .
•
(854 + 7) + 3
... ... E
1.
( 626 + 2) + 4
--------- N
2.
3.
(748 + 4) + 9
.......... u
4 . (833 + 7)- 3
.. ....... C
5.
( 744 + 3) + 5
........ ...0
6. (862 + 6)- 5
.......s
7.
(852 + 2) +5
........... A
8. (471 + 3) -7
...... ..T
9. (810 + 3) + 8
..........w
10. (840 + 3)- 7
. ....... D
11 . (648 +4) + 6
. ..........H
Show them the boxes below. Tell them to write the letter for each answer in the box that
is above the answer.
There are two types of mathematicians
Ii5o I~68 I~53
I ~39 I T25
I~~6 I ~31 1~17
I;;8 I ~68 I ~53
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I~31 I~17 I~73
I I 16,253 , 196,317,150
1278 1 168 , 241
I~~6 I~31 l ~~7 Iiso
Answer: Those who can count and those who cant
16
Activity 2
Missing Numbers
Solve each equation
85 + 2 = -------------
l.
= 10 R 1
2.
---------- + 7
3.
58+ ....... = 11R3
4.
89 + 8
5.
. ....... + 4 = 11 R 1
= ------------
-------- = 32 R 1
6.
97
7.
68 + 3
8.
--------
= ------6 = 11 R 3
9. 85
------ = 21 R 1
10. 87
2 = ----------
11.
..........
12.
63
13.
87 .,. 4 = ---------
------- = 10R3
14.... ......
15.
89
9 = lOR 7
5 = 11R4
------- = 22 R I
Answers:
(1) 42Rl (2)71 (3) 5 (4) llRl (5)45 (6)3 (7)22R2 (8)69 (9)4
(10) 43RI (11) 97 (12) 6 (13) 2 1R3 ( 14) 59 (15) 4
17
Activity 3
Missing Numbers
Solve each equation
1.
8.5 + 2
2.
---------- + 7 = 10. 1
3.
60.20 + 2
= ........
4.
56.8 + 8
= ------------
5.
. ...... . + 4
=
=
--------------
0.11
6.
97.5 + -------- = J.25
7.
390 + 1.3 = ----------
8.
--------- + 6 = 0.71
9.
8.1 + ------
=9
10. 87 + 2 = ----------
•
11.
.......... + 9 = 2.01
12.
63 + ------- = 10
13.
8.250 + 0.5 = ---------
14.
1.44 + 1.2 = ...... .. .
15.
99.09 + ------- = 11.01
Answers:
(1) 4.25 (2) 70.7 (3) 30.10 (4) 7.1 (5) 0.44 (6) 30 (7) 300 (8) 4.26 (9) 0.9
(10) 43.5 (11) 18.09 (12) 6.3 (13) 16.5 (14) 1 (15) 9
18
1.8 HCF and LCM
Activity 1
HCF: Following an Example.
Teacher will assist the students as they do the following activities:
1.
Write the factors of 8? (1, 2, 4 ,8)
Write the factors of 12. (1, 2, 3, 4, 6, 12)
•
2.
What are the common factors of 8 and 12? (1, 2, 4)
3.
What is the highest common factor of8 and 12? (4)
4.
What is the greatest number that can divide 8 and 12 without remainders? (4)
Now do the following :
5. Find the highest common factor of(a) 42 and 30? (6) (b) 60 and 64? (4)
7.
The highest common factor (HCF) of28 and 42 is 14. Show that this is a true
statement by listing the factors of 28 and then the factors of 42. Next list the
common factors and choose the HCF.
Activity 2
Complete the factor tree below:
•
Answers:
Third row 7; last row 2, 7.
19
Activity 3
LCM
Teacher will ensure that students copy the incomplete chart below:
Row 1
Row2
Row3
Row4
RowS
Row6
Row7
RowS
Row9
Row 10
Multiples of 2
Multiples of 3
Multiples of 4
Multiples of 5
Multiples of 6
Multiples of 7
Multiples of 8
Multiples of 9
Multiples of 10
Multiples of 15
t
2, 4, 6, 8,----,----,-----, --3, 6, 9,' 12,----,----,----,--4, 8, 12,16,----,----,----, --5,10, 15, 20----,----,--6, 12, 18, 24 ----,----,----,--7, 14, 21, 28,---,----,-----, --8, 16, 24, 32,----,----,-----, --9, 18,27,36, ----,----,---,--10, 20,30,40,----,----,-----, --15, 30, 45, 60, ----,----,----, -
--
1. Ask students to complete all the rows by filling in the bla.nks.
2.
Let them select two common multiples from Row 1 and Row 2 after filling in the
blanks. (6,12)
3. Let them decide what is the lowest common multiple of2 and 3. (6)
4. Have them play in groups of three to find L.C.M of not more than three of the
numbers. They can extend the multiples in any of the rows in the chart .
•
Answers:
(1)
Rowl
Row2
Row3
Row4
RowS
Row6
Row7
RowS
Row9
Row 10
.
Multiples of 2
Multiples of 3
Multiples of 4
Multiples of 5
Multiples of 6
Multiples of 7
Multiples of 8 .
Multiples of 9
Multiples of 10
Multiples of 15
20
2, 4, 6, 8, 10, 12, 14,...
3, 6, 9, 12, 15, 18, 21,--4,8,12,16,20,24,28-5,10, 15, 20, 25, 30, 35, 40,-6,12,18,24,30,36,42~-
7, 14, 21, 28, 35, 42, 49, --8, 16, 24,32, 40, 48 56,--9, 18, 27 36, 45, 54, 72,--10,20~0,40,50,60,70,--
15,30,45,60,75,90,105,-
F Al\1 ASTIC FRACTIONS
Activity 2
Finding 000.
Teacher will copy the exercises below on the chalkboard and ask students to do the
fractions with U1e activities.
4~
-
5~
6
')4,. -l
6
12_2_
14
12
3
-- 2·-
- --··-
12
9.!3.
102.
16
15
7
- 715
- g2_
16
4
l'".) -9
9
15 -12
3
9
-10-
1
- 4 --
12
---
- -·--
- 9-1
- -14
14
6
7
3
- 117
132.
15
1
- 9-
--- 15
}>Iace an () next to the ..~ollov.ring answers: 2-2 2-1 )- -L 4 ·-2 and an X next to
3' g' 4 ' 15
2
1 I
4
3
.
9- , 2- , 3-, 3- . 3 - . ldentifv three answers one after the other that have O's.
3
3 2
7. 7
.
Answers:
123.0
3-.!_X
2.!.x
2.!_0
3
8
93. x
5_!_ 0
-4
3
3
2
3~ X
7
32 x
7
4~ 0
15
22
· 2 2 2!
3' 8'
42
15
Activity 3
Fraction Shuffle: Addition
Teacher will give each group of three students, number cards as shown below:
1.
Ask students to use the cards to make as many different fractions as they can
e.g.
2.
Guide the students in making addition exercises e.g.
+
3.
Let students make addition exercises and solve them.
23
Activity 4
Fraction Shuffle
Teacher will give each group of three students, number cards as shown below:
1.
0
Ask students to use the cards to make as many different fractions as they can
e.g.
OJ
2.
3.
Guide the students in making subtraction exercises e.g.
Let students make subtraction exercises and solve them.
24
1.10 Multiplication and Division of Fractions
Objectives include
(i) Multiplying and dividing fractions using proper and improper fractions
(ii) Multiply and dividing mixed numbers.
Activity 1
Multiplication and Division of Fractions
Teacher will copy the exercises on the chalkboard for students to do.
Write < , > , or = on each blank to make the equation true.
1.
1
- X - ------
4
2
-X-
5
3
5 3
3.
-
9
16
X
4 ------
3
-x3
5.
2
11
4
3
4
4
2.
3
2
6
7 3
21
- X - ----- -
4
5 3
4
4.
- X - ----- -
6.
- X -
5 3
7 9
9 7
Teacher will explain, with examples, that
X -
4
------
~
4
1
means 1+
~ . Remind them that
3
2
3
1+-
=
3
2
lx - .
Ask them to simplify the following fractions.
7.
1
8.
5
4
.1
1
2
9.
1
1
8
10.
Answers:
(1) > (2)
=
(3) < (4) > (5) > (6)
= (7) ~
25
(8) 2 (9) 8 (10)
~
7
3
1.11 Convert Fractions and Decimals to Percentages.
Objectives include:
(i) Convert fractions to percentages
(ii) Convert decimals to percentages.
Activity 1
Write each decimal or fraction as a percent.
2. 0.67 = ...------
3.
-------
6. 0.065
= -------
7.
0. 80 = -------
10. 0.35
= -------
1.
0.55
5.
-
=
2
100
9.
-----
0.075
11.
= ------
70
100
-
4.
-----
56
=
100
-
--------
8. 0.46 = ---------
0.90 = ------ 12. 0.4 == ------
PUZZLES
1.
~ is---------~
2. Find 20 ~ of 96.
3. _!_ of _!_ would be _ _
this~' you have all but -101 of. it.
5. This many thousandths is
5
4. Ifyou have
2
6. This many hundredths equals 52 %.
9.
8.
Answers: (1)
55~
(7) 70 ~
Puzzles: (1) 20
hundredths
(7) 33
~
~
7. 67
9. 10 ~ of310
(2) 67 ~ (3) 7.5
~
10.
~
~less
~
than 100 ~-
of 50~ of 80
(4} 56~ (5) 0.02
(8) 46 ~ (9) 80 ~ (10) 35
(2) 19.2 (3) 25
50~
2
~
(6) 6.5
~
(11) 90 ~ (12) 40%
(4) 90 ~ (5) 800 thousandths (6) 52
(8) 125 ~ (9) 31 (10) 20.
26
~
80~.
Activity 2
Change percentages to fractions and decimals
Teacher will copy the table on the chalkboard for students to complete
%
23
Percent fraction
Decimal
23
100
0.23
-
0.07
7
13
9
10
16
Answers:
%
23
7
Percent fraction
Decimal
23
100
0.23
7
0.07
-
100
13
9
10
16
-
0. 13
13
100
9
100
10
100
0.09
0. 10
0. 16
16
-
100
27
1.12 Patterns and Sequences
Ojectives include:
(i) Indentifying patterns and sequences
(ii) Establishing rules for patterns and sequences.
Activity 1
Teacher will copy the table below on the chalkboard and ask students to complete it.
2
2
2
2
2
2
X
X
X
X
X
X
1
2
3
5
6
7
Product
2
Reduced number
2
4
4
6
10
12
14
6
1
3
5
2X 8
2X 9
2
2
X
10
X ]}
2 X 12
2x13
Answers:
2 X }
2 X 2
2 X 3
2 X 5
2 X 6
2x7
2 X 8
2 X 9
2 X 10
2 X 11
2 X 12
2xl3
Product
2
4
6
10
12
14
16
18
20
22
24
26
Reduced number
2
4
6
I
3
5
7
9
2
4
6
8
28
Activity 2
Teacher will write the following on cards for each group of three. Students will complete
the "triangle".
1.
1
1
1
1
2
3
1
3
1
Teacher will guide the students in doing the following:
2.
In how many ways can the letters A, B, C be arranged?
Arrange the letters in all possible ways. Two ways are done for you: ABC, ACB.
3.
How many squares are there in each of the diagrams below?
4. Persons are in different rooms. Each person in each room shakes hands with every
other person exactly once. How many total handshakes happen if:
- two persons are in a r~om
- three persons are in a room
- four persons are in a room
.
.
- stx persons are m a room
Answers:
(1) 1 4
6 4 1 (2) 6 ways: ABC, ACB, BAC, BCA, CAB, CBA.
(3) 5, 14. (4) two persons- I; three persons- 3; four persons - 6;
six persons-15.
29
Unit2
Geometry
2.1
Triangle, square, rectangle, parallelogram, pentagon and hexagon
Objectives include:
(i)
Recognition of plane shapes - triangle, square, rectangle,
parallelogram, pentagon and hexagon.
(ii)
Determination of the properties of plane shapes - sides, angles,
vertices
Activity 1:
Measuring_angles of polygons
1.
2.
G
c
Sum of angles= _ _ _
3
Sum of angles= _ __
4.
n..------J
L
R
K
Sum of angles =
Teacher:
Sum of angles =
_ __
Distribute a worksheet with the above polygons to each student or
draw shapes as shown above and let students copy same in their
exercise books.
Instmct student to use their protractor to measure the size of each
angle and then find the sum of the angles for each polygon.
Each student is to record his/her angle sums on the table that
follows.
30
Have each student record his/her angle surns on the table below according to the
number of sides of each polygon
Number
.sides
---·--- -----·- -of
---
Sum of _a n_,g.._l_es__ _ _
3
4
----·------··-----~-------·---·---
5
- - - - - - - - --·--------+----·---·-----·-··- ·--4.
6
------~------~-
Give guidance to students as necessary
Answers to given polygons
- - --------·------...---·--- ----- - - · - - - - ,
Numbe:r of sid·es
Sun1of ._
a_
n~
gl_e_
s ______
-------------3
180°
----------·- -- - - 4
360°
· -- 5
540°
-- -- -- - - ---·---·--1------- - - - - 6
720°
-------------·..-··-·-·---'---------
.
-
31
,--_..;..;.
A_cltivi!;Y.~~:..___:!vfatching -:.TI?s can be used
for evaluatio=
n_ _
1\
i.....
Circle
·-··-]
[
I•entagon
~
·--
Hexagon
r-J
. . . . ''
...._
Triangle
......
4....
Square
Teacher:
Copy the above on chalkboard,, chart or worksheet
Have students draw a line to match each shape to its name.
32
Answers on next page
Circle
Pentagon
Hexagon
Rectangle
Square
33
Activity 2:
Properties of Polygons
so1ve each r1.ddle and wn'te the name ofth e polygon
l
th e rme.
1. I have two pairs of parallel lines.
All my sides are equal in length.
All my angles are right angles.
My diagonals are equal in length.
Who ami?
2. I have no parallel sides.
3. I have 3 sides.
I have 3 angles
The sum of my angles is 180°
Who ami?
4. My opposite sides are parallel
5. All my sides are equal in length.
All my angles are obtuse.
I have 3 pairs of parallel sides.
I have 6 angles
Who ami?
-6. · I have 2 pairs of parallel sides.
My opposite sides are equal in length.
All my angles are equal in size.
Who ami?
I have 5 vertices.
All my sides are equal in length.
· All my interior angles are equal.
..... Who ami?
My opposite sides are equal.
My opposite angles are equal.
None of my angles are right angles.
Who ami?
•
Teacher:
Answers:
Write the above on the chalkboard or chart.
Have students copy in there exercise books and solve the riddles.
1.
Square
2.
Pentagon
3.
Triangle
4.
Parallelogram 5.
Hexagon
6.
Rectangle
.
·•
34
2.2
Symmetrical shapes
Objectives include:
(i)
Recognition of symmetrical shapes and their properties.
(ii)
The properties of symmetrical shapes
Activi
1:
Draw in
1.
;,.
2.
5
3.
6
Teacher:
Copy the shapes above on the chalkboard, chart or worksheets.
Have individual students drawn the line of symmetry on each
shape.
35
Answers to drawing lines of symmetry on the given shapes
1.
4
2.
5
3.
6
-.
36
Activi
2:
lden ·
es with no lines of
A
B
c
'·
D
t:
J
\
E
F
[
HS
G
Teacher:
Copy the shapes above on the chalkboard, chart or worksheets.
Have students identify the shapes that do not have lines of
I
symmetry.
Answers:
J
B
c
F,
G
37
Activity 3:
Investigating some letters of the English Alphabet for lines of
Symmetry
Letters
Number of lines
of Symmetry
A
s
E
H
N
B
0
;..
z
Teacher:
Copy the table above on the chalkboard, chart or
worksheets.
Have students copy the table in their exercise books.
Let the students look at each letter and write the number of
lines of symmetry.
38
Answers:
Letters
Number of lines
of Symme-try
A
1
s
0
1:
12
-
H
N
B
0
0
1
Infi11ite
0
z
39
Unit 3
Statistlies
3.1
PiictogrUI[)h
Objectives indude:
(i)
Interpretation of data on a pictograph.
(ii)
Interpretation of data on a bar graph.
Activity 1:
Inte:rpr elting data on a pitctograph
The pic1ograph below shows how much was e:ar:nc!d by a vendor.
-·- - - - - - -------r----·---- · -
Mo~nt!!y Ec:arn~ed
D•1y·
·-··-----------·---+---·---·-~
..J~IItC,~Idcty ____
$ $ $ $ $
·ruE~sday'
$ $ $ $ $ $
·- - - - ·-------+· - - 'WVednesday'
$ . $ .$ $ $ $ $
- - - -- - - - --:-- ·--- - - -- ---l·h~~·rsday
.$ $ $ $
f:l•fiday'·
$ $ s· $ $ $ $
------$ ()1111e ·t h~ousandl
=
doll a•·s
1.
How much money did the vendor earn on Monday?
2.
How much money did the vendor earn on Wednesday?
3.
How much money did the vendor ecun on Monday and
VVed.ne.sday?
4.
On wlhich day did the vendor earn the~ least' money?
5.
On which day did the V<!ndor earn the most money?
6.
How much more money di'd the vendor ~!am on Friday than
Monday?
Teacher:
Copy the pictograph and questions above on the chalkboard or
chart.
Let students wTite the answers in their exercise books.
40
$
Discuss answers with students giving guidance where necessary.
Answers to questions on pictograph
1.
$5000
2.
$8000
4.
Thursday
5.
Wednesday
41
3.
6.
$13 000
$2000
3.2
Bar Graph
Objectives include the :interpretation of data on a bar graph.
Activity 2:
Interpreting d ata on a bar graph
The bar graph below shows the favourite colours of a group of students.
Favourite Colours of Students
Red
White
Green
Blue
Yellow
Colours
1.
How many students' favourite colour is red?
2.
How many students' favourite colour is green?
3.
How many students' favourite colours are red and white?
4.
How many students' favourite colours are blue and yellow? _ __
5.
Which is the most favourite colour for the students?
6.
Which is the least favourite colour for the students?
Teacher:
Copy the bar chart and questions above on the chalkboard or chart.
Let students write the answers in their exercise books.
Discuss answers with students giving guidance where necessary.
Answers to questions on bar chart.
1.
10
4.
4
4.
18
5.
Blue
42
3.
6.
18
Green
3.3
Tally Chart, Pictograph and Bar Graph
Objectives include:
(i)
Construction of Tally charts
(ii)
Construction of bar graphs
Activity 1:
Constructing a Tally Chart
The students in Miss King's class took a Mathematics quiz and got scores
out of 10, which are listed below:
3
6
5
7
7
3
4
6
8
7
8
9
6
1
10
6
4
5
3
8
8
7
6
9
9
10
5
8
2
6
7
3
7
9
8
5
5
3
9
7
Comp.ete the Ta11y Chart be1ow:
Fre·q uency
Score Tally
1
I
1
2
3
4
5
6
7
8
9
10
Teacher:
Copy the data and Tally Chart on the chalkboard.
Have the students copy the Tally Chart and complete same in their
chequered line exercise books
Discuss answers with students giving guidance where necessary.
43
Answer :
Score
Tally
1
I
I
2
3
Frequency
1
1
5
TTl/
4
II
2
5
trrl
5
6
-rm
7
~II
I
I
6
7
8
'--Hfr
9
m-r
5
10
II
2
44
6
Activity 2:
Constructing a bar graph
Construct a bar graph for the data below. Give your graph a title.
Number of Hours a Student Slept
Wednesday
Thursday
Friday
Saturday
Sunday
Teacher:
8 hours
8 hours
7 hours .
6 hours
9 hours
Copy the information above on the chalkboard.
Have the students construct the bar graph in their chequered line
exercise book. ·
Give guidance where necessary.
Suggested answer :
Number of Hours Student Slept
Wednesday Thursday
Friday
Saturday
Days
45
Sunday
.3.4
Mean, Median and mode
Objectives include the calculation ofthe mean, median and·mode of a set of
scores
Activity 1:
Calculating the mean, median and mode
In the space on the right, determine the mean, median and mode for each set of
data.
20,20, 13,20,20,26, 19, 19,26,17
Mean =
Median =
Mode =
96,68,86,67,92,92, 7,4
Mean =
Median =
Mode=
3.
6, 20, 20, 21, 21, 17, 10, 10, 10, 10,31
Mean=
Median =
Mode=
4.
14, 13, 18, 13, 15, 15, 15, 20,21
Mean =
Median=
Mode =
5.
18, 1, 1, 1, 10, 26, 18, 7, 9, 9,
Mean =
Median =
Mode=
1.
2.
46
In the space on the right, determine the mean, median and mode for each set of
data.
6.
24, 3, 11, 14, 26, 26, 7, 26, 16
7.
21, 3, 3, 20, 3, l., 20, 12, 5, 2
Mean =
Median =
Mode =
Mean =
JV.[edian =
Jv.[oCie =
:.V[ea.n =
8.
21, 12, 4 , 8, 12, 16, 3, 15, 10, 19
~\l£edian
~\l£ocle
9.
=
=
Mean =
Median=
Mode =
10, 19, 11, lO, 20, 13, 10, 9, 15
Mean =
10.
5,30,26,
5~ 26 :
10, 26, 10, 22, 20
Median =
Mode =
Tcach•~r:
Copy the above on the chalkboard, chart or worksheet.
Invite the studc~nts to find the mean, median and mode fi)r each set
of data, then compare answers with their peers.
47
Answers:
20,20, 13,20,20,26, 19, 19,26,17
Mean=
Median=
Mode=
20
20
20
64
96,68,86,67,92,92,7,4
Mean =
Median =
Mode=
6, 20, 20, 21, 21, l7, 10, 10, 10, 10,3 1
Mean=
Median=
Mode =
16
17
10
4.
14, 13, 18, 13, 15, 15, 15, 20,21
Mean =
Median=
Mode =
16
15
15
5.
18, 1, 1, 1, 10, 26, 18, 7, 9, 9,
Mean=
Median =
Mode =
10
9
1
1.
2.
3.
48
77
92
6.
24, 3, 11, 14, 26, 26, 7, 26, 16
Mean =
Median =
Mode =
17
16
26
21,3,3,20,3, 1,20, 12,5,2
Mean=
Median=
Mode=
9
7.
4
3
21, 12,4, 8, 12, 16,3, 15, 10,19
Mean=
Median =
Mode =
12
12
12
9.
10, 19, 11 , 10, 20, 13, 10, 9, 15
Mean =
Median =
Mode=
13
11
10
10.
5,30,26, 5,26, 10,26, 10, 22,20
Mean =
Median =
Mode =
18
21
26
8.
49
Unit4
Consumer Arithmetic
4.1
Simple Interest
Objectives include: the calculation of Simple Interest.
Activity 1:
Calculatine; Simple Interest
Number of Years
Interest ($)
1
2
3
5
7
9
50
100
150
The table shows the simple interest of $1 000 at 5% per annwn for a number of
years. Copy and complete the table and use it to find the interest on $1000 at 5%
for:
1.
3 years
2.
5 years
7 years
3.
9 years
4.
6 months
5.
3 months
6.
What would be the interest on $2000 for 2 years at the same rate?
7.
What
would be the interest on $2000 for 5 years at the same rate?
8.
What w ouJd be the interest for 5 years at double the rate?
9 ..
10.
.
What would be the interest for 5 years at half the rate (2
Teacher:
•
1
%)?
2
Copy the abov.e on the chalkboard, chart or worksheet.
Have the students use the ready reckoner to find answers to the
exercises .
Answers:
1.
4.
7.
10.
150
450
200
250
2.
5.
8.
50
250
25
500
3.
6.
9.
350
12.5
1000
4.2
..
Percentage increase or decrease
Objectives include the calculation of percent increase or decrease of given data
Activity 2:
Calculating percentage increase or decrease.
Solve the problems below using your knowledge of percent increase and
decrease.
1.
The price of a ticket to a concert increased from $500 to $600.
What was the percent increase?
A student answered 20 questions right on his first quiz and 25
2.
questions right on his second quiz. What was his percent increase?
3.
The amount of time Mia spent studying for her mathematics
examination went from 5 hours to 8 hours per week. What was the
percent increase?
4.
The selling price of a house moved from $5 000 000 to $8 000
000. What was the percent increase?
The number of students in a class dropped from 32 to 24. What
5.
was the percent decrease?
6.
At a sale the price of a DVD recorder was marked down from $20
000 to $15 000. What was the percent decrease?
7.
The number of spectators at a cricket match dropped from 10 000
to 8000. What was the percent decrease?
8.
The selling price of a house dropped from $6 000 000 to $5 900
000. What was the percent decrease to 1 decimal place?
Teacher:
Copy the above on the chalkboard, chart or worksheet.
Encourage the students to solve the problems.
Answers:
1.
4.
7.
20%
60%
20%
2.
5.
8.
51
25%
25%
1.7%
3.
6.
60%
25%
Unit 5: Measurement
5.1
Time Periods
Objectives include:
(i)
(ii)
Calculating duration over a period of time
Recognizing various units for using time.
Activity 1
Time Periods Sense
Teacber will ask the students to say whether the following statements make sense or not
and discuss their responses to help them to develop skills in selecting answers that make
the most sense.
.-
Say whether the statement makes sense or does not make sense .
1.
Allan went to bed at 13:00 hours after staying up late in the night to study.
2.
Amelia spoke for 30 minutes from 15:00 hours to 16:00 hours.
3.
Jimmy found out that there are 24 hours in a day.
4.
The minibus left Patentia at 08:30 hand arrived at 7:45 h on the same day.
5.
"There are exactly 24 months in a year," said Mr. Manny.
6.
Johnny left home at 08:00 h. He arrived at school30 minutes later.
He arrived at school at 08:30 h.
7.
Our lunch hour at school is at 16:00 h.
8.
I leave for school at 08:30 h to·reach at 09:00 h.
Answers: (1) Does not make sense (2) Does not make sense (3) Makes sense
(4) Does not make sense (5) Does not make sense ( 6) Makes sense.
(7) Does not make sense (8) Makes sense.
52
'•
Activity 2
Activity
Measurement Sense
Teacher will ask the students to say whether the following statements make sense or not
and discuss their responses to help them to develop skills in selecting answers that make
the most sense.
Say whether the following statements make sense or does not make sense.
1.
Pamela drank a glass of milk this morning. The glass held three litres of milk.
Makes sense/ does not make sense
2.
Amelia ran in the 1000 kilometres race and came in first.
Makes sense/ does not make sense
~
..
3. Jimmy measured the length of his desk. It was 100 millimetres long .
Makes sense/ does not make sense.
4. The distance around the racing track was about 400 metres.
Makes sense/ does not make sense.
5. "There are exactly 10 millimetres in one centimetre," said Mr. Moses.
Makes sense/ does not make sense.
6.
The length of a garden plot is 10 metres.
Makes sense/ does not make sense.
~
7. Mary drew a line 1 metre long in her exercise book.
8.
The tree was 2000 kilometres in height.
Answers: (1) Does not make sense (2) make sense (3) Does not makes sense
(4) Makes sense ( 5) Does not make sense ( 6) Makes sense (7) Does not
makes sense (8) Does not make sense.
5.2 Perimeter and Area of Plane Shapes
53
Objectives include:
(i) Finding perimeter of plane shapes
(ii) Finding the area of plane shapes.
Activity 1
Teacher will guide students step by step as they do the following exercises.
1. A rectangle (not a square) has a perimeter of36 em.
Which of the following cannot be that rectangle? You are free to draw rectangles to
find your answer.
(i) length 17 em, width 1 em
(ii) length 16 em, width 2 em
;
(iii) length 15 em, with 3 em
(iv)
length 14 em, width 4 em
(v)
length 13 em, width 5 em
(vi)
length 12 em, width 6 em
(vii)
length 11 <;m, width 7 em
(ix)
length 10 em, width 8 em
(x)
length 9 em, length 9 em .
..
2.
Find the area, in em2, of (i), (ii) and (iii) above.
Answers: ( 1) x ( 2) 17 cm2 , 32 cm2,45 cm2 .
54
5.3
Volume of C uboids and their Combinations
Objectives include
(i) Understanding the concept of volume
(ii) Calculating the volume of cuboids and their combinations.
Activity 1
1. Teacher will discuss with the children what is Volume.
2.
Teacher will remind students that volumes are measured in cubic units.
3.
Show the students models of a cube with volume 1 em 3 . Let them handle them.
4.
I I I I I
,
Teacher will draw a two by four rectangle ( two rows with four squares in each
row) on the chalkboard and ask students to say how many cubes are needed to
build cuboids 2 layers high on the rectangle.
•
5.
6.
.. .
Repeat with a four by four rectangle shown below for 5 layers of cubes.
Let students explain how they arrive at their answer for (4) and (5). Guide them to
an understanding that they can find the number of squares in the rectangle and
multiply the answer by the number of layers to find the number of cubes .
.
Answers: (4) 16 (5) 80
56
Activity 2
Teacher will ask students to find the volwne , in cubes, of lhe following:
1.
A 4 by 2 rectangle with two layers of cubes.
2.
A 3 by 2 rectangle with two layers of cubes.
3.
A 4 by 3 rectangle with two layers of cubes.
4.
A 3 by 3 recumgle
'~.rith
3 layers of cubes.
5.
--
-
[~-------- - - - - -l.
--
---
6 cm
14cm
Guide students to an understanding that 6layers of cubes are placed on a 14 by 8
rectangle.
Let them find the volume of the cuboid, in cm3.
6.
Let them identify (i) what is th(! length of the cuboid (ii) what is the width
(iii) what is the height.
7.
Let them explain what they dld to arrive at their answers.
,
Answers: ( 1) I 6 ~ubes (2) 12 cubes (3) 24 cubes ( 4) 27 cubes (5) 672 cm3 .
...
(6) (i) 14 em (ii) 8 em (iii) 6 em (7) Some possible responses: length x width
x height; area ofbase x height; 8 x 14 x 6
57