1. 6th Grade Primary Mathematics
October 23, 2012

2. Algebraic Expressions
Algebraic expression can be used to describe an existing relationship.
Amelia was born when her mother was 25 years old.
25 years
Amelia’s Age
Mother’s Age

3. X
25 years
Amelia’s Age
Mother’s Age
X + 25
Will Amelia’s mother always be 25 years older than Amelia?
Amelia's Age
Her mother’s age 1
1+ 25 = 26 5
5+ 25 = 30 8
= 33 14
= 30 22
= 27 X
X + 25

4. John takes all of his dollar bills to the bank to exchange them for quarters. How many quarters will he receive?
Number of Dollars
Number of Quarters 1
1 x 4 = 4 2
2 x 4 = 8 5
5 x 4 = 20 10
10 x 4 = 40
100
100 x 4 = 400 D
D x 4 = 4D

5. Graphs of Functions
Sally’s allowance is $5 per week. Her parents give her an additional $1 for each chore that she does.
Number of Chores
Sally’s allowance
5 + 0 = 5 1
5 + 1 = 6 3
5 + 3 = 8 7
5 + 7 = 12 x
5 + x 10
Sally’s Allowance ($) 5 5 10
Number of Chores

6. How old will Dylan be when Ellen is 10?
How old will Ellen be when Dylan is 10?
Ellen’s Age Dylan’s Age
= 4
= 5
Dylan’s Age (years)
x x + 3
= 13 7
Ellen’s Age (years)
Primary Mathematics Textbook 6A page 26

7. Writing Expressions T + 3 T 3
Joel has three more rabbits than turtles.
If Joel has T turtles, how many rabbits does he have?
If Joel has R rabbits, how many turtles does he have?
T + 3 R
Number of Rabbits
Number of Turtles T 3
R - 3

8. G 4 x G There are four times as many boys on the track team as girls.
If there are G girls on the track team, how many boys are on the team?
If there are B boys on the tract team, how many girls are on the team?
If there are X number of athletes on the track team, how many are girls and how many are boys? G
Number of Girls
Number of Boys
4 x G

9. B ÷ 4 B There are four times as many boys on the track team as girls.
If there are G girls on the track team, how many boys are on the team?
If there are B boys on the tract team, how many girls are on the team?
If there are X number of athletes on the track team, how many are girls and how many are boys?
B ÷ 4
Number of Girls
Number of Boys B

10. There are four times as many boys on the track team as girls.
If there are G girls on the track team, how many boys are on the team?
If there are B boys on the tract team, how many girls are on the team?
If there are X number of athletes on the track team, how many are girls and how many are boys?
1 5 X
Number of Girls X
Number of Boys
4 5 X

11. Equations
An equation is a mathematical statement of equality between algebraic expressions.

12. There are four times as many boys on the track team as girls.
If there are 30 athletes on the team, how many girls and boys are there?
x + 4x = 30
There are 6 girls and 24 boys on the team. X
5x = 30
x = 6
Number of Girls 6 30
Number of Boys 6 6 6 6 4X

13. Method 1 2+ 3 = 5 2 y + 3 y + 3 + y = 7 2y + 3 = 7 7 2y = 4 y 3 y = 2
Joel has three more rabbits than turtles. If he has 7 animals in all, how many rabbits does he have?
Method 1
y + 3
y y = 7
2+ 3 = 5
Number of Rabbits
2y + 3 = 7 7 2
Number of Turtles
2y = 4 y 3
y = 2
Joel had 2 turtles and 5 rabbits.

14. Method 2 5 5 – 3 = 2 w w + w – 3 = 7 2w – 3 = 7 7 2w = 10 w = 5 3
Joel has three more rabbits than turtles. If he has 7 animals in all, how many rabbits does he have?
Method 2 w
w + w – 3 = 7 5
Number of Rabbits
2w – 3 = 7 7
5 – 3 = 2
Number of Turtles
2w = 10
w = 5 3
w - 3
Joel had 2 turtles and 5 rabbits.

15. Morris spent $115. 70 on CD’s and Video Games. If he spent $87
Morris spent $ on CD’s and Video Games. If he spent $87.95 on Video Games, how much did Morris spend out CD’s?
$115.70
Video Games
CD’s x
$87.95
x =
x = 27.75
Morris spent $27.75 on CD’s.

16. y = 1 2 (12) + 4 10 = 1 2 (8) + 4 Use the graph to solve for y
𝑦= x + 4 10
y = (12) + 4 5
10 = (8) + 4 5 10 12

17. Use the graph to solve for x10
1 2 x + 4 = 7
1 2 (6) + 4 = 7 5
1 2 x + 4 = 10 5 6 10
1 2 (12) + 4 = 10 12

18. Algebraic Expressions II
There are x pens in a box and y pencils in a box. If Mrs. Smith purchased 5 boxes of pens and 3 boxes of pencils, how many writing implements did she buy? x x x x x
Number of Pens = 5x
Pens
Pencils
Number of Pencils = 3y y y y
Mrs. Smith bought 5x + 3y writing implements in all.

19. s t Mrs. Smith purchased 8s + 10t writing implements in all.
There are 8 pens in a box and 10 pencils in a box. If Mrs. Smith purchased s boxes of pens and t boxes of pencils, how many writing implements did she buy? s
Number of pens = 8s
Pens
Pencils
Number of pencils = 10t t
Mrs. Smith purchased 8s + 10t writing implements in all.

20. At a farm, Ben and Kathy were each given a bucket that weighed x grams
At a farm, Ben and Kathy were each given a bucket that weighed x grams. Ben picked y grams of blueberries. The blueberries Kathy picked were three times as heavy as Ben’s. x y
Ben
Kathy x y y y

21. ? x y Ben Kathy x y y y The total weight of both buckets is 2x + 4y
At a farm, Ben and Kathy were each given a bucket that weighed x grams. Ben picked y grams of blueberries. The blueberries Kathy picked were three times as heavy as Ben’s. What is the total weight of both buckets? x y
Ben ?
Kathy x y y y
The total weight of both buckets is 2x + 4y

22. ? x y Ben Kathy x y y y Kathy’s bucket weighs 2y more grams than Ben’s
At a farm, Ben and Kathy were each given a bucket that weighed x grams. Ben picked y grams of blueberries. The blueberries Kathy picked were three times as heavy as Ben’s. How much more does Kathy’s bucket weight than Ben’s bucket? ? x y
Ben
Kathy x y y y
Kathy’s bucket weighs 2y more grams than Ben’s

23. Darryl has $7700 in his investment account after a year
Darryl has $7700 in his investment account after a year. He earned 10% of it as interest. How much did he have in his account at first?
10% of the original amount
Amount Darryl had at first
Darryl’s
money after
a year
$7700
11 units = $7700
1 unit = $700
10 units = $7000
Darryl had $7000 in his account at first.
Primary Mathematics Workbook 6A page 73

24. Mr. Arasim sold a bed frame for $625
Mr. Arasim sold a bed frame for $625. The selling price was 25% more than the cost price. What is the cost price of the bed frame?
25% of the cost price
Cost price of the bed frame
Selling price of the bed frame
$625
5 units = $625
1 unit = $125
4 units = $500
The cost price of the bed frame is $500.
Primary Mathematics Workbook 6A page 74

25. 100% ?
15%
40%
45%
? = 100 – 15 – 40
? = 45
Primary Mathematics Textbook 6A page 77 Problem 3

26. 45% = 1800 tickets 1800 tickets are priced at $50 4000 seats $120 $80?
15%
40%
45%
45% = 1800 tickets
100% = 4000 tickets
10% = 400 tickets
5% = 200 tickets
40% = 4(10%) = 4(400)=1600
1800 tickets are priced at $50
Primary Mathematics Textbook 6A page 77 Problem 3

27. The figure is made up of two rectangles. Find the area of the figure.
PM 4A
30 feet
Area = 10 x 8
Area = 80 square feet
8 feet
Area = 20 x 20
Area = 400 square feet
20 feet
10 feet
Area =
20 feet
The area of the figure is 480 square feet.

28. The figure is made up of two rectangles. Find the area of the figure.
PM 4A
30 feet
Area = 30 x 8
Area = 240 square feet
8 feet
20 feet
Area = 20 x 12
Area = 240 square feet
12 feet
20 feet
Area =
Area= 480 square feet

29. The ratio of pens to pencils is 3 : 2
Number
of pens
Number
of pencils
The ratio of pens to pencils is 3 : 2
Primary Mathematics Textbook 6A page 95.

30. $ 453.60 $27 $27 $27 Cost of mileage Cost of mileage = 453.60 – 3 (27)=
Primary Mathematics Textbook 6A page 137.

31. $
$27
$27
$27
$372.60
x = 621 miles
Primary Mathematics Textbook 6A page 137.