6th Grade
Primary Mathematics
October 23, 2012
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
25 years
X
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
8 + 25 = 33
14
14 + 25 = 30
22
22 + 25 = 27
X
X + 25
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
1x4=4
2
2x4=8
5
5 x 4 = 20
10
10 x 4 = 40
100
100 x 4 = 400
D
D x 4 = 4D
Graphs of Functions
Sally’s allowance is $5 per week. Her parents give
her an additional $1 for each chore that she does.
Sally’s Allowance ($)
Number of
Chores
0
1
3
7
x
10
5
0
5
Number of Chores
10
Sally’s
allowance
5+0=5
5+1=6
5+3=8
5 + 7 = 12
5+x
How old will Dylan be when Ellen is 10?
How old will Ellen be when Dylan is 10?
1
2
x
10
Dylan’s Age
1+3=4
2+3=5
x+3
10 + 3 = 13
Dylan’s Age (years)
Ellen’s Age
7
Primary Mathematics Textbook 6A page 26
Ellen’s Age (years)
Writing Expressions
Joel has three more rabbits than turtles.
(a)If Joel has T turtles, how many rabbits
does he have?
(b)If Joel has R rabbits, how many turtles
does he have?
T +R 3
Number of Rabbits
Number of Turtles
R -T3
3
There are four times as many boys on the track team as girls.
(a) If there are G girls on the track team, how many boys are on the team?
(b) If there are B boys on the tract team, how many girls are on the team?
(c) 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
4xG
There are four times as many boys on the track team as girls.
(a) If there are G girls on the track team, how many boys are on the team?
(b) If there are B boys on the tract team, how many girls are on the team?
(c) 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
There are four times as many boys on the track team as girls.
(a) If there are G girls on the track team, how many boys are on the team?
(b) If there are B boys on the tract team, how many girls are on the team?
(c) If there are X number of athletes on the track team, how many are girls
and how many are boys?
1
X
5
Number of
Girls
X
Number of
Boys
4
X
5
Equations
An equation is a mathematical statement of equality
between algebraic expressions.
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
5x = 30
x=6
X
Number of
Girls
6
There are 6 girls and
24 boys on the team.
30
Number of
Boys
6
6
6
4X
6
Joel has three more rabbits than turtles. If
he has 7 animals in all, how many rabbits
does he have?
Method 1
y+3
Number of Rabbits
Number of Turtles
y+3+y=7
2+ 3 = 5
7
2
y
2y + 3 = 7
2y = 4
3
Joel had 2 turtles and 5 rabbits.
y=2
Joel has three more rabbits than turtles. If
he has 7 animals in all, how many rabbits
does he have?
Method 2
w
Number of Rabbits
Number of Turtles
w+w–3=7
5
7
5–3=2
w-3
2w – 3 = 7
2w = 10
3
Joel had 2 turtles and 5 rabbits.
w=5
Morris spent $115.70 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
$87.95
CD’s
x
87.95 + x = 115.70
x = 27.75
Morris spent $27.75 on CD’s.
Use the graph to solve for y
𝑦=
1
2
x+4
10
1
2
y = (12) + 4
5
1
2
10 = (8) + 4
0
5
10
12
Use the graph to solve for x
𝑦=
10
5
0
5
6
10
12
1
2
x+4
1
2
x+4=7
1
2
(6) + 4 = 7
1
2
x + 4 = 10
1
2
(12) + 4 = 10
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.
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.
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
x
y
Ben
Kathy
y
y
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
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
x
y
?
Ben
Kathy
y
y
Kathy’s bucket weighs 2y more grams than Ben’s
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?
Amount Darryl had at first
10% of the
original amount
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
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?
Cost price of the bed frame
25% of the
cost price
Selling price of
the bed frame
5 units = $625
1 unit = $125
4 units = $500
$625
The cost price of the bed frame is $500.
Primary Mathematics Workbook 6A page 74
100%
15%
40%
?
45%
? = 100 – 15 – 40
? = 45
Primary Mathematics Textbook 6A page 77 Problem 3
4000 seats
$120
$80
?
15%
40%
45%
100% = 4000 tickets
10% = 400 tickets
5% = 200 tickets
40% = 4(10%) = 4(400)=1600
45% = 1800 tickets
1800 tickets are
priced at $50
Primary Mathematics Textbook 6A page 77 Problem 3
The figure is made up of two rectangles.
Find the area of the figure.
PM 4A
30 feet
8 feet
Area = 10 x 8
Area = 80 square feet
Area = 20 x 20
Area = 400 square feet
20 feet
10 feet
Area = 80 + 400
20 feet
The area of the figure is 480 square feet.
The figure is made up of two rectangles.
Find the area of the figure.
PM 4A
30 feet
8 feet
Area = 30 x 8
Area = 240 square feet
20 feet
12 feet
Area = 240 + 240
Area= 480 square feet
Area = 20 x 12
Area = 240 square feet
20 feet
Number
of pens
Number
of pencils
The ratio of pens to pencils is 3 : 2
Primary Mathematics Textbook 6A page 95.
$ 453.60
$27 $27 $27
Cost of mileage
Cost of mileage = 453.60 – 3 (27)
= 372.60
Primary Mathematics Textbook 6A page 137.
$ 453.60
$27 $27 $27
$0.60 $372.60

1 mile x miles
$372.60
x = 621 miles
Primary Mathematics Textbook 6A page 137.