6th GradePrimary Mathematics

October 23, 2012

Algebraic ExpressionsAlgebraic expression can be used to describe an existing relationship.

Amelia was born when her mother was 25 years old.

Amelia’s Age

Mother’s Age

25 years

Amelia’s Age

Mother’s Age

25 years

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

X + 25

X

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

Graphs of FunctionsSally’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

0 5 + 0 = 5

1 5 + 1 = 6

3 5 + 3 = 8

7 5 + 7 = 12

x 5 + x

0 5 10

5

10

Number of Chores

Sally

’s Al

low

ance

($)

Primary Mathematics Textbook 6A page 26

Ellen’s Age Dylan’s Age

1 1 + 3 = 42 2 + 3 = 5x x + 3

Ellen’s Age (years)

Dyl

an’s

Age

(yea

rs)

How old will Ellen be when Dylan is 10?How old will Dylan be when Ellen is 10?

10 10 + 3 = 13

7

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?

Number of Rabbits

Number of Turtles

3T

T + 3R

R - 3

Writing Expressions

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?

Number of Girls

Number of Boys

G

4 x G

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?

Number of Girls

Number of Boys

B

B ÷ 4

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?

Number of Girls

Number of Boys

X

X

X

EquationsAn 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?

Number of Girls

Number of Boys

30

X

4X

x + 4x = 305x = 30

x = 6

6

6

66 6

There are 6 girls and 24 boys on the team.

Joel has three more rabbits than turtles. If he has 7 animals in all, how many rabbits does he have?

Number of Rabbits

Number of Turtles

3

7

Method 1

y

y + 3

y + 3 + y = 7

2y + 3 = 7

2y = 4

y = 2

2

2+ 3 = 5

Joel had 2 turtles and 5 rabbits.

Joel has three more rabbits than turtles. If he has 7 animals in all, how many rabbits does he have?

Number of Rabbits

Number of Turtles

3

7

Method 2

w

w - 3

w + w – 3 = 7

2w – 3 = 7

2w = 10

w = 5

5

5 – 3 = 2

Joel had 2 turtles and 5 rabbits.

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

$87.95 x

CD’sVideo Games

87.95 + x = 115.70 x = 27.75

Morris spent $27.75 on CD’s.

50

5

10

10

x + 4

Use the graph to solve for y

y = (12) + 4

12

10 = (8) + 4

50

5

10

10

x + 4

Use the graph to solve for x

x + 4 = 7

6 (12) + 4 = 1012

(6) + 4 = 7

x + 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?

Pens

Pencils

x

y

x x x x

y y

Number of Pens = 5x

Number of Pencils = 3y

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?

Pens

Pencils

s

t

Number of pens = 8s

Number of pencils = 10t

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.

Ben

Kathy

x y

yyyx

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?

Ben

Kathy

x y

yyyx

?

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?

Ben

Kathy

x y

yyyx

?

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?

$7700

Darryl’s money after a year

Amount Darryl had at first 10% of the original amount

11 units = $77001 unit = $70010 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?

Selling price of the bed frame

$625

Cost price of the bed frame 25% of the cost price

5 units = $6251 unit = $1254 units = $500 The cost price of the bed frame is $500.

Primary Mathematics Workbook 6A page 74

Primary Mathematics Textbook 6A page 77 Problem 3

100%

15% 40% ?? = 100 – 15 – 40? = 45

45%

Primary Mathematics Textbook 6A page 77 Problem 3

4000 seats

15% 40%

100% = 4000 tickets10% = 400 tickets 5% = 200 tickets 40% = 4(10%) = 4(400)=1600

45%

$120 $80 ?

45% = 1800 tickets1800 tickets are priced at $50

The figure is made up of two rectangles. Find the area of the figure.

30 feet

20 feet

20 feet

8 feet

10 feet

Area = 20 x 20Area = 400 square feet

Area = 10 x 8Area = 80 square feet

The area of the figure is 480 square feet.

Area = 80 + 400

PM 4A

The figure is made up of two rectangles. Find the area of the figure.

30 feet

20 feet

20 feet

8 feet

12 feet

Area = 30 x 8Area = 240 square feet

Area = 20 x 12Area = 240 square feet

Area = 240 + 240Area= 480 square feet

PM 4A

Primary Mathematics Textbook 6A page 95.

Number of pens

Number of pencils

The ratio of pens to pencils is 3 : 2

Primary Mathematics Textbook 6A page 137.

$ 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 $372.60

milesx

60.372$

mile 1

60.0$ x = 621 miles