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**6th Grade Primary Mathematics**

October 23, 2012

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**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

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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

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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

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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

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**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

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**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

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**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

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**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

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**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

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

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**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

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**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.

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**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.

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**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.

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**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

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**Use the graph to solve for x**

10 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

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**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.

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**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.

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**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

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**? 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

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**? 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

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**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

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**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

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

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**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

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**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.

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**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

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**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.

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**$ 453.60 $27 $27 $27 Cost of mileage Cost of mileage = 453.60 – 3 (27)**

= Primary Mathematics Textbook 6A page 137.

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

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Division ÷ 1 1 ÷ 1 = 1 2 ÷ 1 = 2 3 ÷ 1 = 3 4 ÷ 1 = 4 5 ÷ 1 = 5 6 ÷ 1 = 6 7 ÷ 1 = 7 8 ÷ 1 = 8 9 ÷ 1 = 9 10 ÷ 1 = 10 11 ÷ 1 = 11 12 ÷ 1 = 12 ÷ 2 2 ÷ 2 =

Division ÷ 1 1 ÷ 1 = 1 2 ÷ 1 = 2 3 ÷ 1 = 3 4 ÷ 1 = 4 5 ÷ 1 = 5 6 ÷ 1 = 6 7 ÷ 1 = 7 8 ÷ 1 = 8 9 ÷ 1 = 9 10 ÷ 1 = 10 11 ÷ 1 = 11 12 ÷ 1 = 12 ÷ 2 2 ÷ 2 =

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