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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 = 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 = 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.