Gregg Velatini Dianna Spence 2010 GCTM Transitions in Bar Modeling Leveraging Elementary Singapore Math Strategies in Upper Grade Levels Gregg Velatini Dianna Spence 2010 GCTM

Solving Simple Fraction Problems Brad spent 1/3 of his money on Beanie Babies and 1/2 of it on Nascar collectables. What fraction of his money did he spend altogether? What fraction did he have remaining? 1/3 1/2 Brad’s Money Beanies Nascar 1/6 Brad spent 5/6 of his money. Brad had 1/6 of his money remaining.

Simple Ratios and Proportions The lengths of three rods are in the ratio of 1:3:4. If the total length is 72 inches find the length of the longest rod. 72 inches Rod 1 9 Rod 2 9 9 9 72 / 8 = 9 inches Rod 3 9 9 9 9 9 x 4 = 36 inches The length of the longest rod is 36 inches

Simple Percentages Sherry made 250 donuts. She sold 80% of them. How many donuts did she left? 250 / 10 = 25 25 x 2 = 50 250 Donuts Sherry’s Donuts 25 80% ? = 50 Donuts Sherry had 50 donuts left.

Solving a Simple Algebraic Equation Three more than twice a number is eleven. What is the number ? 2x + 3 = 11 2x = 8 x = 8/2 x = 4 8 4 1 1 1 11 The number is 4

Ratios and Proportions The ratio of Clinton’s baseball cards to Jesse’s baseball cards was 3:4. After Clinton bought another 40 baseball cards, he had twice as many baseball cards as Jesse. How many baseball cards did Clinton have at first? Clinton 3 Parts Jesse 4 Parts

Set this up as a “Before and After” problem. The ratio of Clinton’s baseball cards to Jesse’s baseball cards was 3:4. After Clinton bought another 40 baseball cards, he had twice as many baseball cards as Jesse. How many baseball cards did Clinton have at first? Set this up as a “Before and After” problem. 8 8 8 Clinton 8 x 3 = 24 Before 3 Parts Clinton had 24 cards to begin with Jesse 4 Parts 40 Cards 40/5 = 8 Clinton 8 2 Parts After Jesse 1 Part

Percentages Before After Karen’s cat condo boards cute calicos for companionless curmudgeons. In September, the condo boarded 200 cats, 60% of which were female. In October, another 150 cats were added to the condo, and the percentage of female cats was reduced to 50%. How many of the new cats were female? Before 200 Cats Cats 20 60% = 120 females After 350 Cats Cats 35 50% = 175 females 175 – 120 = 55 of the new cats were female.

The combined weight of Brad, John and Gregg is 409 lbs The combined weight of Brad, John and Gregg is 409 lbs. Gregg is 32 lbs heavier than Brad and Brad is 17 lbs lighter than John. Find John’s weight. Brad John Gregg 17 lbs 409 lbs 32 lbs Brad John Gregg 17 lbs 409 - 17 - 32 lbs = 360 lbs 32 lbs 360 lbs / 3 = 120 lbs John 17 lbs 120 lbs John weighs 120 + 17 = 137 lbs 137 lbs

Solving Fraction Equations Robb’s kids got 240 pieces of candy on Halloween. After performing a “safety check” on the candy, he let his kids keep 3/4 of their haul, took 1/3 of the remainder for “further inspection”, and threw away the rest. How many pieces did he throw away? 3/4 = 180 pcs 1/3 = 20 pcs Throw Away remainder 240 pcs 60 60 60 60 20 60 60 pcs Robb threw away 40 pieces of candy.

Solving Fraction Equations Robb’s kids got 240 pieces of candy on Halloween. After performing a “safety check” on the candy, he let his kids keep 3/4 of their haul, took 1/3 of the remainder for “further inspection”, and threw away the rest. How many pieces did he throw away? Candy

Solving Fraction Equations Robb’s kids got 240 pieces of candy on Halloween. After performing a “safety check” on the candy, he let his kids keep 3/4 of their haul, took 1/3 of the remainder for “further inspection”, and threw away the rest. How many pieces did he throw away? Candy 1/4

Solving Fraction Equations Robb’s kids got 240 pieces of candy on Halloween. After performing a “safety check” on the candy, he let his kids keep 3/4 of their haul, took 1/3 of the remainder for “further inspection”, and threw away the rest. How many pieces did he throw away? 1/3 Candy 1/4

Solving Fraction Equations Robb’s kids got 240 pieces of candy on Halloween. After performing a “safety check” on the candy, he let his kids keep 3/4 of their haul, took 1/3 of the remainder for “further inspection”, and threw away the rest. How many pieces did he throw away? 1/3 of Remainder Robb’s Candy Candy Kid’s Candy Thrown Away 20 240 / 12 =20 3/4 Thrown Away = 20 x 2 = 40 pieces

Rate of Work Problems Sue can paint a mailbox in 2 hours. It takes Bill 3 hours to paint the same mailbox. How long will it take them to paint three of the mailboxes working together? 1/2 Mailbox per hour Bar represents one mailbox Sue Bill 1/3 Mailbox per hour Sue and Bill can paint 5/6 of a mailbox in one hour if they work together. Both 5/6 Mailbox per hour

Rate of Work Problems Sue can paint a mailbox in 2 hours. It takes Bill 3 hours to paint the same mailbox. How long will it take them to paint three of the mailboxes working together? 1 hour Sue and Bill can paint 5/6 of a mailbox in one hour if they work together. Both 12 Min 5/6 Mailbox per hour 1 mailbox 12 First Hour Second Hour Third Hour 36 min

Ratios and Proportions What amount and concentration of acid solution must be added to 1 gal of 60% acid solution in order to get 3 gal of 80% acid solution? 3 gal -1 gal = 2 gal 2 gal ? gal 1 gal 3 gal ? % 60 % + = 80 % There are 24 shaded units here. 6 come from the first bucket. 18 must come from the second bucket. Shading each gallon equally to get 18 total shaded units results in each gallon with 9 of 10 shaded units 2 gal of 90% acid solution must be added to 1 gal of 60 % acid solution to yield 3 gal of 80% acid solution.