Transitions in Bar Modeling

Leveraging Elementary Singapore Math Strategies in Upper Grade Levels

Gregg Velatini

Dianna Spence2010 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?

1/6

1/3

Brad spent 5/6 of his money.

Brad’s Money

1/2

Beanies Nascar

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.

Rod 2

9 x 4 = 36 inches

Rod 1

72 inches

72 / 8 = 9 inchesRod 3

9

9 9 9 9

The length of the longest rod is 36 inches

9 9 9

Simple Percentages

Sherry made 250 donuts. She sold 80% of them. How many donuts did she left?

80%

250 Donuts

25

?

250 / 10 = 25

25 x 2 = 50

= 50 Donuts

Sherry’s Donuts

Sherry had 50 donuts left.

Solving a Simple Algebraic Equation

Three more than twice a number is eleven. What is the number ?

11

82x + 3 = 11

2x = 8

x = 8/2

x = 4

4 1 1 1

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

Jesse

3 Parts

4 Parts

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.

Clinton

Jesse

Clinton

Jesse

After

3 Parts

4 Parts

Before

40 Cards

2 Parts

1 Part

8 40/5 = 8

8 x 3 = 248 8 8

Clinton had 24 cards to begin with

Percentages

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?

Cats

After

60% = 120 females

Before 200 Cats

20

Cats

50% = 175 females

35

350 Cats

175 – 120 = 55 of the new cats were female.

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.

409 lbs

32 lbs

17 lbs

Brad

John

Gregg

409 - 17 - 32 lbs = 360 lbs

32 lbs

17 lbs

Brad

John

Gregg 360 lbs / 3 = 120 lbs

John 17 lbs120 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?

240 pcs

60

3/4 = 180 pcs

60 60 60

60 pcs

1/3 = 20 pcs

20 20 20

remainder Throw Away

60

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?

Candy

1/3

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?

Candy

Thrown Away = 20 x 2 = 40 pieces

3/4

20240 / 12 =20

Kid’s Candy

Robb’s Candy

Th

row

n

Aw

ay

1/3 of Remainder

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?

Sue

Bill

Both

1/3 Mailbox per hour

1/2 Mailbox per hour

Bar represents one mailbox

5/6 Mailbox per hour

Sue and Bill can paint 5/6 of a mailbox in one hour if they work together.

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?

Both

5/6 Mailbox per hour

Sue and Bill can paint 5/6 of a mailbox in one hour if they work together.

12 Min

1 hour

12

1 mailbox

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?

+ =

1 gal ? gal 3 gal

60 % ? % 80 %

3 gal -1 gal = 2 gal2 gal

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.