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Transitions in Bar Modeling Leveraging Elementary Singapore Math Strategies in Upper Grade Levels

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Transitions in Bar ModelingLeveraging Elementary Singapore Math Strategies in Upper Grade Levels

Gregg Velatini

Dianna Spence

2010 GCTM

- 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.

72 inches

9 x 4 = 36 inches

- 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.

9

Rod 1

9

9

9

Rod 2

72 / 8 = 9 inches

Rod 3

9

9

9

9

The length of the longest rod is 36 inches

250 Donuts

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

250 / 10 = 25

25 x 2 = 50

Sherry’s Donuts

25

?

80%

= 50 Donuts

Sherry had 50 donuts left.

8

11

1

1

1

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

2x + 3 = 11

2x = 8

x = 8/2

x = 4

4

The number is 4

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?

Clinton

Jesse

40 Cards

2 Parts

1 Part

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

40/5 = 8

8

Clinton

After

Jesse

200 Cats

350 Cats

- 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

20

Cats

60% = 120 females

After

35

Cats

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

50% = 175 females

409 - 17 - 32 lbs = 360 lbs

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.

John

John

17 lbs

17 lbs

17 lbs

Brad

Brad

Gregg

Gregg

32 lbs

32 lbs

360 lbs / 3 = 120 lbs

John weighs 120 + 17 = 137 lbs

John

120 lbs

137 lbs

- 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

Throw Away

1/3 = 20 pcs

remainder

20

20

60

20

60

60

60

60

240 pcs

60 pcs

- Robb threw away 40 pieces of candy.

- 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

- 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

1/3

Candy

1/4

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

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?

Rate of Work Problems

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

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?

Rate of Work Problems

1 hour

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

Both

12 Min

1 mailbox

12

5/6 Mailbox per hour

Second Hour

Third Hour

First Hour

36 min

- 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

? %

80 %

60 %

+

=

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.