1. 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

2. 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.

3. 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

4. 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.

5. 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

6. 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

7. 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

8. 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.

9. 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
lbs = 360 lbs
32 lbs
360 lbs / 3 = 120 lbs
John
17 lbs
120 lbs
John weighs = 137 lbs
137 lbs

10. 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.

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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.