Multiple-Choice Items:

1. How many total pieces would be created in a paper-folding activity used to model ?

A  7

B  12

C  42

D  48

2. Which expression would be a multiplication sentence used to represent the following area model?

3. What answer is represented by the following area model?

4. Simplify the following expression: .

5. Which of the following equations will give you the quotient ?

6. Gretchen walked 6 miles one day at the park. Gretchen rested every  of a mile. How many times did she rest during her 6-mile walk?

A  8 times

B  9 times

C  4 times

D  6 times

If it would be helpful, draw a pictorial representation to help solve problems 7, 8, and 9.

7. An oil mechanic can change the oil in a car in  of an hour. If he works a  hour shift, for how many cars can he change the oil?

A  7 cars

B  11 cars

C  20 cars

D  22 cars

8. You decide to make bookmarks out of a wide leather material to give to some of your friends. You have 38 inches of the leather material. Each bookmark will be  inches long. How many bookmarks can you make from this material?

A  5 bookmarks

B  7 bookmarks

C  8 bookmarks

  D  9 bookmarks

9. Jake went jogging. He ran four miles and noticed he ran for  of an hour. How many miles can he jog per hour if he keeps his current pace?

Multiple-Choice Answer Key:

1. C
2. A
3. B
4. B
5. C
6. B
7. D
8. C
9. A

Short-Answer Items:

10. A box of 24 cupcakes is arranged so that there are 4 rows of 6 cupcakes each. Three-fourths of the cupcakes are vanilla, and  of the vanilla cupcakes have chocolate frosting. Create a visual representation of an area model using a table array or paper folding to show what fraction of the total number of cupcakes is vanilla with chocolate frosting. Explain your model.

11. Draw a model of the expression  and simplify it or solve through repeated subtraction.

12. Create a division word problem using the following numbers:  and . Solve the problem using a picture representation.

Short-Answer Key and Scoring Rubric:

10. A box of 24 cupcakes is arranged so that there are 4 rows of 6 cupcakes each. Three-fourths of the cupcakes are vanilla, and  of the vanilla cupcakes have chocolate frosting. Create a visual representation of an area model using a table array or paper folding to show what fraction of the total number of cupcakes is vanilla with chocolate frosting. Explain your model.

11. Draw a model of the expression  and simplify it or solve through repeated subtraction.

Possible explanation:

See following rubric.

12. Create a division word problem using the following numbers:  and . Solve the problem using a picture representation.

Possible explanation: Brenda had  cups of brown sugar. The recipe for the batch of cookies she was making needed  of a cup. How many batches of cookies could she make with this amount of brown sugar?

Answer: 3 for any problem set up as or  for any situation with

See following rubric.

Use this scoring rubric for questions 10–12.

Performance Assessment:

Part I

A baker is making doughnuts. He has  cups of batter left. Each doughnut requires  cup of batter. Write an expression that shows how many doughnuts can be made with the remaining batter.

________________________________________________________________________

A baker had some boxes of doughnuts. He took  of the boxes for samples. He put  of the doughnuts from each box on a sample tray. Write an expression that shows the fraction of the doughnuts the baker put on the sample tray.

________________________________________________________________________

A teacher bought some doughnuts and of them had chocolate frosting. Only  of the doughnuts had cream filling. Write an expression to show the fraction of chocolate doughnuts with cream filling the teacher bought.

________________________________________________________________________

Using one of the expressions, create a picture representation and solve.

How is using a picture representation helpful in solving word problems?

Part II

To keep the doughnuts fresh in the boxes and to stop the doughnuts from sticking to the insides of the boxes, the bakery owner decided to line the insides of the boxes. Each box that fits 6 doughnuts requires  inches of liner. One roll of liner is 21 feet long. How many boxes can be lined from one roll?

Identify the important information you need to solve this problem.

______________________________________________________________________________

How do you know what operation to use to solve this problem?

______________________________________________________________________________

Solve the this problem using any method you choose. Be sure to include all the necessary steps.

Part III

The owner of the bakery across the street wanted to know the fraction of various kinds of doughnuts left over after a day’s business. At the end of the day,  of the doughnuts had chocolate frosting. If  of the doughnuts with chocolate frosting also had rainbow sprinkles, what fraction of the leftover doughnuts had both chocolate frosting and rainbow sprinkles? Use the area model to solve.

Performance Assessment Key:

Part I: Solution

A baker is making doughnuts. He has  cups of batter left. Each doughnut requires  cup of batter. Write an expression that shows the number of doughnuts that can be made with the remaining batter. 

A baker had some boxes of doughnuts. He took  of the boxes for samples. He put of the doughnuts from each box on a sample tray. Write an expression that shows the fraction of the doughnuts the baker put on the sample tray.

A teacher bought some doughnuts and of them had chocolate frosting. Only  of the doughnuts had cream filling. Write an expression to show the fraction of chocolate doughnuts with cream filling the teacher bought.

Using one of the expressions, create a pictorial representation and solve.

There are 12 s in . The answer: The baker can make 12 doughnuts.

How is using a picture representation helpful in solving word problems?

When you use a pictorial representation, you can visualize what happens when dividing fractions. You can “see” what the answer is when you are done without necessarily using an algorithm. Unfortunately, it might not always be practical or easy to represent a problem pictorially.

Part II: Solution

To keep the doughnuts fresh in the boxes and to stop the doughnuts from sticking to the insides of the boxes, the bakery owner decided to line the insides of the boxes. Each box that fits 6 doughnuts requires  inches of liner. One roll of liner is 21 feet long. How many boxes can be lined from one roll?

Identify the important information you need to solve this problem.

 inches for each box. Roll has 21 feet. Need to make feet into inches. 12 × 21 = 252 inches.

How do you know what operation to use to solve this problem?

I need to divide because I have been given a total amount (21 feet). I need to break up that amount into -inch pieces.

Solve this problem using any method you choose. Be sure to include all the necessary steps.

Part III: Solution

The owner of the bakery across the street wanted to know the fraction of various kinds of doughnuts left over after a day’s business. At the end of the day,  of the doughnuts had chocolate frosting. If  of the doughnuts with chocolate frosting also had rainbow sprinkles. What fraction of the leftover doughnuts had both chocolate frosting and rainbow sprinkles? Use the area model to solve.

Answer:

 (or ) of the doughnuts have both chocolate frosting and rainbow sprinkles.

Performance Assessment Scoring Rubric: