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Open-Ended Template

Names: Catherine Elder, Barb Sleith, Doaquin Smith, Kathy Semanko

Grade Level: 6 – 8 Content Area: Probability/Predictions

PA standard(s) addressed: NCTM standard(s) addressed:

2.7.8C Analyze predictions Data Analysis & Probability

2.4.8B Combine numeric relationships

to arrive at a conclusion

Problem Name: Ice Cream Social

Problem:

Class Ice Cream Survey

Item	Cost	Frequency
Popsicle	$.40 each	3
Chocolate Bar	$.50 each	3
Ice cream sandwich	$.60 each	8
Dreamsicle	$.75 each	10

Ms. Jones randomly surveyed 24 students to determine their favorite ice cream treats. The total population at Miller School is 288 students.

A. How many of each treat are needed for the entire school?

B. How much would it cost to purchase all the treats based on your answer from part A?

Directions:

For full credit, you must do the following:

1. show OR describe each step of your work, even if you did it in your head (“mental math”) or used a calculator,

AND

2. write an explanation stating the mathematical reason(s) WHY you chose each of your steps.

Problem Name: Ice Cream Social

Grade Level: 6 – 8 Content Area: Probability/Prediction

Problem Solution:

1A. 3/24 = x/288 1. To predict the number of each treat

x = 36 popsicles needed for the entire school

and x = 36 chocolate bars

10/24 = x/288

x = 120 Dreamsicles

8/24 = x/288

x = 96 ice cream sandwiches

2A. .40 x 36 = $14.40 2. Multiply cost/item times number of

.50 x 36 = 18.00 items to find the total cost of 288

.75 x 120 = 90.00 treats.

.60 x 96 = 57.60

$180.00

Alternate Solutions

1B. 288/24 = 12

12 x 3 = 36 popsicles

and 36 chocolate bars

12 x 8 = 96 ice cream sandwiches

12 x 10 = 120 Dreamsicles

1C. 3/24 = 1/8 1/8 of 288 = 36 popsicles

and 36 chocolate bars

8/24 = 1/3 1/3 of 288 = 96 ice cream sandwiches

10/24 = 5/12 5/12 of 288 = 120 Dreamsicles

OR

2B. .40 x 36 + .50 x 36 + .75 x 120 + .60 x 96 = $180

(Subtotals need not be shown.)

Problem Name: Ice Cream Social Problem

Grade Level: 6-8 Content Area: Probability/Predictions

Specific Rubric:

5: Advanced Understanding, Excellent

Correct answers and labels with correct procedures and calculations shown or described AND explanations for both finding the number of each treat needed for the entire school and finding the total cost of 288 treats. Only one calculation needed to find number of chocolate bars and popsicles due to same frequency. Subtotals ($14.40, 18.00, 90.00, and 57.60) do not need to be shown.

4: Satisfactory Understanding

A. Correct answers and labels with all correct procedures and calculations shown BUT insufficient or no explanation. Subtotals ($14.40, 18.00, 90.00, and 57.60) do not need to be shown.

B. Correct answers and labels with most procedures/calculations shown

AND some explanation.

(Example: Student does not show or explain that popsicles and chocolate bars are the same.)

3: Almost Satisfactory Understanding

A. Correct answers and labels with half or more correct procedures and calculations shown AND no explanation.

B. Correct answers and labels with few correct procedures and calculations shown AND some explanation.

C. Incorrect answers with correct procedures shown or described, some explanation with one calculation or copying error carried throughout the problem.

2: Partial Understanding

A. Correct answers with few correct procedures and calculations shown OR some explanation.

B. Incorrect answers but with two or more item totals correct (36 popsicles, 36 chocolate bars, 120 Dreamsicles, 96 ice cream sandwiches) with half or more correct procedures and calculations shown or described AND some or no explanation.

C. Incorrect answers with correct procedures shown or described AND no

explanation AND with no more than two calculation or copying errors

carried throughout the problem.

1: Minimal Understanding

A. Correct answers with procedures, calculations and explanations that are not legible, not understandable, or missing or incorrect.

B. Incorrect answers with at least one correct procedure shown or described or explained. If there is a calculation with a procedure, it MUST be correct.

0: No Understanding

Incorrect answers with no correct procedures, calculations or explanations

shown or described. May, also, include a question mark or two (??) or “I

don’t know” written on page.