- Four friends want to share 10 cupcakes evenly. How many cupcakes does each person get? Show how you got your answer.
- Four friends want to share 7 pizzas so each person gets the same amount and there is no pizza left over. How much pizza should each person get? Show how you got your answer.
- Abdi, Kate, and Sarita want to share 7 cups of juice evenly. How many cups of juice should each receive? Show how you got your answer.
- 6 children want to equally share 4brownies. If all the brownies are the same size, how much of a brownie will each person get? Show how you got your answer.
- Eight students in Mrs. Day’s class equally shared 3 candy bars. Sixteen students in Mr. Morris’s class equally shared 6 candy bars. All the candy bars were the same size. Who would receive more candy bar, a student in Mrs. Day’s class or a student in Mr. Morris’ class? Explain why your answer is correct.
Recording Student Responses
The assessment items were developed from work described by various researchers. Please give this assessment to at least one class that you are teaching. The assessment will take students approximately 20-25 minutes to complete. The students are not allowed to use a calculator on this assessment. Please do not help the students as they take the Summative Assessment. Use the scoring grids below to record the results of your students. To facilitate comparison, the Summative Assessment questions are all related to the same numbered question on the Baseline Assessment.
- Four friends want to share 10 cupcakes evenly. How many cupcakes does each person get? Show how you got your answer.
Response: Q1 (4 share 10) / Number of responses
correct response
or
or
cupcakes / Picture showing all cupcakes broken in halves and each person receiving 5 halves
Additive Coordination
Picture showing each person receiving 2 whole cupcakes, with remaining two cupcakes broken in half and shared
Additive Coordination
Division (10÷ 4) used to justify answer
Multiplicative Coordination
10 sharing 4 the same as 5 sharing 2, so each person receives or cupcakes
Ratio
Correct answer; no justification
incorrect or incomplete response / 2
2 R 2
Other incorrect
No response/ don’t know
- Four friends want to share 7 small pizzas so each person gets the same amount and there is no pizza left over. How much of a pizza should each person get? Show how you got your answer.
Response: Q2 (4 share 7) / Number of Responses
correct response
;
or ;
or 1.75;
or 1 + ½ + ¼ of a pizza / Picture showing each pizza split in fourths, each person gets 7 fourths
Additive Coordination
Picture showing each person receiving 1 whole pizza, plus either ¾ or ½ + ¼ of a pizza
Additive Coordination
Division shown as justification
Multiplicative Coordination
Other correct answer, including correct answer with no explanation
incorrect or incomplete response / pizza each (with remainder thrown away)
Non-Anticipatory Sharing
1 R 3
Picture with pizza split in 4 equal pieces, but student is unable to determine the size of those pieces
other incorrect
No response / don’t know
- Abdi, Kate, and Sarita want to share 7 cups of juice evenly. How many cups of juice should each receive? Show how you got your answer.
Response: Q3 (3 share 7) / Number of Responses
correct response
or 2 /
Picture showing 7cupsdivided in thirds, with each student receiving 7 thirds
Additive Coordination
2
Picture showing person receiving 2 whole cupsand of the remaining cup
Additive Coordination
Division used to justify correct answer
(possibly with work showing =2)
Multiplicative Coordination
Other correct, including correct with no explanation
incorrect or incomplete response / 2
Non-Anticipatory Sharing
2
(remainder gets ignored or thrown away)
Non-Anticipatory Sharing
2 R 1
other incorrect
No response / don’t know
- 6children want to equally share 4 pizzas. If all the pizzas are the same size, how much pizza will each person get? Show how you got your answer.
Response: Q3 (6 share 4) / Number of Responses
correct response
or / Picture showing 4 pizzas divided in sixths, with each child receiving 4 pieces
Additive Coordination
Reasons that 6 sharing 4 is the same as 2 sharing 3
Ratio
Division shown as justification
Multiplicative Coordination
Other correct, including correct with no explanation
incorrect or incomplete response / or 1 ½ or 1.5
Non-Anticipatory Sharing
other incorrect
No response / don’t know
- Eight students in Mrs. Day’s class equally shared 3 candy bars. Sixteen students in Mr. Morris’s class equally shared 6 candy bars. All the candy bars were the same size. Who would receive more of a candy bar, a student in Mrs. Day’s class or a student in Mr. Morris’ class? Explain why your answer is correct.
Response: Q6 / Number of Responses
Correct response
“Each person gets the same amount of a candy bar” / Drawing or explanation showing that Mr. Morris’ class can be thought of as 2 groups of 8 students sharing 3 candy bars, and so they get the same amount.
Reasoning based on Ratio
Explanation showing that 6 ÷ 16 gives students the same amount as 3 ÷ 8.
Reasoning based in Fractions as Quotients
Other correct answer (including those with incomplete or no explanation)
Incorrect response / Mrs. Day’s students get more
Mr. Morris’ students get more
No response / don’t know