# data[].attributes.body
Malik wants to give candy bars to his twelve friends. He wants to give them three-fourths of a candy bar each. How many candy bars will he need?
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Problem Type:
Multi-Groups-Multiplication
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Rationale:  High-Level problem because it is a number sentence, using 3/4 instead of 1/4 or 1/2, and the total is not given, must find it.  Student will need to multiply by a fraction.

Students solved two Equal Sharing problems correctly.  This problem changes format and gives the number of friends as well as the fraction each friend will received, but asks the students to find the number of candy bars that will be shared.
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Anticipated Responses:
1.  three-fourths may not be represented properly as 3/4.  Maybe 34.
2.  Guess and check:  Student may just guess that they need to multiply 12 and 3/4.
3.  Repeated addition - add 3/4 together 12 times and reduce.
Direct Modeling - draw the candy bars as 3/4 and add for 12.
Transitional - when adding the 3/4's  recognize that 3/4 + 3/4 is 1 1/2 so add 1 1/2 6 times.
Multiplicative 12 * 3/4 is 9 candy bars.
Questioning:
Explain the information that is given.
Can you explain again the strategy that you used.
Can you write a number sentence for this problem?
Could you have done this a different way? If so, how?
What does 12 represent?
What does 3/4 represent?
How can you solve this problem?

# data[].attributes.body
There are 8 people who want the same type of fabric.  If each person is given 2/3 yards, what is the total amount of fabric that is to be shared?
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Problem Type:
Multiple Groups - Multiplication
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Rationale: This is a high-level problem because it asks student to partition the group into 2/3rds and to also distribute a remainder that is a fraction.  This problem requires students to find the total amount of fabric to be shared rather than the amount of fabric that each person would receive.

This is a bit more challenging than previous problems. Students are given this problem if they've had minor success solving previous Equal Sharing problems.
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Anticipated Responses:
1.Multiply 2/3 x 8 = 5 1/3 CORRECT
2.  Model 2/3 eight times. CORRECT.
3. Divide 8 by 2/3. INCORRECT.
---------------------------------Questioning:
Can you explain again the strategy that you used?
Can you write a number sentence for this problem?
Could you have done this a different way? If so, how?
Explain the information that is given.
What does 8 represent?
What does 2/3 represent?
Is this a division or multiplication problem

# data[].attributes.body
2 children were sharing 5 sandwiches.  If the students shared the sandwiches equally, how many sandwiches would each student get?
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Problem Type:
Equal Sharing
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Number Sets (# is the 2nd number: 3, 5, or 7)
Newcomer: (2, 3)
OGL: (2, 5)
AGL: (2, 7)
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Rationale:
Lower level question that asks students to share equally and share the remainder giving a fraction of 1/2

Students did not solve the first two Equal Sharing problems correctly, so this problem has a smaller number of groups to work with.
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Anticipated Responses:
1. Divide # by 2 = CORRECT (less likely since did not solve previous problem
2. Additive Coordination, one item at a time, with each child receiving 1 1/2 sandwiches.  CORRECT.
3. Divide 2 by # =   INCORRECT
4. No Coordination between sharers and shares: They create equal shares but do not use up everything. Incorrext
5. Strategies: Direct modeling, Repeated Addition, or Trial and Error or guessing for students who are having difficulty with the language or fractions.
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Questioning:
After each child received the whole sandwich(es), how much is left?
What do you do with the leftover sandwich?
Explain what you know about solving this problem.
Can you identify the dividend and the divisor?
Do you think representing the problem by  drawing a picture will help you solve the problem easily?
Can you write a similar problem like this one.
What does 2 represent?
What does 5 represent?
How can you solve this problem?

# data[].attributes.body
Kito and Frida have 5 cookies.  If they share the cookies equally, how many cookies would each person get?
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Problem Type:
Equal Sharing
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Rationale: This problem is a low level problem because the only fraction is 1/2.  May understand better with less cookies to share

Students are given this problem if attempts to solve the previous problems have all been unsuccessful.
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Anticipated Responses:
1. Divide 5 by 2 - 2 1/2.  CORRECT.
2. Solve additively.  Each child would receive cookies until there is only 1 cookie left that they would split.  CORRECT.
3. Distribute the cookies evenly with 1 cookie left over. INCORRECT.
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Questioning:
What type of problem is this?
How do you know?
In what other ways can we solve this problem?
How do you know your answer is right?
What does 5 represent?
How many people are sharing the cookies?
How many groups are there?
Can you write this as a number problem?
Can you write another problem similar to this one?

# data[].attributes.body
4 kids were sharing 5 small pizzas. How much pizza would each kid get if they shared the pizza equally?
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Problem Type:
Equal Sharing
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Number Set (# is the second number, 1, 5, or 9)
Newcomer: (4, 1) - Answer 1/4
OGL: (4, 5) - Answer 1 1/4
AGL : (4, 9) - Answer 2 1/4
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Rationale:
This is a low level question that asks students to share equally and share the remainder giving a fraction of 1/4

Students did not solve the first equal sharing problem correctly, so this problem has a similar situation with a smaller number of items to share.
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Anticipated Responses:

1. Divide # (2nd number in number set by 4)
CORRECT (multiplicatively - less likely)

2. Additive Coordination with one item at a time. CORRECT
3. Divide 4 by # = 4/# INCORRECT
4. No coordination between sharers and shares: They create equal shares but do not use up everything.
5. Strategies: Direct Modelling, Repeated Addition, or Trial and Error, or guessing for students who are having difficulties with the language or fractions.
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Questioning:
Is the question the same/different as the previous problem?
Explain in your own words how you solved this problem.
Is there another strategy you could have used?
Can you solve this problem with/without a picture (number sentence)?
What does 4 represent?
What does 5 represent?
How can you solve this problem?

# data[].attributes.body
Tim Gunn has 15 pounds of beads. He wants to distribute the 15 pounds of beads among 10 containers. How many pounds will each container hold?
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Problem Type:
Equal Groups
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Rationale:
This problem goes back to forming equal groups to solve,  where the number of items being shared is larger than the number of containers being used.

Students are given this problem after solving all Equal Sharing problems correctly, but making a mistake in solving the Multi-Groups problem given previously.
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Anticipated Responses:
1. Divide 15 by 10 = 1 5/10 or 1 1/2 CORRECT.
2. Create a fraction 15/10 = 1 5/10 or 1 1/2 CORRECT.
3. Additive Coordination, one item at a time, with each child receiving 1 1/2 pounds of beads.  CORRECT.
4. Multiplicative Coordination, with each child receiving 15/10, or 1 1/2 pounds of beads.  CORRECT
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Questioning:
In what two ways can we solve this problem?
Can this problem be written as a division problem?
Explain your thinking.
Can you write a similar problem ?
What does 15 represent?
What does 10 represent?
How can you solve this problem?

# data[].attributes.body
Jayden has 7 sour cherry strips. He put the strips into two bags.  How many pieces of fruit strip are in each bag?
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Problem Type:
Partitive Division
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Rationale: Student was not able to distribute three times and divide remaining into fourths.  Try dividing remaining into halves
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Anticipated Responses:
1. Divide 7 by 2 = 3 1/2 CORRECT.
2. Divide 2 by 7 = .3 INCORRECT.
3. Additive Coordination by Distributing three times and dividing the remaining fruit strip into halves. CORRECT.
4. Distributing the fruit strips evenly, with 1 strip left over.  INCORRECT.
----------------------------------------Questioning:
Can you explain again the strategy that you used?
Can you write a number sentence for this problem?
Could you have done this a different way? If so, how?
Explain the information that is given.
What does 7 represent?
What does 2 represent?
How could you solve this problem?
Is this a division or multiplication problem?

# data[].attributes.body
Jayden has eighteen bags.  He put fruit strips into the bags.  If each bag contains one-fifth of the total amount of fruit strips, how many bags can he fill?
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Problem Type:
Multiple Groups-Multiplication
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Rationale:
This is a high-level problem because it is a multi-group problem that uses a fraction that students can't easily split in half and the numbers are in words.

Students receive this problem if they successfully solved a Measurement Division problem.  In the previous problem, the number of groups was missing.  In this problem, the total amount is missing.

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Anticipated Responses:
1. Divide 18 into fourths = 4 1/2 CORRECT.
2. Additively distributing fruit strips four times and then dividing the remainder evenly = 4  2/4 or 4 1/2.  CORRECT.
3. Distribute the fruit strips evenly with 2 strips left over.  INCORRECT.
4. Multiply 18 x 1/4 - 4 1/2 CORRECT.
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Questioning:
Can you explain again the strategy that you used?
Can you write a number sentence for this problem?
Could you have done this a different way? If so, how?
Explain the information that is  given.
What does 18 represent?
What does 1/4 represent?
How could you solve this problem?
Is this a division or multiplication problem?

# data[].attributes.body
Tim Gunn has 20 pounds of beads.  He wants to distribute the beads into containers so that each one will have 3/4 pounds of beads inside.  How many containers can he fill?
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Problem Type:
Measurement Division
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Rationale:
Mid-level question where the number of groups (whole number) is missing which is more challenging to solve.   In previous problems,the fraction was missing.

Students are given this problem after solving all previous problems correctly.
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Anticipated Responses:
1. Multiply 20 x 3/4 = 15 CORRECT.
2. Divide 20 x 3/4 = 80/3 INCORRECT.
3. Model 3/4 20 times.  CORRECT
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Questioning:
What integers do you need to solve this problem?
Can you represent this problem by drawing a picture?
Can you write this problem as a fraction?
How did you solve this problem?
What does 20 represent?
What does 3/4 represent?
How can you solve this problem?

# data[].attributes.body
The teacher has 7 sandwiches.  She gave them to 5 students, with each student receiving the same amount. How many pieces of sandwich will each student get?
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Problem Type:
Partitive Division/Equal Groups
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Rationale: A mid level question where students would use equal groups to solve but also requires them to divide items into smaller parts rather than simply half.

Previous problems required use of Equal Sharing to solve.  To reach this question, one problem was solved incorrectly and one was solved correctly.
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Anticipated Responses:
1. Divide 7 by 5 =  1 2/5 CORRECT.
2. Solve additively using grouping. Each child would receive 1 sandwich.  Then the last sandwich would be shared equally by dividing into fifths. CORRECT.
3. Distribute the sandwiches evenly with two sandwiches left over. INCORRECT.
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Questioning:
Write a number sentence for this problem.
In what other ways can you solve this problem?
Write a similar problem.
How did you solve this problem?
What does 7 represent?
What does 5 represent?
How can you solve this problem?

# data[].attributes.body
There are 15 yards of fabric for 4 people to share.  How many yards of fabric can each person get if they share the fabric equally?
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Problem Type:
Partitive Division/Equal Sharing
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Rationale: it is similar to the previous problem.  The difference is that the fabric problem makes them distribute twice instead of once.

Students are given this problem if they have had minor success solving previous Equal Sharing problems.
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Anticipated Responses:
1.  Divide 15 by 4 = 3  3/4 CORRECT.
2. Solve additively giving each person 3 yards of fabric until there is 1 yards left that need to be distributed evenly by dividing into fourths = 3 3/4 CORRECT.
3. Distribute the fabric evenly with 3 yards left over.  INCORRECT.
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Questioning:
Can you explain again the strategy that you used?
Can you write a number sentence for this problem?
Could you have done this a different way? If so, how?
Explain the information that is given.
What does 15 represent?
What does 4 represent?
How could you solve this problem?

# data[].attributes.body
You have 13 brownies.  If they are put into packages of 4, how many packages can you fill?
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Problem Type:
Multiple Groups: Partitive Division
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Rationale:
A mid level question that is a bit more challenging than forming equal groups, but not too difficult. Students are given the number of groups and the total number, but the fraction is unknown.

Students are given this problem if they were unable to solve the second Equal Sharing  problem correctly.
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Anticipated Responses:
1. Divide 13 by 4 = 3 1/4 CORRECT
2. Additive Coordination by Distributing three times and dividing the remaining brownies into fourths. CORRECT.
3.  Additive Coordination by Grouping - 3 whole and 1/4 of another.  CORRECT.
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Questioning:
What do you need to know to solve this problem?
How can you illustrate this problem?
Do you think you can solve this on a number line?
Can you write this problem as a fraction?
Can you explain your thinking?
If not solved: Is this a division or multiplication problem?
What does 13 represent?
What does 4 represent?
How can you solve this problem?

# data[].attributes.body
4 children want to share 9  sandwiches so that everyone gets the same amount.  How much can each child have?
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Problem Type:
Equal Sharing
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No number sets for this question as it is the beginning of the interview.
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Rationale:
Middle to Low Level Question. 1/2 and 1/4 is low level, Low level and 3/4 and 1/3 and 1/10 is Mid Level. All else is high level.  Distribute twice then share equally as a fraction what is left
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Anticipated Responses:
1. Divide 9 by 4 = 2 1/4 or 2 1/2
2. Divide 4 by 9 = .44 INCORRECT
3. Additive Coordination with Groups - Each student would receive 2 whole sandwiches and 1/4  - CORRECT
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Questioning:
What do you know about this type of problem?
What mathematical operation comes to mind as you read this problem?
Explain in your own words how you solved this problem.
Is there another strategy that you could have used?
Can you solve this problem with/without a picture (number sentence)
What does 4 represent?
What does 9 represent?
How can you solve this problem?

# data[].attributes.body
Avery had 15 cupcakes at her birthday party for 4 children to share equally.  How much cupcake can each child have?
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Problem Type:
Equal Sharing
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Number Sets
Newcomer: (10, 4)
OGL: (15, 4)
AGL: (24, 7)
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Rationale:
Mid-level question where each person will need to split cupcakes that will result in each getting 3.  The fraction that each person will receive is unknown.

Students solved the first Equal Sharing problem correctly.  This problem is a similar format with a bigger number of items to share.
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Anticipated Responses:
1. Divide 20 by 6 = 3 2/6 or 3 1/3. CORRECT
2.  Divide 6 by 20 = .3 INCORRECT
3. Additive Coordination with Groups of Items, or using Multiplicative Coordination, with each child receiving 3 1/3 cupcakes. CORRECT
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Questioning:
What is this question asking you to do?
Can you write this question as a fraction?
Can you solve this problem in a different way?
How did you solve this problem?
What does 15 represent?
What does 4 represent?
How can you solve this problem?

# data[].attributes.body
Kito and Frida have 13 cookies.  If they share the cookies equally, how many cookies would each person get?
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Problem Type:
Equal Sharing
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Rationale: This is a low-level, equal sharing problem where the only fraction students need to create is 1/2.

Students are given this problem if attempts to solve the previous problems have all been unsuccessful.
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Anticipated Responses:
1. Divide 13 by 2 = 6 1/2 CORRECT.
2. Solve additively.  Each child would alternate receiving cookies until there is only 1 cookie left that they would split.  CORRECT.
3. Distribute the cookies evenly with 1 cookie left over. INCORRECT.
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Questioning:
What is this problem asking you to do?
Explain in your own words how to solve this problem.
What is the dividend?
What is the divisor?
Write this problem as a fraction.
What does 13 represent?
How many people are sharing the cookies?