1. By: Chelsey Collins and Emina Susic

2. 5 th /6 th grade: Hanover5 th grade: Henrico  Brought in manipulatives for the first problem  Broke up the students into groups of 2 and had them solve each problem and explain it to the other students  Brought manipulatives for only the first part, wanted to use it for every problem  Had problems understanding how to set up problems, needed help with that

3. 5 th /6 th grade: Hanover5 th grade: Henrico  Stack ◦ At first student A tried working it out without manipulatives. ◦ After using manipulatives she was able to come to the correct solution. ◦ Student B was able to come up with the solution in his head by using mulitiplication and division, he came up with a different answer as student A, but it was still correct.  Stacks ◦ Needed help getting started and setting up the stacks ◦ Played around with the manipulatives in order to be able to find the answer, which was 26

4. 5 th /6 th grade: Hanover5 th grade: Henrico

5. 5 th /6 th grade: Hanover5 th grade: Henrico  The students were able to solve most problems by themselves without the help of manipulatives.  They understood multiplication and division and even ratios.  Were able to explain how they solved each problem as well.  They understood how to multiply and divide the problems

6. 5 th /6 th grade: Hanover5 th grade: Henrico  One student wasn’t able to solve the problem without the help of manipulatives.  Used patterns instead of multiplication and division to solve problem A, which works, but isn’t the most effective.  Didn’t understand ratios  Didn’t know how to divide 60 from 540  Wanted to use manipulatives for every problem

7. 5 th /6 th grade: Hanover5 th grade: Henrico  My student for C was also not able to see that 60 and 540 could be simplified before dividing.  They understood the basics of ratios (what you do to one, you must do to the other), but they did not actually put them in ratio form.  Not being able to simplify two large numbers to solve a problem