Manuel, Philip, and Marina's Work. Choose and display a student work sample to demonstrate how to provide feedback and to clarify the Math Practices Expectations as they relate to this problem. Figures 3–8 show sample sets of work and sample feedback notes for different student groups to help you facilitate this discussion. Masters for display are also available for the student work in these figures.
Reviewing student work samples is a valuable learning experience for children. Student work samples are provided as Masters in this lesson, but it is even more meaningful for students to evaluate the work of their classmates. Classroom work samples are better reflections of classroom instruction, and students have more ownership in them. Be sure to ask permission before displaying a student's work and black out the student's name to provide anonymity.
Give students a few minutes to look at the student work sample selected and then provide feedback on a display of the Class Party Feedback Box Master. Prompts and possible responses for each of the student work samples follow.
Display the Manuel, Phillip and Marina's Work Master. Manuel, Philip, and Marina's work and a review of their work using a Feedback Box are shown in Figures 3 and 4.
- Do you think Manuel, Philip, and Marina know the problem? (Yes, they had a plan that used under $10 for 25 people. However, they added a piñata to their plan even though the problem says to choose from the list.)
- How did they go about solving this problem? (They listed the things they planned to buy for the party and how much they would cost for 25 people. Then they found the total cost of that party plan. They made several tries until they found a plan that spent close to $10 without going over.)
- Did Manuel, Philip, and Marina choose a good strategy? How do you know? (Yes, their strategy to find the total cost and their problem-solving process is organized in a logical order and it is clear. They chose the correct operations and made several tries until they had a good solution. They made good decisions.)
- Tell how Manuel, Philip, and Marina checked if their answer was reasonable. (They did not show if or how they checked the answers for reasonableness. They found a plan that spent the most money, but they added the piñata to do that.)
- How did Manuel, Philip, and Marina check their calculations? (They did not show or tell how they checked their calculations. It's not clear if they checked. All the totals are correct except their chart shows a total in plan 3 of $9.98 and the sentences say it is $9.08, which is the correct total.)
- Did this group show or tell how they solved the problem so you can understand their thinking? (They clearly showed how they came up with the totals for each item and their problem-solving process. But they did not show how they came up with the subtotals for each item. For example, how did they know the lemonade would cost $7.50 for 25 students? The table only tells the cost of the lemonade for 10 servings is $2.50. They also chose an item not listed in the table and did not give a reason for doing that.)
- Did they use appropriate labels? (All the numbers are labeled with the item and they used correct money labels. The totals are also labeled and each step in each party plan is labeled. The money labels are all written correctly except the two cents left over in the last sentence.)
- What feedback would you provide Manuel, Philip, and Marina? (Responses will vary.)
- Based on Manuel, Philip, and Marina's work, what changes would you make to your solution? (Responses will vary.)
Grace and Emma's work. Display the Grace and Emma's Work Master. Grace and Emma's work and a review of their work using a Feedback Box are shown in Figures 5 and 6.
- Do you think Grace and Emma know the problem? (Yes, they figured out that they needed to plan for 25 people and chose different items until they could no longer stay under $10.)
- How did they go about solving this problem? (Grace and Emma wanted to serve ice cream at the party then figured out what else they could buy with the money left from the $10.)
- Did Grace and Emma choose a good strategy? How do you know? (Yes, their sentences explained their strategy clearly. They chose the correct operations and worked until the first solution worked.)
- Tell how Grace and Emma checked if their answer was reasonable. (They did not show if or how they checked the answers for reasonableness, but they did say they got as close to the $10 as they could and showed that with number sentences.)
- How did Grace and Emma check their calculations? (They did not show or tell how they checked their calculations, but all their number sentences are correct.)
- Did this group show or tell how they solved the problem so you can understand their thinking? (Yes, they clearly described which items they chose, how many they would need for 25 people, and how they figured out how much that would cost. Grace and Emma showed the original cost of items from the table and how they used that number to solve the problem. They also showed how they added each item until they got close to $10.)
- Did they use appropriate labels? (Yes and no; the numbers are clearly labeled in the written part in the sentences but not in the addition problems at the bottom of the page. Labeling those numbers would have made their explanation easier to follow. They used all money signs correctly. )
- What feedback would you provide this group? (Responses will vary.)
- Based on Grace and Emma's work, what changes would you make to your solution? (Responses will vary.)
Pete and Matt's work. Display the Pete and Matt's Work Master. Pete and Matt's work and a review of their work using a Feedback Box are shown in Figures 7 and 8.
- Do you think Pete and Matt know the problem? (Yes, they spent most of the $10 on items for 25 people. They did not explain how or why they made those choices though.)
- How did they go about solving this problem? (Pete and Matt seemed to want to give each person a serving of lemonade and then spend the rest of the money on what they could. They chose the right operations but did not show them. They didn't explain how or why they made choices.)
- Did Pete and Matt choose a good strategy? How do you know? (It looks like they use a good strategy because they found a good solution very close to $10, but they didn't show or tell how they made choices or used the information from the table.)
- Tell how Pete and Matt checked if their answer was reasonable. (Pete and Matt did not show or tell how they checked their solution for reasonableness but they did reach a solution that took them close to the $10.)
- How did they check their calculations? (They do not explain how they checked their calculations, but all of their computations are correct.)
- Did this group show or tell how they solved the problem so you can understand their thinking? (They clearly show what numbers they added and what number they ended on, but there are not labels. They also do not show or tell how they made any of their decisions or the items they chose.)
- Did they use appropriate labels? (No, they did not use any labels.)
- What feedback would you provide this group? (Responses will vary.)
- Based on Pete and Matt's work, what changes would you make to your solution? (Responses will vary.)
After discussing Pete and Matt's solution, ask the class to help revise their work. Ask students to add to Pete and Matt's solution so that it better communicates what they did to solve the problem. See Figure 9 for some suggested revisions.
