Problem 45 worked answer
Jules's Nested Workshop Note
Designed for Grade 4 · Grade 5 · Uses Early Grade 5 math · About 6–15 minutes
At a glance
- 1.
- 2.
- 3.
- 4.
- 5. Luna doubles the trays and settings but adds the 5 tags only once. Each of the two cabinets has 5 tags, so the 5 must be inside the group multiplied by 2: .
1. One tray
One tray holds 8 green settings and 4 gold settings. Those two kinds belong together inside one tray:
2. Three trays in one cabinet
Each of the 3 trays has the same group of settings. Parentheses preserve that repeated group:
3. One finished cabinet
The 5 tags are added after all three trays are filled. They belong to the finished cabinet, but they are not repeated for every tray:
4. Two finished cabinets
There are two copies of the entire finished-cabinet group. Brackets make that whole group visible:
Parentheses may replace the brackets if the nesting is still clear: .
5. Diagnose and repair the near miss
Luna's expression
correctly doubles the three trays and all of their settings. However, the sits outside the part multiplied by 2. The expression therefore counts only one cabinet's set of five tags instead of two sets.
Moving the five-tag addition inside the outer group repairs the story:
Check
Each finished cabinet has settings and 5 tags, for 41 objects. Two matching cabinets therefore have objects. The layered equation and the direct check agree.
Technical fit and rating
Algebraic structure and equations
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