Problem 44 worked answer
Rook's Gallery Record
Designed for Grade 2 · Grade 3 · Uses Middle Grade 2 math · About 5–12 minutes
At a glance
- 1.
- 2.
- 3.
- 4.
- 5-6. One equation can be , and the different equation can be .
Equations with addends in the opposite order, such as , are also correct.
1. The delivery total
The word and joins the 12 sun tiles and 7 moon tiles. The word altogether names their total, 19:
The equivalent equation is also correct.
2. Tiles left after filling the high case
Rook starts with 19 tiles and separates 8 into the high case. The 11 tiles that remain are represented by
3. The two cases make the whole delivery
The high case and low case are the two parts. Together they make the 19-tile whole:
The equation says the same thing.
4. Round and square low-case tiles
The 5 round tiles and 6 square tiles are parts of the 11-tile low case:
The equation is equivalent.
5. Show the comparison with addition
The low case has 3 more tiles than the high case. Starting at the high case's 8 and adding the difference gives
6. Show the comparison a different way
The same relationship can be read backward: the difference between 11 and 8 is 3.
A complete response may instead use the subtraction form for part 5 and the addition form for part 6, as long as the equations are different.
Proof that the record is represented completely
Each response can be checked against the nouns in its note: the sun and moon parts make the delivery whole; removing the high-case part leaves the low-case part; the two cases remake the delivery whole; the two shapes remake the low-case whole; and the final addition and subtraction equations both compare the same two cases. Therefore every supplied relationship appears in the equations, and no equation uses a quantity from a different note.
Check
Every equation uses only the numbers from its note, and both sides have the same value. The first four equations match a join or separate relationship. The last two show the same comparison in two different but equivalent ways.
Technical fit and rating
Operations and computation · Algebraic structure and equations
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