Texas Grab-and-Go Substitute Packet · Teacher Answer Key

Answer Key: Multiplication and Fair Shares

Grade: 3 Subject: Mathematics For teacher use only Math

How to use this key

Answers are grouped by section and question number, with the full steps. Accept any correct method that reaches the right answer — drawing dots, skip-counting, repeated addition, or a known fact are all fine at Grade 3. A basic calculator is allowed, so grade the reasoning and the drawing/steps, not just the final number. Watch-for notes flag common misconceptions. Estimated grading time: ~3–5 min per packet.

Start Warm-Up ~1 min

1 Skip-count by 5: 5, 10, 15, ___, ___.

20 and 25. Each number is 5 more than the one before (15 + 5 = 20, 20 + 5 = 25). Watch-for: a student who writes 16, 17 is counting by 1, not by 5.

2 How many in all — 3 groups of 4 dots (Figure 1).

12 dots. 3 groups of 4 = 4 + 4 + 4 = 12, or 3 × 4 = 12. Accept counting all the dots one by one. Alternate: a student may write 4 × 3 = 12; either order is fine here.

Build Study the Math ~1 min

3 Find 5 × 2 (5 groups of 2).

10. 5 groups of 2 = 2 + 2 + 2 + 2 + 2 = 10, so 5 × 2 = 10. Full credit for a drawing of 5 groups with 2 dots each and the answer 10. Alternate: skip-counting by 2 (2, 4, 6, 8, 10) or writing 2 × 5 = 10 is fine.

Apply Use What You Know ~2–3 min

4 Equal groups: 5 bags, 4 apples each.

20 apples. 5 bags × 4 apples = 5 × 4 = 20 (or 4 + 4 + 4 + 4 + 4 = 20). Accept 4 × 5 = 20. Watch-for: a student who writes 5 + 4 = 9 has added instead of multiplied.

5 Array match (Figure 3): 2 rows of 6.

2 rows; 6 in each row; 2 × 6 = 12 (accept 6 × 2 = 12). The array is 2 rows with 6 dots in each row, so there are 12 dots in all. Watch-for: a student who swaps rows and columns (says 6 rows of 2) still reaches 12; gently correct the row/column labels but the product is right.

6 Fair share: 15 crayons shared among 3 friends.

5 crayons each. 15 ÷ 3 = 5. Sharing 15 into 3 equal groups puts 5 in each group. Check with multiplication: 3 × 5 = 15. Accept a drawing of 3 groups with 5 crayons dealt into each. Watch-for: a student who writes 15 ÷ 3 = 12 (subtracted) or divides into the wrong number of groups.

7 Find and fix the mistake (Figure 4): 4, 3, 4 dots.

The mistake: the groups are not equal — Group 1 has 4, Group 2 has only 3, and Group 3 has 4. You can only multiply (3 × 4) when every group has the same number, so 3 × 4 = 12 does not fit this picture.
Correct count: add the groups: 4 + 3 + 4 = 11 dots in all.
Full credit requires (1) naming that the groups are not equal (Group 2 has 3, not 4) and (2) the correct total, 11. Alternate: a student may fix it by saying "if it were really equal groups, add one more to Group 2 to make 3 × 4 = 12" — accept this if they clearly explain the groups were unequal.

Explain Tell How You Know (Q8) ~1–2 min

8 Explain the fair share of 15 crayons among 3 friends.

Model answer. Answer: each friend gets 5 crayons. Picture or numbers: 3 groups with 5 in each group, or 15 ÷ 3 = 5, or the check 3 × 5 = 15. Why it is fair: every group has the same number (5), so no friend gets more or fewer than another — that is what "fair share" means. Full credit requires the correct answer (5) and a reason that the groups are equal / everyone gets the same amount.

Explanation scoring rubric (3 points)

Score	Answer	Picture or numbers	Why (reasoning)
3	Correct: 5 each.	Shows 3 equal groups of 5, or 15 ÷ 3 = 5 (or 3 × 5 = 15).	Clearly says it is fair because every group has the same number.
2	Correct: 5 each.	Some picture or numbers shown, or a small slip.	Reasoning present but incomplete (e.g., "everyone gets 5" without saying why that is fair).
1	Answer attempted, may be wrong.	Little or no picture/numbers.	Weak or missing reasoning.
0	No/incorrect answer.	No work.	No reasoning.

Close ACE ~1 min

ACE Articulate / Connect / Extend.

Articulate: accept any plain-language version of "equal groups means every group has the same number in it."
Connect: items where students multiplied include Q3, Q4, and Q5 (and the check in Q6/Q8). Any correctly named item earns credit.
Extend: any correct equal-groups multiplication fact not in the packet — e.g., 2 × 5 = 10, 3 × 3 = 9, 4 × 2 = 8, 2 × 6 = 12. Check the fact is true and uses equal groups.

Challenge Early Finisher (optional)

EF Draw 6 × 2, then the same as a 2 × 6 array.

6 × 2 = 12. Six groups of 2 dots = 2 + 2 + 2 + 2 + 2 + 2 = 12. As an array, the same 12 dots make 2 rows of 6, so 2 × 6 = 12. Full credit for a labeled drawing of 6 groups of 2 and an array showing 12, with both sentences. Teaching point: 6 × 2 and 2 × 6 give the same total — the array can be turned to show either.

Watch Common misconceptions

Adding instead of multiplying. In Q4, a student may write 5 + 4 = 9 instead of 5 × 4 = 20. Remind them "5 bags of 4" means 4 counted 5 times, not 5 + 4. Drawing the 5 bags with 4 apples each makes it clear.
Unequal groups (the Q7 error). Students see three ovals and multiply 3 × 4 without checking that each group truly holds 4. You can only multiply when the groups are equal; when they are not (4, 3, 4), you must add: 4 + 3 + 4 = 11.
Mixing up × and ÷. In the fair-share problem (Q6), some students multiply 15 × 3 instead of dividing 15 ÷ 3. Anchor the words: "share equally" and "each gets" signal division. Check by multiplying back: 3 × 5 = 15.
Rows vs. columns. In Q5 a student may call it "6 rows of 2." The product (12) is still correct, but coach the labels: rows go across, and here there are 2 rows with 6 in each.
Skip-counting by 1. In Q1, watch for 16, 17 instead of 20, 25 — the student counted by 1, not by 5.

Teacher follow-up based on likely errors

If many students miss Q7, do a quick picture of three equal groups next to three unequal groups so they see multiplication needs equal groups. If Q4 shows 5 + 4 = 9, draw the bags of apples and count. If Q6 shows multiplying instead of dividing, deal out counters (or drawn dots) into 3 groups to model fair sharing, then check with 3 × 5 = 15. The Q8 explanations show who understands why a share is fair — a good warm-up for next class. The separate student packet has all the models printed; this key is for the teacher only.

G03_MATH_MultiplicationShares_01 — Multiplication and Fair Shares Teacher Answer Key