Problem
Count groups several equivalent ways
The beads are arranged in 4 rows of 7. To count them, you could use (A) 7+7+7+7, (B) 7×4, (C) 4×7, or (D) add 7×2 four times — find the choice that is not a correct way to count.
Operations
Your answer
Watch out (B) 7×4 and (C) 4×7 just swap the order of the same two factors, so both equal 28. The wrong one isn't either of them — it's (D).
How to solve
Strategy Draw a Diagram — Picture the array of 7 beads in each of 4 rows, then check each method's result against that array in turn to spot the one whose value doesn't match.
1STEP 1
Read the array as the true total
The beads are 4 rows of 7, so the true total is 7×4=28.
7 × 4 = 28
The array is exactly its four rows put together, nothing missed or doubled, so multiplying 7 per row by 4 rows gives the exact true total.
Draw A Diagram3.OA.A.12STEP 2
Check the addition and product choices
(A) 7+7+7+7, (B) 7×4, (C) 4×7 — all three equal 28.
7+7+7+7 = 28, 7×4 = 28, 4×7 = 28
Adding equal rows and multiplying rows by the row length are just two views of the same array, so they always match. And multiplication gives the same product in either order, so 7×4 and 4×7 both equal 28.
Make Systematic List2.OA.C.43STEP 3
Check choice D
(D) adds 7×2=14 four times to get 56 — not 28, so it is the wrong one.
7×2=14, 14×4=56 ≠ 28
Each row holds 7 beads, not 7×2=14. Doubling every one of the four rows doubles the whole array, inflating the true total of 28 into 56.
Make Systematic List3.OA.A.1Choice D adds 7 x 2 four times and reaches 56, not the 28 beads in the array, so it is not a correct way to count.
Why?
The array truly holds 28 beads, because it is four equal rows of 7.
Why?
Four rows of 7 is four equal groups of 7, and 7 + 7 + 7 + 7 is 28.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The whole array is exactly its four rows put back together, with none left out and none counted twice.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Choice D counts each row as 7 x 2 = 14 instead of 7, so it doubles every row.
Why?
One row is a single group of 7 beads, but 7 x 2 means two groups of 7 — twice as many as are really there.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Doubling all four equal rows doubles the whole, turning the true 28 into 56.
Why?
Adding 7 x 2 four times is the four rows of 7 taken twice, since the factors 4, 7, and 2 give the same product however you group them.
🧱Associativity of multiplicationMultiplying three numbers, grouping any two first gives the same product.
Answer
D
7×2×4 = 56 ≠ 28
Check — (A), (B), and (C) all total 28, but (D) totals 56, twice as many. The wrong one is D.
Takeaway
The same array can be shown with addition or multiplication and still match — but doubling a row breaks the true total.
- 4 rows of 7 truly total 28
- (A), (B), (C) all give 28 — different views of the same array
- (D) adds 7×2 four times to get 56 — doubled, so it's wrong
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested