Problem
Smaller unit, more measured counts
A wooden stick is 6 ft long and a wire is 8 ft long. We want to cover the length of 4 sticks laid end to end. How many wire lengths laid end to end cover that same total?
Measurement & data
Your answer
times
Watch out The wire is longer than the stick, so it needs fewer counts than 4 sticks — not more.
How to solve
Strategy Analyze the Units — First find the total length to cover (4 sticks), then see how many 8 ft wires fit into it. Because the wire is longer than the stick, fewer wires are needed than sticks - the smaller unit needs more counts.
1STEP 1
Total length of 4 sticks
Four 6 ft sticks laid end to end give 24 ft — that's the length to cover.
4 × 6 = 24 ft
Laying equal sticks end to end adds their lengths, giving the total to cover.
2.MD.A.1Identify Subproblems2STEP 2
How many wires fit in 24 ft
Each wire is 8 ft, and 24 ÷ 8 = 3, so 3 wires cover it.
24 ÷ 8 = 3
Counting how many copies of the unit fit into the total is measuring with that unit.
2.MD.A.1Analyze The UnitsThe number of 8-ft wires laid end to end that covers 24 ft is found by dividing 24 by 8.
Why?
Covering 24 ft with equal 8-ft wires means finding how many 8-ft lengths fill 24 ft, so we need the number n of wires with n groups of 8 ft making 24 ft.
Why?
Laying n wires each 8 ft long end to end is n equal groups of 8 ft, which is exactly what n times 8 means.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The wires fill the 24 ft with no gaps or overlaps, so their 8-ft pieces add back to the whole 24 ft.
🧱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?
Knowing n groups of 8 make 24, we recover the number of wires n by splitting 24 back into 8s with 24 divided by 8, because division undoes multiplication.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Answer
3 times
24 ÷ 8 = 3
Check: 3 wires x 8 ft = 24 ft, which equals 4 sticks x 6 ft = 24 ft. The wire (longer unit) needs fewer counts than 4 sticks, as expected.
Takeaway
A longer measuring unit needs fewer counts to reach the same length — Grade 2 measuring sense!
- Total length of 4 sticks
- How many wires fit in 24 ft
Where next?
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