Smaller unit, more measured counts

2.MD.A.1 · adapt · grade 2

Archetype: Length as Sum of Parts with Unit Matching · step in a 7-type progression

A wooden stick is $6\ \text{ft}$ long, and a wire is $8\ \text{ft}$ long. Find how many times you would lay the wire end to end to cover the same length as $4$ lengths of the wooden stick.

Show solution

Understand

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?

Givens

The wooden stick is 6 ft long.
The wire is 8 ft long.
The target length is 4 sticks laid end to end.

Unknowns

How many wire lengths laid end to end equal the length of 4 sticks.

Constraints

Both units (stick, wire) measure the same total length; the count must come out whole.

Plan

#8 Analyze the Units · also uses: #7 Identify Subproblems

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.

Execute

#7 Identify Subproblems 2.MD.A.1

Each stick is 6 ft, and 4 are laid end to end, so multiply.

4 \times 6 = 24 \text{ ft}

Laying equal sticks end to end adds their lengths, giving the total to cover.

#8 Analyze the Units 2.MD.A.1

Each wire is 8 ft, so see how many 8 ft pieces make 24 ft by dividing.

24 \div 8 = 3

Counting how many copies of the unit fit into the total is measuring with that unit.

Answer: 3 times

Review

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.

Look for a Pattern / repeated addition (tool 5): add 8 + 8 + 8 = 24 ft, reaching the target in 3 wire lengths.

Standards · min grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Measuring the same total length with two different unit lengths (stick, wire).

💡 A longer measuring unit needs fewer counts to reach the same length — Grade 2 measuring sense!