Measurement & Time

Problem

Find one handspan from measured counts

A baseball bat is measured in handspans from both ends. Mia counts 5 handspans from the left, Liam counts 3 from the right, and their fingertips meet exactly. Given the bat is 3 ft 9 in long and Mia's handspan is 6 in, find the length of one of Liam's handspans.
Measurement & data
Your answer
in
How to solve
Strategy Work Backwards — Convert everything to inches, find Mia's covered length, subtract from the whole to get Liam's covered length, then divide by his 3 handspans to find one. Working backwards from the total isolates Liam's part.
1STEP 1

Put the bat length in inches

Convert 3 ft 9 in to inches: 3 feet is 36 inches, plus 9 inches.

3 × 12 + 9 = 45 in
2STEP 2

Find Mia's covered length

Mia's 5 handspans are each 6 in, so multiply.

5 × 6 = 30 in
3STEP 3

Find Liam's covered length

Since the two parts meet exactly with no overlap or gap, Liam covers the rest of the bat.

45 - 30 = 15 in
4STEP 4

Find one of Liam's handspans

Liam's 15 in is 3 equal handspans, so divide.

15 ÷ 3 = 5 in
Answer
5 in
Check: Mia 30 in + Liam 3x5 = 15 in totals 45 in = 3 ft 9 in, the full bat. A 5 in handspan is a bit smaller than Mia's 6 in, which is reasonable for a smaller hand.
Takeaway

Turn everything into inches, take away Mia's part, then share what's left into 3 — pure Grade 2 length sense!

  • Put the bat length in inches
  • Find Mia's covered length
  • Find Liam's covered length
  • Find one of Liam's handspans
Where next?
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10 practice problems
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Step back and solidifysuggested
Skip-count by the changing place valueTimes ten adds one place
8 reasoning problems grow out of this type — the bridge toward competition →

▶ Practice — 10 problems