Problem
Putting everything in inches, 3 ft 9 in becomes 45 in.
Mixed units like feet and inches can't be added or subtracted directly. Since 1 ft is 12 in, multiplying 3 ft by 12 and adding the extra 9 in turns the whole bat into one number, 45 in.
2.MD.A.1Analyze UnitsMeasuring LengthMia's 5 handspans at 6 in each cover 30 in.
Equal-length handspans repeated several times can be added all at once with multiplication. Five 6-in handspans in a row give 5 × 6, the length Mia's spans cover.
2.MD.B.5Analyze UnitsMeasuring LengthWith no overlap or gap, subtracting Mia's part from the whole 45 in leaves 15 in.
The two parts meet exactly with no gap and no overlap, so Mia's part and Liam's part together make up the whole 45 in bat. If Mia's 30 in and Liam's part add up to 45 in, then taking Mia's 30 in away from 45 in gives back Liam's part, since subtracting undoes adding.
2.MD.B.5Work BackwardsMeasuring LengthLiam's handspans cover 15 in — the whole bat minus the length Mia's handspans cover.
The two parts meet exactly with no gap and no overlap, so Mia's part and Liam's part together make up the whole 45 in bat.
If Mia's 30 in and Liam's part add up to 45 in, then taking Mia's 30 in away from 45 in gives back Liam's part, since subtracting undoes adding.
Liam's 15 in splits into 3 equal handspans, so one span is 5 in.
The 15 in Liam covered is made of 3 equal-sized handspans. Splitting the total evenly by 3 gives the exact length of one handspan.
2.MD.B.5Work BackwardsMeasuring LengthSubtract the known part from the whole, then split what's left evenly to find one handspan.