← Find one handspan from measured counts · Length as Sum of Parts with Unit Matching

Find one handspan from measured counts · 10 practice problems

2.MD.A.12.MD.B.5

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 4 in

Nora and Eli measured the length of a ribbon using handspans. Starting from the left end, Nora counted off $4$ handspans, and starting from the right end, Eli counted off $2$ handspans. Their fingertips met exactly, with no overlap and no gap.

The ribbon is $2\ \text{ft}\ 4\ \text{in}$ long, and one of Nora's handspans is $5\ \text{in}$ . How many inches long is one of Eli's handspans?

Show solution

1 · Understandwhat's really being asked

A ribbon is measured in handspans from both ends. Nora counts 4 handspans from the left, Eli counts 2 from the right, and their fingertips meet exactly. Given the ribbon is 2 ft 4 in long and Nora's handspan is 5 in, find the length of one of Eli's handspans.

Givens

The ribbon is 2 ft 4 in long.
Nora measures 4 handspans from the left end, each 5 in.
Eli measures 2 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Eli's handspans, in inches.

Constraints

Nora's part plus Eli's part equals the whole ribbon (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Nora's covered length, subtract from the whole to get Eli's covered length, then divide by his 2 handspans to find one. Working backwards from the total isolates Eli's part.

3 · Execute4 carry out the plan

1Put the ribbon length in inches

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

Convert 2 ft 4 in to inches: 2 feet is 24 inches, plus 4 inches.

2 \times 12 + 4 = 28 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Nora's covered length

#8 Analyze the Units 2.MD.B.5

Nora's 4 handspans are each 5 in, so multiply.

4 \times 5 = 20 \text{ in}

Repeated equal handspans add up to a total length.

3Find Eli's covered length

#11 Work Backwards 2.MD.B.5

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

28 - 20 = 8 \text{ in}

The whole minus Nora's part leaves exactly Eli's part.

4Find one of Eli's handspans

#11 Work Backwards 2.MD.B.5

Eli's 8 in is 2 equal handspans, so divide.

8 \div 2 = 4 \text{ in}

Splitting his total evenly among 2 spans gives one span.

Answer: 4 in

4 · Reviewdoes it hold up?

Check: Nora 20 in + Eli 2x4 = 8 in totals 28 in = 2 ft 4 in, the full ribbon. A 4 in handspan is reasonable next to Nora's 5 in.

Another way: Draw a Diagram (tool 1): mark the 28 in ribbon, shade Nora's 4 x 5 in from the left, and the remaining segment split into 2 equal pieces is clearly 4 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Eli's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 2 easy answer: 6 in

Lily and Jack measured the length of a fishing rod using handspans. Starting from the left end, Lily counted off $6$ handspans, and starting from the right end, Jack counted off $4$ handspans. Their fingertips met exactly, with no overlap and no gap.

The fishing rod is $5\ \text{ft}\ 6\ \text{in}$ long, and one of Lily's handspans is $7\ \text{in}$ . How many inches long is one of Jack's handspans?

Show solution

1 · Understandwhat's really being asked

A fishing rod is measured in handspans from both ends. Lily counts 6 handspans from the left, Jack counts 4 from the right, and their fingertips meet exactly. Given the fishing rod is 5 ft 6 in long and Lily's handspan is 7 in, find the length of one of Jack's handspans.

Givens

The fishing rod is 5 ft 6 in long.
Lily measures 6 handspans from the left end, each 7 in.
Jack measures 4 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Jack's handspans, in inches.

Constraints

Lily's part plus Jack's part equals the whole fishing rod (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Lily's covered length, subtract from the whole to get Jack's covered length, then divide by his 4 handspans to find one. Working backwards from the total isolates Jack's part.

3 · Execute4 carry out the plan

1Put the fishing rod length in inches

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

Convert 5 ft 6 in to inches: 5 feet is 60 inches, plus 6 inches.

5 \times 12 + 6 = 66 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Lily's covered length

#8 Analyze the Units 2.MD.B.5

Lily's 6 handspans are each 7 in, so multiply.

6 \times 7 = 42 \text{ in}

Repeated equal handspans add up to a total length.

3Find Jack's covered length

#11 Work Backwards 2.MD.B.5

Since the two parts meet exactly with no overlap or gap, Jack covers the rest of the fishing rod.

66 - 42 = 24 \text{ in}

The whole minus Lily's part leaves exactly Jack's part.

4Find one of Jack's handspans

#11 Work Backwards 2.MD.B.5

Jack's 24 in is 4 equal handspans, so divide.

24 \div 4 = 6 \text{ in}

Splitting his total evenly among 4 spans gives one span.

Answer: 6 in

4 · Reviewdoes it hold up?

Check: Lily 42 in + Jack 4x6 = 24 in totals 66 in = 5 ft 6 in, the full fishing rod. A 6 in handspan is reasonable next to Lily's 7 in.

Another way: Draw a Diagram (tool 1): mark the 66 in fishing rod, shade Lily's 6 x 7 in from the left, and the remaining segment split into 4 equal pieces is clearly 6 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Jack's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 3 medium answer: 6 in

Iris and Cole measured the length of a ski using handspans. Starting from the left end, Iris counted off $7$ handspans, and starting from the right end, Cole counted off $3$ handspans. Their fingertips met exactly, with no overlap and no gap.

The ski is $5\ \text{ft}\ 0\ \text{in}$ long, and one of Iris's handspans is $6\ \text{in}$ . How many inches long is one of Cole's handspans?

Show solution

1 · Understandwhat's really being asked

A ski is measured in handspans from both ends. Iris counts 7 handspans from the left, Cole counts 3 from the right, and their fingertips meet exactly. Given the ski is 5 ft 0 in long and Iris's handspan is 6 in, find the length of one of Cole's handspans.

Givens

The ski is 5 ft 0 in long.
Iris measures 7 handspans from the left end, each 6 in.
Cole measures 3 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Cole's handspans, in inches.

Constraints

Iris's part plus Cole's part equals the whole ski (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Iris's covered length, subtract from the whole to get Cole's covered length, then divide by his 3 handspans to find one. Working backwards from the total isolates Cole's part.

3 · Execute4 carry out the plan

1Put the ski length in inches

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

Convert 5 ft 0 in to inches: 5 feet is 60 inches, plus 0 inches.

5 \times 12 + 0 = 60 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Iris's covered length

#8 Analyze the Units 2.MD.B.5

Iris's 7 handspans are each 6 in, so multiply.

7 \times 6 = 42 \text{ in}

Repeated equal handspans add up to a total length.

3Find Cole's covered length

#11 Work Backwards 2.MD.B.5

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

60 - 42 = 18 \text{ in}

The whole minus Iris's part leaves exactly Cole's part.

4Find one of Cole's handspans

#11 Work Backwards 2.MD.B.5

Cole's 18 in is 3 equal handspans, so divide.

18 \div 3 = 6 \text{ in}

Splitting his total evenly among 3 spans gives one span.

Answer: 6 in

4 · Reviewdoes it hold up?

Check: Iris 42 in + Cole 3x6 = 18 in totals 60 in = 5 ft 0 in, the full ski. A 6 in handspan is reasonable next to Iris's 6 in.

Another way: Draw a Diagram (tool 1): mark the 60 in ski, shade Iris's 7 x 6 in from the left, and the remaining segment split into 3 equal pieces is clearly 6 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Cole's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 4 easy answer: 5 in

Ava and Noah measured the length of a shelf using handspans. Starting from the left end, Ava counted off $4$ handspans, and starting from the right end, Noah counted off $4$ handspans. Their fingertips met exactly, with no overlap and no gap.

The shelf is $4\ \text{ft}\ 0\ \text{in}$ long, and one of Ava's handspans is $7\ \text{in}$ . How many inches long is one of Noah's handspans?

Show solution

1 · Understandwhat's really being asked

A shelf is measured in handspans from both ends. Ava counts 4 handspans from the left, Noah counts 4 from the right, and their fingertips meet exactly. Given the shelf is 4 ft 0 in long and Ava's handspan is 7 in, find the length of one of Noah's handspans.

Givens

The shelf is 4 ft 0 in long.
Ava measures 4 handspans from the left end, each 7 in.
Noah measures 4 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Noah's handspans, in inches.

Constraints

Ava's part plus Noah's part equals the whole shelf (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Ava's covered length, subtract from the whole to get Noah's covered length, then divide by his 4 handspans to find one. Working backwards from the total isolates Noah's part.

3 · Execute4 carry out the plan

1Put the shelf length in inches

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

Convert 4 ft 0 in to inches: 4 feet is 48 inches, plus 0 inches.

4 \times 12 + 0 = 48 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Ava's covered length

#8 Analyze the Units 2.MD.B.5

Ava's 4 handspans are each 7 in, so multiply.

4 \times 7 = 28 \text{ in}

Repeated equal handspans add up to a total length.

3Find Noah's covered length

#11 Work Backwards 2.MD.B.5

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

48 - 28 = 20 \text{ in}

The whole minus Ava's part leaves exactly Noah's part.

4Find one of Noah's handspans

#11 Work Backwards 2.MD.B.5

Noah's 20 in is 4 equal handspans, so divide.

20 \div 4 = 5 \text{ in}

Splitting his total evenly among 4 spans gives one span.

Answer: 5 in

4 · Reviewdoes it hold up?

Check: Ava 28 in + Noah 4x5 = 20 in totals 48 in = 4 ft 0 in, the full shelf. A 5 in handspan is reasonable next to Ava's 7 in.

Another way: Draw a Diagram (tool 1): mark the 48 in shelf, shade Ava's 4 x 7 in from the left, and the remaining segment split into 4 equal pieces is clearly 5 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Noah's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 5 medium answer: 6 in

Zoe and Max measured the length of a yoga mat using handspans. Starting from the left end, Zoe counted off $8$ handspans, and starting from the right end, Max counted off $4$ handspans. Their fingertips met exactly, with no overlap and no gap.

The yoga mat is $6\ \text{ft}\ 0\ \text{in}$ long, and one of Zoe's handspans is $6\ \text{in}$ . How many inches long is one of Max's handspans?

Show solution

1 · Understandwhat's really being asked

A yoga mat is measured in handspans from both ends. Zoe counts 8 handspans from the left, Max counts 4 from the right, and their fingertips meet exactly. Given the yoga mat is 6 ft 0 in long and Zoe's handspan is 6 in, find the length of one of Max's handspans.

Givens

The yoga mat is 6 ft 0 in long.
Zoe measures 8 handspans from the left end, each 6 in.
Max measures 4 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Max's handspans, in inches.

Constraints

Zoe's part plus Max's part equals the whole yoga mat (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Zoe's covered length, subtract from the whole to get Max's covered length, then divide by his 4 handspans to find one. Working backwards from the total isolates Max's part.

3 · Execute4 carry out the plan

1Put the yoga mat length in inches

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

Convert 6 ft 0 in to inches: 6 feet is 72 inches, plus 0 inches.

6 \times 12 + 0 = 72 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Zoe's covered length

#8 Analyze the Units 2.MD.B.5

Zoe's 8 handspans are each 6 in, so multiply.

8 \times 6 = 48 \text{ in}

Repeated equal handspans add up to a total length.

3Find Max's covered length

#11 Work Backwards 2.MD.B.5

Since the two parts meet exactly with no overlap or gap, Max covers the rest of the yoga mat.

72 - 48 = 24 \text{ in}

The whole minus Zoe's part leaves exactly Max's part.

4Find one of Max's handspans

#11 Work Backwards 2.MD.B.5

Max's 24 in is 4 equal handspans, so divide.

24 \div 4 = 6 \text{ in}

Splitting his total evenly among 4 spans gives one span.

Answer: 6 in

4 · Reviewdoes it hold up?

Check: Zoe 48 in + Max 4x6 = 24 in totals 72 in = 6 ft 0 in, the full yoga mat. A 6 in handspan is reasonable next to Zoe's 6 in.

Another way: Draw a Diagram (tool 1): mark the 72 in yoga mat, shade Zoe's 8 x 6 in from the left, and the remaining segment split into 4 equal pieces is clearly 6 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Max's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 6 hard answer: 10 in

Tess and Gus measured the length of a plank using handspans. Starting from the left end, Tess counted off $6$ handspans, and starting from the right end, Gus counted off $2$ handspans. Their fingertips met exactly, with no overlap and no gap.

The plank is $4\ \text{ft}\ 8\ \text{in}$ long, and one of Tess's handspans is $6\ \text{in}$ . How many inches long is one of Gus's handspans?

Show solution

1 · Understandwhat's really being asked

A plank is measured in handspans from both ends. Tess counts 6 handspans from the left, Gus counts 2 from the right, and their fingertips meet exactly. Given the plank is 4 ft 8 in long and Tess's handspan is 6 in, find the length of one of Gus's handspans.

Givens

The plank is 4 ft 8 in long.
Tess measures 6 handspans from the left end, each 6 in.
Gus measures 2 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Gus's handspans, in inches.

Constraints

Tess's part plus Gus's part equals the whole plank (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Tess's covered length, subtract from the whole to get Gus's covered length, then divide by his 2 handspans to find one. Working backwards from the total isolates Gus's part.

3 · Execute4 carry out the plan

1Put the plank length in inches

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

Convert 4 ft 8 in to inches: 4 feet is 48 inches, plus 8 inches.

4 \times 12 + 8 = 56 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Tess's covered length

#8 Analyze the Units 2.MD.B.5

Tess's 6 handspans are each 6 in, so multiply.

6 \times 6 = 36 \text{ in}

Repeated equal handspans add up to a total length.

3Find Gus's covered length

#11 Work Backwards 2.MD.B.5

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

56 - 36 = 20 \text{ in}

The whole minus Tess's part leaves exactly Gus's part.

4Find one of Gus's handspans

#11 Work Backwards 2.MD.B.5

Gus's 20 in is 2 equal handspans, so divide.

20 \div 2 = 10 \text{ in}

Splitting his total evenly among 2 spans gives one span.

Answer: 10 in

4 · Reviewdoes it hold up?

Check: Tess 36 in + Gus 2x10 = 20 in totals 56 in = 4 ft 8 in, the full plank. A 10 in handspan is reasonable next to Tess's 6 in.

Another way: Draw a Diagram (tool 1): mark the 56 in plank, shade Tess's 6 x 6 in from the left, and the remaining segment split into 2 equal pieces is clearly 10 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Gus's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 7 medium answer: 4 in

Emma and Owen measured the length of a table edge using handspans. Starting from the left end, Emma counted off $2$ handspans, and starting from the right end, Owen counted off $4$ handspans. Their fingertips met exactly, with no overlap and no gap.

The table edge is $2\ \text{ft}\ 8\ \text{in}$ long, and one of Emma's handspans is $8\ \text{in}$ . How many inches long is one of Owen's handspans?

Show solution

1 · Understandwhat's really being asked

A table edge is measured in handspans from both ends. Emma counts 2 handspans from the left, Owen counts 4 from the right, and their fingertips meet exactly. Given the table edge is 2 ft 8 in long and Emma's handspan is 8 in, find the length of one of Owen's handspans.

Givens

The table edge is 2 ft 8 in long.
Emma measures 2 handspans from the left end, each 8 in.
Owen measures 4 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Owen's handspans, in inches.

Constraints

Emma's part plus Owen's part equals the whole table edge (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Emma's covered length, subtract from the whole to get Owen's covered length, then divide by his 4 handspans to find one. Working backwards from the total isolates Owen's part.

3 · Execute4 carry out the plan

1Put the table edge length in inches

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

Convert 2 ft 8 in to inches: 2 feet is 24 inches, plus 8 inches.

2 \times 12 + 8 = 32 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Emma's covered length

#8 Analyze the Units 2.MD.B.5

Emma's 2 handspans are each 8 in, so multiply.

2 \times 8 = 16 \text{ in}

Repeated equal handspans add up to a total length.

3Find Owen's covered length

#11 Work Backwards 2.MD.B.5

Since the two parts meet exactly with no overlap or gap, Owen covers the rest of the table edge.

32 - 16 = 16 \text{ in}

The whole minus Emma's part leaves exactly Owen's part.

4Find one of Owen's handspans

#11 Work Backwards 2.MD.B.5

Owen's 16 in is 4 equal handspans, so divide.

16 \div 4 = 4 \text{ in}

Splitting his total evenly among 4 spans gives one span.

Answer: 4 in

4 · Reviewdoes it hold up?

Check: Emma 16 in + Owen 4x4 = 16 in totals 32 in = 2 ft 8 in, the full table edge. A 4 in handspan is reasonable next to Emma's 8 in.

Another way: Draw a Diagram (tool 1): mark the 32 in table edge, shade Emma's 2 x 8 in from the left, and the remaining segment split into 4 equal pieces is clearly 4 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Owen's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 8 medium answer: 6 in

Ruby and Leo measured the length of a curtain using handspans. Starting from the left end, Ruby counted off $3$ handspans, and starting from the right end, Leo counted off $3$ handspans. Their fingertips met exactly, with no overlap and no gap.

The curtain is $3\ \text{ft}\ 6\ \text{in}$ long, and one of Ruby's handspans is $8\ \text{in}$ . How many inches long is one of Leo's handspans?

Show solution

1 · Understandwhat's really being asked

A curtain is measured in handspans from both ends. Ruby counts 3 handspans from the left, Leo counts 3 from the right, and their fingertips meet exactly. Given the curtain is 3 ft 6 in long and Ruby's handspan is 8 in, find the length of one of Leo's handspans.

Givens

The curtain is 3 ft 6 in long.
Ruby measures 3 handspans from the left end, each 8 in.
Leo measures 3 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Leo's handspans, in inches.

Constraints

Ruby's part plus Leo's part equals the whole curtain (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Ruby's covered length, subtract from the whole to get Leo's covered length, then divide by his 3 handspans to find one. Working backwards from the total isolates Leo's part.

3 · Execute4 carry out the plan

1Put the curtain length in inches

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

Convert 3 ft 6 in to inches: 3 feet is 36 inches, plus 6 inches.

3 \times 12 + 6 = 42 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Ruby's covered length

#8 Analyze the Units 2.MD.B.5

Ruby's 3 handspans are each 8 in, so multiply.

3 \times 8 = 24 \text{ in}

Repeated equal handspans add up to a total length.

3Find Leo's covered length

#11 Work Backwards 2.MD.B.5

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

42 - 24 = 18 \text{ in}

The whole minus Ruby's part leaves exactly Leo's part.

4Find one of Leo's handspans

#11 Work Backwards 2.MD.B.5

Leo's 18 in is 3 equal handspans, so divide.

18 \div 3 = 6 \text{ in}

Splitting his total evenly among 3 spans gives one span.

Answer: 6 in

4 · Reviewdoes it hold up?

Check: Ruby 24 in + Leo 3x6 = 18 in totals 42 in = 3 ft 6 in, the full curtain. A 6 in handspan is reasonable next to Ruby's 8 in.

Another way: Draw a Diagram (tool 1): mark the 42 in curtain, shade Ruby's 3 x 8 in from the left, and the remaining segment split into 3 equal pieces is clearly 6 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Leo's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 9 hard answer: 5 in

Mia and Liam measured the length of a baseball bat using handspans. Starting from the left end, Mia counted off $5$ handspans, and starting from the right end, Liam counted off $3$ handspans. Their fingertips met exactly, with no overlap and no gap.

The baseball bat is $3\ \text{ft}\ 9\ \text{in}$ long, and one of Mia's handspans is $6\ \text{in}$ . How many inches long is one of Liam's handspans?

Show solution

1 · Understandwhat's really being asked

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 baseball bat is 3 ft 9 in long and Mia's handspan is 6 in, find the length of one of Liam's handspans.

Givens

The baseball bat is 3 ft 9 in long.
Mia measures 5 handspans from the left end, each 6 in.
Liam measures 3 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Liam's handspans, in inches.

Constraints

Mia's part plus Liam's part equals the whole baseball bat (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

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.

3 · Execute4 carry out the plan

1Put the baseball bat length in inches

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

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

3 \times 12 + 9 = 45 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Mia's covered length

#8 Analyze the Units 2.MD.B.5

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

5 \times 6 = 30 \text{ in}

Repeated equal handspans add up to a total length.

3Find Liam's covered length

#11 Work Backwards 2.MD.B.5

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

45 - 30 = 15 \text{ in}

The whole minus Mia's part leaves exactly Liam's part.

4Find one of Liam's handspans

#11 Work Backwards 2.MD.B.5

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

15 \div 3 = 5 \text{ in}

Splitting his total evenly among 3 spans gives one span.

Answer: 5 in

4 · Reviewdoes it hold up?

Check: Mia 30 in + Liam 3x5 = 15 in totals 45 in = 3 ft 9 in, the full baseball bat. A 5 in handspan is reasonable next to Mia's 6 in.

Another way: Draw a Diagram (tool 1): mark the 45 in baseball bat, shade Mia's 5 x 6 in from the left, and the remaining segment split into 3 equal pieces is clearly 5 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Liam's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!

Variant 10 hard answer: 6 in

Maya and Finn measured the length of a kayak paddle using handspans. Starting from the left end, Maya counted off $9$ handspans, and starting from the right end, Finn counted off $4$ handspans. Their fingertips met exactly, with no overlap and no gap.

The kayak paddle is $6\ \text{ft}\ 6\ \text{in}$ long, and one of Maya's handspans is $6\ \text{in}$ . How many inches long is one of Finn's handspans?

Show solution

1 · Understandwhat's really being asked

A kayak paddle is measured in handspans from both ends. Maya counts 9 handspans from the left, Finn counts 4 from the right, and their fingertips meet exactly. Given the kayak paddle is 6 ft 6 in long and Maya's handspan is 6 in, find the length of one of Finn's handspans.

Givens

The kayak paddle is 6 ft 6 in long.
Maya measures 9 handspans from the left end, each 6 in.
Finn measures 4 handspans from the right end, all equal.
Their fingertips meet exactly, with no overlap and no gap.

Unknowns

The length of one of Finn's handspans, in inches.

Constraints

Maya's part plus Finn's part equals the whole kayak paddle (no overlap, no gap).
1 ft = 12 in.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #8 Analyze the Units

Convert everything to inches, find Maya's covered length, subtract from the whole to get Finn's covered length, then divide by his 4 handspans to find one. Working backwards from the total isolates Finn's part.

3 · Execute4 carry out the plan

1Put the kayak paddle length in inches

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

Convert 6 ft 6 in to inches: 6 feet is 72 inches, plus 6 inches.

6 \times 12 + 6 = 78 \text{ in}

Using one unit (inches) lets us add and subtract lengths directly.

2Find Maya's covered length

#8 Analyze the Units 2.MD.B.5

Maya's 9 handspans are each 6 in, so multiply.

9 \times 6 = 54 \text{ in}

Repeated equal handspans add up to a total length.

3Find Finn's covered length

#11 Work Backwards 2.MD.B.5

Since the two parts meet exactly with no overlap or gap, Finn covers the rest of the kayak paddle.

78 - 54 = 24 \text{ in}

The whole minus Maya's part leaves exactly Finn's part.

4Find one of Finn's handspans

#11 Work Backwards 2.MD.B.5

Finn's 24 in is 4 equal handspans, so divide.

24 \div 4 = 6 \text{ in}

Splitting his total evenly among 4 spans gives one span.

Answer: 6 in

4 · Reviewdoes it hold up?

Check: Maya 54 in + Finn 4x6 = 24 in totals 78 in = 6 ft 6 in, the full kayak paddle. A 6 in handspan is reasonable next to Maya's 6 in.

Another way: Draw a Diagram (tool 1): mark the 78 in kayak paddle, shade Maya's 9 x 6 in from the left, and the remaining segment split into 4 equal pieces is clearly 6 in each.

Standardsmin grade 2

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools — Converting feet and inches into a single unit (inches) for measuring.
2.MD.B.5 Solve word problems involving lengths using same units — Adding, subtracting, and splitting lengths to isolate one of Finn's handspans.

💡Takeaway. Turn everything into inches, take away one person's part, then share what's left -- pure Grade 2 length sense!