Practice · Find the per-unit-weight rate first · Sensim Math

Variant 1 answer: $44

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$6$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$8$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $6 for every 8 oz and pork priced at$ 8 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $6 per 8 oz.
Pork: she buys 2 lb 8 oz, priced at $8 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $6 per 8 oz of tomatoes;$ 8 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is

6 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of

6.

32 \div 8 = 4,\quad 4 \times \$6 = \$24

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

2 lb 8 oz is 2 whole pounds plus half a pound (8 oz = half of 16 oz). At

8 per pound, 2 pounds cost

16 and the extra half-pound costs half of

8, which is

4.

2\times\$8 + \tfrac{1}{2}\times\$8 = \$16 + \$4 = \$20

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$24 + \$20 = \$44

Combining the two subtotals is a single addition of two money amounts.

Answer: $44

Review

Tomatoes $24 and pork$ 20 are both sensible store prices, and the total $44 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $24 +$ 20 to reach $44.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 2 answer: $22

At the produce stand, Mia's mom buys $3\ \text{lb}$ of cherry tomatoes that cost $\$2$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}$ of pork that costs $\$10$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $2 for every 8 oz and pork priced at$ 10 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 3 lb (= 48 oz), priced at $2 per 8 oz.
Pork: she buys 1 lb, priced at $10 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $2 per 8 oz of tomatoes;$ 10 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

3 lb is 48 oz, and the price is

2 for each 8 oz. There are 48 / 8 = 6 portions of 8 oz, so the tomatoes cost 6 groups of

2.

48 \div 8 = 6,\quad 6 \times \$2 = \$12

Converting 3 lb to 48 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

1 lb is 1 whole pound. At

10 per pound, the pork costs 1 x

10 = $10.

1 \times \$10 = \$10

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$12 + \$10 = \$22

Combining the two subtotals is a single addition of two money amounts.

Answer: $22

Review

Tomatoes $12 and pork$ 10 are both sensible store prices, and the total $22 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $12 +$ 10 to reach $22.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 3 answer: $38

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$5$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}$ of pork that costs $\$9$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $5 for every 8 oz and pork priced at$ 9 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $5 per 8 oz.
Pork: she buys 2 lb, priced at $9 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $5 per 8 oz of tomatoes;$ 9 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is

5 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of

5.

32 \div 8 = 4,\quad 4 \times \$5 = \$20

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

2 lb is 2 whole pounds. At

9 per pound, the pork costs 2 x

9 = $18.

2 \times \$9 = \$18

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$20 + \$18 = \$38

Combining the two subtotals is a single addition of two money amounts.

Answer: $38

Review

Tomatoes $20 and pork$ 18 are both sensible store prices, and the total $38 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $20 +$ 18 to reach $38.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 4 answer: $30

At the produce stand, Mia's mom buys $3\ \text{lb}$ of cherry tomatoes that cost $\$3$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$8$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $3 for every 8 oz and pork priced at$ 8 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 3 lb (= 48 oz), priced at $3 per 8 oz.
Pork: she buys 1 lb 8 oz, priced at $8 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $3 per 8 oz of tomatoes;$ 8 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

3 lb is 48 oz, and the price is

3 for each 8 oz. There are 48 / 8 = 6 portions of 8 oz, so the tomatoes cost 6 groups of

3.

48 \div 8 = 6,\quad 6 \times \$3 = \$18

Converting 3 lb to 48 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

1 lb 8 oz is 1 whole pound plus half a pound (8 oz = half of 16 oz). At

8 per pound, 1 pound cost

8 and the extra half-pound costs half of

8, which is

4.

1\times\$8 + \tfrac{1}{2}\times\$8 = \$8 + \$4 = \$12

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$18 + \$12 = \$30

Combining the two subtotals is a single addition of two money amounts.

Answer: $30

Review

Tomatoes $18 and pork$ 12 are both sensible store prices, and the total $30 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $18 +$ 12 to reach $30.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 5 answer: $23

At the produce stand, Mia's mom buys $4\ \text{lb}$ of cherry tomatoes that cost $\$2$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}$ of pork that costs $\$7$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $2 for every 8 oz and pork priced at$ 7 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 4 lb (= 64 oz), priced at $2 per 8 oz.
Pork: she buys 1 lb, priced at $7 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $2 per 8 oz of tomatoes;$ 7 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

4 lb is 64 oz, and the price is

2 for each 8 oz. There are 64 / 8 = 8 portions of 8 oz, so the tomatoes cost 8 groups of

2.

64 \div 8 = 8,\quad 8 \times \$2 = \$16

Converting 4 lb to 64 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

1 lb is 1 whole pound. At

7 per pound, the pork costs 1 x

7 = $7.

1 \times \$7 = \$7

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$16 + \$7 = \$23

Combining the two subtotals is a single addition of two money amounts.

Answer: $23

Review

Tomatoes $16 and pork$ 7 are both sensible store prices, and the total $23 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $16 +$ 7 to reach $23.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 6 answer: $43

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$8$ per $8\ \text{oz}$ . At the butcher, she buys $4\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$6$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $8 for every 8 oz and pork priced at$ 6 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $8 per 8 oz.
Pork: she buys 4 lb 8 oz, priced at $6 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $8 per 8 oz of tomatoes;$ 6 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is

8 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of

8.

16 \div 8 = 2,\quad 2 \times \$8 = \$16

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

4 lb 8 oz is 4 whole pounds plus half a pound (8 oz = half of 16 oz). At

6 per pound, 4 pounds cost

24 and the extra half-pound costs half of

6, which is

3.

4\times\$6 + \tfrac{1}{2}\times\$6 = \$24 + \$3 = \$27

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$16 + \$27 = \$43

Combining the two subtotals is a single addition of two money amounts.

Answer: $43

Review

Tomatoes $16 and pork$ 27 are both sensible store prices, and the total $43 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $16 +$ 27 to reach $43.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 7 answer: $26

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$3$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}$ of pork that costs $\$7$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $3 for every 8 oz and pork priced at$ 7 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $3 per 8 oz.
Pork: she buys 2 lb, priced at $7 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $3 per 8 oz of tomatoes;$ 7 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is

3 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of

3.

32 \div 8 = 4,\quad 4 \times \$3 = \$12

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

2 lb is 2 whole pounds. At

7 per pound, the pork costs 2 x

7 = $14.

2 \times \$7 = \$14

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$12 + \$14 = \$26

Combining the two subtotals is a single addition of two money amounts.

Answer: $26

Review

Tomatoes $12 and pork$ 14 are both sensible store prices, and the total $26 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $12 +$ 14 to reach $26.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 8 answer: $30

At the produce stand, Mia's mom buys $2\ \text{lb}$ of cherry tomatoes that cost $\$4$ per $8\ \text{oz}$ . At the butcher, she buys $3\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$4$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $4 for every 8 oz and pork priced at$ 4 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 2 lb (= 32 oz), priced at $4 per 8 oz.
Pork: she buys 3 lb 8 oz, priced at $4 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $4 per 8 oz of tomatoes;$ 4 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

2 lb is 32 oz, and the price is

4 for each 8 oz. There are 32 / 8 = 4 portions of 8 oz, so the tomatoes cost 4 groups of

4.

32 \div 8 = 4,\quad 4 \times \$4 = \$16

Converting 2 lb to 32 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

3 lb 8 oz is 3 whole pounds plus half a pound (8 oz = half of 16 oz). At

4 per pound, 3 pounds cost

12 and the extra half-pound costs half of

4, which is

2.

3\times\$4 + \tfrac{1}{2}\times\$4 = \$12 + \$2 = \$14

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$16 + \$14 = \$30

Combining the two subtotals is a single addition of two money amounts.

Answer: $30

Review

Tomatoes $16 and pork$ 14 are both sensible store prices, and the total $30 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $16 +$ 14 to reach $30.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 9 answer: $42

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$9$ per $8\ \text{oz}$ . At the butcher, she buys $2\ \text{lb}$ of pork that costs $\$12$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $9 for every 8 oz and pork priced at$ 12 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $9 per 8 oz.
Pork: she buys 2 lb, priced at $12 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $9 per 8 oz of tomatoes;$ 12 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is

9 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of

9.

16 \div 8 = 2,\quad 2 \times \$9 = \$18

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

2 lb is 2 whole pounds. At

12 per pound, the pork costs 2 x

12 = $24.

2 \times \$12 = \$24

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$18 + \$24 = \$42

Combining the two subtotals is a single addition of two money amounts.

Answer: $42

Review

Tomatoes $18 and pork$ 24 are both sensible store prices, and the total $42 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $18 +$ 24 to reach $42.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 10 answer: $31

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$5$ per $8\ \text{oz}$ . At the butcher, she buys $3\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$6$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $5 for every 8 oz and pork priced at$ 6 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $5 per 8 oz.
Pork: she buys 3 lb 8 oz, priced at $6 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $5 per 8 oz of tomatoes;$ 6 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is

5 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of

5.

16 \div 8 = 2,\quad 2 \times \$5 = \$10

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

3 lb 8 oz is 3 whole pounds plus half a pound (8 oz = half of 16 oz). At

6 per pound, 3 pounds cost

18 and the extra half-pound costs half of

6, which is

3.

3\times\$6 + \tfrac{1}{2}\times\$6 = \$18 + \$3 = \$21

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$10 + \$21 = \$31

Combining the two subtotals is a single addition of two money amounts.

Answer: $31

Review

Tomatoes $10 and pork$ 21 are both sensible store prices, and the total $31 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $10 +$ 21 to reach $31.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 11 answer: $19

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$7$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}$ of pork that costs $\$5$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $7 for every 8 oz and pork priced at$ 5 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $7 per 8 oz.
Pork: she buys 1 lb, priced at $5 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $7 per 8 oz of tomatoes;$ 5 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is

7 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of

7.

16 \div 8 = 2,\quad 2 \times \$7 = \$14

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

1 lb is 1 whole pound. At

5 per pound, the pork costs 1 x

5 = $5.

1 \times \$5 = \$5

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$14 + \$5 = \$19

Combining the two subtotals is a single addition of two money amounts.

Answer: $19

Review

Tomatoes $14 and pork$ 5 are both sensible store prices, and the total $19 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $14 +$ 5 to reach $19.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Variant 12 answer: $21.50

At the produce stand, Mia's mom buys $1\ \text{lb}$ of cherry tomatoes that cost $\$4$ per $8\ \text{oz}$ . At the butcher, she buys $1\ \text{lb}\ 8\ \text{oz}$ of pork that costs $\$9$ per pound. How much does Mia's mom spend in all on the cherry tomatoes and the pork?

Show solution

Understand

Mia's mom buys cherry tomatoes priced at $4 for every 8 oz and pork priced at$ 9 per pound. We find each item's cost from its per-unit price, then add the two costs.

Givens

Cherry tomatoes: she buys 1 lb (= 16 oz), priced at $4 per 8 oz.
Pork: she buys 1 lb 8 oz, priced at $9 per pound.
1 lb = 16 oz.

Unknowns

The total amount of money spent on the cherry tomatoes and the pork together.

Constraints

Prices are unit rates: $4 per 8 oz of tomatoes;$ 9 per 1 lb of pork.
Money amounts are in dollars and cents.

Plan

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

This is a money/rate problem, so tracking the units ( $per ounce,$ per pound) keeps the setup correct. It splits naturally into two subproblems (tomato cost, pork cost) that are added at the end.

Execute

#8 Analyze the Units 3.MD.A.2

1 lb is 16 oz, and the price is

4 for each 8 oz. There are 16 / 8 = 2 portions of 8 oz, so the tomatoes cost 2 groups of

4.

16 \div 8 = 2,\quad 2 \times \$4 = \$8

Converting 1 lb to 16 oz so the weight matches the 8 oz unit of the price is just unit sense a third grader builds with measurement.

#7 Identify Subproblems 3.OA.A.3

1 lb 8 oz is 1 whole pound plus half a pound (8 oz = half of 16 oz). At

9 per pound, 1 pound cost

9 and the extra half-pound costs half of

9, which is

4.50.

1\times\$9 + \tfrac{1}{2}\times\$9 = \$9 + \$4.50 = \$13.50

Matching the pork weight to its per-pound price is a within-100 multiplication/division word-problem skill.

#7 Identify Subproblems 3.OA.A.3

Add the tomato cost and the pork cost to get the total spent.

\$8 + \$13.50 = \$21.50

Combining the two subtotals is a single addition of two money amounts.

Answer: $21.50

Review

Tomatoes $8 and pork$ 13.50 are both sensible store prices, and the total $21.50 is a reasonable grocery sum for the two items.

Use repeated addition to confirm each subtotal, then add $8 +$ 13.50 to reach $21.50.

Standards · min grade 3

3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Converting pounds to ounces (and 8 oz to half a pound) to match the price units.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding each item's cost from its unit rate and adding the subtotals.

💡 Match the weight to the price's unit, find each cost, then add - that's just Grade 3 unit sense!

Find the per-unit-weight rate first · 12 practice problems

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