← Choose round up or round down in context · Divisibility and Remainder Reasoning

Choose round up or round down in context · 12 practice problems

4.NBT.B.44.NBT.B.54.OA.A.34.NBT.B.6

Generated variants — 12

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

Variant 1 easy answer: 1970 notebooks

Riverside Elementary School has $188$ boys and $205$ girls. As a Field Day gift, the school plans to give every student $5$ notebooks. If the store sells notebooks only in packs of $10$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 188 boys and 205 girls, and each of them gets 5 notebooks. Notebooks come only in packs of 10. We need the smallest number the school can buy and still have enough.

Givens

188 boys and 205 girls.
Every student gets 5 notebooks.
Notebooks are sold only in packs of 10.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

188 + 205 = 393

393 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 393 students gets 5.

393 \times 5 = 1965

1965 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

1965 is not a whole number of packs. Rounding down to 1960 would leave students without notebooks, so the school must round up to the next multiple of 10.

1965 \div 10 = 196 \cdots 5 \Rightarrow 197\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

197 packs of 10 is 1970 notebooks, which covers the 1965 needed with 5 to spare.

197 \times 10 = 1970

The school must buy 1970 notebooks.

Answer: 1970 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 1960, which is less than the 1965 needed -- so 1970 really is the smallest that works.

Another way: Round the need up to the nearest 10 directly: 1965 sits between 1960 and 1970, and only 1970 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 393 students by 5 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 1965 by 10 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 2 easy answer: 3450 notebooks

Riverside Elementary School has $233$ boys and $259$ girls. As a Field Day gift, the school plans to give every student $7$ notebooks. If the store sells notebooks only in packs of $10$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 233 boys and 259 girls, and each of them gets 7 notebooks. Notebooks come only in packs of 10. We need the smallest number the school can buy and still have enough.

Givens

233 boys and 259 girls.
Every student gets 7 notebooks.
Notebooks are sold only in packs of 10.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

233 + 259 = 492

492 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 492 students gets 7.

492 \times 7 = 3444

3444 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

3444 is not a whole number of packs. Rounding down to 3440 would leave students without notebooks, so the school must round up to the next multiple of 10.

3444 \div 10 = 344 \cdots 4 \Rightarrow 345\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

345 packs of 10 is 3450 notebooks, which covers the 3444 needed with 6 to spare.

345 \times 10 = 3450

The school must buy 3450 notebooks.

Answer: 3450 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 3440, which is less than the 3444 needed -- so 3450 really is the smallest that works.

Another way: Round the need up to the nearest 10 directly: 3444 sits between 3440 and 3450, and only 3450 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 492 students by 7 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 3444 by 10 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 3 easy answer: 3620 notebooks

Riverside Elementary School has $295$ boys and $308$ girls. As a Field Day gift, the school plans to give every student $6$ notebooks. If the store sells notebooks only in packs of $10$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 295 boys and 308 girls, and each of them gets 6 notebooks. Notebooks come only in packs of 10. We need the smallest number the school can buy and still have enough.

Givens

295 boys and 308 girls.
Every student gets 6 notebooks.
Notebooks are sold only in packs of 10.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

295 + 308 = 603

603 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 603 students gets 6.

603 \times 6 = 3618

3618 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

3618 is not a whole number of packs. Rounding down to 3610 would leave students without notebooks, so the school must round up to the next multiple of 10.

3618 \div 10 = 361 \cdots 8 \Rightarrow 362\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

362 packs of 10 is 3620 notebooks, which covers the 3618 needed with 2 to spare.

362 \times 10 = 3620

The school must buy 3620 notebooks.

Answer: 3620 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 3610, which is less than the 3618 needed -- so 3620 really is the smallest that works.

Another way: Round the need up to the nearest 10 directly: 3618 sits between 3610 and 3620, and only 3620 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 603 students by 6 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 3618 by 10 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 4 easy answer: 2370 notebooks

Riverside Elementary School has $274$ boys and $317$ girls. As a Field Day gift, the school plans to give every student $4$ notebooks. If the store sells notebooks only in packs of $10$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 274 boys and 317 girls, and each of them gets 4 notebooks. Notebooks come only in packs of 10. We need the smallest number the school can buy and still have enough.

Givens

274 boys and 317 girls.
Every student gets 4 notebooks.
Notebooks are sold only in packs of 10.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

274 + 317 = 591

591 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 591 students gets 4.

591 \times 4 = 2364

2364 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

2364 is not a whole number of packs. Rounding down to 2360 would leave students without notebooks, so the school must round up to the next multiple of 10.

2364 \div 10 = 236 \cdots 4 \Rightarrow 237\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

237 packs of 10 is 2370 notebooks, which covers the 2364 needed with 6 to spare.

237 \times 10 = 2370

The school must buy 2370 notebooks.

Answer: 2370 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 2360, which is less than the 2364 needed -- so 2370 really is the smallest that works.

Another way: Round the need up to the nearest 10 directly: 2364 sits between 2360 and 2370, and only 2370 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 591 students by 4 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 2364 by 10 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 5 medium answer: 2240 notebooks

Riverside Elementary School has $356$ boys and $389$ girls. As a Field Day gift, the school plans to give every student $3$ notebooks. If the store sells notebooks only in packs of $10$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 356 boys and 389 girls, and each of them gets 3 notebooks. Notebooks come only in packs of 10. We need the smallest number the school can buy and still have enough.

Givens

356 boys and 389 girls.
Every student gets 3 notebooks.
Notebooks are sold only in packs of 10.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

356 + 389 = 745

745 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 745 students gets 3.

745 \times 3 = 2235

2235 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

2235 is not a whole number of packs. Rounding down to 2230 would leave students without notebooks, so the school must round up to the next multiple of 10.

2235 \div 10 = 223 \cdots 5 \Rightarrow 224\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

224 packs of 10 is 2240 notebooks, which covers the 2235 needed with 5 to spare.

224 \times 10 = 2240

The school must buy 2240 notebooks.

Answer: 2240 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 2230, which is less than the 2235 needed -- so 2240 really is the smallest that works.

Another way: Round the need up to the nearest 10 directly: 2235 sits between 2230 and 2240, and only 2240 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 745 students by 3 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 2235 by 10 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 6 medium answer: 3125 notebooks

Riverside Elementary School has $376$ boys and $401$ girls. As a Field Day gift, the school plans to give every student $4$ notebooks. If the store sells notebooks only in packs of $25$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 376 boys and 401 girls, and each of them gets 4 notebooks. Notebooks come only in packs of 25. We need the smallest number the school can buy and still have enough.

Givens

376 boys and 401 girls.
Every student gets 4 notebooks.
Notebooks are sold only in packs of 25.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

376 + 401 = 777

777 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 777 students gets 4.

777 \times 4 = 3108

3108 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

3108 is not a whole number of packs. Rounding down to 3100 would leave students without notebooks, so the school must round up to the next multiple of 25.

3108 \div 25 = 124 \cdots 8 \Rightarrow 125\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

125 packs of 25 is 3125 notebooks, which covers the 3108 needed with 17 to spare.

125 \times 25 = 3125

The school must buy 3125 notebooks.

Answer: 3125 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 3100, which is less than the 3108 needed -- so 3125 really is the smallest that works.

Another way: Round the need up to the nearest 25 directly: 3108 sits between 3100 and 3125, and only 3125 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 777 students by 4 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 3108 by 25 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 7 medium answer: 1690 notebooks

Riverside Elementary School has $423$ boys and $418$ girls. As a Field Day gift, the school plans to give every student $2$ notebooks. If the store sells notebooks only in packs of $10$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 423 boys and 418 girls, and each of them gets 2 notebooks. Notebooks come only in packs of 10. We need the smallest number the school can buy and still have enough.

Givens

423 boys and 418 girls.
Every student gets 2 notebooks.
Notebooks are sold only in packs of 10.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

423 + 418 = 841

841 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 841 students gets 2.

841 \times 2 = 1682

1682 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

1682 is not a whole number of packs. Rounding down to 1680 would leave students without notebooks, so the school must round up to the next multiple of 10.

1682 \div 10 = 168 \cdots 2 \Rightarrow 169\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

169 packs of 10 is 1690 notebooks, which covers the 1682 needed with 8 to spare.

169 \times 10 = 1690

The school must buy 1690 notebooks.

Answer: 1690 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 1680, which is less than the 1682 needed -- so 1690 really is the smallest that works.

Another way: Round the need up to the nearest 10 directly: 1682 sits between 1680 and 1690, and only 1690 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 841 students by 2 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 1682 by 10 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 8 medium answer: 2740 notebooks

Riverside Elementary School has $447$ boys and $462$ girls. As a Field Day gift, the school plans to give every student $3$ notebooks. If the store sells notebooks only in packs of $20$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 447 boys and 462 girls, and each of them gets 3 notebooks. Notebooks come only in packs of 20. We need the smallest number the school can buy and still have enough.

Givens

447 boys and 462 girls.
Every student gets 3 notebooks.
Notebooks are sold only in packs of 20.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

447 + 462 = 909

909 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 909 students gets 3.

909 \times 3 = 2727

2727 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

2727 is not a whole number of packs. Rounding down to 2720 would leave students without notebooks, so the school must round up to the next multiple of 20.

2727 \div 20 = 136 \cdots 7 \Rightarrow 137\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

137 packs of 20 is 2740 notebooks, which covers the 2727 needed with 13 to spare.

137 \times 20 = 2740

The school must buy 2740 notebooks.

Answer: 2740 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 2720, which is less than the 2727 needed -- so 2740 really is the smallest that works.

Another way: Round the need up to the nearest 20 directly: 2727 sits between 2720 and 2740, and only 2740 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 909 students by 3 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 2727 by 20 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 9 hard answer: 2000 notebooks

Riverside Elementary School has $512$ boys and $487$ girls. As a Field Day gift, the school plans to give every student $2$ notebooks. If the store sells notebooks only in packs of $25$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 512 boys and 487 girls, and each of them gets 2 notebooks. Notebooks come only in packs of 25. We need the smallest number the school can buy and still have enough.

Givens

512 boys and 487 girls.
Every student gets 2 notebooks.
Notebooks are sold only in packs of 25.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

512 + 487 = 999

999 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 999 students gets 2.

999 \times 2 = 1998

1998 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

1998 is not a whole number of packs. Rounding down to 1975 would leave students without notebooks, so the school must round up to the next multiple of 25.

1998 \div 25 = 79 \cdots 23 \Rightarrow 80\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

80 packs of 25 is 2000 notebooks, which covers the 1998 needed with 2 to spare.

80 \times 25 = 2000

The school must buy 2000 notebooks.

Answer: 2000 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 1975, which is less than the 1998 needed -- so 2000 really is the smallest that works.

Another way: Round the need up to the nearest 25 directly: 1998 sits between 1975 and 2000, and only 2000 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 999 students by 2 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 1998 by 25 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 10 hard answer: 2136 notebooks

Riverside Elementary School has $539$ boys and $528$ girls. As a Field Day gift, the school plans to give every student $2$ notebooks. If the store sells notebooks only in packs of $12$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 539 boys and 528 girls, and each of them gets 2 notebooks. Notebooks come only in packs of 12. We need the smallest number the school can buy and still have enough.

Givens

539 boys and 528 girls.
Every student gets 2 notebooks.
Notebooks are sold only in packs of 12.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

539 + 528 = 1067

1067 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 1067 students gets 2.

1067 \times 2 = 2134

2134 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

2134 is not a whole number of packs. Rounding down to 2124 would leave students without notebooks, so the school must round up to the next multiple of 12.

2134 \div 12 = 177 \cdots 10 \Rightarrow 178\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

178 packs of 12 is 2136 notebooks, which covers the 2134 needed with 2 to spare.

178 \times 12 = 2136

The school must buy 2136 notebooks.

Answer: 2136 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 2124, which is less than the 2134 needed -- so 2136 really is the smallest that works.

Another way: Round the need up to the nearest 12 directly: 2134 sits between 2124 and 2136, and only 2136 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 1067 students by 2 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 2134 by 12 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 11 hard answer: 3590 notebooks

Riverside Elementary School has $618$ boys and $577$ girls. As a Field Day gift, the school plans to give every student $3$ notebooks. If the store sells notebooks only in packs of $10$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 618 boys and 577 girls, and each of them gets 3 notebooks. Notebooks come only in packs of 10. We need the smallest number the school can buy and still have enough.

Givens

618 boys and 577 girls.
Every student gets 3 notebooks.
Notebooks are sold only in packs of 10.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

618 + 577 = 1195

1195 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 1195 students gets 3.

1195 \times 3 = 3585

3585 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

3585 is not a whole number of packs. Rounding down to 3580 would leave students without notebooks, so the school must round up to the next multiple of 10.

3585 \div 10 = 358 \cdots 5 \Rightarrow 359\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

359 packs of 10 is 3590 notebooks, which covers the 3585 needed with 5 to spare.

359 \times 10 = 3590

The school must buy 3590 notebooks.

Answer: 3590 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 3580, which is less than the 3585 needed -- so 3590 really is the smallest that works.

Another way: Round the need up to the nearest 10 directly: 3585 sits between 3580 and 3590, and only 3590 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 1195 students by 3 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 3585 by 10 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.

Variant 12 hard answer: 3700 notebooks

Riverside Elementary School has $631$ boys and $594$ girls. As a Field Day gift, the school plans to give every student $3$ notebooks. If the store sells notebooks only in packs of $50$ , find the smallest number of notebooks the school must buy.

Show solution

1 · Understandwhat's really being asked

There are 631 boys and 594 girls, and each of them gets 3 notebooks. Notebooks come only in packs of 50. We need the smallest number the school can buy and still have enough.

Givens

631 boys and 594 girls.
Every student gets 3 notebooks.
Notebooks are sold only in packs of 50.

Unknowns

The smallest number of notebooks the school must buy.

Constraints

Every student must get their full share, so running short is not allowed.

2 · Planchoose the strategy

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

Three small steps: how many students, how many notebooks they need, and then how many packs cover that. The last step is a decision about rounding, not a calculation.

3 · Execute4 carry out the plan

1Count all the students

#7 Identify Subproblems 4.NBT.B.4

Boys and girls together are the number of students.

631 + 594 = 1225

1225 students in all.

2Find how many notebooks are needed

#8 Analyze the Units 4.NBT.B.5

Each of the 1225 students gets 3.

1225 \times 3 = 3675

3675 notebooks are needed.

3Decide whether to round up or down

#7 Identify Subproblems 4.OA.A.3

3675 is not a whole number of packs. Rounding down to 3650 would leave students without notebooks, so the school must round up to the next multiple of 50.

3675 \div 50 = 73 \cdots 25 \Rightarrow 74\ \text{packs}

The context decides the rounding, not the digits.

4Check it in packs

#8 Analyze the Units 4.NBT.B.6

74 packs of 50 is 3700 notebooks, which covers the 3675 needed with 25 to spare.

74 \times 50 = 3700

The school must buy 3700 notebooks.

Answer: 3700 notebooks

4 · Reviewdoes it hold up?

One pack fewer would be 3650, which is less than the 3675 needed -- so 3700 really is the smallest that works.

Another way: Round the need up to the nearest 50 directly: 3675 sits between 3650 and 3700, and only 3700 is enough.

Standardsmin grade 4

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Adding the boys and girls to get the student count.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 1225 students by 3 notebooks each.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Deciding that the context forces rounding up.
4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends — Dividing 3675 by 50 to count the packs needed.

💡Takeaway. When running short is not allowed, always round up -- even when the digits say to round down.