← Bigger addend, bigger sum · Pin Down a Number from Digit and Range Conditions

Bigger addend, bigger sum · 10 practice problems

3.NBT.A.23.OA.A.4

Generated variants — 10

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

Variant 1 easy answer: 426

$73 + \square < 500$

Find the greatest number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the greatest whole number for the box so that 73 plus the box stays < 500.

Givens

The fixed number is 73.
The bound is 500.

Unknowns

The greatest whole number that fits in the box.

Constraints

The sum must be < 500.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

500 - 73 = 427

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

73 + 427 = 500 \not< 500

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the greatest side of the boundary.

73 + 426 = 499 < 500

One step past the tipping point is the extreme value that still works.

Answer: 426

4 · Reviewdoes it hold up?

499 is < 500, and the next step would break the inequality, so 426 is the greatest.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 2 easy answer: 449

$150 + \square < 600$

Find the greatest number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the greatest whole number for the box so that 150 plus the box stays < 600.

Givens

The fixed number is 150.
The bound is 600.

Unknowns

The greatest whole number that fits in the box.

Constraints

The sum must be < 600.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

600 - 150 = 450

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

150 + 450 = 600 \not< 600

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the greatest side of the boundary.

150 + 449 = 599 < 600

One step past the tipping point is the extreme value that still works.

Answer: 449

4 · Reviewdoes it hold up?

599 is < 600, and the next step would break the inequality, so 449 is the greatest.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 3 easy answer: 456

$285 + \square < 742$

Find the greatest number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the greatest whole number for the box so that 285 plus the box stays < 742.

Givens

The fixed number is 285.
The bound is 742.

Unknowns

The greatest whole number that fits in the box.

Constraints

The sum must be < 742.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

742 - 285 = 457

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

285 + 457 = 742 \not< 742

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the greatest side of the boundary.

285 + 456 = 741 < 742

One step past the tipping point is the extreme value that still works.

Answer: 456

4 · Reviewdoes it hold up?

741 is < 742, and the next step would break the inequality, so 456 is the greatest.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 4 medium answer: 554

$248 + \square < 803$

Find the greatest number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the greatest whole number for the box so that 248 plus the box stays < 803.

Givens

The fixed number is 248.
The bound is 803.

Unknowns

The greatest whole number that fits in the box.

Constraints

The sum must be < 803.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

803 - 248 = 555

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

248 + 555 = 803 \not< 803

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the greatest side of the boundary.

248 + 554 = 802 < 803

One step past the tipping point is the extreme value that still works.

Answer: 554

4 · Reviewdoes it hold up?

802 is < 803, and the next step would break the inequality, so 554 is the greatest.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 5 medium answer: 690

$199 + \square > 888$

Find the least number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the least whole number for the box so that 199 plus the box stays > 888.

Givens

The fixed number is 199.
The bound is 888.

Unknowns

The least whole number that fits in the box.

Constraints

The sum must be > 888.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

888 - 199 = 689

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

199 + 689 = 888 \not> 888

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the least side of the boundary.

199 + 690 = 889 > 888

One step past the tipping point is the extreme value that still works.

Answer: 690

4 · Reviewdoes it hold up?

889 is > 888, and the next step would break the inequality, so 690 is the least.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 6 medium answer: 486

$420 + \square > 905$

Find the least number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the least whole number for the box so that 420 plus the box stays > 905.

Givens

The fixed number is 420.
The bound is 905.

Unknowns

The least whole number that fits in the box.

Constraints

The sum must be > 905.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

905 - 420 = 485

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

420 + 485 = 905 \not> 905

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the least side of the boundary.

420 + 486 = 906 > 905

One step past the tipping point is the extreme value that still works.

Answer: 486

4 · Reviewdoes it hold up?

906 is > 905, and the next step would break the inequality, so 486 is the least.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 7 medium answer: 487

$512 + \square < 1{,}000$

Find the greatest number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the greatest whole number for the box so that 512 plus the box stays < 1000.

Givens

The fixed number is 512.
The bound is 1{,}000.

Unknowns

The greatest whole number that fits in the box.

Constraints

The sum must be < 1{,}000.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

1{,}000 - 512 = 488

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

512 + 488 = 1{,}000 \not< 1{,}000

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the greatest side of the boundary.

512 + 487 = 999 < 1{,}000

One step past the tipping point is the extreme value that still works.

Answer: 487

4 · Reviewdoes it hold up?

999 is < 1{,}000, and the next step would break the inequality, so 487 is the greatest.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 8 hard answer: 575

$367 + \square > 941$

Find the least number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the least whole number for the box so that 367 plus the box stays > 941.

Givens

The fixed number is 367.
The bound is 941.

Unknowns

The least whole number that fits in the box.

Constraints

The sum must be > 941.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

941 - 367 = 574

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

367 + 574 = 941 \not> 941

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the least side of the boundary.

367 + 575 = 942 > 941

One step past the tipping point is the extreme value that still works.

Answer: 575

4 · Reviewdoes it hold up?

942 is > 941, and the next step would break the inequality, so 575 is the least.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 9 hard answer: 573

$367 + \square < 941$

Find the greatest number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the greatest whole number for the box so that 367 plus the box stays < 941.

Givens

The fixed number is 367.
The bound is 941.

Unknowns

The greatest whole number that fits in the box.

Constraints

The sum must be < 941.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

941 - 367 = 574

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

367 + 574 = 941 \not< 941

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the greatest side of the boundary.

367 + 573 = 940 < 941

One step past the tipping point is the extreme value that still works.

Answer: 573

4 · Reviewdoes it hold up?

940 is < 941, and the next step would break the inequality, so 573 is the greatest.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.

Variant 10 hard answer: 559

$640 + \square < 1{,}200$

Find the greatest number that can go in the box $\square$ so that the statement above is true.

Show solution

1 · Understandwhat's really being asked

Find the greatest whole number for the box so that 640 plus the box stays < 1200.

Givens

The fixed number is 640.
The bound is 1{,}200.

Unknowns

The greatest whole number that fits in the box.

Constraints

The sum must be < 1{,}200.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

Undo the addition to find the exact boundary, then step one past or short of it to land on the right side of the inequality.

3 · Execute3 carry out the plan

1Find the boundary

#11 Work Backwards 3.NBT.A.2

Subtract to see what box value makes the two sides equal.

1{,}200 - 640 = 560

Equality is the tipping point of the inequality.

2Test the boundary

#6 Guess and Check 3.NBT.A.2

The boundary itself makes the sides equal, so it fails the strict inequality.

640 + 560 = 1{,}200 \not< 1{,}200

We need strictly one side, not equal.

3Step to the answer

#6 Guess and Check 3.OA.A.4

Move one step to the greatest side of the boundary.

640 + 559 = 1{,}199 < 1{,}200

One step past the tipping point is the extreme value that still works.

Answer: 559

4 · Reviewdoes it hold up?

1{,}199 is < 1{,}200, and the next step would break the inequality, so 559 is the greatest.

Another way: Guess a few values near the boundary and check each sum.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and place value. — Subtracting to find the boundary.
3.OA.A.4 Determine the unknown whole number in an addition or subtraction equation. — Pinning the unknown box value.

💡Takeaway. Solve the equal case first; the answer is always one step away from it.