Bigger addend, bigger sum

3.OA.A.43.NBT.A.2 · take · grade 3

Archetype: Pin Down a Number from Digit and Range Conditions · step in a 9-type progression

$367 + \square < 941$

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

Show solution

Understand

We have the inequality 367 + (box) < 941. We must find the largest whole number that fits in the box so the total stays below 941.

Givens

The addition statement is 367 + box < 941
367 is one fixed addend

Unknowns

The greatest whole number that can go in the box

Constraints

The sum 367 + box must be strictly less than 941 (not equal to it)

Plan

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

The result of the addition is bounded, so we work backwards from 941: find what plus 367 gives exactly 941, then step down by one to satisfy the strict 'less than'. A quick guess-and-check confirms the boundary case.

Execute

#11 Work Backwards 3.NBT.A.2

First find the box value that would make the sum exactly 941 by subtracting 367 from 941. This is the largest sum allowed if 'less than' were 'at most'.

941 - 367 = 574

Subtraction undoes addition, so it tells us exactly how big the box could be at the boundary.

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

If the box were 574, the sum would be 367 + 574 = 941, but the statement needs the sum to be LESS than 941, not equal to it. So 574 is too big.

367 + 574 = 941 \not< 941

Testing the boundary shows equality fails the strict inequality, so we must step down.

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

The next whole number below 574 is 573. Then 367 + 573 = 940, which is less than 941. So 573 is the greatest value that works.

367 + 573 = 940 < 941

Since whole numbers increase by 1, the largest one keeping the sum under 941 is just one below the boundary.

Answer: 573

Review

573 is a three-digit number near 600, and 367 + 573 = 940, which sits just one below 941. Using 574 would hit 941 exactly, so 573 is indeed the largest that stays strictly under. The magnitude makes sense.

Convert to algebra (tool 13): box < 941 - 367 = 574, so the greatest whole number is 573. This confirms the work-backwards result.

Standards · min grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Computing 941 - 367 and verifying 367 + 573 within 1000
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the unknown box value that satisfies the relationship

💡 Find the exact match by subtracting, then drop down one because the sum must stay UNDER the target!