Bar Diagram Subtraction: A Whole, a Part and a Question Mark

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6 problems. Bar diagram subtraction within 100: find the missing part. Sheet 49R1W8, with its answer key.

Bar diagram subtraction within 100: find the missing part

Name Date Score / 6

The top strip is the whole and the strips under it are its parts. Subtract to find the part with the question mark.

  1. 1.3113?31 − 13 = ________
  2. 2.4433?44 − 33 = ________
  3. 3.256?25 − 6 = ________
  4. 4.3825?38 − 25 = ________
  5. 5.7450?74 − 50 = ________
  6. 6.4536?45 − 36 = ________

Sheet 49R1W8 · Made at homeroomtools.com

Answer key. Bar diagram subtraction within 100: find the missing part

  1. 1.31131831 − 13 = 18 (13 + 18 = 31)
  2. 2.44331144 − 33 = 11 (33 + 11 = 44)
  3. 3.2561925 − 6 = 19 (6 + 19 = 25)
  4. 4.38251338 − 25 = 13 (25 + 13 = 38)
  5. 5.74502474 − 50 = 24 (50 + 24 = 74)
  6. 6.4536945 − 36 = 9 (36 + 9 = 45)

Sheet 49R1W8 · Made at homeroomtools.com

Next step More grade 2 subtractionPractice regrouping in columns

How it works

Each bar diagram subtraction here draws the whole as one long bar over two shorter ones: a part you know and a part marked with a question mark. Pupils subtract to find it.

Read the full guide

How to read the bars

The top bar is the whole, say 62. Under it sit two parts that fill the same length: 56 and a question mark. The missing part is 62 − 56 = 6, and the key writes the check, 56 + 6 = 62. The known part is drawn to scale wherever its number fits inside it.

Pick the size of the numbers

Within 20: a whole, a part and a question mark suits a first lesson. Within 100, regrouping every time: 62 − 38 and Within 1,000: a 3-digit whole and part follow. Common Core 2.OA.1 asks for take-apart problems within 100 solved with drawings and equations.

  • Have pupils cover the question mark and say the whole and the known part aloud before they write.
  • Use the whole tens sheet to show that 80 − 50 is the same picture as 8 − 5.

Questions and answers

What is a bar diagram in subtraction?

A drawing of rectangles: one bar for the whole and, under it, a bar cut into the part taken away and the part left. Subtracting finds the part with the question mark, as in 70 − 61 = 9.

Is bar diagram math subtraction the same as a tape diagram?

Yes. Wikipedia's article on the tape diagram lists divided bar model, strip diagram and length model as other names for the same drawing of rectangles.

Does the key show the diagrams filled in?

Yes. The answer key prints as the last page with the missing part written in its bar, the subtraction, and an addition that checks it. Untick Answer key before you press Print to leave it out.

Are there comparison bar diagrams, with two bars?

Not here. Every diagram on this page is a whole and its two parts. Diagrams that set two separate bars side by side, to ask how many more or fewer, are not drawn by this tool.

All 12 sheet types

Within 100 7

  • A small part taken away: 38 − 7 The known part has one digit, so most of the bar is the question mark: 38 − 7 = 31. Counting back works here. Where a number would not fit in so short a part, the part is drawn wider.
  • Bar diagram subtraction within 100: find the missing part The top bar is the whole, 62. Under it are two parts that fill the same length: 56 and a question mark. Pupils write 62 − 56 = 6, and the key adds the check, 56 + 6 = 62. Six diagrams, with and without regrouping.
  • From 100: the part that goes with 67 The whole is always 100 and one part is given: 100 − 67 = 33, 100 − 14 = 86. Pupils find the partner that completes the hundred, and the key checks it, 67 + 33 = 100.
  • Nearly the whole taken away: 70 − 61 The known part is almost the whole bar and the question mark is a sliver: 70 − 61 = 9. Pupils see that counting up from 61 to 70 is quicker than taking 61 away.
Show all 12 sheet types (8 more)

Within 100, continued

  • Whole tens on a bar: 80 − 50 Every number is a whole ten: 80 − 50 = 30, 60 − 20 = 40. The picture is the same as for 8 − 5 and 6 − 2, which is the point of the sheet: tens subtract like ones.
  • Within 100, no regrouping: 97 − 37 Each digit of the part is no larger than the digit above it, so no ten is taken apart: 97 − 37 = 60, 70 − 10 = 60. The diagram shows why the answer is what is left of the top bar.
  • Within 100, regrouping every time: 62 − 38 The ones of the part are larger than the ones of the whole, as in 62 − 38 = 24, so a ten is taken apart each time. Pupils check on the diagram: 38 + 24 = 62 fills the whole bar.

Within 20 and within 10 3

  • Copy a number bond into a bar A number bond with circles stands beside empty bars. Pupils write the whole in the long bar and the two parts in the cut bar: whole 10, parts 9 and 1, so 10 − 9 = 1. It ties the bar picture to bonds they know.
  • Within 10: number bond bars drawn to scale A bar for a whole of 10 or less, cut into two parts with one number missing: whole 9, one part 2, so the other is 9 − 2 = 7. The cut is drawn where the numbers say, so the longer part is the larger number.
  • Within 20: a whole, a part and a question mark Small numbers for a first lesson: a whole of 17 over the parts 5 and a question mark, so 17 − 5 = 12. Pupils learn to read the three bars before the numbers grow.

Within 1,000 2

  • From a whole hundred: 700 − 102 The whole is 200, 300 or another whole hundred, so the subtraction crosses zeros: 700 − 102 = 598 and 600 − 591 = 9. The check on the key, 102 + 598 = 700, is often the easier way to the answer.
  • Within 1,000: a 3-digit whole and part Three-digit numbers on the same picture: 974 − 378 = 596, checked by 378 + 596 = 974. The working is done beside the diagram; the bars only show which number is the whole and which are parts.

How this list was compiled: The sheet types and worked examples were written for this page; every diagram and answer is made by the sheet generator, and every worked example was computed by script on 2026-10-01. The other names of the drawing follow Wikipedia, Tape diagram, https://en.wikipedia.org/wiki/Tape_diagram, read the same day. Where the problems sit in school was read in the full text of the Common Core State Standards for Mathematics (California Department of Education copy, https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf), read on 2026-10-01: 2.OA.1 asks grade 2 to solve problems of taking from, taking apart and comparing within 100, for example by using drawings and equations with a symbol for the unknown number. Licence: own work

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