These bar model multiplication worksheets print the bars, so pupils label and solve, not rule rectangles. Sheets cover equal parts, a missing part, times as many, word problems to draw and blank frames.
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One bar, three questions
A bar model is a rectangle cut into equal parts. For 4 × 6, draw 4 parts of 6 and bracket the whole bar: 24. Hide a different number and the same bar asks for division: 24 ÷ 4 finds the size of one part, and 24 ÷ 6 finds how many parts.
Comparison bars and times as many
A comparison model stacks two bars, lined up at the left edge. The short bar is 1 unit and the long bar is as many units as the multiplier. So 4 times as many as 7 is 4 units of 7, or 28. The Common Core places these problems in grade 4 (4.OA.2).
Have pupils label each bar in words, such as rolls on one tray, before any number goes in.
Count the parts aloud on Bars with 6 to 10 parts. A miscount turns 7 × 8 into 48 or 64.
Print Times as many or more than? first: 4 times as many as 6 is 24, 4 more is 10.
Questions and answers
Is a bar model the same as a tape diagram?
Yes. The Common Core glossary defines a tape diagram as a drawing that looks like a segment of tape. It lists strip diagram, bar model, fraction strip and length model as other names. Texas standards 3.5(B) and 4.5(A) say strip diagram.
Which grade are bar model multiplication sheets for?
Grades 3 to 6. Equal parts and a missing part match grade 3 (Common Core 3.OA.3, Texas 3.5(B)). Comparison bars match grade 4 (4.OA.2). Fraction of a number on a bar is grade 5 (5.NF.4) and Ratio bars is grade 6 (6.RP.3).
Are the bars drawn to scale?
Within one problem, yes. Equal parts have equal width, and a comparison bar for 4 times as many is 4 units long. Different problems share no scale: 2 × 3 at the scale of 9 × 10 would be too small to write in.
All 25 sheet types
Equal parts, total unknown 6
Bars for 2-digit × 1-digit4 parts of 23. A dotted line cuts each part into 20 and 3, so the bar shows 4 × 20 = 80 and 4 × 3 = 12, and 80 + 12 = 92. It is the area model laid out in a line, and Texas sets this size in grade 3.
Bars of tens4 parts of 30 make 120, because 4 × 3 tens is 12 tens. Every part is a multiple of 10 from 10 to 90, the range standard 3.NBT.3 sets for grade 3. The bar looks the same as the bar for 4 × 3, and that is the point.
Bars with 6 to 10 parts7 parts of 8: 7 × 8 = 56. With this many parts only the first one carries its number, and the rest are read from their width. A pupil who miscounts the parts writes 48 or 64, so the key prints the number of parts beside each answer.
Show all 25 sheet types (22 more)
Equal parts, total unknown, continued
Draw the bar for a factThe sheet gives 3 × 7 and an empty bar. The pupil cuts it into 3 parts, writes 7 in each and puts the total, 21, on the bracket. Read 3 × 7 as 3 parts of 7, the way standard 3.OA.1 reads 5 × 7 as 5 groups of 7.
One fact drawn two ways3 × 8 is drawn as 3 parts of 8, and under it 8 × 3 as 8 parts of 3 on a bar of the same length. Both brackets hold a question mark, and both answers are 24. Two bars that end at the same place are a picture of the commutative property, with no rule to memorize.
Read the bar and write the factA bar is cut into 4 equal parts with 6 written in each, and a bracket over the whole bar holds a question mark: 4 × 6 = 24. Every part on a bar has the same width, because equal width stands for equal value. The page opens on this sheet, 8 bars to a page.
A part or the number of parts unknown 4
Any of the three numbers unknownAll three unknowns on one page. One bar hides the total (5 × 9 = 45), the next hides the part (45 ÷ 5 = 9) and the next hides the number of parts (45 ÷ 9 = 5). Pupils have to find the question mark before they choose × or ÷.
Find the number of partsThe total is 24 and the first part is marked 6, but the rest of the bar is left uncut. The pupil steps along in sixes, 6, 12, 18, 24, and draws the lines: 4 parts. That is ? × 6 = 24, or 24 ÷ 6 = 4, the number of groups unknown.
Find the value of one partThe bracket says 24 and the bar has 4 equal parts, each holding a question mark. 4 × ? = 24, so each part is 6. The Common Core glossary calls this reading of division group size unknown: 24 ÷ 4 = 6.
Four facts from one barA finished bar, 4 parts of 6 with 24 on the bracket, and four blank lines. The pupil writes 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4. A bar of 5 parts of 5 gives only two facts, 5 × 5 = 25 and 25 ÷ 5 = 5.
Comparison bars: times as many 6
Comparison bars with a differenceOne amount is 3 times the other and 18 more. The long bar sticks out 2 units past the short one, so 2 units are 18, 1 unit is 9, and the amounts are 9 and 27. The extra length is one unit fewer than the multiplier: 3 units against 1 leaves 2.
Comparison bars with a totalOne amount is 3 times the other and together they make 48. A bar of 1 unit over a bar of 3 units is 4 units in all, so 1 unit is 48 ÷ 4 = 12, and the two amounts are 12 and 36.
How many times as many?Two bars drawn to scale, 6 and 18, with no unit lines on the long one. The pupil marks lengths of 6 along it and finds 3 of them, so 18 is 3 times as many as 6, and 3 × 6 = 18.
Times as many or more than?Each problem is a pair with the same numbers: 4 times as many as 6, and 4 more than 6. The first needs 4 units of 6 and makes 24. The second needs one bar of 6 with 4 added and makes 10. Standard 4.OA.2 asks pupils to tell the two comparisons apart.
Times as many: find the larger amountThe short bar is 1 unit and is marked 7. The long bar under it is 4 of those units, lined up at the left edge: 4 × 7 = 28. The long bar is drawn exactly 4 units long, so the picture itself says 4 times as many.
Times as many: find the smaller amountThe long bar is marked 28 and is 4 units long. The single unit above it holds the question mark: 28 ÷ 4 = 7. A pupil who multiplies and writes 112 has read the word times and stopped looking at the bars.
Word problems to draw 4
Two-step problems on one bar'4 boxes hold 6 pencils each, and 5 pencils are loose.' The bar has 4 equal parts of 6 and one odd part of 5: 4 × 6 = 24, then 24 + 5 = 29. Both sets of standards ask grade 3 for two-step problems, and Texas 3.5(B) names strip diagrams for them. Totals stay within 100.
Word problems: comparison bars to draw'A sunflower is 9 inches tall. A young tree is 5 times as tall. How tall is the tree?' The pupil draws 1 unit of 9 over a bar of 5 units and writes 5 × 9 = 45. Heights, prices, distances and weights take turns down the page.
Word problems: equal parts to draw'A baker fills 6 trays with 8 rolls each. How many rolls is that?' comes with an empty bar and an equation line. The pupil draws 6 parts of 8 and writes 6 × 8 = 48. One story in three asks for the part or for the number of parts, so the drawing has to come first.
Write a story for the barThe bar is finished: 5 parts of 8 and 40 on the bracket. The pupil writes a word problem that fits it and the equation 5 × 8 = 40. It is the usual task in reverse, and standard 3.OA.1 asks for it: describe a context for 5 × 7. The key gives the equation and one sample story.
Matching, fractions, ratios and blank frames 5
Blank comparison bar framesSix pairs of empty bars: a 1-unit bar over a bar of 2 to 6 units, lined up at the left edge, with a label space beside each bar. Pupils write whose amount is whose before any number goes in. No answer key, 1 page.
Blank part-whole bar framesSix empty bars, already cut into 2 to 10 equal parts, each with a bracket for the total and an equation line under it. For problems from a textbook or the board. There is no answer key, because there are no set problems, so the print is 1 page.
Fraction of a number on a bar3/4 of 24: cut the bar for 24 into 4 equal parts of 6 and shade 3 of them, 3 × 6 = 18. Standard 5.NF.4 describes a fraction times a whole number the same way, as a parts of a partition of the number into b equal parts.
Match the bar to the equationEach bar has its number in the first part only and three equations under it, and the pupil circles the one that matches. One wrong choice always makes the same total another way, such as 4 × 6 = 24 under a bar of 8 parts of 3. Working out totals is not enough. The pupil has to count the parts.
Ratio barsA bar of 3 units over a bar of 2 units, and 40 for both together: 5 units are 40, so 1 unit is 8, and the amounts are 3 × 8 = 24 and 2 × 8 = 16. Red beads to blue beads at 3 to 2 is a problem of this kind. Standard 6.RP.3 lists tape diagrams among its tools for ratio problems.
How this list was compiled: Sheet types, story wording and worked examples are own work. Every worked example was computed twice by script on 2026-09-19. What a bar model is and its other names were checked 2026-09-19 against the glossary of the Common Core State Standards for Mathematics (national copy, https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf, read again 2026-09-20), which defines a tape diagram as 'a drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model', and against https://en.wikipedia.org/wiki/Bar_model (a redirect to the Tape diagram article, which also gives the ratio 3 to 2 example). The whole-part and comparison models, the multiplication example of one bar cut into four equal parts, and the concrete, pictorial, abstract sequence were checked the same day against https://en.wikipedia.org/wiki/Singapore_math. The three unknowns of a multiplication situation (unknown product, group size unknown, number of groups unknown) and the compare rows come from Table 2 of the same Common Core glossary. Standard numbers and wording checked 2026-09-19 against the full Common Core text above (3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.6, 3.OA.7, 3.OA.8, 3.NBT.3, 4.OA.1, 4.OA.2, 4.OA.3, 4.NBT.5, 5.NF.4, 6.RP.3) and the Texas Essential Knowledge and Skills for Mathematics, 19 TAC chapter 111 subchapter A (https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf: 3.4(G), 3.4(H), 3.4(J), 3.4(K), 3.5(B), 3.5(C), 3.5(D), 4.5(A)). The two standards texts and the Tape diagram article were read again on 2026-10-03. Licence: own work