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What is a tape diagram? A parent’s guide to bar models

If your child’s homework says “draw a tape diagram,” it means a row of boxes that stands for the numbers in a word problem. It is the same thing as a bar model, and it takes about a minute to learn.

By The Kizupi team · Written · Updated

Key findings

  • The Common Core glossary defines a tape diagram as a drawing that looks like a segment of tape, used to show how numbers relate, and lists bar model, strip diagram and length model as other names for it [1].
  • From Grade 2, the standards ask children to solve word problems by using drawings and equations with a symbol for the unknown number [2].
  • In Grade 6, tape diagrams are named outright as one way to reason about ratios [3].

What a tape diagram is

A tape diagram is a rectangle split into parts, drawn so that bigger amounts take more room. The Common Core’s glossary calls it “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 [1]. Singapore-style books say bar model; many US worksheets say tape diagram. They are the same picture.

It turns a story into a shape. Once the boxes are on paper, the question is usually easy to see: which box is missing, and what is it worth?

Why your child is asked to draw one

The standards ask for it. Grade 2 and Grade 3 both ask children to solve word problems “by using drawings and equations with a symbol for the unknown number to represent the problem” [2]. In Grade 6 the standards name tape diagrams directly, next to tables and double number lines, as a way to reason about ratios [3].

So the drawing isn’t extra busywork. It is the step that shows the child understood the story before doing any arithmetic.

Example 1: a part is missing (Grade 1 and up)

Hana read 13 pages in two days. On day one, Hana read 5 pages. How many pages did Hana read on day two?

5?13 pages

Draw one bar for the whole 13, and split it into the two days. Day one is 5. The other part is what’s left: 13 − 5 = 8. Kizupi’s hint for this one, under the problem on its worksheet, is a question, not the answer: “What is the whole here? What is one part?”

Example 2: “times as many” (Grade 3)

Wei and Jade have 35 marbles together. Jade has 4 times as many as Wei. How many marbles does Wei have?

WeiJadeJadeJadeJade35 marbles

This is where the drawing earns its keep. Give Wei one box. Jade has 4 times as many, so Jade gets four boxes the same size. That is 5 equal boxes for 35 marbles, so one box is 35 ÷ 5 = 7. Wei has 7. Kizupi’s hint: “If Wei has one box of marbles, how many boxes does Jade have?”

Without the picture, most children divide 35 by 4 and get stuck. With it, they count the boxes.

Example 3: how much more? (Grade 3)

A red ribbon is 8 cm long. A blue ribbon is 4 times as long. How much longer is the blue ribbon than the red one?

8888blue ribbon, 4 × 8 = 32 cm

Draw the red ribbon as one box of 8 and the blue as four of them. The red ribbon lines up with the first box, so the difference is the other three: 3 × 8 = 24 cm. The question asks for the difference, not the blue ribbon, which is the trap Kizupi’s hint points at: “Are we looking for the blue ribbon, or the difference?”

How to help at home

  1. Read the story and name the things. Pages, marbles, ribbons. One bar for each thing, or one bar for the whole.
  2. Draw the boxes before any numbers. Same-size boxes for “times as many,” a longer box for a bigger amount. It doesn’t need a ruler.
  3. Write what you know, and a ? for what you don’t. Put the total under a bracket.
  4. Ask which box is the question. Then the arithmetic is one step: subtract a part, or divide by the number of boxes.

Then try a few more. Kizupi’s free Grade 3 two-step word problem sheets include bar model problems like the two above, and the Grade 1 addition and subtraction sheets include part-whole ones, each with a hint and an answer key.

Questions parents ask

Is a tape diagram the same as a bar model?

Yes. The Common Core glossary lists bar model, strip diagram, fraction strip and length model as other names for a tape diagram [1].

What grade are tape diagrams taught in?

Simple part-whole drawings show up in Grades 1 and 2, when word problems are solved with drawings and equations [2]. “Times as many” bars come in Grade 3, and Grade 6 uses them for ratios [3].

How do you draw a tape diagram for “times as many”?

Draw one box for the smaller amount, then that many same-size boxes for the larger one. Divide the total by the number of boxes to find one box.

My child gets the answer without drawing. Is that OK?

For easy problems, yes. The drawing matters on harder ones, like “together” and “times as many” in the same story, where it shows which number to divide by.

Keep going

Sources

  1. Common Core State Standards Initiative, Mathematics Glossary: Tape diagram. Read November 5, 2026.
  2. Common Core State Standards Initiative, Grade 3, Operations and Algebraic Thinking (3.OA). Read November 5, 2026.
  3. Common Core State Standards Initiative, Grade 6, Ratios and Proportional Relationships (6.RP). Read November 5, 2026.

Cite this page: The Kizupi team, “What is a tape diagram? A parent’s guide to bar models,” Kizupi, updated November 5, 2026, https://kizupi.com/guides/tape-diagram-bar-model.

Want a tutor that asks “how do you know?” every day? Kizupi’s pixel owl reads each problem aloud, hints one small step at a time and never hands over the answer. Grades 1–6.

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