Summary: A bar model, also called a tape diagram, draws a whole and its two parts as boxes and hides one of the three numbers. This guide shows how to read a bar model, a ten frame and a number line, and how to turn each drawing into the number sentence that finds the missing number.
Want ready-made sheets? Visual Math Models generates bar model worksheets with answer keys, ready to print.
Overview
Every problem on a bar model worksheet is built from three numbers that belong together: a whole and the two parts that make it. Each problem shows two of them, and the child writes the missing one in the box under the drawing. Once a child can see which of the three is missing, they know whether to add or subtract. This guide is for teachers, parents and anyone making worksheets.
The Part-Whole Model
The whole is the two parts put together: whole = part + part. From the numbers 12, 18 and 30 you get three questions at once: 12 + 18 = ☐, 30 − 12 = ☐, and 12 + ☐ = 30 (“what do I add to 12 to make 30?”). A bar model problem always shows two of the three numbers and hides one. Every part is at least 1, so both boxes always hold something.
This is why teachers reach for bar models in word problems. Take “Sam had 12 stickers, got some more, and now has 30. How many did he get?” The 30 is everything Sam has at the end, so it goes in the top box as the whole. The 12 goes in one part box, and the question mark goes in the other. The drawing turns the story into 12 + ☐ = 30.
How to Read a Bar Model (Tape Diagram)
- The top box is the whole. It is shaded on the default sheet and stretches across the full width of the drawing, because the whole covers both parts.
- The two boxes underneath are the parts. Together they line up exactly under the whole.
- The question mark is the missing number. Where it sits tells you what to do: in the top box, the whole is missing; in a bottom box, a part is missing.
- On these sheets the two part boxes are the same width. That is a choice these worksheets make on purpose: the drawing shows where each number belongs, never how big it is, so the picture cannot give the answer away. Read the numbers, not the lengths. When children draw their own bar models, they often make the bigger number the longer box, and that is a good habit too.
On these worksheets a missing part is always the right-hand box, so the part you are given is always the left-hand one.
Finding the Missing Number
When the whole is missing
Add the two parts. The number sentence reads 12 + 18 = ☐, and the answer is 30.
When a part is missing
Take the part you know away from the whole: 30 take away 12 leaves 18. The same question can be written two ways, and a sheet may use either or both:
- Addition with a gap: 12 + ☐ = 30. “What do I add to 12 to make 30?” Children who count on from 12 can jump to 20 (that is 8), then on to 30 (10 more): 8 + 10 = 18.
- Subtraction: 30 − 12 = ☐. “What is left of 30 after the 12?” The answer is 18 again.
Both sentences describe the same bar, which is the point: the drawing shows a child that a gap addition and a subtraction are one question asked two ways.
The answer key writes each answer once, in its box. The question mark stays in the drawing, so the key shows exactly the page the child worked on.
Solving Any Bar Model, Step by Step
- Find the question mark. (On a ten frame the box always asks for the total, so go straight to step 3.)
- Decide what is missing. A question mark in the top box means the whole; in a bottom box, a part.
- Whole missing: add. Put the two parts together.
- Part missing: subtract or count on. Take the known part away from the whole, or count up from the known part to the whole.
- Write the answer in the box, then check it. The two parts must add up to the whole. If 12 + 18 really makes 30, the 18 is right.
The same steps work on the ten frame and the number line below.
Reading a Ten Frame
Ten frames come with the Creative edition of Visual Math Models and up, and you can move up to a higher edition at any time after you buy.
A ten frame is a 2 × 5 grid of squares with one counter for every unit. The counters fill the top row from left to right, then the bottom row, and a total above 10 carries on into a second frame underneath. The first part’s counters come first in a dark colour and the second part’s follow in a light one, so the two parts stay easy to tell apart, even on a black-and-white copy.
To find the total, read a full frame as 10 at a glance and count on from there: one full frame and four more counters is 14. The number sentence under the frame names both parts — 8 + 6 = ☐ — and the child writes the total in the box. Ten-frame sheets count up to 10 (one frame) or up to 20 (one frame or two, depending on the total), which makes them the gentle first step before bigger numbers.
Reading a Number Line
Number lines also come with the Creative edition and up, and they reach the same numbers as the bar model, up to 1,000. A number line problem starts at 0 and makes two jumps:
- The first jump lands on the first part, and its label says how far it went (+12).
- The second jump ends at the whole, labelled with the second part (+18).
- The three marks under the line read 0, the first part, and the whole.
A question mark shows what is missing. Under the last mark, the whole is missing: add the two jumps. On the second jump (+?), a part is missing: work out how far it is from the first mark to the whole. The three marks are evenly spaced on purpose, so the line shows the order of the jumps without giving the answer away, and the labels carry the sizes. Read the labels.
One Sum, Three Drawings
The same addition, 9 + 7, looks different in each model, and seeing them side by side helps a child connect them. The ten frame is the most concrete — the child can count every counter. The number line shows counting on. The bar model shows the structure itself, and with the number line it keeps working when the numbers reach the hundreds.
Number Ranges
Bar model and number line sheets come in three bands:
- Easy: wholes up to 20.
- Medium: wholes up to 100.
- Hard: wholes up to 1,000.
Ten-frame sheets have their own two bands: totals up to 10 on one frame, and totals up to 20 using one or two frames.
When the whole is the missing number, the two parts can be equal (1 + 1 = ☐ can appear). When a part is missing, the two parts are always different, so the answer is never just a copy of the number already shown.
Answer Tiles
With answer tiles switched on, the sheet prints a band of answer tiles below the problems: one tile per problem, carrying that problem’s answer, shuffled. No two answers on the sheet are the same, so each tile matches exactly one problem. A child can cut the tiles out and lay each one next to its problem, or cross a tile off as each answer is found. When every tile has found its problem, the whole page checks out.
Try It Online
On screen, a bar model plays just like the printed sheet: pick a problem’s answer box and type the missing number. Play one here — no download, nothing to install. The general player controls, including checking your answers and resetting, are covered once in How to Play Puzzles Online.
FAQ
What is a bar model in math?
A drawing of a part-whole relationship: a long box for the whole and two boxes underneath for its parts. A question mark marks the one number that is missing, and the child works out whether to add or subtract to find it.
Is a bar model the same as a tape diagram?
Yes. “Tape diagram” (common in US classrooms) and “bar model” (from Singapore maths) name the same picture of a whole and its parts.
Are the boxes drawn to the size of the numbers?
Not on these sheets. Both part boxes are drawn the same width and a number line’s marks are evenly spaced, on purpose, so the drawing never gives the answer away and the numbers carry the sizes. When children draw their own bar models, a bigger number often gets a longer box.
What is the difference between 12 + ☐ = 30 and 30 − 12 = ☐?
Nothing in the answer: both ask for the missing part, 18. The first asks “what do I add?”, the second asks “what is left?” — practising both shows a child that addition and subtraction are two views of one fact.
How does a child check an answer?
Put the numbers back into the drawing: the two parts must add up to the whole. If they do, the answer in the box is right.
Further Reading
- How to Create Bar Model Math Worksheets in Puzzle Maker Pro
- How Visual Fractions Worksheets Work
- How to Create Visual Fractions Worksheets in Puzzle Maker Pro
- How to Play Puzzles Online
- How Puzzle Maker Pro Works: From One Puzzle to a Finished Book
Make Your Own Bar Model Worksheets
Now that you know how a bar model works, make your own: a fresh sheet every time, from totals to 20 up to totals to 1,000, each with its answer key, ready for a lesson, a homework pack or a workbook.
Create your own bar model worksheets with Visual Math Models
Not ready yet? Try the free demo first — it covers every module.