What Is a Strip Diagram? Multi-Step Word Problem Examples

How to draw and label a strip diagram

1. Name the quantities and units. Are you counting stickers, students, dollars or hours?
2. Identify the relationship. Parts make a whole; equal groups have equal-size parts; a comparison shows how much more one quantity has.
3. Draw the bars. Label known values and use a letter or question mark for an unknown. Draw equal quantities with equal lengths.
4. Write and solve an equation. Let the picture guide the operation instead of choosing an operation from one keyword.
5. Check the story. Substitute your answer, include units and make sure it answers the question.

You can sketch bars by hand; they do not need to be measured precisely. Keep their relative lengths sensible and show equal parts consistently. The labels and relationships determine the answer, not a ruler.

Example 1: give some away, then get more

Sam has 20 stickers. He gives 5 to his sister, then receives 8 from a friend. How many stickers does he have now?

Step 1: Split the original 20 into the stickers remaining, R, and the 5 given away.

R + 5 = 20, so R = 20 − 5 = 15 stickers.

Step 2: Join the 15 remaining stickers and the 8 new stickers.

N = 15 + 8 = 23 stickers. Check: 20 − 5 + 8 = 23. The first bar represents the original collection; the second represents the new collection.

Example 2: equal groups, then subtract

A baker fills 4 trays with 12 cookies on each tray, then sells 20 cookies. How many cookies are left?

Four equal parts give C = 4 × 12 = 48 cookies. Now split that whole into sold and remaining cookies.

20 + L = 48, so L = 28 cookies. Check: 20 + 28 = 48.

Example 3: a comparison with a total

Tom has 5 more marbles than Jerry. Together they have 27. How many does each person have?

Let J be Jerry’s number. Tom has an equal J-part plus 5. Their combined total therefore contains two equal J-parts and one extra 5.

J + J + 5 = 27. Remove the extra 5: 27 − 5 = 22. Divide the remaining total into two equal parts: 22 ÷ 2 = 11. Jerry has 11 marbles; Tom has 16. Check both facts: 16 − 11 = 5 and 11 + 16 = 27.

Common strip-diagram mistakes

Confusing a part with the whole: in the sticker example, 5 is part of the original 20, not an extra 5 to add. Drawing unequal “equal” groups: each cookie tray needs the same-size part because each holds 12. Stopping early: finding 48 cookies does not answer how many remain after the sale.

For comparisons, show the extra amount only once. If one person has 5 more, subtracting 5 from both people’s amounts would change the story. For quantities that count whole people or objects, check that the answer makes sense as a whole number.

Practice: draw first, then check

Sketch a strip diagram and write an equation for each problem. Open the explanations when you are ready.

Keep practicing with the multi-step word-problem method, choose printable practice from our free Grade 4 math worksheets, or browse lessons in the Grade 4 Online Center.

Optional video

For parents: Math4Texas guidance from Education Service Center Region 11 connects strip diagrams with equations and unknown quantities in fourth-grade multi-step problems. The worked examples above are separate from its activity.