Problem
Gaps are one fewer than the objects
Five posts stand in a row, evenly spaced. We need to count how many gaps (spaces between neighboring posts) there are.
Measurement & data
Your answer
gaps
Watch out It is easy to give each post its own gap and count five gaps, but the empty spaces fall only between neighbors, so there is one fewer.
How to solve
Strategy Draw a Diagram — Draw the row of posts and mark each space. Each gap sits between two posts, so the count of gaps is always one fewer than the count of posts. A quick small-case pattern confirms the rule.
1STEP 1
Picture the posts and spaces
Draw 5 posts in a line: the empty spaces appear only between neighbors, never past the two ends.
5 posts → spaces between neighbors
Seeing the line of posts makes it clear the ends have no gap beyond them.
2.MD.B.5Draw A Diagram2STEP 2
Spot the pattern: gaps are one fewer
2 posts make 1 gap, 3 posts make 2 gaps, 4 posts make 3 gaps — so the number of gaps is the number of posts minus 1.
gaps = posts - 1
A repeated small-case pattern reveals the simple rule without listing every gap.
2.MD.B.5Look For A PatternThe number of gaps is always one fewer than the number of posts.
Why?
You can match every gap with the single post standing just to its left, and no two gaps ever grab the same post.
Why?
Each gap pairs with exactly one post and each of those posts with exactly one gap, so the gaps and the matched posts have to be the same size.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
The last post on the right has no gap after it, so it never gets matched, and the matched posts are every post except that last one.
Why?
The whole row splits with no overlap into the one leftover post and the matched posts, so the matched posts count one below the whole row.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
3STEP 3
Apply the rule
With 5 posts, subtract 1 to get the number of gaps.
5 - 1 = 4
Subtracting one matches the four spaces we drew between the five posts.
2.MD.B.5Draw A DiagramAnswer
4 gaps
We can directly count the four spaces between the five posts in the picture, so 4 is correct and the unit (gaps, a count) matches the question.
Takeaway
Spaces are always one fewer than the posts — Grade 2 counting sense you can see in the picture!
- Picture the posts and spaces
- Spot the pattern: gaps are one fewer
- Apply the rule
Where next?
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