Problem
Gaps are one fewer than the objects
5 wooden posts stand in a straight line, evenly spaced. Find the total number of gaps between the posts.
Measurement & data
Your answer
Watch out Don't just carry the post count 5 over as the gap count — there's no gap beyond the first or the last post.
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 the spaces
Draw the 5 posts in a row — empty spaces only appear between neighboring posts.
1-2, 2-3, 3-4, 4-5
Sketching the posts makes it clear the outer ends have nothing beyond them, so no gap forms there.
Draw A Diagram2.MD.B.5Measuring Length2STEP 2
Spot the pattern: gaps are one fewer
2 posts→1 gap, 3→2, 4→3. The gap count is always one fewer than the post count.
2→1, 3→2, 4→3
Every gap can be paired with the single post standing just to its left. Only the last post on the right is never paired, since nothing follows it — so the gap count is exactly one less than the post count.
Look For A Pattern2.MD.B.5Gaps One Fewer Than ObjectsThe 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, 5 − 1 = 4 gaps.
5 − 1 = 4
Plugging 5 posts into the rule 'gaps = posts − 1' gives the same four spaces we counted in the picture.
Draw A Diagram2.MD.B.5Measuring LengthAnswer
4 gaps
5 − 1 = 4
Check — counting each neighbor pair (1-2, 2-3, 3-4, 4-5) directly gives exactly 4 gaps.
Takeaway
A gap only ever sits between two neighboring posts, so the gap count is always one fewer than the post count — giving 4 gaps.
- Drawing the 5 posts in a row shows spaces only between neighbors
- Small cases (2, 3, 4 posts) confirm gaps = posts − 1
- 5 − 1 = 4 gaps
Where next?
Another one like thissuggested
Same look, different logicsuggested
Step back and solidifysuggested