Problem
Look at the counts under each shape: 1, 4, 7, 10. Each one is 3 more than the one before, because every new shape adds 3 counters (up, right, diagonal).
The same three counters appear at every step, so the count grows by a steady 3.
4.OA.C.5Look For A PatternThe counts under the shapes — 1, 4, 7, 10 — climb by the same 3 at every step.
Each new shape keeps all the counters of the shape before it and only adds fresh ones, so its count is the earlier count plus however many were added.
The new shape splits with no gaps and no overlaps into two parts — the old counters and the freshly placed ones — so those two parts add back to the new total.
The amount added is 3 at every step, because each step drops one counter up, one to the right, and one on the diagonal — the same three moves each time.
The three new counters placed at one step pair up one for one with the three placed at any other step, so every step adds a group of the very same size.
Add 3 to the 4th shape's 10 counters to get the 5th shape's count.
One more step means one more group of 3 counters added on.
4.OA.C.5Look For A PatternStart from the 4th shape (10 counters) and place one new counter up, one to the right, and one on the diagonal corner, extending the L into a larger right-angled cluster. Counting all the counters in the drawn shape gives 13.
Drawing it shows the growth literally: the starting 1 plus four rounds of 3 makes 13.
3.OA.D.9Draw A DiagramEach new shape just adds 3 more counters, so after 10 comes 13: count up by 3 and you have the fifth shape!