A medium question on counting shapes for P3–P4, with a step-by-step solution, diagrams and the answer. Every year of the Hua Xia Cup, P1 to P6, has shape-counting questions. The hard part is counting each shape once and missing none.
The question
A sheet of squared paper has 2 rows of 3 squares, and one square has a dot in it, as shown.
How many rectangles in the picture contain the dot? (Squares count as rectangles.)
Show the hints (2)
💡Hint 1: Every rectangle is made by two upright lines and two across lines. To hold the dot, which upright lines could be its left side?
💡Hint 2: There are 2 upright lines to the left of the dot (the edge included) for the left side, and 2 to its right. Count the top and bottom the same way.
Worked solution
Have a go first, then read the solution step by step.
1.The rectangle's left side: 2 upright lines to the dot's left; its right side: 2 to its right.
2.Top: 2 across lines above the dot; bottom: 1 below it.
3.One line for each side makes a rectangle holding the dot (the green one is one of them). Each side is chosen on its own: 2 × 2 × 2 × 1 = 8.
⚠️Common mistake: counting only rectangles in the dot's own row or column. A rectangle can stretch up, down, left and right at once.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download