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Counting Squares

Alignments to Content Standards: 1.G.A.2


How many squares are in this picture?


IM Commentary

This task is intended to be a simpler form of 1.G.A.2 Overlapping Rectangles. The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares, and stimulate interest as students compete to try to find the most squares. Furthermore, older students may also benefit from such an exercise as well, which could be aligned with 2.G.1.

This task includes an experimental GeoGebra worksheet, with the intent that instructors might use it to more interactively demonstrate the relevant content material. The file should be considered a draft version, and feedback on it in the comment section is highly encouraged, both in terms of suggestions for improvement and for ideas on using it effectively. The file can be run via the free online application GeoGebra, or run locally if GeoGebra has been installed.

Attached Resources

  • Geogebra File
  • Solution

    In addition to the nine small squares, there are four $2 \times 2$ squares (shown below), and one $3 \times 3$ square, for a total of 14 squares.


    Julie Boss says:

    over 5 years

    A great extension for this is to find all of the rectangles in addition to the squares.

    Kristin says:

    over 5 years

    Nice suggestion.

    HTChance says:

    almost 6 years

    I think this exercise is very age appropriate. It facilitates analytical thinking to identify the number of squares presented in the diagram by the student. A prerequisite activity for first graders would be to construct figures with cubes and consider the number of squares they can create.