Building Squares and Cubes

Overview: Students time themselves building squares and cubes. Then predict the effect on time needed to build the squares and cubes if the side length is increased.

Curriculum Expectations

• Number sense and algebra: Solve problems involving proportional reasoning
• Measurement and geometry: Solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures

Learning Goal:

• If the side length of a square doubles the area is four times larger.
• If the side length of a cube doubles the volume is eight times larger.
• The time it takes to build a square or cube will be proportional to its area or volume
  

Timing and sequencing: This activity will take one period. This acts as a good review of area and volume from lower grades. Students may need to be refreshed on proportional thinking, but it could also come out of this activity.

Classroom constructs: Students work in groups of three.

Materials:

• Each group needs 64 linking cubes.
• Each group needs a phone or stopwatch for timing

Description:

Question to pose to students: If it takes you _____s to build a square with a side length of 4 units, how long will it take you to build a square with a side length of 8? What about a side length of 6?

• Do several trials building the square with a side length of 4 until a consistent approach is obtained.
• Students make a prediction for time required to build a square with 6 and 8 units and explain their reasoning.
• Check their results.
• Share class data on the board and look for trends. Students should explain what they notice and why their predictions were correct on incorrect.

Question to pose to students: If it takes me _____s to build a cube with a side length of 2 units, how long will it take me to build a cube with a side length of 4? What about a side length of 3?

• Repeat the process that was done with squares with building cubes.

Resources:

http://threeacts.mrmeyer.com/bubblewrap/

Teacher notes:

• The method needs to be consistent so it is important to practice the “building” method before attempting bigger squares or cubes. If the building method changed, go back and repeat the smaller squares or cubes with the same method.
• I liked this activity because students had to think about how many linking cubes were needed to build the various shapes. This brought in some spatial thinking.
• When the side length of the square was doubled from 4 to 8, it was very easy to show how 4 of the smaller squares fit into the larger one, as the students will have the visual representation in front of them.