Proportions

Curriculum Goal

Measure, using non-standard units of the same size, and compare objects, materials, and spaces in terms of their length, mass, capacity, area, and temperature, and explore ways of measuring the passage of time, through inquiry and play-based learning (#16).

Set out two shapes: a rectangle and a longer rectangle (Appendix A). Ask students what they notice about these two shapes.
Allow students to share their observations about the two rectangles. Common observations include one is bigger than the other, they are both rectangles, etc.
Ask students how to fill up space on the longer rectangle using the shorter rectangle.
Have students prove their theories.
Bring out another shape – a small square (Appendix B). Ask students what they notice about that shape when compared to the two other shapes.
Have students share their ideas and prove them using the materials provided.
Ask students how many squares it will take to fill up the small rectangle and then the larger rectangle.
Show students a bigger square (Appendix C). Repeat the process above by asking students what they notice about the shapes. Have them prove their ideas.
Show students a bigger rectangle (Appendix D). Repeat the process above by asking students what they notice about the shapes. Have them prove their ideas.
By this point students will be able to fill the bigger rectangle with many different combinations.

What observations do children make about the different shapes and how the smaller shapes can be used to fill up larger shapes?
How do children show how smaller shapes fill up a larger shape?

Students can be challenged with more shapes of various sizes added into the activity.

Supports concepts of area and size in a “real-life” scenario.