Curriculum – Geometry and Spatial Sense and Measurement
For students to describe, sort, classify, and compare two-dimensional shapes, and describe the location and movement of objects through investigation.
For students to measure and compare length, mass, capacity, area, temperature of objects/materials, and the passage of time, using non- standard units, through free exploration, focused exploration, and guided activity.
Students and the teacher begin by sitting on the floor in a circle.
- Magnetic square tiles (at least 9 single colour tiles per student)
- Download: Pre-cut shapes posted on cookie sheets
- Introduce the lesson with a narrative about a sister and brother whom have been asked by their parents to make their own garden patio.
- Hold up the cookie sheet with two shapes side-by-side and explain that the design on the left (the square) was created by the sister and that the design on the right (irregular shape) was created by the brother.
- Explain that the parents had a disagreement over whether the two garden patios took up the same amount of space.
- Ask children to look closely at the two shapes and try to determine whether or not the garden patios do in fact take up the same amount of space.
- After hearing several children’s suggestions/conjectures, prompt children to further imagine whether there is something that can be done to one shape to make it look just like the other.
- You might want to point to the shape on the right and ask, “Is there something you can do to this shape to make it look the exact same as this shape (pointing to the shape on the left).”
- Continue the narrative by explaining that it might be helpful if there was a way to figure out the number of tiles needed to build the garden patio on the left (the square patio built by the sister).
- Provide each student with a single square tile, in addition to his or her own cookie sheet with the pre-attached shapes placed side-by-side.
- Ask children if there is any way of using the tile to predict the number of tiles needed to fill the entire space. Invite students to share their predictions as a whole group.
- Alternatively, if you do not wish for students to influence one another with their predictions, have students whisper their predictions to a neighbour.
- Provide students with an additional 2 tiles (each child should have 3 total) and have students to now use all 3 tiles to make their predictions of how many tiles are needed to create the garden patio.
- Let students know that it is okay to change their initial predictions. As a class, have children share and discuss their predictions. Ask children to show you and others how they reasoned over the number of tiles required
- Look for different strategies, including iteration, unitization (do they make a unit of units), seeing structures of rows and columns, different placement of 3 tiles, etc.).
- Facilitate discussion to eventually focus on the fact that the area of the square is 9 square units.
- Next, provide each student with 9 square tiles and ask children to reaffirm the area of 9 square units. (This is done to consolidate the 9 and to give kids opportunity to see the array in full).
- Next, ask students to look at the second patio shape.
- Have students predict the number of tiles it will take to cover the shape.
- Some students may recall that the two shapes can be made to look the same through decomposition/ composition and use this information to reason that the irregular shape will also require 9 square tiles to fill.
- After listening to and discussing various students’ predictions, provide children with 9 tiles and have them cover (tile) the irregular shape.
- Facilitate another discussion about how and why the two different shapes contain the same area and thus can be covered with 9 square tiles.
- Ask students to use their 9 tiles to create their own shape/patio design.
- Explain to students that they are welcome to design any shape they wish so long as tiles are adjoined along their entire edge/side (e.g., tiles cannot be connected at corners or along only a portion of the edge).
- Model for students an example of a design that conforms to the “all edges must be touching” rule and one that does not.
- Once students are finished creating their own patio designs, invite students to share with their classmates.
- To end, have students turn over their trays and reconstruct the original 3 x 3 square.