Curriculum – Geometry and Spatial Sense
For students to describe, sort, classify, and compare two-dimensional shapes and three-dimensional figures, and describe the location and movement of objects through investigation.
Students and the teacher begin by sitting on the floor in a circle. After the teacher has explained the game, students will go off in pairs.
- Whiteboard with a line of symmetry and markers
8.5 x 11 paper with different shapes on each paper, folded (Appendix A)
- Magnetic board (cookie sheets work well) with a line of symmetry
- Magnetic shapes
For appendix, download the lesson plan here.
- Show students a half of a heart drawn on a sheet of paper. Ask students what they think would happen if you cut that shape out and opened it up.
- After gathering some ideas, cut the shape out and show them the result.
- Repeat these two steps with different shapes.
- Turn their attention to the whiteboard with the line of symmetry on it. Draw attention to the line of symmetry.
- Proceed by explaining that they are going to be playing a game where one person puts a shape down and the other person needs to put the same shape down in a way that follows the rules of the symmetry game.
- Demonstrate this on the whiteboard.
- After students have showed they understand how to play, explain that they will be getting their own board, and playing this game with a partner.
- Have students play this game with their partner.
- Gather the students in a circle again. Have them look at other designs made playing the symmetry game.
- Take a picture of the design and see how it can be recreated using other pattern blocks (composing and decomposing 2D shapes)
- Measure the area and describe your area in terms of triangles
- Cut a piece of grid chart paper to fit on the cookie sheet. Design a symmetrical creation over top of the paper. Look at the negative space and try to figure out its area. Create questions involving negative space: How many triangles could you fit in the negative space?
- Use your design to talk about slides and flips. Which shapes don’t have to be flipped to get the symmetrical image?
- Exploring fractions by comparing shapes: What fraction of the hexagon is a trapezoid? Triangle? Rhombus?
- Memory test: Look at another person’s design and try to reconstruct it
- Puzzles: Create a base shape, trace the shape and give it to other students. Tell them how many pieces are required to fit the puzzle or give a list of the actual shapes used and ask students to fill in the shape.
- Assigning a value to each 2D shape. For example, if the triangle is worth $1, what would the hexagon be worth? ($6). How much does your entire design add up to?
- Stack the pieces in shape groups to create a 3D graph of how many of each type were used in the image.
- Pattern identification: Are there repeating patterns?
- Language Arts connection: Invite students to create personalities and names for the images/designs they’ve created and to make a story
- Identifying larger shapes out of smaller shapes (e.g., a larger triangle made with four triangles; a trapezoid made with three triangles)
- measure the perimeter of this new shape
- See who has the biggest perimeter. How would need to move your pieces if you wanted to make your perimeter smaller or bigger without changing the number of pieces?
*These extension ideas were generated by OISE’s second-year Master of Teaching Students in Susan London McNab’s mathematics course. Thanks to you all!
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