Page 197 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

• cylinder and cone with the same height and base area:
Instructional Tips
Teachers can:
• create tasks that enable students to make sense of the relationships between prisms and pyramids, and between cylinders and cones, through manipulating solids and pouring materials;
• support students in generalizing the relationships by having them experiment with a variety of base shapes, including regular bases, irregular bases, and objects with different-shaped bases, such as a heart-shaped box;
• support students in identifying the precision to which measurements are needed based on the context of the problem;
• use appropriate representations and materials to reinforce students’ understanding that the relationship stays the same whether it is capacity (mL) or volume (cm3) that is being measured.
Note
The volume of a pyramid is one third the volume of a prism with the same base and height. The same relationship holds for cones and cylinders.
Teacher Prompts
• If you know the volume of a prism, how can you determine the volume of a pyramid with the same height and base as the prism?
• If you know the volume of a cone, how can you determine the volume of a cylinder with the same height and base as the cone?
Sample Tasks
1. Provide students with several different sizes of prism and pyramid containers with the same height and base. Also provide cylinder and cone containers with the same height and radius. Provide students with a filling substance such as water or sand, and ask them to determine how many
196