RatioLesson

EXPLORING RATIO OF AREA and VOLUME of SIMILAR FIGURES

LESSON PLAN:

Class : 8^th grade Geometry (2 years advanced)

Time period: 45 minutes

Objectives:

Students will use Geomoeter's Sketchpad to explore geometry.

Students will determine ratios of areas of similar figures

Students will determine ratio of volumes of similar figures

Prior Knowledge:

Students should have an understanding of, and be familiar with the definition of similar figures.

Students should be familiar with the basic functions of Geomoeter's Sketchpad..

Procedures:

Review what it means to have figures that are similar.

Have students make conjectures about what they think the ratio of areas of similar figures would be.

Have students group up at computer stations and work on Sketchpad Activity "Investigation: Proportions with Area".

Have students discuss findings and argue in favor of their conjectures.

Have students make a hypothesis about what they think the ratio of volumes will be.

As a whole class complete the chart below:

**Figures A and B are similar figures.**

2 Similar figures	Ratios of sides	Ratio of Area	Ratio of Volume
FIGURE 1: (Two similar 2-D squares (A and B) or Two similar 3-D cubes (A and B) depending on if you are dealing with area or volume)	Side of square A Side of square B	area of square A area of square B	volume of cube A volume of cube B
FIGURE 2: (Figure A and figure B are similar spheres)	radius of sphere A radius of sphere B	area of sphere A area of sphere B	volume of sphere A volume of sphere B
FIGURE 3: (Figure A and B are similar cylinders)	radius of cylinder A radius of cylinder B	area of cylinder A area of cylinder B	volume of cylinder A volume of cylinder B

Students will question if this will work for any pair of similar figures. Encourage them to try some similar figures on their own and report their findings.

Some Questions to Ask:

What is the relationship between ratio of sides of cubes and ratio of their volumes?

If you know area of two similar prisms, how would you find ratio of volumes?

Are all cubes similar?

Are all spheres similar?

Are all cylinders similar?