# Giving meaning to volume and surface area

This lesson is designed to help students give meaning to volume and surface area by solving problems using a meaningful situation rather than formulas.

**A lesson plan for grades 7–8 Mathematics**

## Learning outcomes

Students will be able to determine the volume and surface area of rectangular prisms.

## Teacher planning

### Time required for lesson

2 days

### Materials/resources

- Transparencies of the 3 activity sheets
- Copies of the 2 activity sheets found in Vol & S A.pdf
- Unlined paper
- Cubes would be useful, e.g., cm cubes (students could use enough cubes to help their thinking, but not enough to solve the problem - no more than 30 cubes per pair)

### Technology resources

Overhead projector

## Activities

- Begin the lesson using the two figures in the Quick Draw file (10 min). “I will show you a figure for two seconds. Draw what you saw.” Show the figure a second time after they have made their attempt. Then uncover the figure and ask students to describe what they saw. There are no “wrong” answers. Show enthusiasm for all responses.
- “If we had a box that was 3 cm wide, 4 cm long and 5 cm high, how many one cm cubes would fit in the box?” Ask student to explain how they decided on their answer. After several explanations, organize the class into pairs, putting students of a similar mathematical level together. Distribute the first page of the Vol&SA activity sheet and ask the pairs to solve the problems and be prepared to explain their solutions to the class.
- While students are solving the problems, move around the room listening to the discussions but avoid answering questions directly. Do not tell students whether they are right or wrong and don’t give hints. This is an important learning time for you.
- When a pair has finished the first activity sheet, give them page two. Some pairs may not get to page two.
- Allow 15-20 minutes for discussion. Have the class come together and call on pairs to explain how they solved the problems. Feel free to ask clarifying questions but do not judge or tell students they are right or wrong. You may not have time for all problems to be discussed. The lesson could be spread over two days. There are many ideas to be discussed.

## Assessment

Give them the dimensions of a rectangular prism and have them find its volume and surface area.

## Supplemental information

Attachments:

### Comments

This lesson utilizes an instructional strategy called Problem Centered Learning. The teacher does not explain but students develop their own solution methods.

- Common Core State Standards
- Mathematics (2010)
#### Grade 7

- Geometry
- 7.G.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

- Geometry

## North Carolina curriculum alignment

### Mathematics (2004)

#### Grade 8

**Goal 2**: Measurement - The learner will understand and use measurement concepts.**Objective 2.01**: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

**Goal 3**: Geometry - The learner will understand and use properties and relationships in geometry.**Objective 3.01**: Represent problem situations with geometric models.**Objective 3.02**: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.