Perimeter, Area, Volume, and All That: A Study of Measurement

Teaching Activities

Here are some examples of hands-on activities that can be used to instruct these concepts:

• Have students create rectangles and squares on dot paper, geoboard, tiles or graph paper and have them determine the perimeter and the area of each one.
• The instructor draws irregular shapes to have students find the perimeter and area.
• Students write the definitions of perimeter and area in their own words.
• Students investigate hexominoes to find perimeter and area.

In using the hexomino investigation, give each student a set of 6 individual tiles and have students look at the common attributes of the models. In the activity, students will create polygons according to the instructions of using all six tiles to make different polygons. Students then find the area and perimeter of each of the polygons they created. I like to have students explain what they noticed about the areas and perimeters of the polygons.

Allow students to start out by working independently writing down their process. Ask questions such as:

1. How many different figures did you make?
2. Which model has the greatest perimeter measurement?
3. Which model has the least perimeter measurement?
4. What are some strategies that were used to arrive at this solution?

This activity allows students at every level to experience success. When the students come together after working independently, group students for a discussion to share strategies and solutions. This will allow students to learn from each other as well as developing an in-depth understanding of the learning outcome.

To make a connection to area or as an extension with this activity, students will be placed in small cooperative learning groups to come up with answers to the following questions:

1. What is the area of the figure? 
2. Construct as many different rectangles as you can with an area of 24. 5. Do they all have the same perimeter?
3. Construct as many different rectangles as you can with a perimeter of 16.
4. Do they all have the same area?

Activity: To develop a strong foundational understanding of geometric concepts, which will involve activities in creating concrete models, discussions, hands-on activities, and practice.  Using nets to find surface area of three dimensional shapes and have students trace each side of the solid to determine its net (a two-dimensional figure that when folded forms the surface of a three-dimensional object) Students could then construct the object from the net. Another strategy is to have students draw a net and have them fold their net to investigate if it makes a three dimensional shape.

Activity: Next students will investigate Three-dimensional concepts

In teaching geometric solids to middle school students, my students will benefit from using hands on activities for learning surface area and volume. I will start by showing students a container, such as a cereal box. I will ask these questions prior to starting the hands on activity:

1. What is the math term for this object? (show the cereal box)
2. How many faces does it have? Vertices? Edges?
3. What shapes make up the faces?
4. Turn to your partner and explain the difference between surface area and volume of the container?
5. How would we measure the surface area of the container?

Next, ask students to imagine the net of the container, or the two-dimensional flat piece, that when folded will result in the three-dimensional container you are holding. When I use a cereal box, I point out that it is actually made by being folded up from a net (with a couple of extra flaps). After demonstrating and discussing the possible net of the container, have students use graph paper to sketch other possible net for the container. While they are completing this task cut the cereal box to reveal a net. Make sure to cut off any excess pieces that don’t belong to the net of the container. Next, have students discuss in their small groups how the net can be used to find the surface area of the container. I will listen to their conversations to make sure part of the discussion is about surface area as the sum of the area of all the faces on the net. I will use think-pair-share strategy at this point to have students share their ideas. After this guided instruction, in the next activity, I will pair the students and have them choose a container to answer the questions and allow them to investigate, as I monitor and give them support if needed.

First have each pair of students choose a container then have them complete the questions on the sheet which are:

1. What do you know about surface area?
2. Measure the dimensions of the object using mathematical tools.
3. Draw a mathematical net for the container and determine each area of the faces.
4. Explain the process you used to find the surface area of the container.

Authentic tasks such as this offer realistic problem solving that target students’ preferences and interests. More importantly the task allows students to work collaboratively and assess one another’s’ understanding.