Hands on Math Activities on Proportions

Proportions are used every day by engineers and designers.

Proportions are a real world math concept that people use all the time. Think about how many times people say, "It must have been three times the original size," or phrases like it. Hands-on activities involving proportions should draw upon real world applications and help students understand the complexity of building or city planning. The activities should also help students understand the size of objects that are perhaps too big to see altogether, whether it's a building or a city.

Playground Proportions

Proportions can be found all around the school. Applying proportions to the real world is a successful way an educator can make proportions a hands-on activity. Students studying proportions can be assigned to find different geometric shapes of different sizes in the playground. The students can measure the geometric shapes and find out the proportions the different-size shapes have among one another. The area and perimeter can be calculated and proportioned out as well. To make the assignment even more interactive, make it a contest, and divide the students into groups.

State vs. State

Each state has a calculated amount of square feet that can be found online or in an encyclopedia. In order for students to understand proportions, the students can learn the size of each state compared to the country as a whole or compared to other states. The activity is hands-on but simple. The students pick a state or several states and research the size of the state in square feet. Then look up the country as a whole. The students can them calculate several proportions based on the size of states. For example, they can answer, 'What is the proportion of Texas to the United States versus North Carolina to the United States?" Students will be amazed by the different sizes of the states and better understand the size of the country as a whole.

How Tall?

Divide the students into groups of three and have one student in the group stand against a wall. Have another student stand a couple feet away, holding up a pencil, aligning the pencil's height with the first student's. The third student in the group will measure the following three items: the distance to the top of the pencil from the floor, the distance of the pencil from the student who is holding it to his eyes, and the distance between the second student's eye and the first student. The students will then use these measurements in two ratios to find, through proportions, the height of the first student. The ratios are: height of pencil is to height of student 1 as distance between eye and pencil is to distance between eye and student 1.

Proportion World

Have the students draw the map of their house or school. However, everything in the drawing has to be completely proportional to the size of the building. If the activity is in the classroom, help students measure the room they chose to draw. If the assignment is for homework, instruct students to seek help from their parents. The students must keep a consistent key and on a separate paper write the exact measurements of the house and drawing, as well as the ratio the two have toward each other.

References

• The Futures Channel: How Tall?

Resources

• Hands on Math: Song Lyrics and Proportions