Extreme Makeovers: Math Edition
Standards Met: CCSS.Math.Content.7.G.A.1; 7.G.B.6
What You Need: Floor plans, flooring and paint samples, yardsticks, graph paper, pencils
What to Do: Classrooms, bedrooms, and pretty much any room can be broken down into a collection of shapes when looking at a floor plan. Even if a room isn’t perfectly rectangular, by drawing lines, it can be made to be so—this will create additional, non-rectangular shapes. To explore this, have students measure a room of their choice, such as a classroom or their bedroom, and create a scale floor plan using graph paper. They should determine what scale works best—possibly one graph square equaling a six-inch square—and convert their measurements using this scale.
Next, provide your class with various flooring and paint samples and ask them to calculate how much of their chosen flooring and paint color they would need to renovate their room. Students will need to find the area of the floor and walls to determine how much of each material they need to create the room of their dreams.
To expand on this activity, provide a budget and challenge your students to determine the largest room they could fully renovate without exceeding their given budget.
The Big Event
Standard Met: CCSS.Math.Content.6.SP.B.5
What You Need: Data on the costs of different events, paper, pencils
What to Do: The phrase “the average cost” is frequently used to discuss how much one might spend on a special event such as a birthday party or a wedding. But is the “average” the best way to show a typical price for a given type of event? Put this question to your students and ask them to decide!
First, provide them with the mean, median, and range of total costs for a certain type of celebration (e.g., a wedding) in a few different states or countries. (You can find this data online.) Then, assign each student a locale and ask him or her to figure out the cost based on the mean, median, or range for the particular area, with the goal of planning a representative event. When students have created their budgets, which should include food, venue, and decorations, give them a more detailed breakdown on typical costs for those items in your area, so they can see how their budgets compare with those for actual events close to home.
Working in groups, have kids compare their different budgets and discuss which value—the mean, median, or range—best represents the amount that most kids in the class spent on their event, while explaining how other measures could provide an inaccurate perspective. For example, if one student plans an extravagant holiday party, the median will be the most representative value and they’ll find that a so-called “average” cost will be due to the exception, not the rule!
Proportions in Pop
Standard Met: CCSS.Math.Content.7.RP.A.3
What You Need: Bottle of soda, bags of candy, drawing paper, pencils, markers
What to Do: After realizing that her eighth-grade students needed extra practice with proportions, Sarah Carter, now at Drumright High School in Oklahoma, decided to use sodas and snacks to get them engaged. She modified an activity built around a video, 3 Act Math, from former math teacher Dan Meyer’s website, which challenges students to use proportions to determine how many packets of sugar are in a bottle of soda. Although students initially focused on the 20-ounce size, they soon realized that the key to solving the problem was in setting up a proportion between how much sugar was in the soda bottle based on the nutrition label and how much sugar was in a single sugar packet. Carter then challenged students to find out how many packets of sugar were in a variety of types of soda and bags of candy.
After her students determined how many sugar packets were in each item, Carter asked them to present their findings in a data display. She had students work in groups to foster discussion as they determined what type of data display would best represent their information.
“For once, they didn’t complain about having to solve proportions,” says Carter, who blogs at Math = Love. “I enjoyed the process of helping students discover a method to solve a real-world problem.” And who knows? Your students may even discover an aversion to sugary sodas and candies after conducting this experiment!
Standard Met: CCSS.Math.Content.7.G.A.2
What You Need: Colored markers, pencils, drawing paper, construction paper, clay
What to Do: Whether or not there’s snow outside, building a snowman can provide a fun challenge—especially if you invite students to get creative!
Divide your students into teams, and assign each team a shape. In addition to the traditional circles and spheres, suggest that students use some less conventional snowman-building shapes, such as squares, cubes, triangles, pyramids, and trapezoids. Then ask each team to design a snowman using only its assigned shape. They can draw their model, craft it out of construction paper, or build it using clay. (Sculpting provides an added challenge, since the model needs to be architecturally sound.)
Once your students have designed their shape-specific creation, have each group determine how much snow by volume it would need to actually build its snowman. To do so, students will need to measure the volume of each shape in their model and then scale their figure up to life size. To further encourage out-of-the-box thinking, have them vote for the most unique snowman!
Image: Naphat Jorjee/iStock