 # Math Lesson Plans for Middle School Students

A large part of middle school math involves ratios and proportional relationships. Below, you will find sample lesson plans for sixth and eighth grade with hands-on activities and real-world applications. ## Middle School Lesson Plans in Math

### Sixth Grade Lesson

In sixth grade, one goal is for students to comprehend what a ratio is and to use the term to describe the relationship between two numbers. This lesson plan will explore the relationship between a rectangle's length and width.

1. They will use a variety of units of measure to measure a rectangle.
2. They will post their measurements on a coordinate plane, making a graph.
3. They will analyze the graph, make predictions based on it and make deductions about the ratios.

Each student will be given a paper with a rectangle drawn on it. Students will measure the length (longer side) and width (shorter side) of the rectangle in at least five different ways. Measurement options could include:

1. Inches
2. Centimeters
3. Paper clips
4. Nails

You may use your imagination to give students more varieties, such as pennies or finger widths. Each student should receive enough materials to measure the length of the rectangle. They may have to estimate decimals if the 'rulers' don't give exact amounts - for example, if a little less than half of a paper clip extends beyond the edge of the rectangle, they may estimate the length as '5.4 paper clips.'

Have the students keep a record of their measurements. Students will then plot the various measurements on a graph, with the length on the x-axis and the width on the y-axis. Beside each point they place on the graph, they will write what the unit of measurement was. Then, have the students:

1. Estimate where the line would go if all measurements were exact. Next, they will draw the line with a ruler.
2. Recognize the ratio between length and width.
3. Find ways to express the ratio. For example, the length is always 1.25 times the width, which can be written as an equation: L = 1.25W.

Ultimately, students should understand that the ratio is always the same (e.g., 1:1.25) no matter what the unit of measurement is. Then, the students can apply this knowledge by figuring out how many feet wide the rectangle would be if it were 15 feet long.

### Eighth Grade Lesson

In this lesson, students will:

1. Solve linear equations that have one variable.
2. Graph proportional relationships.

Begin the lesson with a word problem: Billy got a cell phone for his birthday. For one year, his parents will pay \$20 each month for a pre-paid program. Ask your students to analyze which of the following two program options Billy should choose.

Program I costs 10¢ a minute for calls and 5¢ for each text message.
Program II costs 5¢ a minute for calls and 15¢ for each text message.

Discuss with the students what they would need to know to discover which program is best for Billy. Answers should include:

1. Whether the students think Billy would be more likely to make calls or send text messages.
2. How many calls each program option would allow Billy to make each month if he only made calls.
Program I: \$20 x \$.10 = 200 calls
Program II: \$20 x \$.05 = 400 calls
3. How many monthly text messages each program option would allow Billy if he only sent text messages.
Program I: \$20 x \$.05 = 400 texts
Program II: \$20 x \$.15 = 133 texts

Have students figure how many texts could be sent given various situations. For example, if Billy talked on the cell phone for one hour, how many texts would he still be able to send that month?

• Program I: One hour (60 minutes) at 10¢ per minute costs \$6.00 (60 x \$0.10 = \$6.00), leaving \$14.00 for texts. \$14 ÷ \$0.05 = 280 texts
• Program II: One hour (60 minutes) at 5¢ per minute costs \$3.00 (60 x \$0.05 = \$3.00), leaving \$17.00 for texts. \$17 ÷ \$0.15 = 113 texts

Using x to represent the number of voice minutes and y to represent the number of text messages, ask the students to make an equation for each program that would depict the number of voice minutes and the number of text messages available to Billy for \$20 per month.

• Program I: 20 = 0.10x + 0.05y
• Program II: 20 = 0.05x + 0.15y

Using these two equations, the students can make a graph. The x-axis would be labeled Voice Minutes, and the y-axis would be Text Messages. Students would use the totals found above. Explain to the students that the place on the graph where the two lines intersect shows at which point the two programs would allow the same number of voice minutes and text messages.

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