Solving Proportions Using Formal Strategies Lesson Plan Example for 7th Grade Students

Topic:Solving Proportions Using Formal Strategies

Objectives & Outcomes

Understand how to solve proportions using formal strategies.

Materials

Two sets of parallel rulers

Calculator

Worksheets with problems for practice and review

Warm-up

Review what proportion is and what it represents. A proportion is an equation that shows equivalent ratios between two quantities. It is a way of showing that two ratios are equal. For example, if a cake recipe calls for 1 cup of flour and 2 cups of flour, the proportion would be 1:2, which can also be written as 1:2 or 1/2. The equal sign means that the two ratios are equal.

Have students work in pairs to solve a few simple proportion problems. Have them use a calculator and parallel rulers to draw a line of equality through the solutions.

Direct Instruction

Introduce the formal strategies for solving proportions.

Solving by cross-multiplying: This is the most straightforward way of solving proportions. It involves multiplying both sides of the proportion by the same number, which will result in two fractions that are equal. For example, if a recipe calls for 1 cup of flour and 2 cups of flour, we can solve by cross-multiplying by multiplying both sides by 2, which gives us 2 x 1 = 2 x 2, or 2 = 2, which means that 2 cups of flour is equivalent to 1 cup of flour.

Solving by multiplying by 1: This is a slightly more difficult way of solving proportions, but it can be helpful to know in some cases. It involves multiplying both sides of the proportion by 1, which will result in a fraction that is equal to 1. For example, if a recipe calls for 1 cup of flour and 2 cups of flour, we can solve by multiplying both sides by 1/2, which gives us 1 x 1 = 1 x 2, or 1 = 1, which means that 1 cup of flour is equivalent to 1 cup of flour.

Solving by cross-multiplying and then dividing: This is a more advanced method of solving proportions, and it is only necessary in certain cases. It involves first solving the proportion by cross-multiplying, and then dividing by the conjugate of the numerator of the resulting fraction. For example, if a recipe calls for 1 cup of flour and 2 cups of flour, we can solve by cross-multiplying and then dividing by 2, which gives us 1 x 2 = 2 x 1, which is not a fraction, so we can then divide by the conjugate of the numerator, which is 2/1, which gives us 1 = 2/1, or 1/2, which means that 1 cup of flour is equivalent to 2/1 cups of flour.

Have students work in pairs to solve a few simple proportions using formal strategies. Have them use a calculator and parallel rulers to draw a line of equality through the solutions.

Guided Practice

Give students a few more complex proportions to solve using formal strategies.

Have them work in pairs to solve the problems, providing assistance as needed.

Have students present their solutions to the class, using the formal strategies they used.

Independent Practice

Give students a worksheet containing additional complex proportions to solve.

Have them work independently to solve the problems, using the formal strategies they learned.

Have students review their solutions with a partner, check their work, and submit the worksheet.

Closure

Review the key concepts of solving proportions using formal strategies.

Ask students to share one thing they learned about solving proportions during the lesson.

Assessment

Observe students during the independent practice activity to assess their understanding of solving proportions using formal strategies.

Collect and review the formal equations written by the students as part of the independent practice activity.

Give a quiz on solving proportions to assess students' understanding of the concept.

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