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Lesson Plan Template

  • Grade

  • Subject

  • Section

Fifth

Math

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  • Competency

Multiply mixed numbers

  • Aligned Standards

Number and Operations—Fractions

  • Strand

5.NF.B.4a

  • Vocabulary

  • Mixed number: A number that consists of a whole number and a fraction.
  • Improper fraction: A fraction where the numerator is greater than or equal to the denominator.
  • Numerator: The top number of a fraction, representing the number of parts being considered.
  • Denominator: The bottom number of a fraction, representing the total number of equal parts.

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Multiply Mixed Numbers by Fractions

Prerequisite Skill

Multiply Mixed by Whole Numbers

Materials and Preparation

  • Fraction strips or visual aids
  • TeachTastic Worksheet Pack for Multiplying Mixed Numbers by Fractions
  • Whiteboard and markers for demonstrations
  • Calculators (optional)

Learning Objectives

  • Students will convert mixed numbers into improper fractions.
  • Students will multiply a mixed number by a fraction.
  • Students will simplify the resulting fraction and convert it back into a mixed number if needed.

Introduction

Begin the lesson by reviewing what a mixed number and an improper fraction are. Explain that when multiplying mixed numbers by fractions, it is often easier to first convert the mixed number to an improper fraction. Provide a simple example on the board, such as multiplying 2122 \frac{1}{2} by 34\frac{3}{4}, and walk through the steps of the process.

Explicit Instruction/Teacher modeling

  • Convert the Mixed Number: Demonstrate how to convert a mixed number into an improper fraction. For example, to convert 4 1/4 into an improper fraction, multiply the whole number (4) by the denominator (4) and then add the numerator (1), resulting in 17/4.

  • Multiply the Fractions: Once the mixed number is converted, multiply the numerators together and the denominators together. For example, 17/4×1/2 gives 17×1/4×2=17/8.

  • Simplify the Fraction: If necessary, simplify the resulting fraction or convert it back to a mixed number. In this example, 17/8 simplifies to 2 1/8.

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Guided Practice

Use the TeachTastic Worksheet Pack to work through several examples with the class. Guide the students step-by-step, ensuring they understand how to convert mixed numbers to improper fractions, multiply, and simplify. Encourage them to use visual aids like fraction strips if they need a concrete understanding of the process.

Independent Practice

Students will complete the remaining problems in the TeachTastic Worksheet Pack independently. These problems should include a variety of mixed numbers and fractions to give students ample practice with the concept. Encourage students to check their work by converting their answers back into mixed numbers where applicable.

Differentiation

Support

  • Provide additional practice problems with step-by-step solutions for students who need extra help.
  • Use visual aids like fraction strips or pie charts to help students better understand the concept of multiplying fractions.
  • Pair students who are struggling with a peer tutor for additional practice and support.

Extension

  • Challenge advanced students to solve word problems involving the multiplication of mixed numbers and fractions in real-world contexts, such as recipes or measurements.
  • Introduce problems that involve multiplying more than two fractions to extend the concept.
  • Have students explore how multiplying by fractions greater than 1 vs. less than 1 affects the product.

Assessment

Use the assessment section of the TeachTastic Worksheet Pack to formally evaluate students' ability to multiply mixed numbers by fractions. This could include a mix of computation problems and word problems.

Review and closing

Review the steps for multiplying a mixed number by a fraction, focusing on common errors such as incorrectly converting the mixed number or forgetting to simplify. Summarize the key points and invite students to ask any remaining questions.

Misconceptions

  • Misconception: Students might forget to convert the mixed number to an improper fraction before multiplying. Correction: Emphasize the importance of converting the mixed number first as the initial step.

  • Misconception: Students may not simplify the final answer or incorrectly simplify. Correction: Reinforce the steps of simplifying fractions and converting back to a mixed number if needed.

  • Misconception: Students might confuse the process of adding fractions with multiplying fractions. Correction: Clearly differentiate between addition and multiplication of fractions, and emphasize that multiplying involves the numerators and denominators directly.

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