Lesson plan
|Math Lesson: Model Multiplication and Division of Fractions |Grade Level: 6 |
|Lesson Summary: Students will understand how to multiply and divide fractions. Advanced students will be able to determine what operation to use in solving word |
|problems, and struggling students will focus on basic fractions to model and solve problems. |
|Lesson Objectives: |
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|The students will know that… |
|multiplication and division situations involving fractions and decimals can be represented with models and visual representations. |
|a quotient may be larger than the dividend when the divisor is a fraction. |
|solutions to fraction and decimal computations can be justified. |
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|The students will be able to… |
|represent multiplication and division situations involving fractions and decimals with models and visual representations. |
|recognize that a quotient may be larger than the dividend when the divisor is a fraction. |
|perform fraction and decimal computations and justify their solutions. |
|Learning Styles Targeted: |
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|Visual |
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|Auditory |
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|Kinesthetic/Tactile |
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|Pre-Assessment: |
|Use this quick assessment to see if students can simplify fractions and to convert decimals to fractions. |
|Write each fraction in simplest form. |
|1. [pic] ([pic]) 2. [pic] ([pic]) 3. [pic] ([pic]) 4. [pic] ([pic]) |
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|Write each decimal as a fraction in simplest form. |
|5. 0.8 ([pic]) 6. 0.24 ([pic]) 7. 0.17 ([pic]) 8. 0.55 ([pic]) |
|Note students who do not get the correct answers. |
|Whole-Class Instruction |
|Materials Needed: Grid paper, colored pencils or markers, 1 copy of the Worksheet* per student, writing utensils |
|Procedure: |
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|Discuss the pre-assessment with the class, making sure that students understand how to simplify a fraction and how to convert a decimal to a fraction in simplest |
|form. |
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|Use a rectangular model to multiply fractions. Explain that the area of a rectangle is the same regardless of how you cut up the parts. For example, to solve [pic]|
|follow these steps: Draw a rectangle and use horizontal lines to divide it into 4 equal rows. Shade 3 rows. This represents the fraction [pic]. Next use vertical |
|lines to divide the rectangle into 5 equal columns. Shade 2 columns in another color. This represents the fraction [pic]. Now count the number of sections that are|
|shaded with both colors. There are 6 sections. Count the total number of sections that the rectangle has been divided into. There are 20 sections. The |
|fraction[pic]is the solution to [pic]. Be sure to write the fraction in simplest form. [pic][pic] |
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|To divide fractions, like [pic], follow these steps: Draw a rectangle and use a vertical line to divide it into 2 equal columns. Shade 1 column. This represents |
|the fraction[pic]. [pic] |
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|Next divide the rectangle into 8 equal columns. In the shaded section there are 4 eighths. [pic][pic]. |
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|Also provide examples for students of problems that are decimals so that students reinforce the skill of converting decimals to fractions. |
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|Guided Practice: |
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|Divide the students into groups. Have the students solve the following problems using the rectangular area models. |
|a) [pic] ([pic]) b) [pic] ([pic]) c) [pic] ([pic]) d) [pic] ([pic]) |
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|Independent Practice: |
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|Have students work on their own to complete the Worksheet. |
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|Closing Activity: |
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|Have students create their own multiplication and division problems. Then have them work in pairs to take turns solving their partner’s problem. |
|Advanced Learner |
|Materials Needed: Grid paper, colored pencils or markers |
|Procedure: |
|Teacher Guided: |
|Ask students to determine what operation should be used to solve the following problem and then have them solve the problem: Kasey has[pic] pizza left over from |
|dinner. If she has [pic]of the entire pizza for lunch, how much of the original pizza will remain? (multiplication, [pic]) |
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|Have students solve the following problem. Be sure to have them write out the problem and explain how they got their solution. |
|Suppose a recipe calls for[pic]teaspoon of salt. If you want to cut the recipe in half, how much salt do you need? (division,[pic]) |
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|Discuss with your students how a quotient may be larger than the dividend when the divisor is a fraction. |
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|Have students work in pairs to write and solve multiplication and division word problems involving fractions. |
|Struggling Learner |
|Materials Needed: Grid paper, colored pencils or markers |
|Procedure: |
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|Ask students to make and use a rectangular model to represent the following basic fractions: [pic]. Have them compare the models to see how the fractions are |
|related. |
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|Have students use these models to help solve the following problems. |
|a) [pic] ([pic]) b) [pic] ([pic]) c) [pic] ([pic]) d) [pic] ([pic]) |
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|Be sure that students understand that [pic] means “In [pic], how many eighths are there?” |
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|Have students work in pairs to write and solve multiplication and division problems involving fractions. |
*see supplemental resources
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