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Equivalent Fractions Using Area Models
Students will be able to create equivalent fractions by multiplying by different fraction forms of 1 whole and draft an accompanying area model.
- Ask your class what is 6 x 1 and 21 x 1? Continue until they realize that any number you give, multiplied by 1, results in the number itself.
- Tell your students that this concept has a name, the identity property, and in this lesson, we will use this concept as we generate equivalent fractions. Equivalent means of equal value.
Explicit Instruction/Teacher modeling(10 minutes)
- Explain to your class that the lesson's goal is to generate equivalent fractions by multiplying a fraction by 1, but 1 in fraction form, where 1 is expressed as a fraction.
- Point out that the identity property states a number remains the same, or equivalent, when multiplied by 1. Even though 1 may take different forms, when multiplied by a fraction the value remains the same.
- Show your students an area model display of 2⁄2 = 1 as a rectangle, split in half with both sides shaded. Note how the rectangle is in 2 parts: ½ shaded + ½ shaded = 1 whole shaded. Repeat demonstrations for 3⁄3 and 4⁄4.
- Write the fraction 2⁄3 x 1 on the board, then write 2⁄3 x 2⁄2 just below it. Have students turn and tell a neighbor what the two expressions have in common. Share reponses as a whole class, and note connections that 2⁄2 is equivalent to 1.
- Present the expression 2⁄3 x 2⁄2 to your class.
- In front of your students, draft an area model for the equation, by drawing a rectangle partitioned as ⅔ vertically shaded. Share with your students that by multiplying by two halves, you want two equal parts of a whole. Cut the ⅔ area model in half horizontally (because you want two equal parts of a whole) with a dotted line.
- The result shows 4 equal parts shaded out of 6. Hence, 2⁄3 x 2⁄2 = 4⁄6.
Guided Practice(10 minutes)
- Enlist your students to solve the equations of 2⁄3 x 3⁄3 and 2⁄3 x 4⁄4, along with drafted area models for each. Make sure your students record their work in their math journals or on their papers.
- Summarize with your class how you've shown the equivalent fractions for 2⁄3 as: 4⁄6, 6⁄9, and 8⁄12 (all by multiplying with different fraction forms of 1).
- Review the fraction forms of 1 used (i.e., 2⁄2, 3⁄3, and 4⁄4), noting that any fraction with the same numerator and denominator is equivalent to 1 whole.
Independent working time(15 minutes)
- Present the following fractions on the board: ¼, ⅓, ⅖, ⅗, 2⁄6.
- Assign your students to show 2 equivalent fractions for each by multiplying with different fraction forms of 1, and to demonstrate each with area models.
- Post a chart with steps to drafting equivalent fractions:
- Step one: Write 1 in an equivalent fraction form like 2/2, 3/3, or 4/4.
- Step two: Multiply the fraction you want an equivalent form of times a fractional form of 1.
- Step three: Draft an area model.
- Refer students to the poster with a study buddy (using their notes as well).
- See resources for multiplying fractions with fractions for students who need additonal practice.
- Challenge students to use equivalent fraction representations for 1 using digits larger than 6.
- Interactive whiteboards make for an engaging presentation for drafting area models with students.
- Write the following three fractions on the board: ½, 2⁄2, and 3⁄3. Ask your students to tell you which of them is a fractional equivalent to 1. Follow up with what an equivalent fraction would be for ⅜ , using the proper fractional equivalent to 1 (i.e., 2⁄2 x ⅜ would be 6⁄16 or ⅜ x 3⁄3 would be 9⁄24).
Review and closing(10 minutes)
- Have your class place their work on their desks and perform a "gallery walk." This is where students tour the class, view one another's work in silence, then return to their seats. Tell them they will be asked to share one thing they noticed or had questions about during the walk.
- Hold a discussion with your students about what they noticed, learned, liked, and had questions about. Make sure to note academic language and review the lesson's objective.