1. Model and Represent Equivalent Fractions
Unit of Study: 7
Global Concept Guide: 4 of 4

2. Content Development
Models should be used to help students identify equivalent fractions. Sentence strips or stripes of paper cut into congruent rectangles can be used to model the idea of equivalency. Number lines should be HEAVILY emphasized as it is an efficient strategy for finding equivalent fractions. Do NOT rely on tips and tricks for teaching equivalent fractions. Students should make comparisons in real world situations.

3. Content Development
“…procedural responses are efficient but do not indicate conceptual understanding. All students should eventually be able to write an equivalent fraction for a given fraction. At the same time, the procedures should never be taught or used until the student understands what the result means…In a problem-based classroom, students can develop an understanding of equivalent fractions and also develop from that understanding a conceptually based algorithm. As with most algorithms, it is a serious instructional error to rush too quickly to the rule. Be Patient! Intuitive methods are best at first…To write a fraction in simplest terms means to write it so that numerator and denominator have no common whole-number factors…Notice that the phrase reducing fractions was not used. Because this would imply that the fraction is being made smaller, this terminology should be avoided. Fractions are simplified, not reduced.”
Elementary and Middle School Mathematics, John Van de Walle

4. Day 1 How can you find equivalent fractions using models?
Have students use fraction tiles to create equivalent fractions.
Sample question: How many eighths are equivalent to ¾?

5. Day 2 How can you find equivalent fractions using number lines?
Students can take their understanding of using models (such as fraction tiles) to create equivalent fractions. They can apply this understanding to number lines
when finding equivalent fractions.
Folding paper is an excellent task to
make this connection.
How can you find equivalent fractions using number lines?

6. Day 3
How can you use models to name equivalent fractions, including fractions greater than one?
Students can use any strategy (using manipulatives, number lines etc.) to find equivalent fractions.
Have students look for patterns in multiplication tables to determine equivalent fractions. (See following slide)

7. Looking for Patterns × 1 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20 22 24 15 21 27 30 33 36 28 32 40 44 48 25 35 45 50 55 60 42 54 66 72 49 56 63 70 77 84 64 80 88 96 81 90 99
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144

8. Enrich/Reteach
For students who are struggling with this concept, utilize hands on materials and number lines. Students can jump to the same spot on a number line to help with the idea of equivalency. Also use Reteach Activity p. 365B
To extend students thinking, select four or five fractions for students to put in order from least to greatest (make sure you include at least one pair of equivalent fractions). Have them place them on a number line. Students should be able to articulate placement on a number line and justify reasoning behind their placement. av

9. Literature for your Classroom Library