Teacher Guide: Fraction Equivalence

@ Learning Objective 5-10 min lesson

Students will: Identify and generate equivalent fractions using multiplication and division, simplify fractions to lowest terms, and compare/order fractions using benchmark fractions (1/2, 1/4, 3/4).

Why this matters for FAST: Fraction equivalence is foundational for all fraction operations. Students must recognize equivalent fractions, simplify, and compare fractions with different denominators - all common FAST question types.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Fraction strips or tiles
Colored pencils
Number line printout
Multiplication chart (optional)

! Common Misconceptions to Address

Misconception #1: Adding Same Number to Numerator and Denominator

Students think 1/2 = 2/3 because they add 1 to both (1+1=2, 2+1=3). They confuse multiplication with addition.

How to Address:

"To create equivalent fractions, we MULTIPLY (or divide) both parts by the SAME number. Think of it as multiplying by 1 in a special form: 2/2 = 1, 3/3 = 1. So 1/2 x 2/2 = 2/4."

Misconception #2: Larger Numbers Mean Larger Fractions

Students believe 3/8 > 2/4 because 3 and 8 are "bigger numbers" than 2 and 4.

How to Address:

"Use benchmarks! Is 3/8 more or less than 1/2? (Less - because 4/8 = 1/2). Is 2/4 equal to 1/2? (Yes!) So 2/4 > 3/8."

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Draw two fraction bars: one showing 1/2, one showing 2/4. Ask: "Are these the same amount? How do you know?" Establish that different fractions can represent the same value.

2

Introduce the Concept (2 min)

SAY THIS:

"Equivalent fractions are different ways to show the same amount. To find an equivalent fraction, multiply or divide BOTH the numerator AND denominator by the SAME number. It's like multiplying by 1!"

1/2 = ?/4

Multiply top and bottom by 2:

1 x 2 = 2 | 2 x 2 = 4

1/2 = 2/4

1/2

1/4

3

Teach Simplifying (2 min)

Explain: "Simplifying is finding equivalent fractions by DIVIDING. We divide both parts by a common factor." Example: 6/8 - both 6 and 8 can be divided by 2, so 6/8 = 3/4.

SAY THIS:

"To simplify, find a number that goes into BOTH the numerator and denominator evenly. Keep going until you can't divide anymore - that's the simplest form!"

4

Introduce Benchmark Fractions (2 min)

Show students the benchmarks 0, 1/4, 1/2, 3/4, and 1 on a number line. Explain how to compare any fraction to these benchmarks.

Is 3/8 more or less than 1/2? (Less, because 4/8 = 1/2)
Is 5/6 closer to 1/2 or 1? (Closer to 1)

5

Guided Practice (2-3 min)

Work through these together:

Find an equivalent fraction for 2/3 with denominator 12
Simplify 8/12 to lowest terms
Compare 5/8 and 3/4 using benchmarks

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"Which fraction is equivalent to 3/4?"

A) 6/12 B) 9/12 C) 4/5 D) 6/9

Correct answer: B) 9/12 (3x3=9, 4x3=12)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Find equivalent fractions using models Find equivalent fractions Write fractions in lowest terms Compare fractions using benchmarks Compare fractions with different denominators

^ Differentiation & Extension

For struggling students: Use fraction strips to physically show equivalence. Start with halves, fourths, and eighths before moving to thirds and sixths.

For advanced students: Challenge them to find ALL equivalent fractions for 1/2 with denominators up to 12. Introduce comparing fractions by finding common denominators.

For home: Send Parent Activity sheet. Families can explore equivalent fractions using pizza slices and measuring cups.