Grade 4 Teacher Guide

Unit 2

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Unit 2: Fraction Equivalence and Comparison

Goals

In this unit, students will learn to think about fractions that are equal (called "equivalent fractions"), even when they look different. They will also compare and put fractions in order when the fractions have these bottom numbers, called denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.

About This Unit

This unit builds on what students learned in Grade 3 about fractions. Back then, students split shapes into equal parts and named each part with a "unit fraction" — a fraction like 1/4 that shows one equal part out of the whole. They learned that any unit fraction comes from splitting 1 whole into equal parts.

Students then used unit fractions to build bigger fractions, including fractions greater than 1, using fraction strips (paper strips folded into equal parts) and tape diagrams (rectangle drawings split into equal parts). In Grade 3, the bottom numbers of these fractions were only 2, 3, 4, 6, and 8. Students also placed fractions on a number line and learned that fractions are numbers, and that equivalent fractions land on the very same point on the number line.

In this unit, students use the same tools — fraction strips, tape diagrams, and number lines — to understand the size of fractions. But now they will work with more denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Students will learn an important idea: one fraction is equivalent to another fraction when each equal part is split into the same number of smaller equal parts. This makes each new part smaller, but there are more of them, so the fraction stays the same size. For example, if you split each fifth into 2 smaller parts, you now have twice as many shaded parts (tenths instead of fifths), but each part is half as small. So the fraction still represents the same amount.

As the unit goes on, students use equivalent fractions and "benchmark" fractions — easy-to-picture fractions like 1/2 and 1 — to figure out where fractions belong on a number line, and to compare and order them.

Throughout the Unit

Students keep practicing mental multiplication — building on skills from Grade 3 and using multiplication properties (rules) to make math easier. Short daily "Number Talks" in this unit help with this skill, focusing on the numbers 2, 4, 5, 6, 8, 10, and 12.

Students practice strategies like doubling and halving numbers. These strategies connect to folding fraction strips and splitting tape diagrams into smaller equal parts.

Here are some example Number Talk warm-ups used in this unit: one in Lesson 5, one in Lesson 9, and one in Lesson 16.

These numbers were picked on purpose to help students get comfortable with the unit fractions used in this unit. By noticing patterns between these numbers and their products during Number Talks, students get faster and better at finding equivalent fractions and comparing fractions with these denominators.

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Materials Needed

Here is a quick list of materials for each lesson.

Lesson	Materials to Gather	Materials to Copy
Lesson 1	Straightedges (rulers or similar tools) for two activities	Fraction Strips handout (1 copy for every 2 students)
Lesson 2	Straightedges for two activities; materials saved from an earlier lesson	—
Lesson 3	—	—
Lesson 4	Straightedge for one activity	—
Lesson 5	Straightedge for one activity	—
Lesson 6	—	Card Sort: "Where Do They Belong?" cards (1 copy for every 2 students)
Lesson 7	Tools for making a display	—
Lesson 8	Tape (painter's or masking tape)	—
Lesson 9	Rulers or straightedges; sticky notes	"How Do You Know" cards (1 copy for every 15 students)
Lesson 10	—	—
Lesson 11	—	Card Sort: "Fractions Galore" cards (1 copy for every 3 students)
Lesson 12	Colored pencils	—
Lesson 13	—	—
Lesson 14	Tools for making a display	—
Lesson 15	—	—
Lesson 16	—	Fraction Cards with denominators 2, 3, 4, and 6 (1 copy for every 2 students); Fraction Cards with denominators 5, 8, 10, 12, and 100 (1 copy for every 2 students)
Lesson 17	Markers, paper, paper clips, and tape (painter's or masking tape)	—

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Section A: Size and Location of Fractions

Standards Covered

This section builds on fraction skills students learned in Grade 3. It directly teaches new Grade 4 fraction skills and helps prepare students for even more fraction learning later on.

Goals

• Understand fractions with denominators 2, 3, 4, 5, 6, 8, 10, and 12 by using objects and drawings.
• Figure out where fractions belong on a number line.

About This Section

In this section, students go back to ideas about fractions from Grade 3, but now they also work with denominators of 5, 10, and 12. They use real fraction strips, drawings of fraction strips, tape diagrams, and number lines to understand the size of fractions and how fractions relate to each other.

Students think about fractions where one denominator is a multiple of the other — for example, comparing fourths to eighths, since 8 is a multiple of 4. They explore different ways to show these relationships. Students also compare fractions to benchmark fractions like 1/2 and 1.

This work gets students ready to understand equivalent fractions and fraction comparison in the lessons that come next.

Suggested Learning Centers

For Lessons 1 through 6, teachers can use these optional practice centers:

• Get Your Numbers in Order: a game where students order fractions with denominators 2, 3, 4, and 6.
• Mystery Number: a game (for extra