### Grade 4/Chapter 6: Fraction Equivalence and Comparison

Released Items pertaining to unit of study: 4.NF.1, 4.NF.2

Results on 2015:

- MC: 4.NF.1: 44% (4 questions)
- MC: 4.NF.2: 28% (1 question)
- CR: 4.NF.2: 24% achieving 3 points

Online Resource:

- Visnos: http://www.visnos.com/demos
- EngageNY: NF Video
- Fraction Bars
- Khan Academy: Equivalent Fractions (Good conceptual video.)
- Fraction Game from Marilyn Burns

Thoughts on Lessons:

**Tools**: grid/graphing paper, number lines, fraction cards**Models**: ration table (see: pg. 352)bar model/tape diagram, open number line diagram**Strategies**: common numerators, common denominators, benchmark fractions,- Center ideas: Equivalence Center
- Fluencies: Stage 4
- recognizing that 1 can be renamed and written an 2/2, 3/3, 4/4, etc.
- connecting the identify property and multiplying by 1 written in fractional form.

- Show What You Know:
**Provided limited and insufficient information**about student understanding of fractions. Would add additional information – Pre/Post Vocabulary, 1/6 is five ways. - Lesson 6.1:
**2-Day Lesson**: If we are going to explore, then explore. Eliminate the complete guiding that is done by the book. Ask students, “What do you know?” or “What do you think?” Adjust the problem so that you can use authentic materials, i.e. a cake, paper, chocolate bar, etc. The question below is from introduction of lesson 5.1…I adjusted:*“Joe cut a pan of brownies into third-size pieces. He kept 1/3 and gave the rest away. Joe will not eat his part all at once. How can he cut his part into smaller, equal-size pieces? Using fractional terms, what would I call each of the pieces? Why? How would I model that using graph paper?*The challenge that you are going to face here is that students will not see the entire whole…it has been given away. So we must model the amounts. Focus on the visual models and relating to a number line and bar model. Do not say, “Multiply by 2, when you mean multiplying by 1, but using the equivalency of 2/2). If students do the Advanced Learners, then they need to make a model.**Day 1: Focus on why and how the fractions are equivalent using visual models. Day 2: Focus on comparing fractional amounts to determine if the fractions are equivalent using a bar model with equal sized wholes or using 2 number lines comparing congruent line segments spans of zero to one.** - Lesson 6.2: Do after Day 1 of Lesson 6.1. Student should be able to generate equivalent fractions, before they begin to compare fractions. Look at comments on lesson 6.3.
- Lesson 6.3: CCSS never mention simplest form explicitly. (See: http://commoncoretools.me/forums/topic/simplifying-fractions/) For this lesson focus on using division by 1 to generate equivalent fraction, not the simplest form. Also, emphasize the idea of ratios relationships. For example, if I shade in 3 circle for every group of 12, that means that I am shading in 1 for every 4 pieces. Also it is important to note that equivalent fraction of improper fractions should be shown/represented, i.e. 3/2 is equivalent to 6/4.
- Lesson 6.4: Should be taught before Day 2 of Lesson 6.1. Finding common denominators (visually using a models and arithmetically) are strategies that students need to compare fractions. Use C-R-A model. Provide opportunities to find common denominators, not just lowest common denominators. Strategy #1: Mix, Freeze, Group. Strategy #2: Match and Compare.
- Lesson 6.5: Make into an exploration and have students make visuals and act out using concrete tools. Can infuse throughout unit after lesson 6.2.
- Lesson 6.7: This is about reasoning with fractions using 1/2 as a benchmark, but students should be able to compare fractions with like denominators and like numerators from Grade 3…check for this. Also students should compare fractions by looking where closet to zero or one as benchmarks. Strategy: Quiz, Quiz, Trade – students compare fractions using benchmark amounts. One-third of class should have unit fractions, 1/3 should have fractions that are one-unit fraction away from 1-whole, and the last third should have fractions that are just below or about a half.
- Lesson 6.8: All throughout the unit have a routine where students have to order fraction on a number line using the strategy or strategies being taught. This lesson is an opportunity to talk and reason about how students determined where a fraction belonged on the number line. Do not ignore mixed and improper fractions.

Activities:

- How do we model and explain equivalent fractions?
- Mix, Freeze, Group for common denominators. For example, the numbers are 1/2 and 1/3, make a group to show a common denominator. Students could possibly make a group of 6 or 12. Show visuals when doing this activity.
- Match and Compare: Can be use to compare fractions, to determine common denominators, to generate equivalent fractions, etc.