Chapter 6 Add and Subtract Fractions with Unlike Denominators
Stage 4 Fluencies:
- Generating equivalent fractions for benchmark fractions.
- Decomposing fractions
- Skip counting by fractional amounts and converting between mixed fractions and improper fractions as you go.
- Generating equivalent fractions.
Thoughts on Lessons:
- Tools: fraction bars,
- Models: number lines, bar model,
- Strategies: common denominators
- Show What You Know: Vital! Also do a vocabulary formative assessment and see what students know.
- Lesson 6.1: Make this into a game. Different ways to make 1 whole with two different fraction units. You could have each group with 1 constant, e.g., students have to make 1 whole with 1/4 as 1 on the addends and they have to find different ways to make the whole, but always using 1/4 and some other fraction unit. The should record and chart the amounts. The strategy that they will be able to see is that 1/4 + 3/4 (in various forms) is 1 whole. In a guided group, explore why we cannot combine unlike units, by using a chart, similar to a place value chart. Use problem 13 on pg. 354 as an example during your guided math group. Use the problems on page 355 to make a Tic Tac Toe game for students to play. 2-days on this!
- Lesson 6.2: Use food and concrete examples in guided math groups. For example, If we got a pizza pie, which was cut into 8 equal pieces or 1/8 of the whole and I ate 1/8 of the pizza pie. Later my mother each slice into 2 equal pieces. So now really each slice was 1/16 of the whole pizza pie. I ate 3/16. Now how much pizza was left? Have students visualize and act out and prove. Use concrete objects and act out the situations and examples in the book. Subtraction of fractions really help us think about why we might generate equivalent fractions before we subtract. The other idea is to think about when and were we might be able to subtract accurately with out making equivalent fractions. For example, 1 7/8 – 3/4. We want students to see the relationships, so I might say, “Well I can see that 3/4 from 1 is going to leave me with 1/4 and 1/4 is really just 2/8, so if I add what is left I would combine 2/8 and 7/8, which is 9/8 or 1 1/8. I did not need to convert both fractions to equivalent, like denominators. 2-days on this!
- Lesson 6.3: Would not do. Would have students talk about what they know about the fractions and how they see them on a number line. Would make the first problem on page 365 an exploration, but use more realistic numbers and situations. One that students can better relate to or experience. For example the 40-mile bike trail could be $40. Later on it could be 40-mile bike trail, when you revisit the problem.
- Lesson 6.4: CCSS does not ask for the LCD, only a common denominator. The standards want students to have a conceptual understanding of what this strategy means and why it is being used and students being flexible enough to have several common denominators that could be used. Stress the understanding about common denominator and ways to figure out the common denominators. From lesson #1 and #2 begin looking at how we can record the fraction equivalences, so that students discover the pattern. Make a visual for students using a paper folding technique.
- Lesson 6.5: CCSS does not ask for simplest form. The key here is the let students see and understand that some one could say an answer that is correct, but it is presented in an equivalent format…and students have to recognize them.
- Lesson 6.5/6.6: Make into centers and guided groups. Centers should focus on use of concrete tools, math models and students discussing and proving why the sums and differences. We should also make the connection to adding/subtracting with whole numbers. Use a number bond and use examples to make a game. Solve collaboratively – one paper, one pen.
- Lesson 6.7: Strategies modeled by book are regrouping and making improper fractions. These concepts are important, but not as a procedure and a way to develop flexibility with fractions and operations. Present worked problems to students and ask them to explain what was done. Explicitly show using number bonds where the regrouping in taking place. Students need to ability to decompose fractions. Discourse is vital! 2-days on this!
- Lesson 6.8: Infuse this lesson as a routine…look at skip counting by fractional amounts using concrete models and showing on the number line. Later adjust the count to be skip counting by different units. For example, begin at 1/3 and skip count by 1/2. Show on a number line. Make the “On Your Own” into a game.
- Lesson 6.9: Infuse throughout unit.
- Lesson 6.10: Infuse from lesson #1. For example, 2/3 + 1/4 = 8/12 + 3/12 = 8/12 + 2/12 + 1/12…I can add these numbers in any order and arrive at the same sum. Also, 2 3/4 + 2 1/8 = 2 + 6/8 + 2 + 1/8 = 2 + 2 + 6/8 + 1/8. Apply the Associate Property of Addition and the Commutative Property of Addition from the very beginning.
- End-of-Chapter Exam: Must review carefully. Compare the released items and EngageNY Module Exam. Many question unnecessarily confusing and poorly constructed.