Grade 4/Chapter 7: Adding and Subtracting Fractions
Thoughts on Lessons:
- Tools: fraction bars, pattern blocks, number lines, fraction cards, chart
- Models: area model, bar model, number line, number bonds
- Strategies: common numerators, common denominators, benchmark fractions
- Unit Focus/Big Ideas:
- Making connection that when we add or subtract we combine or separate like units.
- Make connections to the work done with whole numbers, especially when regrouping.
- Make connections to the idea that fractions can be renamed into different, but equivalent forms.
- Infuse the different problems types of Results Unknown, Start Unknown and Change Unknown
- Stage 3 Fluencies:
- Stage 4 Fluencies:
- Vocabulary, use Frayer Model and VVWA to help students make connections
- Routine: Skip counting by fractional amounts.
- Center ideas: Look at “Prerequisite Skills” on pg. 383 I and Game, pg. 384 A to make into centers. For the Name It activity…be precise and ask students to make proper fractions, opposed to improper fractions. Do not tell students to look, “use the greater number” as the denominator, as this reinforces the idea that fractions are made up of a whole number on top and another whole number on bottom.
- Lesson 7.1 (Infuse lesson 7.3): Use the problems in this lesson to create concrete experiences for students to explore. Have them act out the information and justify their thinking. I would turn this lesson into centers:
- A: Word Problems – Act it out
- B: Build it and Add – students select fractions with like denominators and then add the amounts. Students should use concrete tools, then make diagrams of the objects.
- C: Build it on a Number Line – similar to above activity, but students should show the work on a number line.
- D: Find and Fix My Error – Show how students worked out word problems, but each solution is in correct based upon the misconception of adding the denominators. Do not tell students that that is the error, let them discover it.
- Lesson 7.2 (Infuse lesson 7.3): Use number bonds and other models here. Make this lesson idea into a game that can later be a center. For example, Give 3 students 1 fractional amount which indicates the sum, they have to create a different equation to how to get that sum using 2 or 3 addends. Improper fractional amounts are encouraged.
- Lesson 7.3: Should be infused into previous lessons and not taught separately. Look at “Advanced Learners” pg. 398…this could be used as a quick “Do Now” or center/small-group activity where you have students make their own riddles.
- Lesson 7.4: Similar to lesson 7.1 make this into a lesson where word problems are used to help students make sence of what is happening. Act out the problems. Possible Instructional Idea: Have a different problem at each table. Students have to work in groups of 3 or 4. Each group has 5 minutes to solve and justify the problem given. Use the collaboration strategy of “Two Talk” – where 2 students in a group of 4 can talk about what they are thinking or doing. The other two can guester or make sound to indicate if the others are going in the correct direction, but they cannot speak.
- Lesson 7.5: While the problem on page 412 is useful, it is not needed for the Grade 4 CCSS Standards. This lesson can be infused into other lessons or skipped. The ideas of renaming the sum or difference in another way is useful and should be done throughout the entire unit. For example, problem #18, pg. 411 can be a quick Do Now and discussion. Problem #14, pg. 14 can be presented as a Two Arguments problem, by saying that one student said the answer was ¾ gallons, but another student said the answer was “one and 2/8 gallons”. This exploration can be a 20 to 30 minute lesson.
- Lesson 7.6: Use number bonds. Focus on renaming, especially the whole. Ensure that students use concrete and visual models to build and see what it happening. Focus on what the denominator tells us about the whole. Do an activity where a mixed or improper fraction is presented and ask the students, “What do you know?”, then list what is known and add additional items to the list, as needed to help students focus on the big concepts. Look at pg. 420 #20…this a good idea for a center, where students can make matching games. Additional Game Idea: Assign 2 students the same number. Give a yellow index card or give a blue index card. The yellow card should have numbers that are mixed numbers, while the blue cards should have numbers that are improper fractions. Students have to find the other students that are their match.
- Combine Lesson 7.7/7.8: Spend at least 3 days on these lessons. Visit the idea of regrouping in a guided math group. Use number bonds. Use concrete tools and charts. Make into a game. Do Find and Fix My Errors on Day 3. Provide students with the chance to identify when they have to regroup.
- Lesson 7.9: Infused the ideas in this lesson in lessons 7.1 – 7.3, but use simpler numbers and begin without regrouping. Make combinations obvious. For example, if adding 2 ⅞ + 2 ⅝ + 1 ⅛ a student can say that they are going to use a partial sum strategy by adding the whole numbers, then the fractional amounts and next. They would be employing the Associative Property of Addition. They could also say that they are going to add the ⅞ and ⅛ to make a whole, then add the ⅝, they would be employing the Commutative Property.
- Lesson 7.10: Infuse throughout unit. But look at the problems carefully. For example, in the Enrich 7.10 #1…this is a good for an exploration and discussion, but it is not directly addressing the standard. #2 address the standard and would be good during lesson 7.2 or 7.3.
- End-of-Unit Exam: Exam #17. Use as formative assessment. This can be solved using addition, but it would be a multi-step problem. And more effeciently we would like students to recognize that this is division situations. How many groups of 6/4 miles are in 3 miles or 3 divided by 6/4? Be on the look out for these kinds of problem throughout the unit, especially in lessons 7.9 and 7.10.