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# Adding & Subtracting Fractions

Lesson 12 of 16

## Objective: SWBAT add and subtract fractions with common denominators.

## Big Idea: Students will use an interactive computer application to model the addition and subtraction of fractions.

*100 minutes*

#### Opening

*20 min*

**Today's Number Talk**

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using a number line model, Student Number Line, and a hundreds grid, Hundred Grids. For each task today, students shared their strategies with peers (sometimes within their group, sometimes with someone across the room). It was great to see students inspiring others to try new methods and it was equally as great to see students examining each other work for possible mistakes!

**Getting Started**

Prior to the lesson, I placed magnetic money and fractions on the board to help students conceptualize our number talk today.

I invited students to join me on the front carpet with their number lines. I then drew a number line on the board, Number Line on the Board, and marked 0, 1, and 2 on the line. I asked students to do the same on their own number lines.

**Task 1: Compare 3/10 x 2 to 1/4 x 3**

For the first task, I asked students to compare 3/10 x 2 to 1/4 x 3. I asked: *Which fraction is greater? Which is smaller? How do you know? Please show your thinking on your number line. Prove it to me! *

Here are a couple examples of student work during this time: Student Number Line 6:10 < 3:4 and Student Hundreds Grid 6:10<3:4.

After students had time to share their work with others, I invited a couple students to share their thinking on the board: Student Identifying 3:10 x 2 and Student Identifying 1:4 x 3.

**Task 2: Compare 5/100 x 9 to 20/100 x 4**

For the final task, students compared 5/100 x 9 to 20/100 x4. I loved listening to this student explain how $0.05 = half of $0.10 because half of 1/10 is 5/100: 5:100 = 0.05.

Again, students did a great job showing their thinking on their own mats: Student Number Line 45:100 < 80:100 and Student Hundreds Grid 80:100 > 45:100.

To save time, I modeled student thinking on the board, which I forgot to capture on film.

##### Resources (11)

#### Resources

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#### Teacher Demonstration

*20 min*

**Goal**

To begin today's lesson, I introduced the goal: *I can add and subtract fractions with common denominators. *I explained: *Now that we understand how to represent and compare fractions, we are going to move on to fraction computation. First, we will focus on adding and subtracting fractions. Then, we will focus on multiplying a fraction by a whole number. *

**Introduction**

To provide students with the opportunity to explore fraction addition and subtraction on their own, I designed an activity using the following interactive Computer Application at the Think Central iTools Site.

I wanted to students to engage in Math Practice 2 (Reason abstractly and quantitatively) by conceptualizing the process of adding and subtracting fractions. Within this application, students are able to click on "Activities" and then choose "Add" or "Subtract." However, I quickly discovered a limitation to this tool: Students are unable to add and subtract mixed numbers and improper fractions or sets of three fractions. In order to compute a variety of fractions, I showed students how to use the "Explore" tab. Later, a student discovered that the "Show" tab was much easier to work with than the "Explore" tab.

Using this computer application, students would also be engaged in Math Practice 3 (Construct viable arguments and critique the reasoning of others) as they would often use the program to justify their thinking.

To model how to use this application, I asked students to join me on the front carpet. I wrote the following Problems on the Board:

- 1/2 + 2/2
- 4/5 - 2/5
- 3/4 + 3/4 + 2/4

As we solved and discussed each task above, I passed around a student white board (flat surface) and a mouse for students to model the problem using the computer application: Modeling Subtraction.

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#### Student Practice

*60 min*

**Choosing Partners**

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. Before students began working, I asked them to discuss how they would like to support each other today. I gave them many examples: *Do you want to take turns talking out loud? Do you want to solve quietly and then check with each other? Or do you want to turn and talk anytime you get stuck? *Students always love being able to develop a "game plan" with their partners!

**Part 1 Practice**

I provided students with addition and subtraction practice by asking partners to work together to find the solutions to the problems on this page: Adding & Subtracting Fractions. To encourage teamwork, I only gave one page to each set of partners. I explained: *Today, I am looking for pairs of students, working together to **represent each problem on their computers. Make sure you discuss each answer before recording it on the paper. *

**Monitoring Student Understanding**

Once students began working, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3).

*What did you do first?**What do you need to always remember?**Does that feel right?**What mixed number does that equal?**Is this simplest form?**What makes more sense to you?**Does that always work?**What's your next step?*

**Conferences**

Here, a student adds three fractions at a time: Adding Three Fractions at a Time. Students loved being able to click the "Line Up" button to organize the fractions! This computer application was perfect for showing students that 8/4 is equivalent to 2 wholes.

This student liked the circle area model better than the rectangular area model: Using a Circle Model.

Another student used the "Show" tab instead of the "Explore" tab: Student Modeling 8:4 + 8:4 + 2:4.

**Completed Work**

Here's an example of student work doing this time: Completed Page. Some students simplified fractions. Other's did not. The main goal of this lesson was to add and subtract fractions correctly!

**Part 2 Practice**

To provide students with further practice, I printed two practice pages (Adding & Subtracting Practice Pages) from New York Engage Module 5. I explained: *For continued practice today, I'd like for you to continue adding and subtracting fractions using this computer application! *Students couldn't wait! They liked the computer application even more than I expected!

**Conferences**

Here, I support a student with checking her work: Checking Work. This computer application was a very powerful visual tool for this ELL student.

I also conferenced with this student, Erasing to Subtract. I showed him how to use the eraser to "take away" fractional parts. Next, we discussed how to represent his thinking using number bonds.

**Completed Work**

Most students were very successful with this activity, especially once they got the hang of it. Here are examples of completed work: Student Page 1 and Student Page 2.

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- UNIT 1: Measuring Mass and Weight
- UNIT 2: Measuring Capacity
- UNIT 3: Rounding Numbers
- UNIT 4: Place Value
- UNIT 5: Adding & Subtracting Large Numbers
- UNIT 6: Factors & Multiples
- UNIT 7: Multi-Digit Division
- UNIT 8: Geometry
- UNIT 9: Decimals
- UNIT 10: Fractions
- UNIT 11: Multiplication: Single-Digit x Multi-Digit
- UNIT 12: Multiplication: Double-Digit x Double-Digit
- UNIT 13: Multiplication Kick Off
- UNIT 14: Area & Perimeter

- LESSON 1: Decomposing Submarine Sandwiches
- LESSON 2: Exploring Unit Fractions 1/2, 1/3, 1/4
- LESSON 3: Exploring Unit Fractions 1/5, 1/6, 1/7
- LESSON 4: Exploring Unit Fractions 1/8, 1/9, 1/10, 1/100
- LESSON 5: Exploring Equivalent Fractions
- LESSON 6: Decomposing Pizza Fractions
- LESSON 7: Decomposing & Composing Fractions
- LESSON 8: Investigating Fractions with Smarties
- LESSON 9: Criss Cross Comparison
- LESSON 10: Area Model Comparison
- LESSON 11: Common Denominator Comparison
- LESSON 12: Adding & Subtracting Fractions
- LESSON 13: Measuring & Comparing the Lengths of Objects
- LESSON 14: Pencil Measurements
- LESSON 15: Fraction Multiplication with Clocks
- LESSON 16: Fraction Multiplication Recipes