Adding Fractions by Thinking about Decimals

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Objective

SWBAT add fractions with denominators 10 and 100.

Big Idea

Students will add fractions by thinking about decimals and using a variety of tools: equivalent fractions, a number line model, a money model, and an area model.

Opening

20 minutes

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 and hundreds 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 get a Student Number Line and Hundred Grids. I then drew a 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: 3/10 + 20/100

To begin, I asked students to add 3/10 +20/100 on their number lines and hundreds grids. During this time, some students chose to work alone while others worked with a partner in their math groups. I took this time to conference with students. Here are a few examples of student work during this time: 3:10 + 20:100 Number Line and 3:10 +20:100 Hundreds Grid

I modeled several students' thinking on the board: Number Line Demonstration 3:10 + 20:100

Task #2: 70/100 + 6/10

Next, we moved on to adding 70/100 + 6/10. Once again, students showed their thinking using a number line, 70:100 + 6:10 Number Line, and hundreds grids, 70:100 +6:10 Hundreds Grid.

I then modeled another student's thinking on the board: Number Line Demonstration 70:100 + 6:10

 

Teacher Demonstration

30 minutes

Goal & Lesson Introduction 

To begin, I introduced the goal for today's lesson: I can add fractions with denominators 10 and 100. I explained: Today, we are going to use several models to represent the addition of two fractions. 

Choosing Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills.

Handouts 

I passed out handouts to each pair of students: a student number line and hundreds grids (from our Number Talk) and two different colored mats (colored papers placed inside sheet protectors). 

I asked students to label one colored mat "Equivalent Fractions" and another colored mat "Money Model." 

Altogether, each pair of students will have four "mats," one for each of the following models: 

  • Number Line Model
  • Place Value Model (Hundreds Grids)
  • Equivalent Fractions
  • Money Model

By incorporating multiple models with this lesson, students will naturally engage in Math Practice 2: Reason abstractly and quantitatively. It is particularly important for students to conceptualize the abstract process of adding fractions using models in order to make sense of quantities and their relationships. 

Modeling the Models

After introducing the goal, I drew a large chart on the board in order to model each tool the students would be using today. Here's what the completed chart will look like at the end of this demonstration: Teacher Demonstration of Models.

 I showed students how to add 1/10 + 1/00 by finding an equivalent fraction to 1/10 (1/10 = 10/100). Next, we added 10/100 + 1/100 to get 11/100. 

Next, we discussed how to add 1/10 +1/100 on the number line. I modeled how to take a jump of 10/100 (starting on 0) and a jump of 1/100 to land on 11/100. 

Then, we discussed the Money Model. While gathering student input, I modeled the value of 1/10 and 1/00 using a penny and a dime. We then wrote an equation: 0.01 + 0.10 = $0.11. 

Finally, we colored in the hundreds grids to represent the money model. One one grid, we colored in 10/100 squares and on the other grid, we colored in 1/100 squares. 

As I modeled each step, students worked with their partners to complete the same work on their own mats: 

 

Building on Prior Knowledge

Since students have been exposed to adding fractions on the number line and using hundreds grids through our Number Talks, I knew that students would be more than ready to begin practicing this skill on their own and that further teacher demonstration was unnecessary. 

 

Student Practice

50 minutes

Mild, Medium, & Spicy Practice 

To provide students with continued practice adding fractions with denominators 10 and 100, I created three levels of task cards: MildMedium, and Spicy using the following document: Tenths + Hundredths Cards. Each level of task cards increased with difficulty.

First, students started off by cutting out the Mild task cards. Some students chose to write the answer on the cards. Others had an incomplete and complete pile to keep track of which cards they had solved. 

Once students had completed all of the Mild task cards, they moved on to the medium task cards, and then the spicy!

Monitoring Student Understanding

While students were 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). 

  1. Can you explain what you know?
  2. What step did you take first?
  3. Which model do you like best?
  4. Does that make sense to your partner too?
  5. Can you show me your thinking?
  6. What happens as you move down a column? 
  7. Can you simplify that fraction?

Conferences 

Here are examples of students using each of the above models.

One student, explained that 60/100 = 6/10, so you can start at 6/10 and take a jump of 2/10 to add 60/100 + 2/10 on a number line: Using the Number Line Model.

Another student did a beautiful job explaining how to use money to solve 5/10 + 30/100: Using the Money Model. His two partners also solved this problem using other models: Using Equivalent Fractions & the Place Value Model.

Overall, students were very successful with flexibly using a variety of methods.