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