To get students started today, students practice showing their thinking on a number line. This activity asks students to model adding fractions with like denominators (rather than benchmark fractions like yesterday).
I ask the students to solve:
1/3 + 2/3
4/10 + 3/10
6/8 - 2/8
Students work for 5 minutes independently, then collaborate with their group members. Getting the answer is not the challenging part for the students, representing this with a number line is. Also, this activity requires students to set up the number line before starting to show the solution.
I take the time to have students share their models and explain their thinking. We discuss any representations that are incorrect too, because these mistakes help all students learn.
I take this time to talk to the students about the cumulative nature of the fraction skills they are learning. It is essential for students to understand from the start that each of the skills they have practiced in prior grades, and prior lessons, are designed to prepare them for working on more complex problems.
I compare the skills they are learning to building blocks and lead the students in a conversation about building a tower of blocks. Some of the questions I prompt them with are:
• If you want to build a tall tower that is also strong, what do you do?
• If you have a tall strong tower then you remove on of the bottom blocks, what might happen?
Then, I explain that fraction skills are like the blocks that you build with. You need each and very piece to work together. All of the skills that you have practiced over the years are the skills that make the very bottom of the tower, if you want to keep building, you must use these skills every time.
To make this connection more clear, I draw 4 blocks on the board. Then ask students to name various fraction skills they know. I write these skills in the blocks.
• We know fractions are part of a whole, we know how to read them, we know vocabulary words that go with them.
• We know how to estimate fractions using benchmark fractions to help.
• We know how to make equivalent fractions (simplifying too).
• We know how to add and subtract fractions (but only when the denominators are the same).
These foundational skills will help you tackle more and more challenging problems. Today, we are going to learn something new. You will be using all of these skills that you know, to solve problems like 2/6 +1/4.
I am model the process of solving 2/6 + 1/4 using a think-a-loud method. Throughout the process of solving this problem, I refer back to each of the 4 blocks that represent the skills students know about fractions.
Although the end result looks busy. The screen cast will walk you through my think-a-loud method, it also demonstrates the skills that students need in order to access this lesson.
I model one example, using fractions with denominators that required both fractions to be changed. Next, they will have an opportunity to practice on their own.
Students are given a chance to practice pulling together their fractions skills to solve addition equations with unlike denominators.
I give the students 5 problems to work on with a partner.
1) 3/5 + 1/10
2) 8/9 + 1/3
3) 1/2 + 2/3
4) 3/6 + 3/4
5) 1/5 + 2/7
I choose these examples because they gradually become more challenging. In the first two problems, only one fraction must be changed to create equivalent fractions. The third problem has denominators with an easy to identify common denominator. Then, problems four and five become a bit more challenging.
I have not introduced least common denominator at this point. While circulating the room, I encourage students to simplify when possible.
Part of the group share will be to discuss strategies that students used to find common denominators and also the benefits of using an LCD.
For today, I take extra time to focus on the various common denominators that students used to solve the first problem:
3/5 + 1/10
Some students used 10, others 20, and some 50 for the common denominator.
This one example provided rich discussion about taking many paths to get to the correct answer. I explain to the students that using 10 as the common denominator is the most efficient because there was no need to simplify at the end.
In the next lesson, I will introduce least common denominator.