We have been working hard on fractions and I think you guys are ready to see them in an entirely new way. Who has ever baked something at their house? Or used a ruler? Or had their height measured at the doctor? Well then you’ve all seen fractions on a number line!
It is important for students to understand the connection this has to real life. It makes it more meaningful and helps them understand it in the context of things they are familiar with.
Who can tell me what their definition of a number line is?
We create a whole class definition, based on students responses of a number line. We will revisit it and build upon it each day as we do more work to understand number lines.
Who has ever seen a number line that goes from 0, to 5, to 2, to 100, to 72? Why not?
My goal is to help students realize that they already know the numbers on the number line are in consecutive (counting) order and that they follow a pattern.
I give each pair of students a white board and 2 markers for this activity.
Now if you can all draw a line for me and label one side 0 and the other side of the board 1, I want to show you the first pattern you can use to between whole numbers! Work with your partner to divide your line into 4 equal parts, placing a line to show where your 4 parts are. What do you notice?
Here I want students to make the connection that between the whole numbers there are 4 equal sections, and it looks similar to what our work in fractions and representing fractional parts. My goal is to have students draw on their knowledge of fractions to make sense of the number line and its parts (MP1).
Can you all use your other colored marker to color the first section on your line. What part of your whole line is this? What fraction could you use to describe this part?
Students should be able to recognize that this represents 1/4 of their number line and make the connection to the fraction 1/4. We repeat this process for 1/2 and 3/4 points on the number line.
Now that you and your partner have discovered that fractions on a number line follow a pattern just like whole numbers do, we are going to try it out with our tables!
I put butcher paper, makers and post-its on each table and allow students to create number lines. We will put these together at the end of the time in one large number line, as I gave each group 2 whole numbers with fractions only, so each tables work will combine to make a larger number line in consecutive order. I am walking around the room asking students questions about how they chose to divide up their number line, where they think their parts belong, what patterns they notice. I am also helping groups who are struggling to construct a number line to find entry points to a solution. I don't want to give them the answers, I want to help guide them to it themselves.
Now that you have discovered that fractions follow a pattern just like whole numbers do on a number line, I’m wondering who can draw on their knowledge for today and help me solve these problems. There are letters on my number line and I need to figure out what fraction represents this point on the number line.