1. Linear Model Unit of Study 4 : Understanding Fractions Global Concept Guide: 3 of 3

2. Content Development  In the following lessons students will be exploring fractions on a number line.  With linear models, lengths or measurements are compared instead of areas. Either lines are drawn and subdivided, or physical materials are compared on the basis of length. Linear models are closely connected to the real world contexts in which fractions are commonly used-measuring. (Van De Walle, 2010, p.290)  Students will use the number line extensively in future units to compare and order fractions as well as measure objects.

3. Day 1  The focus of Day 1 is using fraction strips/tiles to create a number line.

4. Day 2  The focus of Day 2 is using the linear model to plot and identify fractions on a number line.  Sample Task: What fraction is shown on the number line below? 0 1

5. Day 3  The focus of Day 3 is using a number line to represent mixed numbers and fractions greater than one.  It is important for students to be exposed to open number lines that do not always start at zero.  Sample Task:

6. Day 4  The focus of Day 4 is how the size of a linear whole affects the size of its parts.  Just as students have worked with placing numbers on a number line, we can have them do the same with fractions.  Be sure to use fractions greater than one and mixed-numbers.  After a few fractions have been placed, move the 1 and the 0 farther apart. We have now changed the size of the whole. Are you okay with leaving the fractions where they are? Allow participants to move fractions.

7. Day 4  By the end of Day 4 students should be able to:  Understand the relationship between each interval and the size of the whole(numerator and denominator)  Name linear representations in word and symbol form  Create a linear model based on a given fraction  Represent, name, and identify fractions greater than one using the linear model.

8. Enrich/Reteach/Intervention  Reteach- Have students work with linear models taped to the floor. How does the denominator affect the size of each jump/interval?

9. Enrich/Reteach/Intervention  Enrich- Show students fractions represented on the number line and have them write a linear word problem to match.  Sample Question: Adam lives 1 mile away from school. He has already walked three fourths of the way home. How much further does he have to walk until he gets home?