Session 6 Number Lines Big Ideas Number lines

Session 6 - Number Lines Big Ideas Number lines can be used to help students build an understanding of: • The relative magnitude of fractions; • Unit fractions; • Equivalence; • Operations with fractions; and • The density of rational numbers. (Petit, Laird, Marsden, & Ebby (2016) © 2018 OGAPMath LLC. For non-commercial use only. 1

1) Keep track of the aspects of a number line that you had to consider or helped you to solve each problem. 2) What errors might students make as they solved each problem? © 2018 OGAPMath LLC. For non-commercial use only. 2

Number Line Warm-Up 1. What aspects of the number line did you need to consider to solve these problems? 2. What errors might students make in trying to solve these problems? © 2018 OGAPMath LLC. For non-commercial use only. 3

Instructional Strategy These 2 number lines were used in the same classroom. 1) What is similar and what is different about the 2 number lines? 2) What mathematical concepts was the teacher trying to reinforce/develop? Figure 6. 19 - Chapter 6 © 2018 OGAPMath LLC. For non-commercial use only. 4

Instructional Strategy © 2018 OGAPMath LLC. For non-commercial use only. 5

Integrating visual model (line) and symbols that define unit © 2018 OGAPMath LLC. For

Multiple Units and Sub Units © 2018 OGAPMath LLC. For non-commercial use only. 7

Evidence in Student Work With a partner: Review Student Solutions 1 – 6 on Slides 9 – 14. For each response: – What developing understanding is evidenced that can be built upon? – What errors or misconceptions are evidenced? – What are potential next instructional steps? © 2018 OGAPMath LLC. For non-commercial use only. 8

Student Solution 1 © 2018 OGAPMath LLC. For non-commercial use only. 9

Student Solution 2 © 2018 OGAPMath LLC. For non-commercial use only. 10

Student Solution 3 Figure 6. 21 Chapter 6 (2016) © 2018 OGAPMath LLC. For

Student Solution 4 © 2018 OGAPMath LLC. For non-commercial use only. 12

Student Solution 5 © 2018 OGAPMath LLC. For non-commercial use only. 13

Student Solution 6 © 2018 OGAPMath LLC. For non-commercial use only. 14

Sequential vs. Proportional Reasoning Sequential reasoning Proportional reasoning © 2018 OGAPMath LLC. For non-commercial

Fractional – Transition: Number Lines • • • Figure 6. 22 Figure 6. 17 Figure 6. 10 Figure 6. 11 Figure 6. 20 Figure 6. 29 © 2018 OGAPMath LLC. For non-commercial use only. Where on the progression? What is the evidence? 16

Your Class (or Case Study) Your Class Grade 3 - #2 Grade 4 -

Instructional Materials Review 1) Based on your analysis of your math program in earlier sessions, what can you say about the use of number lines in your math program? 2) Based on your new learning and your findings in your math program, what might be done to strengthen instruction? © 2018 OGAPMath LLC. For non-commercial use only. 18

Measurement and Number Lines • Read the section Measurement (110 – 111): A direct application of number lines. • Answer question 1 – a, b, and c in Looking Back Chapter 6 (p. 111 -112) © 2018 OGAPMath LLC. For non-commercial use only. 19

OGAP Fraction Item Bank • Go to www. ogapmathllc. com • Go to “For OGAP Participating Teachers, Math Coaches, and Leaders” • Click on “Fractions” • Enter Password 2018 FTevidence – • Download File © 2018 OGAPMath LLC. For non-commercial use only. 20

Item Bank Scan ① With a partner briefly scan through the items. a) Describe a couple of ways that the problems vary in this section. ② Choose 1 item that you think will provide important information about your students understanding of number lines. a) Be prepared to discuss the reasons why you selected the item. © 2018 OGAPMath LLC. For non-commercial use only. 21