Overview

Students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module.

Topic C: Slope and Equations of Lines

Topic D: Systems of Linear Equations and Their Solutions

Advanced Preparation

- Scientific calculator
- Online graphing calculator
- Graph paper
- Straightedge
- Personal White boards

Module 5: Examples of Functions in Geometry

Students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life.

Advanced Preparation

- 3D solids: cones, cylinders, and spheres
- Personal White boards

Students are introduced to a function as a rule that assigns exactly one value to each input. In this module, students use their understanding of functions to model the relationships of bivariate data. This module is important in setting a foundation for students’ work in Algebra I.

Topic B: Bivariate Numerical Data

Advanced Preparation

Graphing calculator

Module Tip Sheet for Parents

These documents provide parents an opportunity to see what their children are learning in the current module including:

- Standards
- Key vocabulary
- Example Problems
- Pictorial Models
- Ideas for how to can help children at home
- Coherence of learning with past and future modules

Week 1: February 5

Standards Addressed in Week's Lessons

Topic C

8.EE.B.5

8.EE.B.6

Topic D

8.EE.B.5

8.EE.C.8

Notes:

Lesson 21 (P)

In example 1, consider saving time by having half of class test one point and the other half test second point.

Lesson 22 (P)

Lesson 11 introduced "Constant Rate" and can be referred to for planning lesson scaffolds if needed.

Lesson 23 (E)

The proof of the theorem is optional. The Discussion can end with the theorem, and in place of the proof, students can complete Exercises 4–8.

Lesson 24 (P)

For pacing considerations, consider skipping exercise 3. Exit ticket may take longer than 5 minutes and time can be used there.

Week 2: February 12

Assessment:

Biweekly 1:

Exit ticket from lesson 28. Allow data to form small group review of elimination and substitution method.

Standards Addressed in Week's Lessons

Topic D

8.EE.B.5

8.EE.C.8

Notes:

Lesson 25 (E)

Consider adding the term 'point of intersection' to your word wall and encourage to use throughout this topic.

Lesson 26 (S)

The Discussion is an optional proof of the theorem about parallel lines. Consider asking students to discuss as a closing debrief prior to exit ticket, "How do we know if two equations are parallel and why does this mean they have no solution."

Lesson 27 (P)

In closing, consider having an everybody writes, "How will we know if a system has one, multiple, or no solutions." Have students share answers with an elbow partner and then whole class.

Lesson 28 (P)

Consider after lesson making an anchor chart that shows the difference between substitution and elimination method.

Week 3: February 19

Assessment:

End of Module Assessment

Standards Addressed in Week's Lessons

Topic D

8.EE.B.5

8.EE.C.8

Topic A

8.F.A.1

8.F.A.2

8.F.A.3

Standards Assessed in Assessment

End of Module

8.EE.B.5

8.EE.B.6

8.EE.C.7

8.EE.C.8

Notes:

Lesson 29 (P)

After working through example 1 together, consider doing other examples with class movement; gallery walk, stations, etc. to provide formless whole group and encourage kinesthetic learning.

Lesson 30 Omit

Omitted for pacing. However, lesson is wonderful application of systems and weather, consider doing if time or in small group.

Lesson 31 Omit

Omitted for pacing. Geometry standard will work itself back in during high school geometry. Pythagorean theorem not on E of M assessment.

Two additional days have been added this week for End of Module assessment and remediation.

Lesson 1 (P)

Consider during opening discussion using suggested points to show students when linear equations will not fully tell the story of all math data and therefore something else is needed, 'functions". Video/YouTube will be needed during lesson.

Week 4: February 26

Notes:

Lesson 2 (S)

Two days are provided for lesson. Allow extra time for richer discussion section and exit ticket completion and whole class analysis. A diagram of an input-output machine may help students visualize idea of a function during discussions.

Lesson 3 (P)

For pacing, consider having students do only exercise 1 and spend extra time doing an everybody writes or table discussion for closing section that puts explanation ownership on students.

Lesson 4 (P)

Consider added 'discrete' and 'non-discrete' to the word wall.

Standards Addressed in Week's Lessons

Topic A

8.F.A.1

8.F.A.2

8.F.A.3

Week 5: March 5

Notes:

Lesson 5 (E)

Careful not to include the trick of 'vertical line test' as it does not allow students to conceptualize the meaning of functions.

Lesson 6 (S)

Fluency activity, while not directly related to lesson is essential for continued maintenance of important concepts. Refer to the Rapid White Board Exchanges section in the Module Overview for directions to administer a RWBE.

Lesson 7 (E)

Fluency activity, while not directly related to lesson is essential for continued maintenance of important concepts. Refer to the Rapid White Board Exchanges section in the Module Overview for directions to administer a RWBE.

Lesson 8 (E)

Students may need graph paper to complete these exercises. Students need graph paper to complete the Problem Set.

Week 6: March 12

Module

Topic

Notes:

Lesson 9 (E)

Consider providing formulas for shapes on anchor chart for work with lesson. Parcc provides the formulas during testing.

Lesson 10 (S)

For the demonstrations in this lesson, the following items are needed: a stack of same-sized note cards, a stack of samesized

round disks, a cylinder and cone of the same dimensions, and something with which to fill the cone (e.g., rice, sand,

or water).

Lesson 11 Omit

For pacing consideration, omit lesson on spheres, as it is not a major work of grade and will be seen again in module 7. Therefore, do not include part of question 3a or 3c in End of Module assessment.

Two additional days have been added this week for End of Module assessment and remediation.

Assessment:

Biweekly 3:

Exit ticket from lesson 9

End of Module Assessment

Standards Addressed in Week's Lessons

Topic B

8.G.C.9

Standards Assessed in Assessment

End of Module

8.F.A.1

8.F.A.2

8.F.A.3

8.G.C.9

Week 7: March 19

Module

Topic

Notes:

Lesson 1 (P)

If pacing is an issue, consider omitting exercises 13-16. Instead allow students to turn & talk and then discuss whole group, closing questions prior to trying exit ticket.

Lesson 2 (P)

Rate of change is used to mean constant rate of change in the subsequent lessons. Students also explain whether the rate of change of a linear function is increasing or decreasing.

*Only two lessons due to consideration of PARCC Administration

Standards Addressed in Week's Lessons

Topic A

8.F.B.4

8.F.B.5

Week 8: April 2

Module

Topic

Notes:

Lesson 3 (P)

Consider during closing to have all students turn & talk before cold calling a few students to discuss answers to closing questions as a whole group.

Lesson 4 (P)

Piecewise functions are used in lesson, but the term piecewise function does not need to be defined. This lesson also focuses on linear relationships. Nonlinear examples are presented in the next lesson.

Lesson 5 (P)

Consider to continue to provide all students opportunity to turn and talk about closing questions prior to cold calling a few students to share whole class.

One additional day this week is provided for ANET testing.

Assessment:

ANet

Standards Addressed in Week's Lessons

Topic A

8.F.B.4

8.F.B.5

Standards Assessed in Assessment

ANET

Major

8.EE.C.8

8.F.A.1

8.F.A.2

8.F.A.3

8.F.B.4

8.F.B.5

Supporting

8.SP.A.1

8.SP.A.2

Review

8.EE.B.5

8.EE.C.7

Week 9: April 9

Notes:

Lesson 6 (P)

Note that in this, and subsequent lessons, there is notation on the graphs indicating that not all of the intervals are represented on the axes. Students may need explanation that connects the “zigzag” to the idea that there are numbers on the axes that are just not shown in the graph.

Lesson 7 (P)

Consider allowing students to work in pairs for exercises 2-9 and share answers whole group.