Overview

Module 2: Arithmetic Operations Including Division of Fractions

Students complete their understanding of the four operations as they study division of whole numbers, division by a fraction, and operations on multi-digit decimals.

Topic A: Dividing Fractions by Fractions

Topic B: Multi-Digit Decimal Operations—Adding, Subtracting, and Multiplying

Topic C: Dividing Whole Numbers and Decimals

Topic D: Number Theory—Thinking Logically About Multiplicative Arithmetic

Advanced Preparation:

- Counters
- Fraction Tiles
- Tape Diagrams

Students extend the number line (both horizontally and vertically) in Module 3 to include the opposites of whole numbers.

Topic A: Understanding Positive and Negative Numbers on the Number Line

Topic B: Order and Absolute Value

Topic C: Rational Numbers and the Coordinate Plane

Advanced Preparation:

- Personal Whiteboards
- Graph Paper
- Number Line
- Compass
- Painters Tape

2016-2017 Math Schedule of Assessed Standards (SAS)

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: November 7

Notes:

Lesson 5 (P)

Consider putting the “5 Steps for Creating Division Word Problems” on chart paper posted around the room. Students will need fraction tiles or fraction cut outs as well as visual models showing measurement division.

Lesson 6 (P)

Lesson continues objective of lesson 5 to make partitive division word problems. Students set up a situation based off a model as the last step in creating problem. Directing students to hold off on the situation until the end may help smooth out process.

Week 2: November 14

Assessment

Biweekly #1 from lesson 7 Exit Ticket

Standards Addressed in Week's Lessons

Topic A

6.NS.A.1

Topic B

6.NS.B.3

Notes:

Lesson 7 (S)

Consider adding the terms 'multiplicative inverse' and 'reciprocal' to a Word Wall with their definitions to display for class. Pre-cut fraction strips from end of lesson to support students that struggle to make models.

Lesson 8 (P)

The memory game that is included in this lesson needs to be cut and prepared for pairs or individual students. During memory game, consider having students keep track of cards on separate paper to avoid doing same problems more than once.

Lesson 9 (P)

Consider doing only one exit ticket question and asking students to add to answer, which solution method they used, fraction or decimal model, and why they found it easier.

Lesson 10 (P)

Stations are used in this lesson. Therefore, some prep work needs to be completed. Prepare stations before class, and have a stopwatch available. Students if needed can support their mental multiplication math through using an area model or future distribution where needed. For example 800x12, can be turned into 800x10 + 800x2.

Week 3: November 21

Notes:

Lesson 11 (E)

To complete this lesson, students need large poster paper and markers so that they can present their detailed solutions to the Exploratory Challenge. Prioritize the discussion section over the exercises to help build understanding for students.

Week 4: November 28

Assessment

Mid Module: administer after lesson 11

Biweekly #2 from lesson 12 Exit Ticket

Standards Addressed in Week's Lessons

Topic C

6.NS.B.2

6.NS.B.3

Notes:

Two days are provided this week for Mid Module assessment and remediation

Lesson 12 (P)

To support discussion questions, consider keeping a running chart through exercise questions that show the divisor and how far away the estimate is from the exact answer.

Lesson 13 (P)

Consider providing the class with value tables for all classwork problems to assist with pacing. Providing the tables does not take away from students working towards standard being addressed, NS.2.

Standards Addressed in Assessment

Mid Module

6.NS.A.1

6.NS.B.3

Week 5: December 5

Standards Addressed in Week's Lessons

Topic C

6.NS.B.2

6.NS.B.3

Topic D

6.NS.B.4

Notes:

Lesson 14 (P)

For modeling purposes, consider putting the opening exercise and example 1 on the board side by side for an easy comparison and discussion.

Lesson 15 (P)

For opening questions, consider allowing students to use multiple methods to solve and explain their mental math, rather than initially providing the example given in the lesson.

Lesson 16 Omit

This lesson is a review of previously learned content. Consider including a quick review of even and odd numbers as an opening activity in Lesson 17.

Lesson 17 (S)

Consider having students build a divisibility chart throughout the lesson, quickly entering the easier rules, 10s,5s,and 2s. And building to the 3s and 9s that will be discussed in the closing debrief.

Lesson 18 (P)

If more than 3 members in a group, consider making all additional members recorders to keep them involved in lesson. Material organization will be key for lesson and should be carefully consulted beforehand.

Week 6: December 12

Assessment

End of Module: administer after lesson 19

Biweekly #3 from lesson 1 Exit Ticket

Notes:

Lesson 19 (P)

For pacing considerations, prioritize examples 1 and 4 to help students conceptualize the GCF rule through the area model.

Two days are provided this week for End of Module assessment and remediation.

Lesson 1 (E)

The lesson allows students to conceptually see the number line horizontally or vertically, if some students need it, they can turn the horizontal exit ticket number line on it's side to see it vertically.

Standards Addressed in Week's Lessons

Topic D

6.NS.B.4

Topic A

6.NS.C.5

6.NS.C.6a

6.NS.C.6c

Standards Addressed in Assessment

End of Module

6.NS.A.

6.NS.B.2

6.NS.B.3

6.NS.B.4

Week 7: December 19

Notes:

Lesson 2 (P)

Consider challenging students to come up with common misconceptions on their own for the opening exercise if a natural opportunity does not arise to display from student work.

Lesson 3 (E)

Consider again, asking students to identify common misconceptions while working through problems. This can be done whole group as well as during teacher circulation.

Lesson 4 (P)

Consider creating a floor model of a number line prior to the lesson with painters tape so students can visualize and walk off answers as needed.

Week 8: January 9

Module

Notes:

Lesson 5 (P)

The lesson outcome leads directly into students conceptual understanding of why a negative times a negative is a positive.

Lesson 6 (S)

To help students visualize a number line with rational numbers. Consider posting a traditional number line first and then show how it can be expanded out to fit fractions and decimals in between whole numbers.

Lesson 7 (P)

For pacing purposed consider prioritizing game, discussion, and exercises 1-4 before closing and exit ticket.

Lesson 8 Omit

This lesson shares the same Student Outcomes with Lesson 7.

Lesson 9 (P)

Students complete an activity during Example 2 that requires preparation. The Activity Cards (attached to the end of the lesson) need to be prepared before the delivery of this lesson.

Standards Addressed in Week's Lessons

Topic A

6.NS.C.5

6.NS.C.6a

6.NS.C.6c

Week 9: January 16

Module

Topic

Notes:

Lesson 10 (P)

Consider referencing the coherence map to understand how students have experienced inequalities in previous grades, 5.NBT.A.3, 4.NF.C.7.

Lesson 11 (P)

Consider referencing lesson 5 from this module to see how finding the opposite of a number on a number line leads into finding the absolute value of a number.

Lesson 12 (P)

Prior to presenting the lesson, prepare sticky notes containing a balanced variety of positive and negative integers ranging from −50 to 50. Each pair of students requires a set of ten integers including five negative values, zero, and four positive values.

Standards Addressed in Week's Lessons

Topic B

6.NS.C.6c

6.NS.C.7

Week 10: January 23

Module

Notes:

One day is provided this week for ANet testing

Lesson 13 (P)

After quick whole group discussion for rotation exercises 1-4, consider having the answers ready to post for all to see as a conclusion to the discussion. If time is an issue, consider using only 2 or 3 questions for this activity rather than 4.

One day is provided this week for Mid Module assessment.

Lesson 14 (P)

Before starting the lesson, the teacher must make copies of the scenarios in Example 2 and cut them apart in order to provide each group with exactly one scenario.

Assessment

ANet

Mid-Module Assessment: administer after lesson 13

Standards Addressed in Week's Lessons

Topic B

6.NS.C.6c

6.NS.C.7

Topic C

6.NS.C.6b

6.NS.C.6c

6.NS.C.8

Standards Addressed in Assessments

ANet

Major

6.NS.C.5

6.NS.C.6a,b,c

6.NS.C.7a,b,c,d

6.NS.C.8

Additional

6.NS.B.2

6.NS.B.3

6.NS.B.4

Review

6.NS.A.1

6.RP.A.2

Mid Module

6.NS.C.5

6.NS.C.6a

6.NS.C.6c

6.NS.C.7

Week 11: January 30

Notes:

Lesson 15 (P)

Consider preparation for lesson: hang posters on the wall, each containing one of the following terms: x-axis, y-axis, x coordinate, y-coordinate, origin, and coordinate pair.

Lesson 16 (P)

Consider helping students understand symmetry of a coordinate plane by continuously referencing absolute value in the discussion.

Lesson 17 (P)

Consider prioritizing correct set up organization of a coordinate graph, labeling x and y axis. Also, give students time to talk to each other for this key question, "Discuss ways in which the point (18, 5) could be graphed without changing the size of the grid."