Overview

Module 5: Area, Surface Area, and Volume Problems

In this module, students utilize their previous experiences in order to understand and develop formulas for area, volume, and surface area. Students use composition and decomposition to determine the area of triangles, quadrilaterals, and other polygons.

Topic B: Polygons on the Coordinate Plane

Topic C: Volume of Right Rectangular Prisms

Topic D: Nets and Surface Area

Advanced Preparation

- Coordinate Planes
- Nets
- Prisms
- Rulers

In this module, students move from simply representing data into analysis of data. Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data. Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape.

Topic A: Understanding Distributions

Topic C: Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range

Topic D: Summarizing and Describing Distributions

Advanced Preparation

- Dot plots
- Histograms
- Box plots

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: April 16

Assessment:

EOM starts the quarter

Standards Addressed in Week's Lessons

6.G.A.1

Standards Assessed in Assessments

End-of-Module

6.EE.A.1

6.EE.A.2

6.EE.A.3

6.EE.A.4

6.EE.B.5

6.EE.B.6

6.EE.B.7

6.EE.B.8

6.EE.C.9

Notes:

One day provided for administering End of Module 4 assessment. Start the quarter with this assessment.

Lesson 1 (S)

Consider utilizing the parallelogram templates, along with listed supplies (scissors, glue, ruler), for students to utilize during their investigation of area formulas.

Lesson 2 (E)

During this lesson students will develop the formula necessary to calculate the area of a right triangle. Supplies needed: polygon templates, glue, ruler and scissors. Students may benefit from more than one copy of the triangle template.

Week 2: April 23

Assessment:

Biweekly #1 after lesson 5 / 6

Use exit ticket from lesson 6

Standards Addressed in Week's Lessons

Topic A

6.G.A.1

Topic B

6.G.A.3

Notes:

Lessons 3 / 4 (Combined) (M / E)

Provide students practice problem solving with altitudes on the inside and outside of triangles. Consider using shape templates in lesson 4 to demonstrate location of altitudes on a variety of triangles. Select exercises from examples and problem sets for each lesson. Use exit ticket from lesson 4 for assessment.

Lessons 5 / 6 (Combined) (S / E)

Provide students opportunities to investigate solving area problems with decomposing irregular polygons and nested rectangles (lesson 6, problem set 4 and 5). Also consider select exercises from examples and problem sets for each lesson. Use exit ticket from lesson 6 for assessment/bi-weekly #1.

Lesson 7 (P)

Utilizes coordinate plane to find the dimensions of triangles and quadrilaterals; helpful for finding the area of polygons (lesson 8). Reviews absolute value.

Lesson 8 (P)

Utilizes coordinate plane to calculate area by applying distance to find dimensions of various polygons. Also utilizes decomposition to find the areas of pentagons.

Week 3: April 30

Assessment:

Mid-Module: administer before lesson 9

Standards Addressed in Week's Lessons

6.G.A.2

Standards Assessed in Assessments

Mid Module

6.G.A.1

6.G.A.2

6.G.A.3

Notes:

One day provided this week to administer Mid Module assessment.

Lessons 9-10 OMIT

Lesson 9 material is already addressed in lesson 7. Lesson 10 material is already addressed in lesson 6 (which is more rigorous and supports standards more strongly).

Lessons 11 / 12 (Combined) (P)

Provides students opportunities to investigate calculating the volume of cubes with fractional edge lengths. Select exercises from examples and problem sets for each lesson. Use the exit ticket from lesson 12 for assessment.

Lesson 13 (P)

Provides opportunities for students to apply volume to problem solving situations. Connect volume with unit cubes/cubic units.

Lesson 14 (P)

Provides opportunities for students to apply volume to more advanced problem solving situations. Connect volume with unit cubes/cubic units.

Week 4: May 7

Notes:

Lesson 15 (M)

Presents students the opportunity to explore and work with nets (e.g., what net patterns make cubes) and provides net templates for students to manipulate to complete their investigation. Consider reconstructing a cereal box to display in support of the opening exercise.

Lesson 16 (E)

Utilize the cereal box from lesson 15 to demonstrate how dimensions on 3D objects assist in net design. Consider making the net in the opening exercise prior to teaching the lesson, then demonstrate how to design a net from given dimensions. Graph paper will help students with their designs.

Lesson 17 (P)

Provides students with an introduction to finding surface area. Exercises and the problem set provide students opportunities to calculate surface area of nets. Stress the problem solving process of decomposing 3D figures, finding the area of each face, then putting the 3D figure back together (sum of the areas of the faces).

Lesson 18 (P)

Presents the surface area formulas: SA = 2(l)(w) + 2(l)(h) + 2(w)(h) for rectangular prisms and SA = 6s^2 for cubes. Provides students ample practice in computation of surface area. Consider using the exit ticket to assess student understanding.

Standards Addressed in Week's Lessons

6.G.A.2

6.G.A.4

Week 5: May 14

Notes:

Lesson 19 (P)

Provides students the opportunity to complete computation of surface area and volume simultaneously and compare the results. Consider using the exit ticket to assess student understanding.

Lesson 19a OMIT

Lesson repeats computation opportunities completed in lesson 19.

One day provided to administer End of Module assessment.

Lesson 1 (P)

Provides students the opportunity to discuss and formulate their own statistical question such that it yields data. Examples present students with engaging examples on how to implement the data process.

Lessons 2/3 (Combined) (P)

Provides students the opportunity to assemble and analyze data from dot plots. Problem set from lesson 3 presents students ample practice. Consider using the exit ticket from lesson 3 to assess student understanding.

Standards Addressed in Week's Lessons

Topic D

6.G.A.2

6.G.A.4

Topic A

6.SP.A.1

6.SP.A.2

6.SP.B.4

6.SP.B.5

Standards Assessed in Assessments

EOM

6.G.A.1

6.G.A.2

6.G.A.3

Week 6: May 21

Module

Notes:

Lessons 4/5 (Combined) (P)

Students assemble and analyze frequency tables and histograms (lesson 4). Lesson 5 utilizes relative frequency tables and histograms. Select items from each lesson for students to practice. Consider using the exit ticket from lesson 4 as practice since the exit ticket from lesson 5 is utilized as the bi-weekly.

Lesson 6 (P)

Mean discussed in terms of center of data and fair share. Students utilize dot plots and unifix cubes to determine what is the fair share which leads to conceptual understanding of the mean (example 2 and exercises 7-10). Consider using the exit ticket to assess student understanding (provide unifix cubes to support solution process).

Lesson 7 (P)

To demonstrate mean as the center students use rulers and pennies in a balance investigation. Dot plots are incorporated into the investigation. Consider using the exit ticket to assess student understanding.

Lesson 8 (P)

Utilizes dot plots in determining the mean of a set of data. Teacher will need to present the algorithm for computing a mean to students since it is not mentioned in the lesson.

Assessment:

Biweekly #3 after lesson 4 / 5 use exit ticket from lesson 5.

Standards Addressed in Week's Lessons

Topic A

6.SP.A.1

6.SP.A.2

6.SP.B.4

6.SP.B.5

Topic B

6.SP.A.2

6.SP.A.3

6.SP.B.4

6.SP.B.5

Week 7: May 28

Module

Topic

Notes:

Lesson 9 (P)

Presents a formal investigation of variability through the calculation of the Mean Absolute Deviation (MAD) and a visual representation of data using dot plots.

Lessons 10/11 (Combined) (P)

Provides students the opportunity to apply the MAD computations to data sets; continuing to incorporate dot plots into their solutions. Examples and problem sets from each lesson support student learning. Consider using the exit ticket form lesson 11 to assess student understanding.

One day provided to administer Mid Module assessment.

Assessment:

Mid-Module after lesson 10 / 11

Standards Addressed in Week's Lessons

6.SP.A.2

6.SP.A.3

6.SP.B.4

6.SP.B.5

Standards Assessed in Assessments

Mid Module

6.SP.A.2

6.SP.A.3

6.SP.B.4

6.SP.B.5

Week 8: June 4

Module

Notes:

Lesson 12 (P)

Provides students the opportunity to investigate the median (center of a distribution) using dot plots, frequency tables and the median algorithm. Introduction to box plot terms and concepts, quartile and interquartile, that students will utilize in future lessons.

Lesson 13 (P)

Students investigate the IQR (Interquartile Range) of data sets; continues the work they have completed in prior lessons (re: the number of french fries in a bag). Dot plots are utilized to give students a visual representation of where the IQR is. Consider using the exit ticket to assess student understanding.

Lesson 14/16 (Combined) (P)

Students construct box plots on data sets and also analyze completed box plots. Consider using #3 from the problem set in lesson 14 to assess for student learning (replaces exit tickets).

Lesson 15 OMIT

Shares student outcomes with lessons 14 and 16 and is an extension of lesson 14.

Lesson 17 OMIT

Exploration lesson that provides students the opportunity to formulate a statistical question, collect and analyze data in response to that question, and present results. Revisit if time allows.

Lesson 18 (P)

Provides students the opportunity to investigate dot plots and histograms through matching numerical summaries to graphical representations of distributions. Students discuss skewed data and it's impact on analyzing data. Consider using the exit ticket to assess student understanding.

Standards Addressed in Week's Lessons

6.SP.A.2

6.SP.B.4

6.SP.B.5

Week 9: June 11

Assessment:

End-of-Module after Lesson 21

ANet

Standards Addressed in Week's Lessons

6.SP.B.4

6.SP.B.5

Standards Assessed in Assessments

EOM

6.SP.A.1

6.SP.A.2

6.SP.A.3

6.SP.B.4

6.SP.B.5

ANet

Supporting

6.G.A.1

6.G.A.2

6.G.A.3

6.G.A.4

Additional

6.SP.A.1

6.SP.A.2

6.SP.A.3

6.SP.B.4

6.SP.B.5

Review

6.EE.A.2

6.EE.B.7

6.EE.C.9

6.NS.C.7

6.RP.A.3

Notes:

Lesson 19 (P)

Provides students the opportunity to compare data distributions displayed by box plots. Consider using the exit ticket to assess for student understanding.

Lessons 20/21 (Combined) (E)

Given a frequency histogram or a data set, students estimate the values of the mean and mean absolute deviation (MAD) or the median and interquartile range (IQR). Use the exit ticket from lesson 20 to assess for student understanding.

One day provided for to administer end of module assessment.

One day provided to administer ANet test.