Overview

Module 5 : Statistics and Probability

Students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. Probability provides a foundation for the inferential reasoning developed in the second half of this module.

Topic C: Random sampling and Estimating Population characteristics

Topic D: Comparing Populations

Advanced preparation

- Graphing calculator
- Dot plots
- Histograms

Students delve further into several geometry topics they have been developing over the years. Supporting work for unknown angles began in Grade 4, Module 4 (4.MD.C.5–7) and students learned to solve for a missing angle in a pair of supplementary angles where one angle measurement is known.

Topic B: Constructing Triangles

Topic D: Problems involving area and surface area

Topic E: Problems involving volume

Advanced preparation

- Familiar objects and pictures to begin discussions around cross sections, such as an apple, a car, a couch, a cup, and a guitar
- A site on Annenberg Learner that illustrates cross sections

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 17

Notes:

Lesson 15 (P)

Heavy on random sample activities. Consider prioritizing activities based on exit ticket questions and dot plot activities in problem set.

Lesson 16 (P)

In addition to words in children's books included in the lesson notes, consider completing the activity in lesson 16 with a random digit table website or TI-86 calculator.

Lesson 17 (P)

Students need exposure to random digit table in order to complete exit ticket. Save student work for lesson 18.

Week 2: April 24

Assessment:

Biweekly #1: Exit ticket from lesson 19

Standards Addressed in Week's Lessons

7.SP.1

7.SP.2

7.SP.3

Notes:

Lesson 18 (P)

Emphasize terminology (random sample, dot plot sample means, data points, etc). Also create balance between numerical and pictorial representation of data.

Lesson 19 (P)

Utilizing the bag of cubes provides an opportunity for active data collection and analysis for students.

Lesson 20 (P)

Opportunity to investigate middle school survey responses on the website or utilize own data.

Lesson 21 (P)

Prepare data bags for students to investigate mean. Bring discussion findings forward to lesson 22.

Week 3: May 1

Assessment:

EOM: After Lesson 22

Standards Addressed in Week's Lessons

Topic D

7.SP.3

7.SP.4

Topic A

7.G.5

Standards Assessed in Assessments

EOM

7.SP.1

7.SP.2

7.SP.3

7.SP.4

7.SP.5

7.SP.6

7.SP.7

7.SP.8

Notes:

Lesson 22 (P)

Emphasize how to determine whether the difference between the means of two different populations is meaningful or not as this was the emphasis of lesson 23 that is omitted.

One day provided for administering End of Module 5 assessment.

Lesson 23 Omit

Lesson 23 can be omitted if students are successful with Lesson 22 and understand how to determine whether the difference between the means of two different populations is meaningful or not.

Lesson 1 (P)

Provide students ample practice writing and solving equations. Consider designing and posting anchor charts for tables listed in open exercises and discussion.

Lessons 2 & 3 Combine (P)

Both lessons provide ample practice for students to write and solve equations to calculate missing angle measures. Consider using the exit ticket from lesson 3 to check for student understanding.

Week 4: May 8

Notes:

Lesson 4 (P)

Concludes Topic A (writing and solving equations for missing angle measures). Consider giving the exit ticket for a culminating task to close out this section.

Lesson 5 (S)

Emphasize notations used to denote congruent parts of triangles so students develop a solid understanding on how to manipulate shapes for similarity.

Lesson 6 (Exploration Lesson)

Compass, protractor and ruler needed. Students explore drawing a variety of polygons under given conditions. Model construction.

Lesson 7 (P)

Protractor, ruler and setsquare needed. Students explore drawing a variety of parallelograms. Model construction.

Standards Addressed in Week's Lessons

Topic A

7.G.5

Topic B

7.G.2

Week 5: May 15

Notes:

Lesson 8 (Exploration Lesson)

Protractor and ruler needed. Students explore drawing a variety of triangles under given conditions. Model construction.

Lesson 9 (E)

Protractor and ruler needed. Consider utilizing straws to scaffold for struggling students. Model construction.

Lesson 10 (E)

Patty or parchment paper needed. Consider practicing construction prior to student instruction. Continues discussion around unique triangles begun in lesson 9.

Lesson 11 (E)

Patty or parchment paper needed. Investigation of what conditions must be present to assemble a triangle. Consider giving the exit ticket to reinforce learning and assess for understanding.

Week 6: May 22

Module

Notes:

Lesson 12 (E)

Protractor, ruler and compass needed. Deep dive into unique triangles and inscription in circles.

Lesson 13 & 14 Combine (P)

Identifying similar triangles. Similar to lesson 5; emphasize markings on the sides and angles and their connection to how to match corresponding parts of triangles to determine if they are identical. Consider using the exit ticket from lesson 14 to check for student understanding.

Lesson 15 (P)

Consider a debate style share out around student responses to example 2 and exercises 1-4; students prepare agree or disagree to a question then provide support (i.e., apply what they have learned in lesson 13/14).

One day provided for administering Mid-Module assessment.

Assessment:

Biweekly #3: Use exit ticket from Lesson 12

Mid-Module: After lesson 15

Standards Addressed in Week's Lessons

Topic B

7.G.2

Topic C

7.G.3

Standards Assessed in Assessments

Biweekly #3

7.G.2

Mid-Module

7.G.2

7.G.5

Week 7: May 29

Module

Notes:

Lesson 16 (P)

Consider clear rectangular prisms with size specific rectangular planes for this lesson and/or display rectangular prism drawings that students can manipulate.

Lesson 17 (S)

Consider models of pyramids, preferably clear ones and/or display pyramid drawings that students can manipulate.

Lesson 18 (P)

Drawings and/or 3D figures will support students envision planes inside prisms.

Standards Addressed in Week's Lessons

Topic C

7.G.3

Week 8: June 5

Module

Notes:

Lesson 19 (P)

Consider using unit cubes and grid paper throughout the examples.

Lesson 20 (S)

Utilize area formulas of a variety of polygons. Consider providing graph paper and a drawing for the exit ticket.

Lesson 21 (S)

Utilizes area models and distributive property.

Lesson 22 (P)

Consider providing an anchor chart with visual representation of circumference, area, diameter and radius.

Standards Addressed in Week's Lessons

Topic C

7.G.3

7.G.6

Week 9: June 12

Assessment:

EOM

ANet

Standards Addressed in Week's Lessons

Topics D & E

7.G.6

Standards Assessed in Assessments

EOM

7.G.2

7.G.3

7.G.5

7.G.6

Anet

Major:

7.EE.4

Supporting:

7.SP.1

7.SP.2

Additional:

7.G.2

7.G.3

7.G.5

7.G.6

7.SP.3

7.SP.4

Review:

7.EE.1

7.EE.3

7.EE.4a

7.EE.4b

7.NS.2c

7.RP.2b

7.RP.3

Notes:

Lesson 23 (P)

Consider providing students with manipulatives to assemble 3D figures and guidance in drawing and labeling 3D figures included in student work.

Lesson 24 OMIT

The three-dimensional figures presented throughout Lesson 23 cover the different types of figures outlined in the standards for surface area. If students are successful with Lesson 23, completing Lesson 24 is unnecessary.

Lesson 25 (P)

Explores and compares volumes of modified 3D figures. Providing models of 3D figures may assist students in their understanding and computations.

Lesson 26 (P)

Builds on work completed in lesson 25 to include composite figures. Drawing and labeling figures will be helpful.

One day provided for administering End of Module 6 assessment.