1 of 37

Online Lessons

A set of lessons students enjoy on learn.thinkcerca.com platform.

Student Guide

A guide for note-taking, discussion, collaboration, and extension activities.

Class Presentation

A student-facing presentation you can

edit for a hybrid, fully online, or fully

in-person class.

(blue slides)

Finding and Making Use of Structure in Mathematics

TEACHER GUIDE

2

3 of 37

TEACHER GUIDE

Finding and Making Use of Structure in Mathematics Affine Ciphers
SKILLS FOCUS	CLOSE READING AND WRITING LESSON
SESSION 1 40 minutes	SESSION 2 40 minutes	SESSION 3 40 -80 minutes	SESSION 4 40-80 minutes	SESSION 5 60 minutes
Direct instruction Lesson	Overview and Connect	Read, Check, Analyze and Summarize	Develop / Build	Draft and Review / Create
Build Your Vocabulary Cornell Notes	Find Your Purpose for Learning Share Your Personal Connection	Share Your Reflections Test Prep Strategy Highlight and Annotate Write a Summary	Share Your Argument Builder	Peer Editing Activity Writing Reflection Optional Extensions

Affine Ciphers — Lesson Overview

ThinkCERCA Platform

(Online)

ThinkCERCA Student Guide Tools

(Off-app, optional)

3

Edit this slide to match your plan for delivering the lesson. One suggestion is provided. See more sample schedules here and a detailed description of steps in the slides following the student presentation.

The CERCA slides describe and support the activities for the lesson, split over a skills focus activity and ThinkCERCA’s multi-step process:

The Skills Focus session provides skill and vocabulary building paired with the lesson, preparing students to engage in the reading and writing activity. Teachers can lead students through the activities, or have students collaborate to complete lessons together.
In Connect students make personal connections to themes that will be present in the text. their reflections on the key themes they will explore in the lesson. Then, they generate their own questions that they can explore as they read. This step is critical in social and emotional development and helps to build community.
In Read, Check, Analyze, and Summarize students review the CERCA question. They read closely, answer multiple choice question, and highlight and annotate the text. They also summarize the text.
In Develop / Build, students review the CERCA question and plan drafts based on the evidence they have found in their close reading. Discussion and collaboration throughout this process clarifies thinking and improves support and organization.
In Draft / Create, students write their draft. They’ll find their personal connection could make a great hook, and their summary helps them transition to their claim. Then, they can pull the rest of their work over and use more custom sentence stems to flesh out the rest of the essay!

All activities can be completed asynchronously for hybrid or remote learning.

Coaching Tip: Before you begin, assign the appropriate lessons to your groups. There are a number of student tools suggested along the way. To edit a tool, first make a copy. Then, have your students copy your version of the tool.

4 of 37

What will students know, understand, and be able to do through this lesson?

Knowledge

What an affine cipher is; how to create an affine cipher; how to write, read, and evaluate expressions in which letters stand for numbers.

Understanding

Ciphers are types of codes developed to protect information.

TEACHER GUIDE

Skills

Understand that a function is a rule that assigns to each input exactly one output; identify central ideas in an informational text; describe the process of creating an affine cipher.

Close Reading & Writing: Affine Ciphers

4

5 of 37

What standards will this lesson help students practice?

TEACHER GUIDE

CCSS CCSS.CONTENT.8.F.A.1; CCSS.PRACTICE.MP.7	BLOOM BLOOM.2.5; BLOOM.2.4; BLOOM.2.1

TEKS TEKS.MATH.8.5(G); TEKS.MATH.8.1(E)	CASEL Framework NA

BEST BEST.MA.8.F.1; BEST.MA.K12.MTR.5.1	Learning for Justice Social Justice Standards NA

5

6 of 37

Affine Ciphers

Encode a secret message of at least 10 letters using an affine cipher. Then, explain how to decode the cipher.

7 of 37

Affine Ciphers

Encode a secret message of at least 10 letters using an affine cipher. Then, explain how to decode the cipher.

Date	Focus/Step	On ThinkCERCA (Online)	Student Guide
X/XX	Build Your Vocabulary Direct Instruction	Complete the Direct Instruction lesson and check your comprehension	Build Your Vocabulary Direct Instruction Cornell Notes
X/XX	Overview and Connect	Read the Topic Overview; Write a brief personal reflection in Connect	Find Your Purpose for Learning Share Your Personal Connection
X/XX	Read and Check	Complete a close reading and answer the multiple choice questions	Pause and Reflect Test Prep Strategy (optional)
X/XX	Analyze / Engage with the Text	Analyze / Engage with the Text	Highlight and Annotate
X/XX	Summarize	Summarize the Reading	Write a Summary
X/XX	Develop / Build	Develop your claim, evidence, and reasoning	Collaborate: Share your argument builder
X/XX	Draft and Review / Create	Complete final draft	Peer Editing Activity�Reflect on Your Writing
X/XX	Extension Activities		Inquiry to Research: Code Talkers (optional) Inquiry to Research (optional) Roundtable Discussion (optional)

7

8 of 37

SKILLS FOCUS

Vocabulary Building and Direct Instruction

Student Guide

Complete Build Your Vocabulary
Complete Cornell Notes: Finding and Making Use of Structure in Mathematics

learn.thinkcerca.com

Complete “Finding and Making Use of Structure in Mathematics” lesson
Check Your Comprehension

8

Talking Point: As we begin our study, we’ll start with a focus on skills and vocabulary that will be important to the upcoming reading and writing activities.

Coaching Tip: Plan to collect answers from students and record them on a shared copy of the of the Cornell Notes and Vocabulary activities. These can be used for later reference as a digital anchor chart and provided for diverse learners who need additional support.

Vocabulary Activity:

Coaching Tip: Students will 15-20 minutes to explore a key conceptual term that will help them deepen their exploration and interpretation of the reading selection.

Introduce the idea that key words will be important as they read, discuss, and write about the selection.

As students complete the Vocabulary Activity for their selected words, they can work alone, in pairs, or small groups. As time permits have groups share out their findings.

Direct Instruction:

Synchronous Delivery (30-40 minutes)

Coaching Tip: Students will need at least 15 minutes to complete the audio-supported lesson independently.

Provide the Cornell Notes activity from the student guide for students to take notes.

You’ll need to make your own copy of the organizer if you want to further tailor it to your students’ needs.

Gradual Release of Responsibility Model:

I Do It: You can project the lesson and the organizer and complete the first part of the graphic organizer with the first 3 slides.
We Do It: Have students work with you to complete the next three slides, taking notes in the organizer.
You Do It Together: Have students work in pairs or small groups to complete the rest of the lesson.
You Do It Alone: Individually, each student summarizes their learning and completes the quiz in ThinkCERCA.

Asynchronous Model:

You Do It Alone: Whether you introduce the lesson in a brief in class overview or not, individually, each student can review the lesson with audio support, summarize their learning, and complete the comprehension check in ThinkCERCA.

9 of 37

Fill in the boxes to map a vocabulary word from the reading.

VOCABULARY BUILDING

Map a Word

9

10 of 37

Take notes on the Direct Instruction lesson online, and practice finding and making use of structure in mathematics.

DIRECT INSTRUCTION GUIDE

Cornell Notes: Finding and Making Use of Structure in Mathematics

10

11 of 37

CLOSE READING AND WRITING

Overview and Connect

Student Guide

Complete Find Your Purpose for Learning
Complete Share Your Personal Connection

learn.thinkcerca.com

Read Topic Overview
Complete Connect Quick Write

11

Talking Point: Have students read the Overview and complete the Finding Your Purpose for Learning reflection in the Student Guide. You’ll need to make your own copy of the Student Guide if you want to further tailor the document to your students’ needs and create a class master copy to use with diverse learners who may require note-taking accommodations.

Consider giving students 10 minutes to share and collaborate before you bring the whole class together for a discussion.

Have students complete the Connect Quick Write, then complete Share Your Personal Connection in the student guide.

Talking Point: Engaging with text is really all about connecting text to one’s self, to others, and to the world. As we continue to build our community of learning together, it’s important to take time to learn more about each other and discover your own purpose for learning. Complete the Connect step of the lesson. Pair with another to share your experiences and use the Share Your Personal Connection worksheet to support your collaboration.

Optional Extension: The Ask Questions of Text extension activity helps students generate questions before reading the text. You can model the process with them using the Gradual Release of Responsibility Model.

Gradual Release of Responsibility Model:

I Do It: You can share questions you have about the essay, the author, etc.
We Do It: Have students work with you to generate a list of questions, taking notes in the organizer.
You Do It: Together: Have students work in pairs or small groups to generate more questions together.
You Do It: Alone: Individually, have each student generate questions.

12 of 37

Read the “Topic Overview”
Answer the questions on the page.

OVERVIEW

Find Your Purpose for Learning

12

13 of 37

Follow the instructions on the page to complete the quick writing activity. Then, pair and share with a peer.
Reflect on your conversation.

CONNECT

Share Your Personal Connection

13

14 of 37

CLOSE READING AND WRITING

Read and Check

Student Guide

Complete Share Your Reflections
Complete Test Prep Strategy (optional)

learn.thinkcerca.com

Read (with audio support and in-text vocab)
Answer multiple-choice questions

14

Talking Point: Students will need at least 30 minutes to complete the reading. “Pause and Reflect” Questions appear throughout the text. Students can use the annotation tool to write answers to these questions. You may choose to have students work together and to collaborate in discussion around the Pause and Reflect prompts using the Student Guide. Each of these questions is designed to help students make disciplinary and personal connections to the text.

To incorporate test preparation into your everyday great instruction, you can ask students to complete an activity to help them acquire test-taking skills. See the Student Guide for the specific activity.

Asynchronous Model:

Preview the reading with students, pointing out the “Pause and Reflect” questions. Encourage students to read independently at their own pace and to use the annotation tools to actively read and respond to the questions.

15 of 37

Follow the instructions on the page to read and answer Pause and Reflect questions.
Record and share reflections connecting the text to self, to other texts, and to the world.

READ

Share Your Reflections

15

16 of 37

Follow the instructions on the page to reflect on your multiple choice answers.

CHECK

Test Prep Strategy (optional)

16

17 of 37

CLOSE READING AND WRITING

Analyze / Engage with the Text

Student Guide

Complete Highlight and Annotate

learn.thinkcerca.com

Analyze / Engage with the Text

17

Coaching Note: If students are learning highlighting, annotation, and other disciplinary literacy strategies for the first time, they can benefit from many times “at-bat,” and the modeling and guidance that the gradual release of responsibility model provides. Here is a sample script of what that might look like.

Gradual Release of Responsibility Model:

I Do It: Project the reading. Follow the highlighting and annotation prompts in the first paragraph, providing a think-aloud that explains why you are selecting a piece of the text and what you think when you read it. “I am highlighting ...;” “I am going to add a note that explains that...makes me think...,” etc.
We Do It: Have students work with you to complete the next paragraph, taking notes in the text in the teacher preview.
You Do It Together: Have students work in pairs or small groups to complete the next several paragraphs or the rest of the lesson.
You Do It Alone (options): Students can continue highlighting and annotating for the last several paragraphs.

Asynchronous Model:

You Do It Alone (options): After observing teacher modeling, students can independently highlight and annotate the remainder of the text.

Alternatively, after highlighting, each student can demonstrate their own achievement by summarizing the reading. If they haven’t already completed it, they can also complete the quiz in Check in ThinkCERCA.

18 of 37

Follow the instructions to closely analyze the text to find evidence for your writing.

ANALYZE / ENGAGE WITH THE TEXT

Highlight and Annotate

18

19 of 37

CLOSE READING AND WRITING

Summarize

Student Guide

Complete Write a Summary

learn.thinkcerca.com

Summarize the Reading

19

20 of 37

Follow the instructions to complete the Summarize step.

SUMMARIZE

Write a Summary

20

21 of 37

CLOSE READING AND WRITING

Develop / Build

Student Guide

Complete Collaborate: Share your Argument Builder

learn.thinkcerca.com

Develop / Build Your Argument

21

Talking Point: The planning step involves a solo or collaborative experience of outlining an argument. Developing a draft claim is the first step. Students then support the claim with reasons, and provide evidence to support their reasoning. After students present a supporting reason+evidence, they should also include an explanation of how the evidence links back to the reason, making their thinking visible. Together the reason-evidence-reasoning sandwiches make up the supporting paragraphs in an argument.

Gradual Release of Responsibility Model:

I Do It: Project the argument-builder step in the teacher preview. Show the claim stem in the Claim box.
We Do It: Have students work with you to complete the sample claim stem. Then ask contributors to improve the claim by making it more specific or general as needed, and encourage students to use more formal language to capture the specific and debatable ideas they have.
You Do It Together: Have students work in pairs or small groups to complete the rest of the argument building or the rest of the lesson, analyzing the major ideas of the text and the details the author uses to support them. Remind students they can arrange and rearrange the argument as they go. Encourage students to test their ideas and share throughout the drafting process.
You Do It Alone (options): Students can refine their final argument during the actual formal drafting step in the lesson.

22 of 37

Follow the instructions online to begin building your argument.
Use the activity to collaborate with others to share reasons, evidence, and reasoning.

DEVELOP / BUILD

Share your Argument Builder

22

23 of 37

CLOSE READING AND WRITING

Draft and Review / Create

Student Guide

Complete Peer Editing Activity
Complete Reflect on Your Writing

learn.thinkcerca.com

Draft / Create
Review / Self-Assess using the Rubric

23

Talking Point: The final step involves creating a complete draft. Student will drop their argument builder outlines into the draft space and use sentence starters to fully flesh out the ideas of their more formal piece of writing.

Gradual Release of Responsibility Model:

I Do It: Project the contents of an argument-builder step in the teacher preview. Drop the outline into the text box. Model how you move from a single statement to a full introduction. You might begin by using the personal connect as a hook and the summary as a transition in order to develop an introduction with significance and a strong claim. Show students how to build the argument’s support using the reason->evidence->reasoning approach, so each point is stated in the reason, supported by evidence, and has a reasoning statement that links the evidence to the overall paragraph and/or argument.
We Do It: Have students work with you to complete an introduction and or a support together.
You Do It Together: Have students work in pairs or small groups to complete another supporting section.. Encourage students to test their ideas and share throughout the drafting process.
You Do It Alone (options): Students can refine their final argument on their own before engaging in peer editing.

24 of 37

Follow the instructions to Create your CERCA.
Evaluate your work using the rubric.
Discuss your work with peers.
Revise your piece.

DRAFT AND REVIEW / CREATE

Peer Editing Activity

24

25 of 37

Follow the prompts to reflect on your writing experience.

DRAFT AND REVIEW / CREATE

Reflect on Your Writing

25

26 of 37

CLOSE READING AND WRITING

Extension Activities

Student Guide

Inquiry to Research: Code Talkers
Inquiry to Research
Roundtable Discussion

learn.thinkcerca.com

NA

26

27 of 37

Use the research activity to dig deeper into a related subject or to ask questions of the topic at hand.

OPTIONAL EXTENSION : INQUIRY TO RESEARCH

Research: Code Talkers

27

28 of 37

Discover how asking questions about author, audience, context, and concepts can lead to greater understanding of a text. This will help you become a critical consumer of information.

OPTIONAL EXTENSION : INQUIRY TO RESEARCH

Ask Questions of the Texts

28

29 of 37

Use the two-part handout to research a topic and prepare to contribute to a roundtable discussion

OPTIONAL EXTENSION : ROUNDTABLE DISCUSSION

Roundtable Discussion

29

30 of 37

Visual Teacher’s Guide

What does a day and a week look like?

30

31 of 37

TEACHER GUIDE

SKILLS FOCUS

Session 1: Direct Instruction and Vocabulary

Purpose: The Skills Focus session provides skill and vocabulary building paired with the lesson, preparing students to engage in the reading and writing activity.

Teacher introduces lesson
Students complete Build Your Vocabulary Activity
Students complete Direct Instruction Lesson (Online)
Students complete Cornell Notes Activity (Student Guide)
Whole class review

In This Session

Finding and Making Use of Structure in Mathematics

Delivery: Synchronous or Asynchronous. See notes below.

Time: ~30-45 min

31

Talking Point: As we begin our study, we’ll start with a focus on skills and vocabulary that will be important to the upcoming reading and writing activity.

Coaching Tip: Plan to collect answers from students and record them on a shared copy of the of the Cornell Notes and Vocabulary activities. These can be used for later reference as a digital anchor chart and provided for diverse learners who need additional support.

Vocabulary Activity:

Coaching Tip: Students will have 15-20 minutes to explore a key conceptual term that will help them deepen their exploration and interpretation of the reading selection.

Introduce the idea that key words will be important as they read, discuss, and write about the selection.

As students complete the Vocabulary Activity for their selected words, they can work alone, in pairs, or small groups. As time permits, have groups share out their findings.

Direct Instruction:

Synchronous Delivery (30-40 minutes)

Coaching Tip: Students will need at least 15 minutes to complete the audio-supported lesson independently.

Provide the Cornell Notes activity from the student guide for students to take notes.

You’ll need to make your own copy of the organizer if you want to further tailor it to your students’ needs.

Gradual Release of Responsibility Model:

I Do It: You can project the lesson and the organizer and complete the first part of the graphic organizer with the first 3 slides.
We Do It: Have students work with you to complete the next three slides, taking notes in the organizer.
You Do It Together: Have students work in pairs or small groups to complete the rest of the lesson.
You Do It Alone: Individually, each student summarizes their learning and completes the quiz in ThinkCERCA.

Asynchronous Model:

You Do It Alone: Whether you introduce the lesson in a brief in class overview or not, individually, each student can review the lesson with audio support, summarize their learning, and complete the comprehension check in ThinkCERCA.

32 of 37

TEACHER GUIDE

CLOSE READING AND WRITING

Session 2: Overview and Connect

Purpose: Students read the Overview to build background knowledge. In Connect, they make personal connections to key themes in the lesson, helping them find their purpose for learning.

In This Session

Time: ~30-40 min

Teacher introduces the lesson
Students read the Overview (Online)
Students complete Find Your Purpose for Learning (Student Guide)
Students complete Connect (Online)
Students complete Share Your Personal Connection reflection (Student Guide)

Affine Ciphers

Delivery: Synchronous preferred. See notes below.

32

Talking Point: Engaging with text is really all about connecting text to one’s self, to others, and to the world. As we continue to build our community of learning together, it’s important to take time to learn more about each other and discover your own purpose for learning. First, you’ll read the Overview and find your purpose for learning. Then, you’ll complete the Connect step of the lesson. Then you’ll pair with another student to share your experiences. Use the Share Your Personal Connection worksheet to support your collaboration.

Coaching Notes: The time you spend on community building is time invested in student engagement and social and emotional learning. We strongly encourage you to do both of these steps, as research shows that determining your own purpose of learning and Think-Pair-Share are research-based best practices that increase student achievement.

Overview and Find Your Purpose Activity:

Have students read the Overview and complete Find Your Purpose for Learning in the Student Guide. You’ll need to make your own copy of the Student Guide if you want to further tailor the document to your students’ needs or create a class master copy to use with diverse learners who may require note-taking accommodations.

Connect and Share Your Personal Connection Activity:

Coaching Tip: Provide the Student Guide after this Connect step has been completed. Students will need at least 5-10 minutes to begin the Think-Pair-Share. An optional whole class debrief is a great way to set up a focus on themes and allow you to transition into the reading.

33 of 37

TEACHER GUIDE

CLOSE READING AND WRITING

Session 3: Read, Check, Analyze, and Summarize

Purpose: Students encounter the CERCA question. They Read closely and Check their comprehension. Then they Analyze and Summarize the text to think critically and deepen learning.

In This Session

Time: ~40-80 min

Teacher previews the reading
Students Read the selection (Online)
Students review Pause and Reflect (Online) and complete Share Your Reflections (SG)
Students complete the Check section (Online)
Students complete Analyze (Online and SG)
Students complete Summarize (Online and SG)

Affine Ciphers

Delivery: Primarily Asynchronous. See notes below.

33

Talking Point: The reading, highlighting and annotating and summarizing steps are all about deepening learning and critical thinking. Needless to say, there are many great opportunities to practice comprehension and disciplinary literacy skills. Some teachers have students wait to answer MCQs until after the analysis step or Summarize.

Asynchronous Model:

Preview the essay with students, pointing out the “Pause and Reflect” questions. Encourage students to independently read the essay at their own pace and to use the annotation tools to actively read and respond to the questions.
Students will need at least 30 minutes to complete the reading.
Students can use the annotation tool to write answers to these questions. You may choose to have students work together and to collaborate in discussion around the Pause and Reflect prompts using the Student Guide. Each of these questions is designed to help students make disciplinary and personal connections to the text.

Additional Learning: To incorporate test preparation into your everyday great instruction, you can ask students to complete an activity in which they predict the correct response. See Test Prep Strategy in the Student Guide.

34 of 37

TEACHER GUIDE

CLOSE READING AND WRITING

Session 4: Develop / Build

Purpose: In the Develop / Build step, students review the CERCA question and build an argument using evidence from the reading. Discussion clarifies thinking and improves support and organization.

In This Session

Time: ~40-80 min

Teacher introduces the session
Students complete Develop / Build step (Online)
Students complete Share Your Argument Builder (SG)

Affine Ciphers

Delivery: Synchronous or Asynchronous. See notes below.

34

Talking Point: At this point, students can begin planning their own essay. The argument builder in Develop / Build prompts students to make a claim in response to the writing prompt. Students then use the tool to assemble reasons, evidence, reasoning, and counterarguments.

Delivery Options:

Have students discuss their drafts. There are several possible options.

Have students collaborate to find evidence.
Have students work independently for 15 minutes or more, then pair up to compare.
Have students generate at least one counterargument for each other to encourage discussion and critical thinking. You can determine later when or not you want students to include the counterargument in their final piece.

Additional Learning:

Throughout this process chatting with peers will allow them to test their thoughts, challenge each other to consider alternative viewpoints, and engage in the deeper learning that is the hallmark of critical thinking. You may want your students to research additional sources. Use the Inquiry to Research extension activity handout to delve deeper.

35 of 37

TEACHER GUIDE

CLOSE READING AND WRITING

Session 5: Draft and Review / Create

Purpose: Students pull their work from the previous step into a Draft, adding an introduction and conclusion to complete their writing. Peer Editing and teacher feedback help with revision.

In This Session

Time: ~60 min

Teacher introduces the session
Students complete Draft / Create step (Online)
Students Review draft using writing checklist (online)
Students collaborate through Peer Editing Activity (SG)
Students revise using feedback received (Online)
Students Reflect on Writing (SG)

Affine Ciphers

Delivery: Synchronous or Asynchronous. See notes below.