Connected Mathematics Project 3 : Differentiating … · Look for links in both Teacher Place and Student Place to digital math ... Share graphics or text that you add to ... Connected

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Differentiating Instruction

Introduction

Planning for Differentiation

This guide explores the features of Connected Mathematics Project 3 (CMP3) which you can use to personalize and differentiate instruction for your students.

It also examines how to support differentiated learning during the Launch, Explore, and Summarize phases.

This guide discovers how CMP3 resources help you identify and address the learning needs of all students in your classroom.

Use the information in the Mathematics Background, Unit Overview, and Investigation Overview sections to begin thinking about how you will differentiate your instruction.

These resources help you understand how the Problems in an Investigation and Unit create a progression that develops key mathematical concepts.

Keep these overarching connections in mind as you plan each lesson.


Problem Overview

Look to the Problem Overview found in your Teacher’s Guide or online on Teacher Place for more specific suggestions about how students can work during a Problem.

Once you have read the Problem Overview, solve the Problem for yourself.

Try to solve it with as many mathematically sound methods as possible. Anticipate incorrect methods that students may try to use. Ensure that you use as many representations as possible. That is, use graphs, symbols, pictures, diagrams, words, numeric patterns, and tables in your solution. Identify questions for each method that will help students work toward solutions in their own way.

Anticipating students’ thinking provides you with insight as to how you can prompt them to make connections between different strategies and concepts. Combine your work with the suggestions in the program’s resources to determine how you can differentiate your instruction.


Cooperative Groups

Resources

Find suggested grouping strategies in the Problem Implementation section. It is important to be thoughtful and purposeful when you determine the groups in your classroom. Arrange your students so that they work with partners with whom they can collaborate productively as they approach Problems together.

Whether students work in partners or small groups, make sure that all students, especially those with special needs, can be active participants in their groups. Consider both your students’ academic strengths and their personalities.

Well-chosen cooperative groups can make even tough mathematical concepts accessible to English language learners and other students with special needs.

Locate the Labsheets and Teaching Aids in the Problem Implementation section. Note that some are labeled with the word “accessibility.” Provide these resources to students who may need more scaffolding as they work through a specific Problem.

Supplement these prepared resources with other guides that you may make to offer students more support when they need it. Expect students to use more scaffolds like these at the beginning of a course, and help your students eventually progress to a point where they feel more confident working without scaffolds.


Launch

Explore

Launch the day’s Problem in a way that best meets yours students’ needs. Many Problems are accompanied by a Launch video, which can help set the tone of the lesson.

Find ideas for how to connect the day’s Problem to your students’ prior knowledge in the Launch section. Draw on your students’ experiences with previous Problems and Investigations to help all students access the ideas in the upcoming Problem.

Use the suggested questions and content information to help address different levels of understanding in your classroom.

Support all learners during the Launch phase by having your students make a list of the tools, models, or strategies that they think they might use in the Problem. With this scaffold, all students practice making sense of the Problems and planning how to solve them. Remove the formal requirement to create this list as students become more confident, independent problem solvers.

Differentiate during the Explore phase by tailoring your questions to your students’ needs. Consider how the Explore phase gives you the opportunity to differentiate.

Find suggestions in Providing for Individual Needs for ways to make the Problem’s mathematical concepts accessible to all students. Note any descriptions of misconceptions or under-developed strategies that your students may be using.

Observe individual differences in how your students approach the Problem.

Use the individual observations to question each student and help guide his or her thinking.

Find suggested questions in this section that can clarify a situation or redirect students to a more fruitful strategy. Combine those with questions that you identified as you planned for the Problem.


Manipulatives and Tools

Provide extra challenges to students who are ready to extend their thinking. Look to the Going Further section for ideas about how to pose questions that will challenge students to develop deeper understandings of the concepts.

Encourage all students to use appropriate manipulatives and tools as they work during the Explore phase. Prepare manipulatives, labsheets, or teaching aids in advance for students who may benefit from extra scaffolding.

Use the suggestions in Teacher Place for ideas about the kinds of manipulatives that are appropriate for each Problem. Look for links in both Teacher Place and Student Place to digital math tools that can help your students visualize the concepts that they explore.

Understand the beneficial role that calculators and technology can play in the math classroom. Allow students to use tools to make computation easier, and let them focus on conceptual understanding. For example, the Expression Calculator tool is a scientific calculator. The Coordinate Grapher and Data and Graphs tools provide students with many functions that a standard graphing calculator would.

These tools are ideal options for students who do not have their own calculators but can log in to Student Place.


Summarize

Practice

Assessment

Reach all learners during the Summarize phase by sequencing the presentation of their work purposefully.

Choose an order that will help everyone in the class build to a more sophisticated level of understanding, regardless of where their understanding began.

Give all students the opportunity to participate in the Summarize discussion. Encourage students to respond to each other to increase thoughtful interaction.

Find opportunities for students who may have struggled with the concepts to present when they have correct answers or strategies that the class will benefit from hearing.

As you observe the variety of strategies that your students use to solve a Problem during the Explore phase, look for different representations of the solution.

Use the variety of CMP3’s practice and assessment resources to differentiate instruction beyond a lesson.

Vary the Applications, Connections, Extensions (ACE) exercises that you assign to students to better meet their individual needs for practice. If your students use the ACTIVe-book, use the Assign feature to assign more, fewer, or different sets of exercises to different students.

Share graphics or text that you add to your ACTIVe-book to provide scaffolded support for individual exercises. Choose to make these supports available to entire classes or individual students.

Take advantage of the many different assessment options that are available in CMP3.

Use the Check Ups and Partner Quizzes to assess students’ understanding after they complete Investigations. Partner Quizzes allow students to feel support by working with a peer. Follow the suggested procedure for Partner Quizzes, which you can find in A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching.


Allow partners to submit their quizzes for feedback. Have partners resubmit the quizzes for a final grade after they address the individualized comments that you provide.

Give students a chance to demonstrate their knowledge in nonstandard ways. Have students complete Mathematical Reflections, Self Assessments, or Unit Projects to supplement traditional assessments like the Unit Test.

Find additional information about all of these features and even more support for differentiation in A Guide to Connected Mathematics 3: Understanding, Implementing, and Teaching.

This guide explained the features of CMP3, which you can use to personalize and differentiate instruction for your students.

It also examined how to support differentiated learning during the Launch, Explore, and Summarize phases.

Finally, this guide discovered how CMP3 resources help you identify and address the learning needs of all students in your classroom.

Review

Connected Mathematics Project 3 : Differentiating … · Look for links in both Teacher Place and Student Place to digital math ... Share graphics or text that you add to ... Connected

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