preparatory mathematics courses in

English and Spanish.

*Core Connections Algebra**Core Connections Geometry**Core Connections Algebra 2**Core Connections Integrated I, II, III*

for students

Study Teams

eTools for Exploration

Learning Logs

MixedSpaced Practice with Homework Help

Math Notes

Checkpoints

Parent Guide

Lesson Mathcasts for Teachers

Study Teams

- Students work in teams of two or four
- Creates environment for student discussion, sharing of ideas, and articulate their thinking
- Provides security to allow students to take risks to refine their ideas, questions, and approaches

eTools for Exploration

- Activities to build conceptual understanding
- CPM proprietary tools, algebra tiles and integer tiles, and Integrated digital activities

Learning Logs

- Prompts students to reflect on their learning
- Students describe their understanding in their own words
- Provide closure to a lesson or clarification of a concept

MixedSpaced Practice with Homework Help

- Provides students practice with past material
- Lays a foundation for future learning
- Multiple opportunities for students to revisit skills
- Homework help linked from eBook provides support for students’ emerging understanding of new topics
- Includes solved problems, hints to get started, and references to previously solved problems

Math Notes

Core ideas are synthesized in “Math Notes” boxes, placed purposefully, often falling one or more lessons after the initial introduction of a concept. This allows students time to explore and build conceptual understanding of an idea before they are presented with a formal definition, algorithm or summary of a mathematical concept.

Checkpoints

Checkpoints indicate to students where fluency with a skill should occur. Each checkpoint problem has the topic clearly labeled and the solution. Checkpoints also offer examples with detailed explanations, complete solution of the checkpoint problem, and more practice problems with answers included.

Parent Guide

- Alternative explanation of key ideas
- Additional practice problems
- Arranged by chapter and topic
- Includes a brief restatement of the idea, typical examples, practice problems, and the answers to those problems

Lesson Mathcasts for Teachers

- Aide in preparing lessons
- Outlines the lesson problems
- Gives suggestions for facilitating the teams

LEARNING LOG

Write a Learning Log entry to summarize what you learned today about the Giant One and its uses. Include examples of how the Giant One is used. Title this entry “The Giant One and Equivalent Fractions” and label it with today’s date.

LEARNING LOG

Make a rectangle from any number of tiles. Your rectangle must contain at least one of each of the following tiles: x^2, y^2 , x, y and xy. Sketch your rectangle in your Learning Log and write its area as a product and as a sum. Explain how you know that the product and sum are equivalent. Title this entry “Area as a Product and as a Sum” and label it with today’s date.

Problem 6-29

Answers to problem 6-29: a: y=3x−105=35x−2, b: x=y−bm, c: r2=Aπ

Rewriting equations with more than one variable may be done in a variety of ways but normally you follow the same steps as you would for solving an equation with a single variable. Commonly, the first step is to multiply all the terms by a common denominator to remove all of the fractions. Then solve in the usual way. Collect like terms. Isolate the specified variable terms on one side and everything else on the other. Finally, divide or undo the exponent so that the variable is alone. The final answer will be an equation that involves variables and possibly numbers.

**Example 1: **Solve for *y*: 2x+3y−9=0

Solution: 2*x* + 3*y* − 9 = 0

problem

3y=−2x+9

subtract 2x, add 9 on each side

y=−2x+93

3 divide by 3

y=−23x+3

simplify

**Example 2: **Solve for *r*: *V* = 43*πr*^{3}

Solution: *V* = 43*πr*^{3}

problem

3*V* = 4*πr*^{3}

multiply by 3 on each side

3V4π=r3

divide by 4π

3V4π3=r

cube root

Now we can go back and solve the original problems.

−3x+5y=−105y=3x−10 y=3x−105 y=x−2

y=mx+by−b=mx+by−bm=x

A=πr2Aπ=r2

Here are some more to try. Solve each equation for the specified variable.

*2x−3y=9(for x)*

2x−3y=9(for y)

5x+3y=15(for y)

4n=3m−1(for m)

2w+2l=P(for w)

2a+b=c (for a)

I=ER(for R)

y=14x+1(for x)

c2=a2+b2(for b2)

V=s3(for s)

S=4πr2(for r2)

m=a+b+c3(for a)

a3+b=c2(for a)

Fa=m(for a)

A=12h(b1+b2)(for b1)

V=13πr2h(for h)

**Answers:**

x=3y+92

y=2x−93

y=15−5×3

m=4n+13

w=P−2l2

a=c−b2

R=EI

x=4(y−1)

b2=c2−a2

s=V3

r2=S4π

a=3m−b−c

a=c2−b3

a=Fm

b1=2Ah−b2

h=3Vπr2

###### Used throughout CPM middle and high school courses

###### Concrete, geometric representation of algebraic concepts.

###### Two-hour virtual session,

###### Learn how students build their conceptual understanding of simplifying algebraic expressions

###### Solving equations using these tools.

###### Determining perimeter,

###### Combining like terms,

###### Comparing expressions,

###### Solving equations

###### Use an area model to multiply polynomials,

###### Factor quadratics and other polynomials, and

###### Complete the square.

###### Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

In **Building on Equity**, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

In **Building on Assessment**, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

In** Building on Discourse**, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.

Correlations

Correlations