Middle School Math Curriculum that Centers Student Problem Solving
• Meaningful Mathematics
• Multimodal program utilizing both digital & print materials
• Dynamic teacher-guided pacing technology
• Intentional mix of digital, print, and manipulatives
• Consumable student book called the Mathematician’s Notebook
• CPM’s time-tested program
• Based on research & CPM’s Three Pillars
• Option of digital and/or print materials
• English and Spanish
• A support class for students who sometimes struggle with mathematics
• Students should be concurrently enrolled in Core Connections, Course 3
• Designed to have:
• No grading
• No homework
• No summative assessments
What does a full blend of print and digital look like? In this multimodal series, digital and print materials work in tandem to maximize student engagement. The choice of medium for each aspect of a lesson is based on how and where students learn best.
A personal notebook where students record the messy work of learning as they highlight key concepts, questions, rough draft thinking, mistakes, corrections, and their inspirations. Diagrams and graphs are included for students to work with, and plenty of space is provided to give students room for error and experimentation.
Concise goals for each lesson are presented to the teacher and to students in the chapter introductions, referenced in the Reflection & Practice problems, and revisited in Chapter Closures. The Mathematician’s Notebook contains a printed copy of the Learning Targets where students can keep track of their progress throughout the course.
Problems are designed to facilitate student learning per the learning intent. To maximize student sensemaking and engagement, lessons have been intentionally constructed using a variety of Venues for student work, such as vertical non-permanent surfaces, external links, embedded technology-enhanced activities, and the Mathematician’s Notebook.
Here are examples of different venues:
Inspiring Connections guides teachers through lessons.
The authors describe how they envision the lesson progressing. These notes are summarized into brief descriptions, which can serve as a reminder after reading the full Authors’ Vision.
The Lesson at a Glance provides a quick orientation to the lesson. It lists things to consider as you begin to prepare to teach the lesson: the overview, learning intent, materials needed for the lesson, aligning standards, and additional resources.
Lessons are designed for students to work in teams during a 45-minute period.
Students collaborate in teams for the large majority of class time. As a means to help all students have a voice and be an integral part of their team, four roles are presented in the Prelude and referred to throughout the curriculum. The roles are Representative, Coordinator, Organizer, and Investigator.
A variety of Study Team and Teaching Strategies (STTS) are suggested in the Authors’ Vision throughout Inspiring Connections. These strategies may be used to help structure team interactions and facilitate engagement. As you gain experience with the curriculum and your students, you will likely develop your own favorite strategies to use regularly.
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0.1.1
Who are my classmates?
0.1.2
How do I work collaboratively?
0.1.3
What questions can I ask?
0.1.4
How can I categorize my words?
0.1.5
How can I communicate my ideas?
0.1.6
How can the team build this together?
0.1.7
What do we need to work togethe
Where do these numbers belong on this line?
1.1.3
How can I use two lines to solve problems?
1.1.4
How can data be used to answer a question?
1.1.5
How are histograms helpful?
1.1.6
How else can data be displayed?
1.2
Shapes and Area,
1.2.1
How can I write equivalent expressions in area and perimeter?
1.2.2
What shapes make up the polygon?
1.2.3
How can I make it a rectangle?
| Opening | 3.OP | Chapter Opening |
|---|---|---|
| Section 3.1 | 3.1.1 | Using the Multiplicative Identity |
| 3.1.2 | Portions as Percents | |
| 3.1.3 | Connecting Percents with Decimals and Fractions | |
| 3.1.4 | Multiple Representations of a Portion | |
| 3.1.5 | Completing the Web | |
| 3.1.6 | Investigating Ratios | |
| Section 3.2 | 3.2.1 | Addition, Subtraction, and Opposites |
| 3.2.2 | Locating Negative Numbers | |
| 3.2.3 | Absolute Value | |
| 3.2.4 | Length on a Coordinate Graph | |
| Closure | 3.CL | Chapter Closure |
| Opening | 4.OP | Chapter Opening |
|---|---|---|
| Section 4.1 | 4.1.1 | Introduction to Variables |
| 4.1.2 | Writing Equivalent Expressions | |
| 4.1.3 | Using Variables to Generalize | |
| Section 4.2 | 4.2.1 | Enlarging Two-Dimensional Shapes |
| 4.2.2 | Enlarging and Reducing Figures | |
| 4.2.3 | Enlargement and Reduction Ratios | |
| 4.2.4 | Ratios in Other Situations | |
| Closure | 4.CL | Chapter Closure |
| Opening | 5.OP | Chapter Opening |
|---|---|---|
| Section 5.1 | 5.1.1 | Representing Fraction Multiplication |
| 5.1.2 | Describing Parts of Parts | |
| 5.1.3 | Calculating Parts of Parts | |
| 5.1.4 | Multiplying Mixed Numbers | |
| Section 5.2 | 5.2.1 | Making Sense of Decimal Multiplication |
| 5.2.2 | Fraction Multiplication Number Sense | |
| Section 5.3 | 5.3.1 | Rearranging Areas |
| 5.3.2 | Area of a Parallelogram | |
| 5.3.3 | Area of a Triangle | |
| 5.3.4 | Area of a Trapezoid | |
| Closure | 5.CL | Chapter Closure |
| Section 5.4 | Mid-Course Reflection Activities |
| Opening | 6.OP | Chapter Opening |
|---|---|---|
| Section 6.1 | 6.1.1 | Dividing |
| 6.1.2 | Fractions as Division Problems | |
| 6.1.3 | Problem Solving with Division | |
| 6.1.4 | Solving Problems Involving Fraction Division | |
| Section 6.2 | 6.2.1 | Order of Operations |
| 6.2.2 | Area of a Rectangular Shape | |
| 6.2.3 | Naming Perimeters of Algebra Tiles | |
| 6.2.4 | Combining Like Terms | |
| 6.2.5 | Evaluating Algebraic Expressions | |
| Closure | 6.CL | Chapter Closure |
| Opening | 7.OP | Chapter Opening |
|---|---|---|
| Section 7.1 | 7.1.1 | Comparing Rates |
| 7.1.2 | Comparing Rates with Tables and Graphs | |
| 7.1.3 | Unit Rates | |
| Section 7.2 | 7.2.1 | Analyzing Strategies for Dividing Fractions |
| 7.2.2 | Another Strategy for Division | |
| 7.2.3 | Division with Fractions and Decimals | |
| 7.2.4 | Fraction Division as Ratios | |
| Section 7.3 | 7.3.1 | Inverse Operations |
| 7.3.2 | Distributive Property | |
| 7.3.3 | Distributive Property and Expressions Vocabulary | |
| 7.3.4 | Writing Algebraic Equations and Inequalities | |
| Closure | 7.CL | Chapter Closure |
| Opening | 8.OP | Chapter Opening |
|---|---|---|
| Section 8.1 | 8.1.1 | Measures of Central Tendency |
| 8.1.2 | Choosing Mean or Median | |
| 8.1.3 | Shape and Spread | |
| 8.1.4 | Box Plots and Interquartile Range | |
| 8.1.5 | Comparing and Choosing Representations | |
| Section 8.2 | 8.2.1 | Statistical Questions |
| Section 8.3 | 8.3.1 | Writing Multiplication Equations |
| 8.3.2 | Distance, Rate, and Time | |
| 8.3.3 | Unit Conversion | |
| Closure | 8.CL | Chapter Closure |
| Opening | 9.OP | Chapter Opening |
|---|---|---|
| Section 9.1 | 9.1.1 | Volume of a Rectangular Prism |
| 9.1.2 | Nets and Surface Area | |
| Section 9.2 | 9.2.1 | Multiplicative Growth and Percents |
| 9.2.2 | Composition and Decomposition of Percents | |
| 9.2.3 | Percent Discounts | |
| 9.2.4 | Simple Interest and Tips | |
| Closure | 9.CL | Chapter Closure |
| Section 9.3 | 9.3.1 | A Culminating Portions Challenge |
| 9.3.2 | Representing and Predicting Patterns | |
| 9.3.3 | Analyzing Data to Identify a Trend |
CP 1: Using Place Value to Round and Compare Decimals
CP 2: Addition and Subtraction of Decimals
CP 3: Addition and Subtraction of Fractions
CP 4: Addition and Subtraction of Mixed Numbers
CP 5: Multiple Representations of Portions
P 6: Locating Points on a Number Line and on a Coordinate Graph
CP 7A: Multiplication of Fractions and Decimals
CP 7B: Area and Perimeter of Quadrilaterals and Triangles
CP 8A: Rewriting and Evaluating Variable Expressions
CP 8B: Division of Fractions and Decimals
CP 9A: Displays of Data: Histograms and Box Plots
CP 9B: Solving One-Step Equations
10.1 | Two Dimensions | |
| 10.1.1 | What can I do with coordinates? |
| 10.1.2 | How can I use mathematics to create art? |
| 10.1.3 | What is the distance from here to there? |
10.2 | Three Dimensions | |
| 10.2.1 | How can I make this? |
| 10.2.2 | How can three-dimensional objects be unfolded? |
| 10.2.3 | How much material do I need? |
| 10.2.4 | How much does it hold? |
| 10.2.5 | How much cash can you stash? |
| 10.2.6 | How are volume and surface area used? |
10.3 | More Data | |
| 10.3.1 | How far away are the data points? |
| 10.3.2 | How else can I measure spread? |
| 10.3.3 | What do I know about data? |
11.1 | Ratios and Proportions | |
| 11.1.1 | How much food is there? |
| 11.1.2 | How much do we need? |
| 11.1.3 | How much is that? |
| 11.1.4 | How can I redesign the classroom? |
11.2 | The Number System | |
| 11.2.1 | Can I determine all the right measurements? |
| 11.23.2 | How can I show my understanding? |
11.3 | Expressions and Equations | |
| 11.3.1 | How can I effectively communicate with my robot? |
| 11.3.2 | How can I use data to help make decisions? |
| Opening | 1.OP | Chapter Opening |
|---|---|---|
| Section 1.1 | 1.1.1 | Visualizing Information |
| 1.1.2 | Perimeter and Area Relationships | |
| 1.1.3 | Describing and Extending Patterns | |
| 1.1.4 | Representing Data | |
| 1.1.5 | Making Sense of a Logic Problem | |
| Section 1.2 | 1.2.1 | Multiple Representations |
| 1.2.2 | Representing Comparisons | |
| 1.2.3 | Characteristics of Numbers | |
| 1.2.4 | Products, Factors, and Factor Pairs | |
| Section 1.3 | 1.3.1 | Attributes and Characteristics of Shapes |
| 1.3.2 | More Characteristics of Shapes | |
| Closure | 1.CL | Chapter Closure |
| Opening | 2.OP | Chapter Opening |
|---|---|---|
| Section 2.1 | 2.1.1 | Dot Plots and Bar Graphs |
| 2.1.2 | Histograms and Stem-and-Leaf Plots | |
| Section 2.2 | 2.2.1 | Exploring Area |
| 2.2.2 | Square Units and Area of Rectangles | |
| 2.2.3 | Area and Perimeter | |
| Section 2.3 | 2.3.1 | Using Rectangles to Multiply |
| 2.3.2 | Using Generic Rectangles | |
| 2.3.3 | Distributive Property | |
| 2.3.4 | Generic Rectangles and the Greatest Common Factor | |
| Closure | 2.CL | Chapter Closure |
| Opening | 3.OP | Chapter Opening |
|---|---|---|
| Section 3.1 | 3.1.1 | Using the Multiplicative Identity |
| 3.1.2 | Portions as Percents | |
| 3.1.3 | Connecting Percents with Decimals and Fractions | |
| 3.1.4 | Multiple Representations of a Portion | |
| 3.1.5 | Completing the Web | |
| 3.1.6 | Investigating Ratios | |
| Section 3.2 | 3.2.1 | Addition, Subtraction, and Opposites |
| 3.2.2 | Locating Negative Numbers | |
| 3.2.3 | Absolute Value | |
| 3.2.4 | Length on a Coordinate Graph | |
| Closure | 3.CL | Chapter Closure |
| Opening | 4.OP | Chapter Opening |
|---|---|---|
| Section 4.1 | 4.1.1 | Introduction to Variables |
| 4.1.2 | Writing Equivalent Expressions | |
| 4.1.3 | Using Variables to Generalize | |
| Section 4.2 | 4.2.1 | Enlarging Two-Dimensional Shapes |
| 4.2.2 | Enlarging and Reducing Figures | |
| 4.2.3 | Enlargement and Reduction Ratios | |
| 4.2.4 | Ratios in Other Situations | |
| Closure | 4.CL | Chapter Closure |
| Opening | 5.OP | Chapter Opening |
|---|---|---|
| Section 5.1 | 5.1.1 | Representing Fraction Multiplication |
| 5.1.2 | Describing Parts of Parts | |
| 5.1.3 | Calculating Parts of Parts | |
| 5.1.4 | Multiplying Mixed Numbers | |
| Section 5.2 | 5.2.1 | Making Sense of Decimal Multiplication |
| 5.2.2 | Fraction Multiplication Number Sense | |
| Section 5.3 | 5.3.1 | Rearranging Areas |
| 5.3.2 | Area of a Parallelogram | |
| 5.3.3 | Area of a Triangle | |
| 5.3.4 | Area of a Trapezoid | |
| Closure | 5.CL | Chapter Closure |
| Section 5.4 | Mid-Course Reflection Activities |
| Opening | 6.OP | Chapter Opening |
|---|---|---|
| Section 6.1 | 6.1.1 | Dividing |
| 6.1.2 | Fractions as Division Problems | |
| 6.1.3 | Problem Solving with Division | |
| 6.1.4 | Solving Problems Involving Fraction Division | |
| Section 6.2 | 6.2.1 | Order of Operations |
| 6.2.2 | Area of a Rectangular Shape | |
| 6.2.3 | Naming Perimeters of Algebra Tiles | |
| 6.2.4 | Combining Like Terms | |
| 6.2.5 | Evaluating Algebraic Expressions | |
| Closure | 6.CL | Chapter Closure |
| Opening | 7.OP | Chapter Opening |
|---|---|---|
| Section 7.1 | 7.1.1 | Comparing Rates |
| 7.1.2 | Comparing Rates with Tables and Graphs | |
| 7.1.3 | Unit Rates | |
| Section 7.2 | 7.2.1 | Analyzing Strategies for Dividing Fractions |
| 7.2.2 | Another Strategy for Division | |
| 7.2.3 | Division with Fractions and Decimals | |
| 7.2.4 | Fraction Division as Ratios | |
| Section 7.3 | 7.3.1 | Inverse Operations |
| 7.3.2 | Distributive Property | |
| 7.3.3 | Distributive Property and Expressions Vocabulary | |
| 7.3.4 | Writing Algebraic Equations and Inequalities | |
| Closure | 7.CL | Chapter Closure |
| Opening | 8.OP | Chapter Opening |
|---|---|---|
| Section 8.1 | 8.1.1 | Measures of Central Tendency |
| 8.1.2 | Choosing Mean or Median | |
| 8.1.3 | Shape and Spread | |
| 8.1.4 | Box Plots and Interquartile Range | |
| 8.1.5 | Comparing and Choosing Representations | |
| Section 8.2 | 8.2.1 | Statistical Questions |
| Section 8.3 | 8.3.1 | Writing Multiplication Equations |
| 8.3.2 | Distance, Rate, and Time | |
| 8.3.3 | Unit Conversion | |
| Closure | 8.CL | Chapter Closure |
| Opening | 9.OP | Chapter Opening |
|---|---|---|
| Section 9.1 | 9.1.1 | Volume of a Rectangular Prism |
| 9.1.2 | Nets and Surface Area | |
| Section 9.2 | 9.2.1 | Multiplicative Growth and Percents |
| 9.2.2 | Composition and Decomposition of Percents | |
| 9.2.3 | Percent Discounts | |
| 9.2.4 | Simple Interest and Tips | |
| Closure | 9.CL | Chapter Closure |
| Section 9.3 | 9.3.1 | A Culminating Portions Challenge |
| 9.3.2 | Representing and Predicting Patterns | |
| 9.3.3 | Analyzing Data to Identify a Trend |
CP 1: Using Place Value to Round and Compare Decimals
CP 2: Addition and Subtraction of Decimals
CP 3: Addition and Subtraction of Fractions
CP 4: Addition and Subtraction of Mixed Numbers
CP 5: Multiple Representations of Portions
P 6: Locating Points on a Number Line and on a Coordinate Graph
CP 7A: Multiplication of Fractions and Decimals
CP 7B: Area and Perimeter of Quadrilaterals and Triangles
CP 8A: Rewriting and Evaluating Variable Expressions
CP 8B: Division of Fractions and Decimals
CP 9A: Displays of Data: Histograms and Box Plots
CP 9B: Solving One-Step Equations
10.1 | Explorations and Investigations | |
| 10.1.1 | How can I make 0? |
| 10.1.2 | What number properties pair well? |
| 10.1.3 | How can you place algebraic expressions on the number line? |
| 10.1.4 | How can I solve it? |
| 10.1.5 | What can you say about the sums of consecutive numbers? |
10.2 | Restaurant Math | |
| 10.2.1 | How can you draw it to scale? |
| 10.2.2 | How can you calculate the cost? |
| 10.2.3 | What do portions have to do with proportions? |
| 10.2.4 | What markdown undoes a markup? |
| Opening | 1.OP | Chapter Opening |
|---|---|---|
| Section 1.1 | 1.1.1 | Visualizing Information |
| 1.1.2 | Perimeter and Area Relationships | |
| 1.1.3 | Describing and Extending Patterns | |
| 1.1.4 | Representing Data | |
| 1.1.5 | Making Sense of a Logic Problem | |
| Section 1.2 | 1.2.1 | Multiple Representations |
| 1.2.2 | Representing Comparisons | |
| 1.2.3 | Characteristics of Numbers | |
| 1.2.4 | Products, Factors, and Factor Pairs | |
| Section 1.3 | 1.3.1 | Attributes and Characteristics of Shapes |
| 1.3.2 | More Characteristics of Shapes | |
| Closure | 1.CL | Chapter Closure |
| Opening | 2.OP | Chapter Opening |
|---|---|---|
| Section 2.1 | 2.1.1 | Dot Plots and Bar Graphs |
| 2.1.2 | Histograms and Stem-and-Leaf Plots | |
| Section 2.2 | 2.2.1 | Exploring Area |
| 2.2.2 | Square Units and Area of Rectangles | |
| 2.2.3 | Area and Perimeter | |
| Section 2.3 | 2.3.1 | Using Rectangles to Multiply |
| 2.3.2 | Using Generic Rectangles | |
| 2.3.3 | Distributive Property | |
| 2.3.4 | Generic Rectangles and the Greatest Common Factor | |
| Closure | 2.CL | Chapter Closure |
| Opening | 3.OP | Chapter Opening |
|---|---|---|
| Section 3.1 | 3.1.1 | Using the Multiplicative Identity |
| 3.1.2 | Portions as Percents | |
| 3.1.3 | Connecting Percents with Decimals and Fractions | |
| 3.1.4 | Multiple Representations of a Portion | |
| 3.1.5 | Completing the Web | |
| 3.1.6 | Investigating Ratios | |
| Section 3.2 | 3.2.1 | Addition, Subtraction, and Opposites |
| 3.2.2 | Locating Negative Numbers | |
| 3.2.3 | Absolute Value | |
| 3.2.4 | Length on a Coordinate Graph | |
| Closure | 3.CL | Chapter Closure |
| Opening | 4.OP | Chapter Opening |
|---|---|---|
| Section 4.1 | 4.1.1 | Introduction to Variables |
| 4.1.2 | Writing Equivalent Expressions | |
| 4.1.3 | Using Variables to Generalize | |
| Section 4.2 | 4.2.1 | Enlarging Two-Dimensional Shapes |
| 4.2.2 | Enlarging and Reducing Figures | |
| 4.2.3 | Enlargement and Reduction Ratios | |
| 4.2.4 | Ratios in Other Situations | |
| Closure | 4.CL | Chapter Closure |
4.1 | Exponents, Part 1 | |
| 4.1.1 | What is exponential growth? |
| 4.1.2 | How can you (re)write it? |
| 4.1.3 | How can notation help you make sense of exponential expressions? |
| 4.1.4 | Are there other exponent properties? |
| 4.1.5 | How can I prevent common exponential expression errors? |
4.2 | Solving Equations | |
| 4.2.1 | How can I check my answer? |
| 4.2.2 | Is there always a solution? |
| 4.2.3 | How many solutions are there? |
| 4.2.4 | How can I solve complicated equations? |
| 4.2.5 | How can I write an equation to meet the criteria? |
4.3 | Exponents, Part 2 | |
| 4.3.1 | What if the exponent is not positive? |
| 4.3.2 | How do you know which exponent properties to use? |
5.1 | Representations of a Line | |
| 5.1.1 | What is the connection? |
| 5.1.2 | How can you show it? |
| 5.1.3 | How does it grow? |
| 5.1.4 | How is the growth represented? |
| 5.1.5 | How can I write the rule? |
| 5.1.6 | How can you make connections? |
| 5.1.7 | How can you use growth? |
| 5.1.8 | What are the connections? |
5.2 | Graphs & Equations of Systems | |
| 5.2.1 | How can I change it to y = mx + b form? |
| 5.2.2 | How can I eliminate fractions and decimals in equations? |
| 5.2.3 | How do I change the line? |
| 5.2.4 | Is the intersection significant? |
| 5.2.5 | What is the equation? |
6.1 | Solving Systems Algebraically | |
| 6.1.1 | Where do the lines intersect? |
| 6.1.2 | When are they the same? |
| 6.1.3 | What if the equations are not in y = mx + b form? |
| 6.1.4 | How many solutions are there? |
6.2 | Slope & Rate of Change | |
| 6.2.1 | What is the equation of the line? |
| 6.2.2 | How does y change with respect to x? |
| 6.2.3 | When is it the same? |
| 6.2.4 | What’s the point? |
| 6.2.5 | Can I connect rates to slopes? |
6.3 | Associations | |
| 6.3.1 | What is the equation for a trend line? |
| 6.3.2 | How can I use an equation? |
| 6.3.3 | What if the data is not numerical? |
| 6.3.4 | Is there an association? |
7.1 | Angles | |
| 7.1.1 | How are the angles related? |
| 7.1.2 | Are there other congruent angles? |
| 7.1.3 | What about the angles in a triangle? |
| 7.1.4 | What if the angle is on the outside? |
| 7.1.5 | Can angles show similarity? |
7.2 | Right Triangle Theorem | |
| 7.2.1 | Can I make a right triangle? |
| 7.2.2 | What is special about a right triangle? |
| 7.2.3 | How can I calculate the side length? |
| 7.2.4 | What kind of number is it? |
| 7.2.5 | How can I use the Right Triangle Theorem to solve problems? |
| 7.2.6 | How can I determine lengths in three dimensions? |
| 7.2.7 | How can I prove it? |
| 8.1 | Introduction to Functions | |
| 8.1.1 | How can you (de)code the message? |
| 8.1.2 | How can a graph tell a story? |
| 8.1.3 | What can you predict? |
| 8.1.4 | Which prediction is best? |
| 8.1.5 | How does the output change based on the input? |
| 8.1.6 | How do you see the relationship? |
8.2 | Characteristics of Functions | |
| 8.2.1 | What is a function? |
| 8.2.2 | How can you describe the relationship? |
| 8.2.3 | How do I sketch it? |
| 8.2.4 | How many relationships are there? |
8.3 | Linear and Nonlinear Functions | |
| 8.3.1 | Is it linear or nonlinear? |
| 8.3.2 | What clues do ordered pairs reveal about a relationship? |
| 8.3.3 | What other functions might you encounter? |
| 9.1 | Volume | |
| 9.1.1 | Given the volume of a cube, how long is the side? |
| 9.1.2 | What if the base is not a polygon? |
| 9.1.3 | What if the layers are not the same? |
| 9.1.4 | What if it is oblique? |
| 9.1.5 | What if it is a three-dimensional circle? |
9.2 | Scientific Notation | |
| 9.2.1 | How can I write very large or very small numbers? |
| 9.2.2 | How do I compare very large numbers? |
| 9.2.3 | How do I multiply and divide numbers written in scientific notation? |
| 9.2.4 | How do I add and subtract numbers written in scientific notation? |
| 9.2.5 | How do I compute it? |
9.3 | Applications of Volume | |
| 9.3.1 | What does a volume function look like? |
| 9.3.2 | What is the biggest cone? |
| 9.3.3 | How do all the items fit together? |
| 10.1 | Explorations and Investigations | |
| 10.1.1 | How close can I get? |
| 10.1.2 | Can you make them all? |
| 10.1.3 | How many triangles will there be? |
| 10.1.4 | What’s my angle? |
| 10.1.5 | Function-function, what’s your function? |
| 10.1.6 | Is it always true? |
| 10.1.7 | What’s right? |
| 10.1.8 | What’s your story? |
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.
PI-10. WAY TO GO!
The map at right shows the streets in Old Town. Assume Jacqueline is standing at the corner of A and 1st Streets. Assume Jacqueline will only walk South or East. The shaded rectangles represent large buildings. Assume Jacqueline will not pass through any buildings.
The number “3” at the intersection of C and 2nd Streets means that there are three different ways she can get there from her starting position. What are those three ways? Describe them in words.
How many different ways can she walk to the corner of F and 4th Streets?
How many different ways can she walk to the corner of D and 5th Streets?
Explain how you can use your answers to parts (b) and (c) to find the number of ways she can walk to the corner of F and 5th Streets. Why does this make sense?
Find the number of different ways she can walk to the corner of I and 8th Streets.
How could you change the map so that Jacqueline has only 7 ways to get to the corner of D and 3rd streets? You can remove blocks or add them.
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.
