CME ALGEBRA & GEOMETRY LESSONS AND INFORMATION BY CHRIS POLLARD & MITCH GROSOFSKY

ALGEBRA 1: EXPRESSIONS & EQUATIONS LESSON 2.2 MODELING GENERAL SITUATIONS BY CHRIS POLLARD

GENERAL SITUATIONS You may hear the Algebra is “full of x’s & y’s.” Using letters to represent numbers lets you describe a general situation easily. Example 1: During a natural disaster, such as an earthquake or flood, many people must leave their home and go to shelters. The table shows three situations. It shows how much food and how many beds a disaster relief group must provide. Write an expression, in words, for how much food and how many beds you will need for any number of people. Relief Camp Supplies Number of PeopleNumber of BedsAmount of Food (lb) 1,0001,0103,000 5,0005,01015,000 10,00010,01030,000

EXPRESSIONS WITH VARIABLES variable There is a simpler way to describe the last situations. Let the variable x represent the number of people needing food and shelter at the relief camp. Here is what the camp needs for x people: (x + 10) beds(3 * x) lbs. of food per day The variable x stands for an unknown number. When the relief group knows the number of people, they can replace x with that number.

FOR DISCUSSION Here is what the camp needs for x people: (x + 10) beds(3 * x) lbs. of food per day For each number of people, how many beds and how much food per day will a relief group need? 1.15,

PROBLEM Ricardo has 3 fewer apples than Jeremy. Let j stand for the number of apples that Jeremy has. Write an expression for the number of apples that Ricardo has. Solution:Think about the steps you take to find how many apples Ricardo has. Suppose Jeremy has 10 apples. Ricardo has 3 fewer apples than Jeremy. 10 – 3 = 7 apples. Suppose Jeremy has 15 apples. Ricardo has 3 fewer apples than Jeremy. 15 – 3 = 12 apples. Now, suppose Jeremy has j apples. Ricardo has 3 fewer apples than Jeremy. Write an expression that equals the number of apples that Ricardo has.

FOR DISCUSSION Hideki says, “I chose a number. I multiplied it by 7. Then I subtracted 4.” Let h stand for Hideki’s starting number. Write an expression for Hideki’s ending number.

CHECK YOUR UNDERSTANDING 1.Mary was born one year before Barbara. No matter how old they are, Mary will always be one year older than Barbara. Find the missing ages in years. Mary’s AgeBarbara’s Age a. 11____________ b. 7____________ c. 53____________ d. 65____________ e. m____________ f._________ n

WRAP UP Everyone needs to write 2 things: 1. A word problem that can be expressed using one variable. Ex) Ricardo has 3 fewer apples than Jeremy. Write an expression that equals the number of apples that Ricardo has. 2. An expression in mathematical notation with one variable. Ex) j – 3 After you have written both of these down, swap with a partner and translate each statement. Translate the first statement into mathematical notation, the second one into English. Verify that your translations are correct with the person you got it from.

GEOMETRY LESSON BY MITCH GROSOFSKY

DISTANCE FORMULA DISCUSSION BETWEEN TWO STUDENTS: HANNAH AND DARREN: GRAPH OF WHAT THEY ARE TALKING ABOUT:

FOR YOU TO DO: FIND THE DISTANCE BETWEEN EACH PAIR OF POINTS: 7.(1,1) AND (-1,-1) 8.(1,1) AND (4,5) 9.(2,4) AND (-4,-2)

MIDPOINT FORMULA BASED ON THEOREM 7.3: EACH COORDINATE OF A MIDPOINT OF A LINE SEGMENT IS EQUAL TO THE AVERAGE OF THE CORRESPONDING COORDINATES OF THE ENDPOINTS OF THE LINE SEGMENTS.

FOR YOU TO DO: 10.FIND THE MIDPOINT OF THE SEGMENT WITH ENDPOINTS (1327,94) AND (-668,17) 11.FIND THE MIDPOINT OF THE SEGMENT WITH ENDPOINTS (1776,13) AND (2000,50)

CME PROJECT DESCRIPTION Developed by EDC’s Center for Mathematics Education (CME) Published by Pearson A four-year, NSF-funded high school mathematics program designed around how knowledge is organized and generated within mathematics. There are three themes: Algebra, Geometry, and Analysis The CME project focuses on these three themes as their centerpieces because they view them as the descriptors for methods and approaches—the habits of mind that determine how knowledge is organized and generated within mathematics itself. They proclaim their philosophy to be: “CME Project makes a conscious choice not to think of each course as a list of topics to cover, but rather as an opportunity to develop mathematical themes in different areas of mathematics. These themes provide students with insight about what it means to “think like a mathematician” and can be applied to many different (even non-mathematical) situations.”

DESIGN OF CURRICULA CME uses the traditional American structure of Algebra, Geometry, Advanced Algebra (Algebra 2), and Precalculus. The problem-based, student-centered program builds on lessons learned from high-performing countries: develop an idea thoroughly and then revisit it only to deepen it. They organize ideas in a way that is faithful to how they are organized in mathematics. They reduce clutter and extraneous topics. CME also employs the best American models that call for struggling with ideas and problems as preparation for instruction, moving from concrete problems to abstractions and general theories, and situating mathematics in engaging contexts.

HOW THEY STRUCTURE THEIR COURSES Algebra 1 Geometry– (making the most/least out of a situation) Algebra 2 Precalculus

HOW CME ADDRESSES CCSS (how they are aligned) Content ordered specifically for the Common Core Traditional Pathway course sequence “Low Threshold/High Ceiling” ensures success for all students Problem-based, student-centered curriculum Engaging lessons that focus on developing students' Habits of Mind Accessible approach to capture and engage students of all ability levels Habits of Mind: establishing the mathematical mindset and rigor so students can solve problems that don’t appear in textbooks Textured Emphasis: separating convention and vocabulary from matters of mathematical substance General Purpose Tools: emphasis on fluency in algebraic calculation, proof, and graphing due to their necessity in mathematics Experience before Formality: allow for grappling and discovery learning High Expectations

TEACHER SUPPORT & RESOURCES Professional Development (none listed at this time) Additional Support on Various Topics Pearson Training - specific to course

PUBLISHER INFORMATION & WEBSITES