CMP Math

Monday  11/16/09

Objective

(Student will…)

•     Gain an intuitive understanding of basic exponential growth patterns

•     Begin to recognize exponential patterns in tables

Teacher Activities & Strategies

Growing, Growing, Growing Unit:  Problem 1.1 (Pg 5) Exponential Growth

Launch:  Describe Chen’s ballot-making task.

Have students cut and stack paper for the first two or three cuts. This provides a visual aid for helping them understand the relationship between the number of cuts and the number of ballots created.

Encourage students to look for the multiplicative pattern in the table.

Summarize:  By asking about patterns in the table relating the number of cuts to the number of ballots, lead the class to a discussion of exponents.

Display the table from Problem 1.1 on the overhead and ask:

•  How did you get the number of ballots for 5 cuts?

Add a third column to the table and illustrate each calculation, showing each factor of 2.

Use the example below to introduce the terms base, exponent, exponential form, and standard form.

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2¹⁰

Explain that 1,024 is the standard form of 2¹⁰.

•  How many ballots are there after 0 cuts?

•  How could we show this in our table?

Student Activities

Bell Work:  Set up paper for Problem 1.1

Growing, Growing, Growing Unit:  Problem 1.1 (Pg 5) Making Ballots

Students will work on problem 1.1 A-D in groups of two or three.

Assessment/Evaluation

Ace Pg 11 #1-4

Academic Vocabulary

• Exponential Form
• Exponent
• Base
• Standard Form

Additional Materials

CMP Math

Tuesday  11/17/09

Objective

(Student will…)

•     Express a product of identical factors in both exponential form and standard form

•     Gain an intuitive understanding of basic exponential growth patterns

•     Begin to recognize exponential patterns in tables, graphs, and equations

•     Write an equation for an exponential relationship

•     Solve problems involving exponential growth

Teacher Activities & Strategies

Growing, Growing, Growing Unit:  Problem 1.2 (Pg 6) Requesting a Reward

Launch: 

 Use the Getting Ready to give students practice with exponents.

Tell the story of the peasant and the king of Montarek.

•  How many rubas will there be on square 1? On square 2? On square 3? On square 4?

•  Which square will have 64 rubas?

Summarize:

Discuss the graph and how it represents the growth pattern. Have students share the methods they used for finding the equation.

Student Activities

Bell Work:  Set-Up page for Problem 1.2

Growing, Growing, Growing Unit:  Problem 1.2 (Pg 6) Requesting a Reward

Students will work in groups of 3 or 4 on Problem 1.2 A-F.

Assessment/Evaluation

ACE Pg 11 #5–7, 10–11, 15–21, 40–42

Academic Vocabulary

Additional Materials

CMP Math

Wednesday 11/18/09

Objective

(Student will…)

•     Continue to recognize exponential patterns in tables, graphs, and equations

•     Compare different exponential growth patterns

•     Understand the role of the growth factor in exponential relationships

•     Make a table from the graph and equation of an exponential relationship

•     Write equations for exponential relationships represented by tables and graphs

•     Solve problems involving exponential growth

Teacher Activities & Strategies

Growing, Growing, Growing Unit:  Problem 1.3 (pg 8) Making a New Offer

Launch:  Have students read about the new plans and study the graph and equation.

•  How many squares are on the board for each new plan?

•  For each plan, how many rubas are placed on the first square?

•  What is the rule for placing rubas on each successive square?

Summarize:

Ask students which plan they think is best for the king and which they think is best for the peasant.

Have students read about the new plans and study the graph and equation.

•  How many squares are on the board for each new plan?

•  For each plan, how many rubas are placed on the first square?

•  What is the rule for placing rubas on each successive square?

Ask students which plan they think is best for the king and which they think is best for the peasant.

Student Activities

Bell Work:  CRT Problem

Growing, Growing, Growing Unit:  Problem 1.3 (pg 8) Making a New Offer

Students will work in groups of 3 or 4 on Problem 1.3 A-F.

Assessment/Evaluation

Pg 17 #47 together in class

Academic Vocabulary

·         exponential growth

·         exponential relationships

• growth factor

Additional Materials

CMP Math

Thursday 11/19/09

Objective

(Student will…)

•     Continue to investigate the role of the growth factor in exponential relationships

•     Compare and contrast exponential and linear growth

Teacher Activities & Strategies

Discuss Bell Work

Growing, Growing, Growing Unit:  Problem 1.4 (pg 8) Making a New Offer

Launch:

Review the terms exponential growth, exponential relationship, and growth factor.

Describe the last chapter in the saga of the king and the peasant.

Summarize:

In a class discussion, talk about groups’ findings for the problem. The important idea to explore here is the distinction between the exponential model (Plan 1) and the linear model (Plan 4).

•  Which plan would you advise the peasant to accept?

•  Do the plans increase in the same way?

•  What would the graphs look like if we extended them?

•  What causes this difference in their patterns of change?

Discuss the fact that Plan 4 favors the peasant for the first six squares, but Plan 1 is much more favorable thereafter.

Ask students about the equations:

•  What do the numbers and variables mean in the equations for Plans 1 and 4?

This question offers an opportunity to review equations for exponential and linear relationships.

Have a student add the information for Plan 4 to the class chart.

Student Activities

Bell Work: CRT Problem

Work in groups of three or four on the problem 4.4 (Pg 52) A-D.

Assessment/Evaluation

ACE Pg 15 #25-30

Academic Vocabulary

Additional Resources

CMP Math

Friday 11/20/09

Objective

(Student will…)

Review all objectives learned in Investigation 1 of Growing, Growing, Growing Unit.

Teacher Activities & Strategies

Growing, Growing, Growing Unit: 

Review Investigation 1 of unit and discuss the Reflection.

Student Activities

Bell Work:  Reflection Pg 19

Additional Practice and Skill Practice Wks in class

Assessment/Evaluation

Assignment:  Additional Practice and Skill Practice Wks

Academic Vocabulary

Monday/9

Objective

(Student will…)

•     Estimate lengths of hypotenuses of right triangles

•     Apply the Pythagorean Theorem to a problem situation

Teacher Activities

Looking for Pythagoras Unit:  Investigation 4.2 – Stopping Sneaky Sally  page 49

LAUNCH:

Introduce the baseball scenario described in the student edition. Talk about the layout of a baseball diamond, which is pictured on Transparency 4.2. The baseball diamond is a square. Let students offer a few estimates.

SUMMARY:

Have several students share their strategies for solving the problem. Look for specific references to the Pythagorean Theorem.

Stress the correct procedure: square each leg length first, add the squares, and then take the square root of the sum to get the length of the hypotenuse.

Student Activities

Bell Work:  Set up paper for Problem 4.2

Students will work in pairs to Explore Pg 49 problems A - C

Assessment/Evaluation

Page 53 # 3-5, 9

Academic Vocabulary

None

Additional Resources

None

Tuesday/10

Objective

(Student will…)

•     Investigate the special properties of a 30-60-90 triangle

Teacher Activities

Looking for Pythagoras Unit   Investigation 4.3 – Analyzing Triangles page 50-51

LAUNCH:

Show a transparency of the Getting Ready for Problem 4.3. Tell the class that triangle ABC is an equilateral triangle and discuss reflection line of symmetry.

Students should discover that line segment AP divides triangle ABC into two congruent triangles. Remind students of the formal and informal meaning of congruent triangles.

In Problem 4.3, students will continue to explore these relationships about angles and side lengths.

SUMMARY:

Let several pairs share their reasoning about each question, demonstrating their work at the board or overhead.

Students should also discover that the length of the side opposite the 30° angle is half the length of the hypotenuse. In Question B, all students should be able to find the length of the third side of the right triangle using the Pythagorean Theorem. Use one of the two possible approaches to help clarify student confusion related to Part B.

Question C of the problems reviews the relationship in a 30-60-90 triangle.

Student Activities

Bell Work:  Simplify square roots.

Students will work in pairs to Explore problems A – C on Pg 51

Assessment/Evaluation

Page 55  #10,  Page 58-59 #32-34,  36-37

Academic Vocabulary

None

Additional Resources

none

Wednesday/11

Objective

(Student will…)

•     Use the properties of special right triangles to solve problems

Teacher Activities

Looking for Pythagoras Unit   Investigation 4.4 – Finding Perimeter Pg 52.

LAUNCH:

Display Transparency 4.4 on the overhead.

Let students offer their ideas.

SUMMARY:

Ask one of the groups to describe how they found the perimeter of ABC.

Move on to the rest of the questions. Once students have discussed how they found the areas of the triangles, ask:

Student Activities

Students will work in groups of 3 or 4 toExplore Problems A – C on Pg 52.

Assessment/Evaluation

Page 59  #35

Academic Vocabulary

None

Additional Resources

none

Thursday/12

Objective

(Student will…)

Review concepts covered in Looking for Pythagoras

Teacher Activities

Looking for Pythagoras Unit   

Pass out unit review.

Grade and discuss unit review.

Student Activities

Have students do unit review or workbook pages.

Assessment/Evaluation

Unit Review

Academic Vocabulary

None

Additional Resources

none

Friday/13

Objective

(Student will…)

Students will recall and use objectives covered in Looking for Pythagoras

Teacher Activities

Discuss Reflection and pass out unit test.

Student Activities

Have students take unit test and do mathematical reflection

Assessment/Evaluation

Unit Test

Academic Vocabulary

None

Additional Resources

none