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

CMP Math

Monday  11/2/09

Objective

(Student will…)

•     Determine whether a triangle is a right triangle based on its side lengths

•     Relate areas of squares to the lengths of the sides

Teacher Activities & Strategies

Looking for Pythagoras Unit:  Problem 3.4(Pg 36)

Discuss the two questions in the introduction to Problem 3.4. Remind students that, so far, they have learned that if a triangle is a right triangle, then its side lengths satisfy the relationship a² + b² = c². However, they do not yet know whether a triangle whose side lengths satisfy this relationship must be a right triangle.

Have students work on the activity in the Getting Ready in pairs, or do the activity as a demonstration.

Summarize:

Have someone demonstrate how to arrange the string, straws, or polystrips to form a triangle with side lengths 3 units, 4 units, and 5 units and to explain how he or she knows it is a right triangle. Explain that this triangle is sometimes called a “3-4-5 right triangle.”

•  Are multiples of a 3-4-5 triangle, such as 6-8-10 and 9-12-15 triangles, also right triangles?

Have students demonstrate each set of lengths on a grid at the overhead, checking for right angles with an angle ruler or a corner of a piece of paper.

•  What about the multiples of 5-12-13? Do these lengths form a right triangle?

Also, discuss the side lengths that did not form a right triangle.

•  Which of these sets of side lengths did not form a right triangle? Does a² + b² = c² for these sets?

Student Activities

Bell Work:  Pg 44 #28-33

Students will work in pairs on Problem 3.4 A-D on Page 37.

Assessment/Evaluation

ACE Pg  40  #15-17

Academic Vocabulary

Additional Materials

Toothpicks

CMP Math

Tuesday  11/3/09

Objective

(Student will…)

Reflect on and summarize their learning at the end of the investigation.

Assess students’ understanding of the mathematics taught in investigation 1, 2 and 3.

Teacher Activities & Strategies

Looking for Pythagoras Unit: 

Discuss Reflection 3 on  Pg 45.

Give Partner Quiz

Student Activities

Bell Work:  Reflection

Partner Quiz

Assessment/Evaluation

Academic Vocabulary

Additional Materials

CMP Math

Wednesday 11/4/09

Objective

(Student will…)

•     Learn the meanings of rational number and irrational number

•     Estimate the values of square roots that are irrational numbers

•     Estimate lengths of hypotenuses of right triangles

Teacher Activities & Strategies

Looking for Pythagoras Unit:   Problem 4.1 (Pg 46) Using The Pythagorean Theorem

Launch:

Introduce the problem by discussing how to find a decimal approximation for a square root.

On a dot grid, draw a square with an area of 2 square units on a number line, with the “bottom vertex” at point 0.

•  What is the length of a side of this square? If we mark off a segment on the number line with the same length as the side, where will the segment end?

•  So,  is approximately equal to 1.4. Is 1.4 exactly equal to ? Suppose we try 1.41. Does 1.41 = ? Try 1.42. Does it equal ? Can you find a number that is closer to  than 1.41 and 1.42 are?

Display the Wheel of Theodorus. Explore with the class how the wheel was constructed and ask for the lengths of the second and third hypotenuses. Cut out the number-line ruler and demonstrate how to transfer these lengths to the ruler.

Summarize:

Display the Wheel of Theodorus. Ask for the lengths of the hypotenuses and write them on the wheel. Then, have students come to the front and mark the length of each hypotenuse on the number-line ruler.

Ask for approximations to the nearest tenth for each length. As a class, check each approximation by squaring it on a calculator.

•  Is this estimate too large? Too small? What might be a better estimate? How do you know?

Take this opportunity to assess students’ understanding of the ordering of decimals.

Ask students to compare their estimates to the numbers they obtained with a calculator. Tell the class that the numbers , , , . . . are called irrational numbers.

Student Activities

Bell Work: Pg 41 #23a

Work in groups of three or four on the problem 4.1 (Pg 47)

Using The Pythagorean Theorem.

Assessment/Evaluation

ACE Pg 53 1-2  pg.57  13-16

Academic Vocabulary

·         irrational number

Additional Materials

CMP Math

Thursday 11/5/09

Objective

(Student will…)

•     review concepts and turn in make-up work

Teacher Activities & Strategies

Looking for Pythagoras Unit:  the student will have a chance to turn in make work and there is also worksheets

Student Activities

Review and makeup:

Students will work on homework and test that they have failed to turn in and also thanksgiving word search. 

Assessment/Evaluation

Worksheets if not done in class.

Academic Vocabulary

Additional Resources

CMP Math

Friday 11/6/09

Objective

(Student will…)

There will be subs for the 8^th grade math department there will be worksheets planned for today. 

Teacher Activities & Strategies

The concepts that have been covered for looking for Pythagoras will be reviewed.

Student Activities

Finish the work sheets if not competed in class.

Assessment/Evaluation

Ws. Pgs. 115, 38, 39, 40

Additional Resources