May

Week of May 7, 2012 to May 11, 2012

Monday May 7, 2012

Objective

(Student will…)

Additional Practice of Linear Equations.  Finish up MSA 3.5

Teacher Activities & Strategies

Student Activities

Make Up Work!!!

 

Assessment/Evaluation

 

Academic Vocabulary

 

Additional Resources

 

Tuesday May 8, 2012

Objective

(Student will…)

Apply concepts learned in MSA, Investigation 3

Teacher Activities & Strategies

MSA 3: Check Up 2

Launch:  Pass out the quiz and answer any questions the students may have.

Explore:  Monitor the students as they complete the quiz independently.

Student Activities

Make Up Work!!!

Class Work: MSA 3: Check Up 2

 

Assessment/Evaluation

Summary: Will grade the quiz and post the class averages on PDSA

Academic Vocabulary

KIM: none

Additional Resources

CMP Book and Notebook

Wednesday May 9, 2012

Objective

(Student will…)

•   Introduce students to the concept of slope as the ratio of vertical change to horizontal change between two points on a line or ratio of rise over run

•   Use slope to sketch a graph of a line with this slope

Teacher Activities & Strategies

MSA 4.1: Using Rise and Run

Launch:  Discuss why stair climbing is a popular aerobic exercise. Ask:

•  Does the steepness of a set of stairs affect the exercise?

•  For homework, examine the stairs in your house, apartment, or school.

•  Do all stairs have the same steepness? How can we find the steepness?

Pose the questions in the Getting Ready.

Let students go out in groups to measure the rise and the run and then find the  ratio of the rise to the run. Tell the groups to measure more than one step in each set of stairs. Compare the ratios. Use different sets of stairs for each group if possible. (See Explore for Alternate Launch.)

Let students work in small groups of three to four people.

Explore: Question A: When the group has recorded its measures of a staircase in the building, have them organize what they have found out about the ratio of rise to run between several of the steps in the staircase.

Question B: Some students may need help in drawing the line that matches the ratio of changes. Grid paper may help. Suggest that the student draw a line that goes through the origin. Then suggest that the student draw a couple of stairs with the ratio given, and connect the top of the stairs to form the desired line.

Student Activities

Make Up Work!!!

Class Work:  MSA 4.1: Using Rise and Run

 

Assessment/Evaluation

Summary:  Question A: Let each group report on stairs they have investigated. Make a class record of the stairs and measures on the stairs, and compare the ratios for various sets of stairs.

•  What is the steepest set of stairs in our list? The least steep set of stairs?

•  Are some stairs steeper than others? If so, how can you tell?

•  Can you order the entire list of stairs from least to greatest in terms of   steepness?

Talk about the Carpenters’ Guidelines with your students. Ask:

•  How do the ratios of the stairs we measured compare to the carpenters’ guidelines? Which ones meet the standards and which ones do not?

•  What do you think influences a builder’s decision on the run/rise of stairs?

Question B: Collect several equations and draw them on a grid on the projector.

•  What do you notice about these lines?

Discuss strategies students used to answer Question B. Use this summary and an illustration of stairs and steps to define slope and launch the next problem. Slope is the ratio of the change in the vertical distance to the change in the horizontal distance between two points on a line or

slope =

Academic Vocabulary

KIM:  slope

Additional Resources

CMP Book, notebook, calculators

Thursday May 10, 2012

Objective

(Student will…)

•   Connect slope to patterns of change   

•   Find the slope of a line from data in table, graph, or equation

•   Find the y-intercept of a line from data in a table, graph, or equation

•   Use the slope m and y-intercept b to write an equation in the form y = mx + b

Teacher Activities & Strategies

MSA 4.2: Finding the Slope of a Line

Launch:  Use the Getting Ready to launch the problem.

•  What is the slope of each line? Explain how we can find it.

•  How do we indicate the change in direction? How do we indicate if the steepness of a line is decreasing or increasing from left to right?

Model how to find the vertical change and horizontal change. For each line, pick 2–3 different pairs of points to find the slope of a line. Show that the ratios are equal.

Repeat the preceding questions for the table in the Getting Ready.

•  Describe the graph of the data.

Students can work on the problems in pairs.

Explore: Check that students are finding the vertical and horizontal changes correctly. Have students show you the changes on the graph. Look for ways that students will find two more points given two points on a line.

•  Start at the point where x is 3. What is the corresponding value for y?

•  Now look at the point where x is -2. What is y? What is the change in the horizontal and the vertical directions between these two points?

•  What does this tell you about the slope of the line representing the equation?

•  If you looked at the ratio of horizontal change to vertical change between two different points on the graph of the line, what would the ratio be? How do you know?

For Question C, ask students to show you or explain to you how the coefficient of x is related to the ratio of vertical change to horizontal change on a graph.

Student Activities

Make Up Work!!!

Class Work:  MSA 4.2: Finding the Slope of a Line

 

Assessment/Evaluation

Summary:  Discuss all of the Questions. Make the connections among the various representations of slope—as the constant rate of change between two variables, the ratio of vertical change to horizontal change between two points of the graph of a linear relationship, and the coefficient m in the equation y = mx + b. See the extended Summarize for suggestions on developing the connection between slope and rate of change, using slope to find points on a line, and methods for finding the y-intercept.

Academic Vocabulary

KIM: None

Additional Resources

CMP Book, notebook, calculators

Friday May 11, 2012

Objective

(Student will…)

•   Explore patterns among lines with the same slope—parallel lines

•   Explore patterns among lines whose slopes are negative reciprocals of each other—perpendicular lines

Teacher Activities & Strategies

MSA 4.3: Exploring Patterns With Lines

LaunchLaunch with the Getting Ready. Students should notice that they can sketch many lines with a slope of 3 that are parallel to their first line drawn.

Ask them for observations on the set of lines in Question A. Students can work in pairs or groups of 3 or 4, and can use their calculators, but each student should keep a sketch of each graph for reference.

Explore:  As you walk around, encourage the students to look for patterns and make conjectures. Then encourage them to think about why their conjectures might work. Use large sheets of graph paper for groups to record their work.

Suggest that they try a different coefficient (slope) for Question A to test their conjectures.

•  What do the graphs of the lines y = 2x + 5 and y = 4x + 10 look like?

•  Do they fit the patterns in Question A?

Going Further: Have students explore the family of lines such as: y = a (horizontal lines) and x = a (vertical lines).

Student Activities

Make Up Work!!!

Class Work: MSA 4.3: Exploring Patterns With Lines

 

Assessment/Evaluation

Summary: Have groups share their conjectures and reasoning. You can refer to the posters and/or use the overhead display of the graphing calculator to show examples from various groups. After you have summarized the problem, ask:

•  Is the line that passes through the points (0, 6) and (2, 12) parallel to the line

y = 3x + b? Why?

•  Are the lines y = 5x + 2 and y = -0.2x perpendicular to each other? Why?

•  Which of the lines are parallel to each other? Which are perpendicular to each other?

       y = 6 – 4x       y = 8 + 2.5x       2y = -8x         

        y = 0.25x – 1                              y = 6 – 0.4x

Academic Vocabulary

KIM: None

Additional Resources

CMP Book, notebook, calculators

 

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