Algebra Grade 9 Lesson Plan

LESSON PLAN EXAMPLE: ALGEBRA, GRADE 9

Date: October 2, 2009 Teacher(s) Name: Mrs. Smith Grade: 9, Algebra I Lesson: Representing patterns as functions Content Area: Mathematics ? Algebra

Description/Abstract of Lesson: Students will extend a variety of patterns. They will generalize the pattern and represent it in multiple ways (tables, graphs, function rules, and in words).

Timeline of Lesson: Two 50-minute periods or one 90-minute period. Additional time will be needed if you have students present their work.

NCTM Standards

Process Strand: Representation Students will use representations to model and interpret physical, social, and mathematical phenomena.

Content Strand: Algebra Students will recognize, use, and represent algebraically patterns, relations, and functions.

Note: There are many additional strands (problem solving, communication, connections, and reasoning and proof) addressed in this lesson. Only the key strands are listed.

Objectives: Upon successful completion of this lesson, students will be able to:

a) explore and extend a pattern; b) complete a data table that describes how the pattern is changing; c) determine and write a function rule for the relationship found in the data table; d) graph the function; and e) identify the dependent and independent variable in the function.

Prerequisite knowledge: graphing ordered pairs, writing algebraic expressions

Introduction:

Begin instruction with a "Do Now" problem. Instruct students to consider the figures below. Draw and describe in words the next figure (n = 4).

The problem could be presented on the SmartBoard as the students entered the class. Students work on the "Do Now" during the taking of attendance, collection of homework, and other administrative tasks. Hide the figure corresponding to n=4 to be revealed after a discussion takes place.

After students have been given an opportunity to explore the problem, bring the class back together to discuss their solutions. Ask students what they noticed about the figures as n changed from 1 to 3. Encourage students to use correct terminology for the shapes (triangle, quadrilateral, pentagon, hexagon, etc.). Most students will describe the nth shape in terms of the (n-1)th shape. Encourage them to describe it in terms of n.

Write the descriptions as students generate them and help students generalize the rule.

The figure at n = 4 is made up of a large red shape with 6 sides. Inside the large red shape is a smaller yellow shape with 7 sides.

Then, ask the students to generalize their rule.

The nth figure is made of up a large red shape with n+2 sides. Inside that shape is a smaller yellow shape with n+3 sides.

Reveal the shape at n = 4 to show that students generated the correct rule.

Tell students that we use mathematics to describe the way things change in the real world. This allows us to generalize rules that will help us predict future events such as weather. The mathematics used to predict future real-world events tends to be very complex and is beyond the scope of this course. However, if students want to become the scientists and engineers of the future, they need to learn how to use the basic tools of mathematics to represent patterns found in nature and the physical world. This will allow them to build good rules for predicting future events.

Lesson Preparation

a) Have the introductory problem and Task 1 (see below) available for presentation via the SmartBoard or overhead.

b) Have the Pattern Activity Handouts attached to baggies containing the materials needed to complete the activities ready to hand out.

c) Assign students to work in homogeneous ability level groups.

Model the Activity

Whole class: The teacher will use the first task to model the activity that follows.

Task 1: Using the pattern blocks, create the first figure. Create the blocks on SmartBoard and build the figures, overhead, with cutouts or draw the figures on the board. Use color to help students see the hexagons and the triangles. Remember that some students cannot see color, so be sure to show how the figures are made of up a triangle and hexagons.

Ask: If each side of the green triangle is one unit, what is the perimeter of the figure at h = 1? (Show that the sides of the green triangle and the hexagon are the same length.) Have the students count the sides as you mark them off. Find the perimeters of the figures at h = 2 and 3. Assume the figures continue to change following the same pattern. Fill out the table below showing how the number of hexagons in the figure relates to the perimeter of the figure generated. State the rule that will allow us to calculate the perimeter for h = n (any number of hexagons).

h = 1

h = 2

h = 3

Complete the following table: Number of Perimeter

Hexagons

(P)

(h)

1

7

2

11

3

15

4

...

100

n

When you have completed the table for P for h = 1, 2, and 3, ask students to predict the perimeter for h = 4. Discuss why they think the pattern is correct. Students should see that each hexagon adds 4 to the perimeter because the new hexagon shares one side with the existing shape and those two sides are removed from the perimeter. Be sure that students understand why the pattern adds 4 and not 5 or 6. This will be difficult for some students to see. Ask different students to explain in their own words how the table and the function relate to the figure. Create the figure for h = 4.

Write a function rule for P, where P is the perimeter of the figure generated for any number h. Reinforce that there is a constant difference between the values for P as h increases by 1. Have students explain how this constant difference relates to the function rule.

Graph the first four points in the table. Have students explain how to label the axis and set an appropriate scale if the numbers are too large for their graph paper. Ask them what they notice about the relationship of the points to one another on the graph? How does the graph relate to the function rule? (They should see that, if connected, the points would form a straight line.)

Remind students that in this figure, the perimeter depends on the number of hexagons.

The number of hexagons is the independent quantity and the perimeter is the dependent quantity. We say "h" is the independent variable and "P" is the dependent variable. Another way to think of this is that P, the perimeter, depends on h, the number of hexagons. (Note: If you use a word wall, you should add "independent variable" and "dependent variable" at this time.)

Have students explain in their own words why "h" is the independent variable and "P" is the dependent variable.

Group Activity:

List the group activity guidelines on the SmartBoard. a) Move to your assigned group. b) Read the instructions on the handout. c) Open the materials and follow the instructions. d) Let your teacher know when you are ready to create your poster.

e) Create and post your poster.

Tell the students that they will work in groups to explore a pattern, complete a data table, graph the data, determine a function rule, and describe the pattern in words. Then, they will create a poster showing their work. The posters will be displayed to other members in the class to review and will be available for their family members to see during "Family Conferences."

Assign one group member to pick up materials for their group. Signal for students to move to their groups and start work.

During the last five minutes of the period during the first day, ask students to put their work together and to collect their materials. Have the materials person return the items.

Ask students to briefly describe one thing they noticed about their pattern. At the end of day two, assign each group to review a poster of their peers and complete the assessment rubric as an exit slip.

Areas Where Students May Struggle

Some students have trouble initially grasping the lesson and are therefore slow to start their work.

Some students have trouble seeing patterns. Some students cannot see color. Some students can't attend to the patterns with only the manipulatives as guides.

Differentiating Instruction

Adaptation 1: Some students will easily complete the introductory activity while others will struggle or be slow to start their work. Add a challenge problem to the introductory activity, "What is does the figure look like at n = 100?" Students can work on the challenge problems when they have free time and drop their solutions into the Challenge Problem Box by the end of the day.

Adaptation 2: Colored pattern blocks are used in the figures for Task 1. The color helps students see the hexagons and triangle in the pattern. This makes it easier for students to identify the sides and determine the perimeter of the figure. Remember that not all students see color and you may need to point to the shapes as well as identify them by color.

Adaptation 3: For the group work activity, select four tasks that range from a basic level (Level A) to a relatively complex level (Level C). Group students homogenously with respect to ability level and assign each group a task that is challenging and doable. The worksheets throughout this lesson are scaffolded, and questions embedded in the lesson are meant to help students get started and to help them think through intermediate steps.

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