Home Forums Grades Pre K-2 Grades 3-5 Grades 6-8 Grades 9-12

Algebra Patterns

Objectives:

· Represent a numerical pattern with an algebraic expression.

Download as Microsoft Word document or Inspiration file:

Instructional Plan

Unit Outline – requires Inspiration

Vocabulary – requires Inspiration

Mathematics Governor’s Institute 2005

Names of Group Members: Karen Tucker, Eugene Wengerd, David Taylor

Topic / Theme: Algebra / Patterns

Level: 8^th or 9^th Grade Algebra

Time Element: 40 – 50 minute class period

NCTM Standards Addressed:

· Generalize patterns using explicitly defined and recursively defined functions.

· Understand relations and functions and select, convert flexibly among, and use various representations for them.

· Create and use representations to organize, record, and communicate mathematical ideas.

PA Math Standards Addressed:

2.8.11.Q

Represent functional relationships in tables, charts and graphs.

2.8.11.A

Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically.

2.8.11.Q

Represent functional relationships in tables, charts and graphs.

PA Math Assessment Anchors Addressed:

M11.D.1.1.1

Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.

M11.D.3.1.1

Identify, describe, and/or use constant or varying rates of change.

M11.D.4.1.1

Match the graph of a given function to its table or equation.

M11.D.4.1.2

Graph linear functions in two variables.

Reading Assessment Anchors Addressed:

R11.A.2

Demonstrate the ability to understand and interpret nonfiction text including textbooks.

Objectives:

· Represent a numerical pattern with an algebraic expression.

Instructional Strategies and Plan:

1. Distribute Growing Dots 1 and pose the problem.

2. Students work on the problem in pairs or small groups.

3. In a guided discussion with the whole group, as students to share their solutions. Develop a table to represent the relationship.

minutes	0	1	2	3	4	5	…	100	…	t
# dots	1	5	9	13	17	21	…		…

4. Develop vocabulary terms constant difference and first difference.

5. Introduce the concept of dependent and independent variables and using an algebraic expression to relate these variables.

6. Students work in pairs or small groups to predict the number of dots after 100 minutes and the number of dots after an unknown t minutes.

7. As a whole-group, ask students to share their solutions and complete the table.

minutes	0	1	2	3	4	5	…	100	…	t
# dots	1	5	9	13	17	21	…	401	…	4t+1

Materials / Resources:

· Handout of the Growing Dots Problem

· Overhead

· Dots (Bingo markers, Smarties, M&M’s, checkers, poker chips, etc.)

Assessment Strategies:

Formative Evaluation

The teacher will check for student understanding throughout the Growing Dots 1 modeling problem.

Summative Evaluation

The Patterns Open-Ended Assessment will be administered to students to determine that the objectives of this lesson were achieved.

Extensions / Enrichment:

Upon completion of the Growing Dots 1 modeling program, Growing Dots 2 is available as an extension or enrichment activity. Individually or in pairs, students complete the activity Growing Dots 2 using the same strategies experienced in Growing Dots 1. A key question to ask students would be: “What are the similarities between Growing Dots 1, Growing Dots 2, and any other pattern that would have a different number of ‘arms’?”

Special Accommodations:

See Accommodations Folder for tools and strategies.

Growing Dots 1

1. Describe the pattern.

2. Assuming the sequence continues in the same way, use your dots to construct the pattern after 3 minutes.

3. How many dots are there in the pattern at 3 minutes?

4. Use the dots to extend the pattern for both 4 and 5 minutes.

5. How many dots are there in the pattern at 4 minutes?

6. How many dots are there in the pattern at 5 minutes?

Minutes

100

Dots

Growing Dots 2

1. Describe the pattern.

2. Assuming the sequence continues in the same way, use your dots to construct the pattern after 3 minutes.

3. How many dots are there in the pattern at 4 minutes?

4. Use the dots to extend the pattern for both 5 and 6 minutes.

5. How many dots are there in the pattern at 5 minutes?

6. How many dots are there in the pattern at 6 minutes?

Minutes

100

Dots

Name:

Patterns Open-Ended Assessment

The table below shows the approximate distance from a lightning strike to an observer based on the time it takes the observer to hear the thunder.

seconds

miles

0.2

0.4

0.6

a. Complete the table.

b. For each increase of one second, what is the constant difference?

constant difference =

c. Use this difference to calculate the distance in miles for 8, 9, and 10 seconds.

seconds

miles

d. The sound of thunder travels 16.4 miles in 82 seconds. Find the distance that the sound travels in 83 seconds. Find the distance that the sound travels in t seconds.

seconds

miles

16.4

Patterns Open-Ended Assessment Solutions and Rubric

Solutions:

seconds

miles

0.2

0.4

0.6

0.8

1.0

constant difference = 0.2

seconds

miles

1.6

1.8

2.0

seconds

miles

16.4

16.6

0.2t

Rubric:

4	Demonstrates a thorough understanding of the concept of constant difference and is able to correctly identify the algebraic expression in part d. All parts of the problem correct.
3	Demonstrates a general understanding of the concept of constant difference but has an incorrect answer due to an error and/or is unable to identify the algebraic expression in part d. Completes a, b, and c with or without calculation error, but not d.
2	Demonstrates a partial understanding of the concept of constant difference. Completes a and b, but not c or d.
1	Demonstrates minimal understanding of the concept of constant difference. Completes a correctly, but not b, c, or d.
0	No response or the response has no correct answer.

Home Forums Grades Pre K-2 Grades 3-5 Grades 6-8 Grades 9-12