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Focus Plan Texarkana Independent School District GRADING PERIOD: Teacher: 3rd Six Weeks PLAN CODE: Tipton Course/subject: Mathematics Grade(s): 8 Time allotted for instruction: 1 – 1 ½ hours Title: What is the Pattern? Lesson TOPIC: Patterns and Sequence TAKS Objective: Objective 6: The student will demonstrate an understanding of the mathematical processes and tools used in problem solving. FoCUS TEKS and Student Expectation: (16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples (5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to: (B) use an algebraic expression to find any term in a sequence Supporting TEKS and Student Expectations: Concepts Pattern Enduring Understandings/Generalizations/Principles The student will understand that A pattern is a recognizable shape or arrangement of things (numbers). Sequence A sequence is an ordered list of numbers. Term A term is an element or number in a sequence. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District I. Sequence of Activities (Instructional Strategies) A. Focus/connections Prior to students entering the class, write the following numbers on the board: 8, 16, 24, 32,…… After students are seated, ask them to look for a pattern that describes the relationship between the numbers. Have the class predict what the next five numbers would be. B. Instructional activities (demonstrations, lectures, examples, hands-on experiences, role play, active learning experience, art, music, modeling, discussion, reading, listening, viewing, etc.) Explain to the class that the purpose of this lesson is to develop skills in the problem solving strategy of discovering and describing patterns in mathematical situations. Students must use inductive and deductive reasoning as they recognize and use patterns to explain, create and predict situations. Write the numbers 1, 3, 5, and 7 on the chalkboard. Ask the students to predict what number comes next. Next ask the students to brainstorm what the 75th number in the sequence would be. Discuss that it would take a long time to find the 75th term by repeatedly adding the common difference. Now show the class how you can find any term by writing an expression that describes the sequence. With the numbers on the board you could create the following table: 1st Term 2nd Term 3rd Term 4th Term 5th Term 1 3 5 7 9 1 + 2(1) 1 + 2(2) 1 + 2(3) 1 + 2(4) Have the class look at the table. What do the expressions for all of the terms have in common? Now have the students predict what the 75th term would be. Next predict what the 150th term in the sequence would be. The class should understand that the study of patterns supports learning to see relationships, to find connections, and to make generalizations and predictions. Understanding patterns nurtures the kind of mathematical thinking that helps students become problem solvers and abstract thinkers. C. Guided activity or strategy Have students get in groups of 2 - 3. Write the following numbers on the board: 1, 2, 4, 7, 11, …. Have the groups work together to determine the following: Find the next 5 numbers in the sequence Write an expression to describe the sequence Find the 62nd term in the sequence After pairs have been given time to work, go over the correct answers with the class. D. Accommodations/modifications Students requiring modifications may work with a peer for the guided activity. E. Enrichment Students requiring enrichment may reteach the lesson in the small group setting for the guided activity.. II. STUDENT PERFORMANCE A. Description Students may complete the Pattern Worksheet individually. B. Accommodations/modifications C. Enrichment Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District iii. Assessment of Activities A. Description Individual student grades may be taken on the Pattern Worksheet. B. Rubrics/grading criteria Grades may be taken based on the Pattern Worksheet Answer Key and Grading Rubric. C. Accommodations/modifications D. Enrichment E. IV. Sample discussion questions Why is it important to know how to work with patterns? In what real world settings do you see patterns? TAKS Preparation A. Transition to TAKS context The teacher will lead the students in a discussion of how pattern or sequence problems may look in test format by placing the following TAKS questions on the overhead/board. B. Sample TAKS questions 1. A pattern of equations is shown below. 1% of 800 = 8 2% of 400 = 8 4% of 200 = 8 8% of 100 = 8 16% of 50 = 8 Which statement best describes this pattern of equations? A. When the percent is doubled and the other number is halved, the answer is 8. B. When the percent is doubled and the other number is doubled, the answer is 8. C. When the percent is increased by 2 and the other number remains the same, the answer is 8. D. When the percent remains the same and the other number is increased by 2, the answer is 8. 2. The expression shown below describes a pattern of numbers. n(n – 1) + 4 If n represents a number’s position in the sequence, which pattern of numbers does the expression describe? A. 4, 6, 8, 10, 12…. B. 1, 4, 6, 10, 16…. C. 4, 6, 10, 16, 24…. D. 4, 10, 18, 28, 40…. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District 3. Which expression can be used to find the nth term in the following arithmetic sequence, where n represents a number’s position in the sequence? Position in Sequence Term A. B. C. D. 1 2 3 4 n 5 9 13 17 ? n+4 3n + 4 5n 4n + 1 4. Let n represent the position of a number in the following arithmetic sequence. 1/2, 1, 3/2, 2, …. Which expression can be used to find any term in the sequence? F. 2n G. 1/2 n H. 3/2 n J. 5/2 n V. Key Vocabulary Pattern, Sequence, Term VI. Resources A. Textbook Math Advantage ~ Middle School II Chapter 6: Writing and Simplifying Expressions Sequences and Expressions, pp. 134-137 Chapter 18: Growing and Shrinking Patterns Repeated Doubling and Halving, pp. 362-363 Patterns in Sequences, pp. 379-381 B. Supplementary materials Pattern Worksheet Pattern Worksheet Answer Key and Grading Rubric C. Technology Students may be taken to the computer lab to utilize the following websites with pattern/sequencing activities: http://www.funbrain.com/cracker/index.html http://www.kidport.com/Grade7/TAL/Patterns.htm VII. follow up activities (reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.) A good follow-up lesson would be one dealing with patterns while using exponents. VIII. Teacher Notes Another good introduction to this lesson would be to read a children’s book that has a predictable pattern that repeats over and over. Examples: The Little Red Hen, The House that Jack Built Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District