Lesson Components Planned Activities

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. 2. Model with mathematics. 3. Use appropriate tools strategically 8. Look for and express regularity in repeated reasoning.

Curriculum Standard Identify the curriculum standard/element to be taught in this lesson.

MCC9-12.F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. (Draw examples from linear and exponential functions.) MCC9-12.F.FIF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Draw connection to F.BF.2 which requires students to write arithmetic and geometric sequences.)

Learning Target Identify the learning skill(s) from the curriculum standard/element that the students will be expected to learn during this lesson.

• Determine if a relation is a function • Recognize arithmetic sequences • Extend and write formulas for arithmetic sequences • Demonstrate mastery of Unit 3 Standards thus far

Lesson Opening Activities Include activities to engage students in the intended instructional outcomes. Differentiated Instruction Methods ! Learning Materials (Content) ! Ways of Learning (Process) ! Ways of Demonstrating Learning (Product)

Teacher Toolkit Assessing Prior Knowledge Activities

❒ Background Knowledge Probe ❒ Entrance & Exit Slips ❒ Quick-Write/Written Conversation ❒ Think-Pair-Share ❒ Graphic Organizers ❒ K-W-L (K and W only) ❒ Cornell Notetaking ❒ Other__Guided Notes_____________

Student Materials:

• Pencil • Interactive notebook • Copy of Arithmetic Sequences Guided Notes • PowerPoint with instructions and expectations

Essential Question (3-5 MINS) Develop a question that reflects the “big idea” of the lesson and used to “hook” students into thinking critically about the content of the lesson through inquiry based discussion or analytical writing.

Review the standard, objective, and target of the day’s lesson. EQ: How do I represent a relation, both as a function and as a sequence?

One or more students will read aloud the standards, objective and target of the lesson. Students will be given 2 minutes to write them in their Interactive Notebooks.

Course: CCGPS Coordinate Algebra Unit: 3 Lesson: Functions and Arithmetic Sequences

Dr. Ronald E. McNair High School Teacher: ________________________________________________ Daily Instructional Lesson Plan

Date: __Monday, 11/5/12 (Week 13) _________________________

Sponge/Warm-Up Activity (3-5 MINS) Include an introductory activity that activities prior knowledge and connects it to the new concept or skill for this lesson.

Activity will be presented on the Promethean Board as the students enter the class. Teacher will circulate the class to monitor the students’ progress. Teacher will go over the warm-up on the board, encouraging student participation and explanation.

Direct Teaching Activity (10-15 MINS) Include a teacher-led activity in which the new concept and/or skill is taught and students take notes

Teacher will hand out the guided notes handout on sequences and go through each example on the board. Teacher will circulate to ensure all students are working the problems out on their paper. Teacher will use thumbs up/down to assess understanding before moving onto the next example.

Students will receive a copy of the Arithmetic Sequences guided notes, and follow along each example with the teacher. Students will work out problems on their papers, and ask questions when confused. Students will participate in thumbs up/down to show understanding of each example before moving on. (The guided notes are copied below, with the solutions in

blue.)

Unit 3: Arithmetic Sequences Guided Notes EQ: How do I represent a relation, both as a function and as a

sequence? Objectives:

• Recognize arithmetic sequences • Extend and write formulas for arithmetic sequences

Example 1: Identify Arithmetic Sequences Determine whether each sequence is arithmetic. Justify your answer.

a) 1, 2, 4, 8, … Not arithmetic because goes up by different amounts each

time.

b) ½, ¼, 0, -1/4, … Arithmetic – goes down by ¼ (or up by – ¼) each time

Example 2: Extend a Sequence Find the next 3 terms of the arithmetic sequence 74, 67, 60, 53, … 46, 39, 32 Example 3: Find a Specific Term KEY: The nth term of an arithmetic sequence is found using the following equation an = a1 + (n – 1) d n = nth term a1 = first term of sequence d = difference between terms in sequence Find the 14th term in the arithmetic sequence 9, 17, 25, 33, …. a14 = a14 = 9 + (14 – 1)*8 = 9 + 13*8 = 9 + 104 = 113 Example 4: Write An Equation for a Sequence Consider the arithmetic sequence 12, 23, 34, 45, … *Write an equation for the nth term of the sequence an = an = 12 + (n – 1)*11 = 12 + 11n – 11 = 11n + 1 Find the 10th term in this sequence a10 = 11(10) + 1 = 110 + 1 = 111 Graph the first five terms of the sequence

n an = 11n + 1 an (n, an) 1 a1 = 11(1) + 1 12 (1, 12) 2 a2 = 11(2) + 1 23 (2, 23) 3 a3 = 11(3) + 1 34 (3, 34) 4 a4 = 11(4) + 1 45 (4, 45) 5 a5 = 11(5) + 1 56 (5, 56)

**Notice that the points fall on a line. The graph of an arithmetic sequence is LINEAR!!!

Lesson Work Period Activities Include activities to engage students in the application of new learning to meet the intended instructional outcomes. Differentiated Instruction Methods ! Learning Materials (Content) ! Ways of Learning (Process) ! Ways of Demonstrating Learning (Product)

Teacher Toolkit Problem-Based Inquiry/Collaborative Activities

❒ Cues and Questions ❒ Question Wall ❒ You Be the Judge ❒ Socratic Seminar ❒ Four Corners Jigsaw ❒ Reciprocal Teaching ❒ Literature Circles ❒ Thinking Map Activity ❒ Cornell Notetaking ❒ Dialogic Journals ❒ Other__Unit 3 Lesson 2 Quiz , KWL_____

Student Materials:

• Pencil • Scientific Calculator • Copy of Unit 3 Lesson 2 Quiz

Guided Practice/Independent Practice (20-55 MINS) • Include an instructional activity that

requires students to apply what was learned during the lesson’s opening and provides the teacher with an opportunity to assess student learning.

• Students (collaboratively or independently) complete a product to be submitted to the teacher for review/assessment.

Teacher will pass out the quiz and a scientific calculator to each student. Teacher will set the timer for 30 minutes and circulate the room to ensure students are working on the Quiz and have their eyes on their own paper

Students will work individually and silently on the Unit 3 Lesson 2 Quiz. Students will write their answers on the quiz and show their work. When students are finished, they will raise their hand and have their quiz collected. Students who finish early will fill in portions of their KWL chart, based on the quiz and previous week’s standards.

. Lesson Closing Activities Include activities to assess the level to which student’s met the intended instructional outcomes. Differentiated Instruction Methods ! Learning Materials (Content) ! Ways of Learning (Process) ! Ways of Demonstrating Learning (Product)

Teacher Toolkit Wrap-Up Activities

❒ 3-2-1 Assessment ❒ Minute Paper ❒ Learning Logs ❒ Three Minute Review ❒ Wows and Wonders ❒ K-W-L (L only) ❒ High Yield Strategies ❒ Other_Flow Map – Explicit Formula________________

Student Materials:

• Pencil • Interactive notebook • Flow Map Template

Closing Activity (5-10 MINS) The lesson is summarized/synthesized through a short instructional activity that involves opportunities for students to demonstrate mastery through reading, writing, thinking, and discussion (i.e. Exit Tickets, thinking maps).

Teacher will have the closing instructions on the Promethean board, as well as a flow map template. Teacher will go over the instructions, and circulate the room to ensure students are properly completing a flow map.

Students will complete a Flow Map on finding the explicit formula for any arithmetic sequence. Selected students will share out their flow maps, explaining how they created the map and how they plan to use it.

Lesson Strategies Incudes strategies to meet the needs of all students

Teacher Toolkit Formative Assessment

❒ Hand Signals ❒ Index Cards ❒ Discussion Questions/Responses ❒ Question Box/Board ❒ Clickers ❒ Projects ❒ Other__Thinking Map______________

Student

Adjustments/Modifications Include any adjustments to the activities to accommodate student learning needs.

Preferential seating Extra time with a timer Visual aids and models (e.g., Thinking Map) Guided notes

Homework

Sequences Worksheet Arithmetic Sequences

(1) Which description shows the relationship between a term and n, its position in the sequence?

A Add 3 to n B Multiply n by 2 and then subtract 3 C Multiply n by 2 and then add 3 D Multiply n by 3 and then subtract 2

(2) Which sequence follows the rule 8n − 4, where n represents the position of a term in the sequence? F 16, 12, 8, 4, 0, … G 8, 16, 24, 32, 40, … H 4, 16, 64, 216, 1,024, … J 4, 12, 20, 28, 36, …

(3) Which description shows the relationship between a term and n, its position in the sequence?

(4) Which rule can be used to find the value of any term in the sequence below where n represents the term position?

A 2n + 4 B 4n + 2 C 3n + 3 D 8n – 2

(5)

(6) Which rule can be used to find the value of the nth term in the sequence, where n represents the term position?

(7) Which table shows the sequence that follows the rule 8n − 2, where n represents the term position in the sequence?

Assessments Identify the formative or summative assessments you will use to determine student progress towards mastery of the lesson’s instructional outcomes.

Unit 3 Lesson 2 Quiz