Sum of an Arithmetic Sequence (Lesson 1.3)
Unit 1: Sequences and Linear Functions
Day 1: Recursive Sequences
Day 2: Applications of Arithmetic Sequences
Day 3: Sum of an Arithmetic Sequence
Day 4: Applications of Geometric Sequences
Day 5: Sequences Review
Day 6: Quiz 1.1 to 1.4
Day 7: Linear Relationships
Day 8: Point-Slope Form of a Line
Day 9: Standard Form of a Linear Equation
Day 10: Quiz 1.5 to 1.7
Day 11: Unit 1 Review
Day 12: Unit 1 Test
Unit 2: Linear Systems
Day 1: Linear Systems
Day 2: Number of Solutions
Day 3: Elimination
Day 4: Larger Systems of Equations
Day 5: Quiz 2.1 to 2.4
Day 6: Systems of Inequalities
Day 7: Optimization Using Systems of Inequalities
Day 8: Quiz 2.5 to 2.6
Day 9: Unit 2 Review
Day 10: Unit 2 Test
Unit 3: Function Families and Transformations
Day 1: Interpreting Graphs
Day 2: What is a function?
Day 3: Translating Functions
Day 4: Quiz 3.1 to 3.3
Day 5: Quadratic Functions and Translations
Day 6: Square Root Functions and Reflections
Day 7: Absolute Value Functions and Dilations
Day 8: Equations of Circles
Day 9: Quiz 3.4 to 3.7
Day 10: Unit 3 Review
Day 11: Unit 3 Test
Unit 4: Working with Functions
Day 1: Using Multiple Strategies to Solve Equations
Day 2: Solving Equations
Day 3: Solving Nonlinear Systems
Day 4: Quiz 4.1 to 4.3
Day 5: Combining Functions
Day 6: Composition of Functions
Day 7: Inverse Relationships
Day 8: Graphs of Inverses
Day 9: Quiz 4.4 to 4.7
Day 10: Unit 4 Review
Day 11: Unit 4 Test
Unit 5: Exponential Functions and Logarithms
Day 1: Writing Exponential Functions
Day 2: Graphs of Exponential Functions
Day 3: Applications of Exponential Functions
Day 4: Quiz 5.1 to 5.3
Day 5: Building Exponential Models
Day 6: Logarithms
Day 7: Graphs of Logarithmic Functions
Day 8: Quiz 5.4 to 5.6
Day 9: Unit 5 Review
Day 10: Unit 5 Test
Unit 6: Quadratics
Day 1: Forms of Quadratic Equations
Day 2: Writing Equations for Quadratic Functions
Day 3: Factoring Quadratics
Day 4: Factoring Quadratics. Part 2.
Day 5: Solving Using the Zero Product Property
Day 6: Quiz 6.1 to 6.4
Day 7: Completing the Square
Day 8: Completing the Square for Circles
Day 9: Quadratic Formula
Day 10: Complex Numbers
Day 11: The Discriminant and Types of Solutions
Day 12: Quiz 6.5 to 6.9
Day 13: Unit 6 Review
Day 14: Unit 6 Test
Unit 7: Higher Degree Functions
Day 1: What is a Polynomial?
Day 2: Forms of Polynomial Equations
Day 3: Polynomial Function Behavior
Day 4: Repeating Zeros
Day 5: Quiz 7.1 to 7.4
Day 6: Multiplying and Dividing Polynomials
Day 7: Factoring Polynomials
Day 8: Solving Polynomials
Day 9: Quiz 7.5 to 7.7
Day 10: Unit 7 Review
Day 11: Unit 7 Test
Unit 8: Rational Functions
Day 1: Intro to Rational Functions
Day 2: Graphs of Rational Functions
Day 3: Key Features of Graphs of Rational Functions
Day 4: Quiz 8.1 to 8.3
Day 5: Adding and Subtracting Rational Functions
Day 6: Multiplying and Dividing Rational Functions
Day 7: Solving Rational Functions
Day 8: Quiz 8.4 to 8.6
Day 9: Unit 8 Review
Day 10: Unit 8 Test
Unit 9: Trigonometry
Day 1: Right Triangle Trigonometry
Day 2: Solving for Missing Sides Using Trig Ratios
Day 3: Inverse Trig Functions for Missing Angles
Day 4: Quiz 9.1 to 9.3
Day 5: Special Right Triangles
Day 6: Angles on the Coordinate Plane
Day 7: The Unit Circle
Day 8: Quiz 9.4 to 9.6
Day 9: Radians
Day 10: Radians and the Unit Circle
Day 11: Arc Length and Area of a Sector
Day 12: Quiz 9.7 to 9.9
Day 13: Unit 9 Review
Day 14: Unit 9 Test
Learning Targets
Find the sum of an arithmetic sequence with a set number of terms.
Interpret summation notation and calculate the sum.
Tasks/Activity | Time |
---|---|
Activity | 20 minutes |
Debrief Activity with Margin Notes | 10 minutes |
QuickNotes | 5 minutes |
Check Your Understanding | 10 minutes |
Activity: The Super Stairs
Lesson Handouts
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Answer Key
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Homework
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Experience First
The goal of today's lesson is for students to create a formula for the partial sum of an arithmetic sequence. That is a lofty goal! You might be thinking, "There's no way you can EFFL this lesson." But guess what, you can! It might take a little more teacher guidance than other lessons, but still, students can come up with the formula without you telling it to them. It will be very tempting to just tell them the formula when they get stuck, but trust the process!
Today's lesson is an adaptation of a lesson created by Dan Meyer, called The Super Stairs. To start, show this video to the class. After that, let students take off! They should be able to work through questions #1-3 pretty quickly. Things start getting tough around #4. Here's where you will want to have your guiding questions all queued up. Guiding Questions: A goal during this time is to get students to notice that when they were adding up 2 + 4 + ... + 14 + 16 for the 8 stairs, they could pair the terms so that each pair equals 18. The first and last terms (2 + 16 = 18) show us what the sum of the pairs should be. Since we're pairing, we take the number of terms and divide it by two to find the number of pairs. This would leave them with 4 pairs of 18. They can use this idea to find the pairs for a staircase with 21 stairs. Another way students can approach this problem is by adding the sequence twice to see the pairs. To get students thinking about this I tell them, "When I do the Super Stairs, I like to start with stair 21 first and work my way down. What would my sequence look like? Write it under the sequence you listed out for Dan. What do you notice? What if you added my sequence with Dan's sequence?" This method requires a bit more teacher guidance but I like to show how either way, we end up with the same total.
Formalize Later
When most groups have completed the front page, it's time to debrief. You'll want to make sure you point out that we are adding an arithmetic sequence. Have students explain their work to the class and how they came up with their total number of steps. If groups solved the problem in a different way, make sure to highlight the variety of different approaches. As a class, talk through how to write a formula for the total number of steps using terms like "first", "last", and "# of steps". Try to keep this all in the context of the problem for question #4. But once you've done that, you can swap in the algebraic version for question #5. And voila, your kids just came up with the formula for the partial sum of an arithmetic sequence! Note: Here is a video showing the solution to the number of steps that it takes Dan to complete the 21 stair Super Stairs.