![]() ![]() ![]() Square Pyramid Data Try to formulate a general equation to represent the pattern you found. STEP 2 Examine the starburst in each row. Next place your orange starburst on the top to finish off our pyramid. Place all your pink on the bottom, and then place your yellow starbursts on top of the pink. Predict how many cannonballs were used to build the figure in the picture?ħ Step 1 Build your pyramid. Predict how many cannonballs are in the 5th row. Common Difference The difference between two numbers in an arithmetic sequence.ġ. Arithmetic Patterns A pattern made by adding the same value to each term. Summation The addition of a sequence of numbers, the result is their sum or total. Series The value you get when you add all the terms of a sequence, this value is called the “sum”. ![]() Each student will need their own copy of the activity packet, but will share the physical material amongst the group.ĥ Terms to know Sequence A list of numbers or objects in a special order. For example, build a function that models that temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.Īctivity packet (1 per student) Starburst: Pink (9 per group) Starburst: Yellow (4 per group) Starburst: Orange (1 per group) Calculator (Optional) The students will be working in groups of 3 to 4 to complete this activity. ![]() b) Combine standard function types using arithmetic operations. a) Determine an explicit expression, a recursive process, or steps for calculation from a context. Write a function that describes a relationship between two quantities. Generalize patterns using explicitly defined and recursively defined functions CCSS: Building Functions F-BF Building a function that models a relationship between two quantities. Understand patterns, relations, and functions 1. The students will calculate the sum of the series. The students will build a summation to represent an arithmetic series. Objective: The students will formulate an equation to represent an arithmetic sequence. The students will demonstrate the ability to recognize patterns in a sequence and derive formulas for the sum of a series. Explicit and recursive formulas are found.1 Hands-On Activity: Exploring Arithmetic Sequences and Seriesīy: Melissa Medici MTH 4040: Coordinating Seminar April 2017 This activity builds the fundamentals of geometric sequences by finding missing terms and then slowly abstracting the process. Explicit formulas are found and the connection between the explicit formula and the slope-intercept form of a line is emphasized.Īrithmetic Sequences Activity 2c – Geometric Sequences This activity builds the fundamentals of arithmetic sequences by finding missing terms and then slowly abstracting the process. Recursion and Abstraction Activity 2b – Arithmetic Sequences If so, students should be encouraged to learn how to express formulas recursively, and writing recursive formulas is a good outcome even for students that are unable to write the explicit formula. Depending on the students’ familiarity with equations of lines, they may be adapt at writing explicit formulas. Students are asked to put results in a table, and may also be able to express formulas. This description should be done in words, and can also be used as an introduction to the mathematically notation for sequences. This activity encourages students to look for patterns and to describe a step-by-step procedure. Activities – Chapter 2 Activity 2a – Recursion and Abstraction ![]()
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