![]() As a result, the total number of grains per 64 cells of the chessboard would be so huge that the king would have to plant it everywhere on the entire surface of the Earth including the space of the oceans, mountains, and deserts and even then would not have enough! The king was amazed by the “modest” request from the inventor who asked to give him for the first cell of the chessboard 1 grain of wheat, for the second-2 grains, for the third-4 grains, for the fourth-twice as much as in the previous cell, etc. According to the legend, an Indian king summoned the inventor and suggested that he choose the award for the creation of an interesting and wise game. ![]() One of the most famous legends about series concerns the invention of chess. 400 years ago, a famous mathematician couldn't confirm his theory computers did it two days ago.Over the millenia, legends have developed around mathematical problems involving series and sequences. How many cannonballs are needed to build the figure in the picture?ġ4 Practice: Let’s practice using the two new formulas that we discovered!ġ5 Practice: How many starbursts would be required to build the 300th figure in this sequence? How many starbursts will be in the 18th row of this square pyramidal? How many starbursts will be in the 100th row of this square pyramidal? How many starbursts would be required to build the 54th figure in this sequence?ġ6 Reflection Melissa Medici Did students struggle with definitions of terms? What vocabulary strategies might make learning these definitions easier for students? What would be the biggest challenge for students with disabilities? What can be used to make that discovering the patterns easier to understand?ġ7 Resources Love, D. Determine how many cannonballs are in the 5th row. Determine how many cannonballs are in the 5th row.Ĭannonball Problem 1. Square Pyramid Data Sequence of the Rows Series of the Square Pyramid Figure 1 1 Figure 2 4 5 Figure 3 9 14 Figure nġ3 1. Sequence of the Rows Series of the Square Pyramid Figure 1 1 Figure 2 4 5 Figure 3 9 14 Figure n ? Square Pyramid Data Try to build a summation to represent the pattern you found. Can we notice a pattern between the figures in this sequence? STEP 3 Now that we have examined the starburst in each row and have discovered a pattern. Sequence of the Rows Series of the Square Pyramid Figure 1 1 Figure 2 4 Figure 3 9 Figure n ?ġ0 Discover the relationship: SQUARE PYRAMIDALS ![]() 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. 1 Hands-On Activity: Exploring Arithmetic Sequences and Seriesīy: Melissa Medici MTH 4040: Coordinating Seminar April 2017
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