Be ready to build on student thinking and use the debrief to discuss both methods. Both of these strategies lead to the same sum formula, though written slightly differently. This sum of 175 will occur 15 times since there are 15 pairings of days. Another strategy is to realize that the days can be summed in any order and the sum of the first and last day is the same as the sum of the second and second to last day, is the same as the sum of the third and third to last day, and so on. Students use the idea of her average run time to find the sum of all 30 days. This idea of a constant (common) difference is critical to the rest of this lesson and ties in important ideas about a constant rate of change and linear functions. We specifically ask for June 29th so students recognize that her running time on that day is exactly five less than her running time on the 30th. While students may use a recursive pattern to find the first few values in the table, they should quickly recognize the need to make use of structure to find values for days later in June. Students identify that her time increases by five minutes every day and use this to fill in her running log. Today students look at Mallory’s running times during the month of June to explore the idea of arithmetic sequences. Day 4: Calculating Instantaneous Rate of Change.Day 3: Calculating Instantaneous Rate of Change.Day 2: Average versus Instantaneous Rates of Change.Day 3: Evaluating Limits with Direct Substitution.Day 7: Infinite Geometric Sequences and Series.Day 6: Geometric Sequences and Finite Series.Day 2: Using Sequences and Series to Describe Patterns.A growing patterns of squares or triangles formed from toothpicks is often used to show linear sequences in a. Day 3: Solving Systems with Elimination Sequences can be derived from shapes and patterns.Day 2: Solving Systems with Substitution.University of Melbourne School of Mathematics and Statistics. Day 15: Parametric Equations (With Trig) Sequences (Dynamic Illustrator) Activity.Day 9: Equations in Polar and Cartesian Form.Day 10: Transformations of Sine and Cosine Graphs.Day 11: Exponential and Logarithmic Modeling.Day 9: Solving Exponential and Logarithmic Equations.Day 3: Compound Interest and an Introduction to "e".Essentially a sequence is an ordered list with the being separated by commas. A sequence is a set of numbers that follow a certain rule. Unit 3: Exponential and Logarithmic Functions Introduction into Series and Sequences Sequence.Day 10: Connecting Zeros Across Multiple Representations.Unit 2: Polynomial and Rational Functions.Day 3: Rates of Change and Graph Behavior.Day 3: Solving Equations in Multiple Representations.
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