problem solution about the element school education of mathematics

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Name____________________________________________ Anchor Task 3: Number Theory -- Consecutive Sums [Section B: Due Tuesday, May 2nd at the start of class. Attach your work to this cover sheet.] Here are examples of sums of consecutive integers. • 3+4=7 • 4 + 5 + 6 + 7 = 22 • 2+3+4=9 In the first, the number 7 is written as the sum of two consecutive integers. In the second, 22 is written as the sum of four consecutive integers. In the last, 9 is written as the sum of 3 consecutive integers. Initial exploration: 1. Try to write each number from 1 to 35 as the sum of consecutive integers. Can you find more than one way for some of the numbers? 2. Explore what numbers can and cannot be made by sums of consecutive integers! Record 2-3 discoveries that you can share with the class. Anchor Task Solution For your write-up of this Anchor Task, record and explain TWO discoveries you’ve made about the sums of consecutive integers. You should use some examples to illustrate each discovery and then make a convincing argument about why you think the discovery is true. You may draw upon the ideas of your classmates. Additional Challenges For this anchor task, engage in one or more of the following additional challenges. A. Record and justify a third discovery about the sums of consecutive integers. B. Work backwards! Without doing any calculations, predict whether the following numbers can be made with 2 consecutive integers, 3 consecutive integers, 4 consecutive integers, etc. Explain your predictions. o 45 o 57 o 62 o 75 o 80 C. Write a shortcut for writing the following numbers as the sum of two or more consecutive numbers. Describe the shortcuts you created and tell how you used them to write each of the numbers below as sums of consecutive integers. o 45 o 57 o 62 o 75 o 80 EDUC 170, Spring 2017 Adapted from: Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide for Teachers, Grades 6-10. Heinemann, 361 Hanover Street, Portsmouth, NH 03801-3912.
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HI there,Attached below please find the complete solution this assignment. All work is displayed.Thanks again,Selenica

Name____________________________________________

Anchor Task 3: Number Theory -- Consecutive Sums
[Section B: Due Tuesday, May 2nd at the start of class. Attach your work to this cover sheet.]
Here are examples of sums of consecutive integers.
• 3+4=7
• 4 + 5 + 6 + 7 = 22
• 2+3+4=9
In the first, the number 7 is written as the sum of two consecutive integers. In the second, 22 is written as the
sum of four consecutive integers. In the last, 9 is written as the sum of 3 consecutive integers.
Initial exploration:
1. Try to write each number from 1 to 35 as the sum ...