Cornerstone Project Consecutive Sums Day 1 Presentation Consecutive

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Cornerstone Project: Consecutive Sums Day 1 Presentation

Cornerstone Project: Consecutive Sums Day 1 Presentation

Consecutive Sums Task The number 18 can be made by adding three consecutive whole

Consecutive Sums Task The number 18 can be made by adding three consecutive whole numbers: 5 + 6 + 7 = 18 Which other numbers can be made by adding three consecutive whole numbers?

What does ‘consecutive’ mean? Question: What do we mean by three ‘consecutive’ whole numbers?

What does ‘consecutive’ mean? Question: What do we mean by three ‘consecutive’ whole numbers? Answer: A sequence of 3 whole numbers with a common difference of one. Example 1: 1, 2, 3 Example 2: 46, 47, 48

What is a ‘conjecture’? Question: What does it mean that you need to state

What is a ‘conjecture’? Question: What does it mean that you need to state a conjecture and prove your conjecture? Answer: A ‘conjecture’ is a statement that you think might be true but which you are not yet absolutely sure of. A conjecture can be tested to see whether or not it is true. Example: At least one person in this room had pasta for dinner yesterday.

Consecutive Sums Task assignment

Consecutive Sums Task assignment

Consecutive Sums Task questions 1 and 2 1. State a conjecture about the sums

Consecutive Sums Task questions 1 and 2 1. State a conjecture about the sums of three consecutive whole numbers. 2. Prove your conjecture (one idea is to experiment with numbers!).

Consecutive Sums Task - SAMPLE ANSWER 1. State a conjecture about the sums of

Consecutive Sums Task - SAMPLE ANSWER 1. State a conjecture about the sums of three consecutive whole numbers. My conjecture is that every time you sum three consecutive whole numbers you get an even number. 2. Prove your conjecture (one idea is to experiment with numbers!). 1 + 2 + 3 = 6 and 6 is an even number 3 + 4 + 5 = 12 and 12 is an even number 11 + 12 + 13 = 36 and 36 is an even number

Clarifying Questions Clarifying Question #1: Clarifying Question #2: Clarifying Question #3: Do you notice

Clarifying Questions Clarifying Question #1: Clarifying Question #2: Clarifying Question #3: Do you notice anything about your sums? Experiment some more and see if you find any patterns! Did you try a variety of different sets of whole numbers?

Consecutive Sums Task assignment

Consecutive Sums Task assignment

Consecutive Sums Task questions 3 and 4 3. Write at least one clarifying question

Consecutive Sums Task questions 3 and 4 3. Write at least one clarifying question (from the cards) that you think will help you to improve your conjecture and/or your proof. 4. Revise your conjecture and/or your proof. Then, explain your proof in writing.

Homework: Consecutive Sums Task 2 Conjecture: The sum of two consecutive whole numbers is

Homework: Consecutive Sums Task 2 Conjecture: The sum of two consecutive whole numbers is always odd. 5 + 6 = 11 1. Investigate this conjecture. 2. Do you think this conjecture is correct? Explain how your investigation supports your answer: