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Generalizing Rules for Even and Odd Numbers

Learn rules for adding/multiplying even and odd numbers using visual models. Practice exercises to master concepts effectively.

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Generalizing Rules for Even and Odd Numbers

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  1. Tuesday

  2. Oct. 20, 2015Day [B] Do now: • (1) Take out your H.W. and packet. • (2) In notebook, copy and fill in the blanks. • Even + even = __________ • Odd + odd = _________ • Odd + even = __________

  3. Oct. 20, 2015Day [B] Today’s Objective: I will be able to generalize rules for adding and multiplying even and odd numbers using “dot models” in order to complete exercises 4-6 with my partner. 6.NS.B.4

  4. Lesson 16: Oct. 20, 2015 What is an even number? (Page 74) • Evenly divided by 𝟐. • Unit (one) digit is 𝟎, 𝟐, 𝟒, 𝟔, or 𝟖 • Multiples of 𝟐

  5. Lesson 16: Oct. 20, 2015 What is an oddnumber? (Page 74) • CANNOT be evenly divided by 𝟐. • Unit (one) digit is 𝟏, 𝟑, 𝟓, 𝟕, or 𝟗 • NOT multiples of 𝟐

  6. Lesson 16: Oct. 20, 2015 Exercise 1 (Pg. 75)

  7. Lesson 16: Oct. 20, 2015 Exercise 1 (Pg. 75)

  8. Lesson 16: Oct. 20, 2015 Exercise 1 (Pg. 75)

  9. Lesson 16: Oct. 20, 2015 Exercise 2 pg. 75 • 2. Why is the sum of two odd numbers even? • a. Think of the problem 11 + 15. Draw dots to represent each number.

  10. Lesson 16: Oct. 20, 2015 Exercise 1 (Pg. 75) • b. Circle pairs of dots to determine if any of the dots are left over. When we circle groups of two dots, there is one dot remaining. When we look at the sum, however, the two remaining dots can form a pair, leaving us with a sum that is represented by groups of two dots. The sum is, therefore, even.

  11. Lesson 16: Oct. 20, 2015 Exercise 1 (Pg. 75)

  12. Lesson 16: Oct. 20, 2015 Exercise 3 pg. 76

  13. Lesson 16: Oct. 20, 2015 Students work in groups to work on p. 77. (15 minutes)

  14. Exploratory ChallengeExercises 4 (Pg. 77) Lesson 16: Oct. 20, 2015 4. The product of two even numbers is even. One example answer: Using the problem 𝟔×𝟏4, students know that this is equivalent to six groups of fourteen, or 14 + 14 + 14 + 14 + 14 + 14 We know that the sum of two even numbers is even; therefore, when adding the addends two at a time, the sum will always be even. This means the sum of six even numbers will be even, making the product even since it will be equivalent to the sum.

  15. Exploratory ChallengeExercises 4-6 (Pg. 77) Lesson 16: Oct. 20, 2015 4. The product of two even numbers is even. One example answer: Using the problem 𝟔×𝟏4, students know that this is equivalent to six groups of fourteen, or 14 + 14 + 14 + 14 + 14 + 14

  16. Exploratory ChallengeExercises 5 (Pg. 77) Lesson 16: Oct. 20, 2015 5. The product of two odd numbers is odd. • One example answer:Using the problem 𝟓x 𝟏5, we know that this is equivalent to five groups of fifteen, or 15+15+15+15+15. • We also know that the sum of two odd numbers is even, and the sum of an odd and even number is odd. • When adding two of the addends together at a time, the answer will rotate between even and odd. • When the final two numbers are added together, one will be even and the other odd. • Therefore, the sum will be odd, which makes the product odd since it will be equivalent to the sum.

  17. Exploratory ChallengeExercises 5 (Pg. 77) Lesson 16: Oct. 20, 2015 5. The product of two odd numbers is odd. One example answer:Using the problem 5 x 15, we know that this is equivalent to five groups of fifteen, or 15+15+15+15+15.

  18. Exploratory ChallengeExercises 6 (Pg. 77) Lesson 16: Oct. 20, 2015 6. The product of an even number and an odd number is even. • One example answer:Using the problem 𝟔 x 𝟕, students know that this is equivalent to the sum of six sevens, or 𝟕+𝟕+𝟕+𝟕+𝟕+𝟕. • You know that the sum of two odd numbers is even, and the sum of two even numbers is even. • Therefore, when adding two addends at a time, the results will be an even number. • Calculating the sum of these even numbers will also be even, which means the total sum will be even. • This also implies the product will be even since the sum and product are equivalent.

  19. Exploratory ChallengeExercises 6 (Pg. 77) Lesson 16: Oct. 20, 2015 6. The product of an even number and an odd number is even. One example answer:Using the problem 𝟔×𝟕, students know that this is equivalent to the sum of six sevens, or 𝟕+𝟕+𝟕+𝟕+𝟕+𝟕.

  20. Lesson 16: Oct. 20, 2015 How do you feel? topic.

  21. Lesson 16: Oct. 20, 2015 Ticket-to-go (in agenda) Determine whether each sum or product will be evenor odd. 1. 56,426 + 17,895 = evenorodd 2. 317,362 × 129,324 = evenorodd 3. 10,481 + 4,569 = evenorodd 4. 32,457 × 12,781 = evenorodd

  22. Lesson 16: Oct. 20, 2015 Problem Set on Page 78

  23. Lesson 16: Oct. 20, 2015 • Accommodations • Read or reread presentation or activity directions, as needed • or after prompting • Use examples to model and act as a guide for emerging learners

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