Problem of the Day 2.1

1. Problem of the Day 2.1 The number on Holly’s house is a 3-digit number. The digit in the hundreds place is twice the value of the digit in the tens place. The tens digit is three more than the ones digit. The sum of the digits is 13. What is the number on Holly’s house? The number on Holly’s house is 841.

2. Properties of Addition • Commutative Property- the order of the addends can change without affecting the sum. • Proof: 2 + 3 = 5 and 3 + 2 = 5 6 + 4 = 10 and 4 + 6 = 10

3. Properties of Addition • Associative Property – in an addition problem using more than two addends, the groupings of the numbers and the order these groups are added will not change the sum. • Proof: (2 + 3) + 7 = 12 and 2 + (3 + 7) = 12 (6 + 4) + 3 = 13 and 6 + (4 + 3) = 13

4. Properties of Addition • Associative Property – in an addition problem using more than two addends, the groupings of the numbers and the order these groups are added will not change the sum. • Proof: (2 + 3) + 7 = ? 2 + (3 + 7) = ? Which of these problems is easier to compute?

5. Properties of Addition • Associative Property – in an addition problem using more than two addends, the groupings of the numbers and the order these groups are added will not change the sum. • Proof: (6 + 4) + 3 = ? 6 + (4 + 3) = ? Which of these problems is easier to compute?

6. Compensation (ishy-oshy-ation) • Compensation allows you to change numbers in the problem as long as you make adjustments in the answer. • Example: 4.25- 3.08 change the problem to 4.25-3.10 (you subtracted .02 more than the problem) 4.25-3.10 = 1.15 (now add the .02 back) 4.25-3.08=1.17

7. Compensation (ishy-oshy-ation) • Compensation allows you to change numbers in the problem as long as you make adjustments in the answer. • Example: $3.47 + $4.35 = compensate the problem to: $3.50 + $4.35 = $7.85 $7.85- (the extra $0.03)=$7.82

8. Partial-Sums Method: *Addition is performed form left to right, column by column *The sum for each column is recorded on a separate line. *The partial sums are added either at each step or at the end. 348 + 177 = ?                               3      4      8  +   1      7      7 400 + 110 + 15 525

9. Partial-Sums Method: .  4.65 + 3.25 = ?   4.       6     5  +3.       2      5 7 + 0.8+ 0.1 7.9

10. Equal Addition Property • Open your textbook to page 32. • Look at problem 27. Explain the Equal Additions Property to a partner. • How is the Equal Addition Property different from Compensation? • Using Equal Addition Property, solve A and B

11. Equal Addition Property • Open your textbook to page 32. • Look at problem 28. • What strategies can you use to solve 28 mentally? • Use one strategy to find the answer.

12. Equal Addition Property • Open your textbook to page 32. • Read problem 29. How can you reorganize the numbers to add the sum mentally? • Explain the strategy you will use to subtract $100.00 from the total.

13. Equal Addition Property • Open your textbook to page 32. • Read problem 30. • Find the answer using a mental math strategy. • Share your answer with a partner. • Explain the strategy you used and how it helped you.

14. Let’s Talk… • About problems 31 and 32 • Think about problem 33. How can partial sums help you find the answer?

15. What About Decimals? • How do these strategies apply to decimals? • What are the possible problems you will have with these methods and decimals?

16. Try some on your own • 66 + 1.8 +2.2 (what two numbers make sense to add?) • 9.7 + 3 + 6.3 • 22 + 4.6 + 4.4 • 23.7 + 1.95 + 2.3 • 3.99 + 3.11 + 6.3

17. Mental Math Rocks • Try some with a partner • Textbook page 31 • Work your way through 1-6 • Mental math only • Write your answers down in your math spiral • Label your answers –Textbook p. 31