1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Write each sum or difference in simplest form.
Warm Up
Write each sum or difference in simplest form. – –1 3 8 __ 5 8 __ 9 10 __ 3 10 __ 3 5 __ 1 1 4 __ 1 4 __ 1 2 __ 3 8 9 __ 2 9 __ 2 3 __ 4

3. Problem of the Day
Students at a school dance formed equal teams to play a game. When they formed teams of 3, 4, 5, or 6, there was always one person left. What is the smallest number of people that there could have been at the dance?
61, the LCM of all the numbers, plus 1

4. Learn to estimate sums and differences of fractions and mixed numbers.

5. 1 2 __
You can estimate fractions by rounding to 0, , or 1.
The fraction is halfway between and 1, but we
usually round up. So the fraction rounds to 1. 3 4 __ 1 2

6. You can round fractions by comparing the numerator and denominator.1 2 __ 1 • •
closer to
Each numerator is about half the denominator, so the fractions are close to . 1 2 __
closer to 1
Each numerator is about the same as the denominator, so the fractions are close to 1.
closer to 0
Each numerator is much less than half the denominator, so the fractions are close to 0. 1 5 __ 2 11 __ 2 15 __ 5 11 __ 4 7 __ 9 20 __ 9 10 __ 16 19 __ 6 7 __ 1 2 __

7. Additional Example 1A: Estimating Fractions
Estimate each sum or difference by rounding to 0, , or 1. + 1 2 __ 6 7 __ 3 8 __ 6 7 __ 3 8 __ 6 7 __ 3 8 __ 1 2 __ +
Think: rounds to 1 and rounds to . 1 2 __ 1 2 __
= 1 6 7 __ 3 8 __ 1 2 __
is about

8. Additional Example 1B: Estimating Fractions
Estimate each sum or difference by rounding to 0, , or 1. – 1 2 __ 9 10 __ 7 8 __ 9 10 __ 7 8 __ 9 10 __ 7 8 __ –
Think: rounds to 1 and rounds to 1.
1 – 1 = 0 9 10 __ 7 8 __
– is about 0.

9. Check It Out: Example 1A
Estimate each sum or difference by rounding to 0, , or 1. + 1 2 __ 5 6 __ 3 7 __ 5 6 __ 3 7 __ 5 6 __ 3 7 __ 1 2 __ +
Think: rounds to 1 and rounds to . 1 2 __ 1 2 __
= 1 5 6 __ 3 7 __ 1 2 __
is about

10. Check It Out: Example 1B
Estimate each sum or difference by rounding to 0, , or 1. – 1 2 __ 13 19 __ 2 11 __ 13 19 __ 2 11 __ – 2 11 __ 13 19
Think: rounds to 1 and rounds to 0.
1 – 0 = 1 13 19 __ 2 11 __
– is about 1.

11. two nearest whole numbers and the nearest .
You can also estimate by rounding mixed numbers. You compare each mixed number to the
two nearest whole numbers and the nearest
Does round to 10, , or 11? 1 2 __ 3 10 __ 1 2 __ 3 10 __ 1 2 __ • 1 10 __ 2 10 __ 4 10 __ 6 10 __ 7 10 __ 8 10 __ 9 10 __ 3 10 __ 1 2 __
The mixed number rounds to

12. Additional Example 2A: Sports Application
About how far did Tosha
walk on Tuesday and Thursday? 1 10 __ 7 8
5 + 5 = 10
She walked about 10 miles on Tuesday and Thursday.

13. Additional Example 2B: Sports Application
About how much farther did
Tosha walk on Sunday than
Thursday? 9 10 __ 7 8 __
8 – 4
9 – 5 = 4
She walked about 4 miles farther on Sunday than on Thursday.

14. Additional Example 2C: Sports Application
Estimate the total distance
Tosha walked on Thursday,
Saturday, and Sunday. 7 8 __ 3 7 __ 9 10 __ 1 2 __ 1 2 __
= 20 1 2 __
She walked about miles on Thursday, Saturday, and Sunday.

15. Jerry’s Roller Skating Distances
Check It Out: Example 2A
About how far did Jerry
skate on Tuesday and Sunday?
Jerry’s Roller Skating Distances
Distance (mi)‏ 3 6 2 8 1 5 __ 7
Day
Tuesday
Thursday
Saturday
Sunday 1 5 __ 6 7 __
3 + 3 = 6
He roller skated about 6 miles on Tuesday and Sunday.

16. Jerry’s Roller Skating Distances
Check It Out: Example 2B
About how much farther did
Jerry skate on Saturday than
Tuesday?
Jerry’s Roller Skating Distances
Distance (mi)‏ 3 6 2 8 1 5 __ 7
Day
Tuesday
Thursday
Saturday
Sunday 1 7 __ 1 5 __
8 – 3
8 – 3 = 5
He roller skated about 5 miles farther on Saturday than Thursday.

17. Jerry’s Roller Skating Distances
Check It Out: Example 2C
Estimate the total distance
Jerry skated on Tuesday,
Thursday, and Sunday.
Jerry’s Roller Skating Distances
Distance (mi)‏ 3 6 2 8 1 5 __ 7
Day
Tuesday
Thursday
Saturday
Sunday 1 5 __ 6 7 3 1 2 __ 1 2 __
= 12 1 2 __
He roller skated about miles on Tuesday, Thursday, and Sunday.

18. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

19. Lesson Quiz: Part I
Estimate each sum or difference by rounding to 0, , or 1. 1

20. Lesson Quiz: Part II
5. The conservation club picked up trash along the road for three weeks. The table shows the number of pounds of trash that was collected. About how many pounds did they collect in weeks 2 and 3?
about 37 pounds

21. Lesson Quiz for Student Response Systems
Estimate the difference by rounding to
A C. 1
B D.

22. Lesson Quiz for Student Response Systems
2. Estimate the difference by rounding to
A C.
B D. 0

23. Lesson Quiz for Student Response Systems
3. Estimate the sum by rounding to
A C. 1
B D. 2

24. Lesson Quiz for Student Response Systems
4. Ben buys fruit every week. The table shows the number of pounds of fruit that he bought in the last month. About how many pounds of fruit did he buy in weeks 2 and 4? A.
B. 40 lb C.
D. 41 lb