Estimating Sums and Differences

Today’s Learning Goals We will continue to use our understanding for

the meaning of fractions to estimate the size of a sum or difference.

Estimating Fractions Below is a recent item from a national test* of

mathematics achievement given to seventh and eighth graders across the country.

Estimate the answer to A. 1B. 2C. 19D. 21E. I don’t know

What do you think was the most popular response?

28%24%7%

27%14%

8

7

13

12

*National Assessment of Educational Progress

Estimating Sums What would you say is a good estimate to ?

Great…this sum is close to 2.

8

7

13

12

Why is 2 a good estimate for this sum?

Yes…because 12/13 is close to 1 and 7/8 is close to 1. So, by rounding the two numbers, we see that this sum is close to 1 + 1 = 2. Estimating usually involves rounding, minimization of calculations, and speed. Often times, we round to whole numbers to make it as easy as possible!

Estimating Sums Libby has 1¾ yards of fabric. Jordan has 2

yards of fabric. How many yards of fabric do they have all together?

85

What is a good estimate for how many yards they have all together?

Yes…about 4½ yards because 1¾ 2 and . So, we have about 2 + 2½ = 4½.

2128

52

What was the idea of addition that was used in this story problem?Great…addition means “put together”.

Estimating Differences Berkley decided to buy 2.65 pounds of lunch

meat at the supermarket. When he got home, he made two sandwiches with .47 pounds of lunch meat. How much lunch meat did he have left?

What is a good estimate for how many pounds of lunch meat was left?Beautiful…about 2 pounds left because 2.65 2.5 and .47 0.5. So we have 2.5 – 0.5 = 2. What was the idea of subtraction that was used in this story problem?Good…subtraction means “take away”.

Estimating Differences Consider the following problem: Jerry walked

miles. Biff walked miles. How many more miles did Jerry walk compared to Biff?

8

73

521

What is a good estimate for how many more miles Jerry walked compared to Biff?Great…2½ because and . So, we have 4 – 1½ = 2½.

2115

21 4873

What was the idea of subtraction that was used in this story problem?Yes…subtraction means “difference between” or “compared to”.

Partner Work You have 20 minutes to work on the following

problems with your partner.

For those that finish early 1. Crissy was doing the problem, 17¼ – 1¾.

She says, “17¼ is ¼ more than 17, and so I will take away ¼ from 17¼, and since I did that to the 17¼, I need to compensate by adding the ¼ to the 1¾. So the new problem is 17 – 2.” a)   Is Crissy’s reasoning correct? Explain why or why not.b)   Will Crissy’s reasoning work for 17 ¼ + 1 ¾? Explain why or why not.

Big Idea from Today’s Lesson Estimating the sums and differences of

fractions is a quick way to get a reasonable answer. Estimating usually involves rounding one or both numbers.

Addition means “put together”. Subtraction means “take away”, “difference

between”, or “compared to”.

Homework Complete Homework Worksheet.