Today we will be estimating sums and differences with fractions and mixed numbers.

Our lesson is

“All about Measurements!”

How about some warm-ups?

Using mental math, can you round each number and estimate:

(a) 263 + 107 + 621

(b) 37 + 21

(c) 898 * 51

(d) 211(29)

Benchmark

• So what is a benchmark?

• A benchmark is an easy to use number by which something is measured or compared.

• Mom use to measure how much we grew each year. For each year she would mark our height on the wall. Last year’s mark served as a benchmark to measure how much we grew in a year.

The benchmarks that we will be using to estimate fractions are 0, ½, and 1.

Let’s compare the numerator to denominator

Compared to the denominator, the numerator is_________.

(a) very small

(b) very big

(c) almost the same

The numerator is very small compared to the denominator.

1, 3, 2, 9 8 16 25 100

Go ahead and plot on this number line.

0 ½ 1

From our plot, we can see that is closest to 0 on the number line.

When the numerator is small compared to the denominator, the

benchmark we use is 0.

1 10

1 10

How do these numerators compare to the denominator?

.

We can see that the numerator is about half of the denominator.

When numerator is about half of the denominator, we

will be using the benchmark ½.

3, 9, 11, 52 8 16 25 100

How about these fractions? Compare the bottom to the top!

In this case, the numerator are very close to the numerator.

When the numerator and denominator are very close, we use

the benchmark 1.

plotted on the line graph shows that it is close to 1.

7, 14, 23, 95 8 16 25 100

7 8

The following is a summary of what we learned so far!

Description Examples Benchmark

Numerator is very small when compared to denominator

1/8, 3/16, 2/25, 9/100 0

Numerator is about one half of the denominator

3/8, 9/16, 11/25, 52/100 1/2

Numerator and denominator are close to each other

7/8,14/16,23/25,95/100 1

Selecting a BenchmarkLet’s choose a benchmark for the measurement inch.

7 is about ½ of 16.½ inch is the benchmark.

How about a benchmark for inch?

8 is very close to 10.1 inch is the benchmark.

7 16

7 16

8 10

8 10

Lets take our benchmarks a little further, by using them to estimate sums and differences.

• Estimate +

Step 1: First replace each fraction with a benchmark. + + 1

Step 2: Then add the benchmarks

1 = + 1

7 12

4 5

7 12

4 5

1 2

1 2

1 2

• Estimate

• First replace each fraction with a benchmark. 1 - 0

• Subtract = 1

12 _ 2 13 25

12 _ 2 13 25

You can also round before estimating the sum or difference of mixed numbers

If a mixed number has a fraction of ½ or more => round up to the next whole number.

Round 7 to the nearest inch. 7

Since > , round up to 8!

9 16

9 16

1 2

9 16

If a mixed number has a fraction less than ½ => whole number stays the same!

Round 6 to the nearest whole number.

6

Since < , round to 6!

1 8

1 8

1 8

1 2

The diameter of a quarter is 24 mm. The diameter of a penny is 17 mm. Estimate the total width of

the coins.

1 5 9

10

• Estimate 24 + 17

24 24 Since < , round to 24

17 18 Since > , round to 18

24 – 18 = 6 Estimate by finding the difference

1 5

9 10

1 5

1 5

1 2

9 10

1 2

9 10

Time for a break!

Word Play!!!

Can you make new words by changing just one letter in each of these words:1. Change BEAR into a fruit.2. Change LINE into a number.3. Change SWAY into a bird.

Can you re-arrange the jumbled letters into an 8-letter word for a large animal? THE PANEL

Can you also use some of the letters to find three 4-letter words with following meanings?1. Story2. Part of a shoe3. Jump

Answers!

1. BEAR - PEAR2. LINE - NINE3. SWAY – SWAN

Jumbled word - ELEPHANT

1. TALE2. HEEL3. LEAP

So, what is a dollar good for these days?

• Why.. to measure stuff, of course! Each US dollar is 6” long. Half a bill is 3” long.

• So next time you need a measuring stick…pull out a buck!

Moving Along,…how about some problems?

1. Choose a benchmark for each fraction. Use 0, ½, or 1.

2. Which of the fractions has a different benchmark than the rest?

3 7 11 45 8 15 57 92

3 7 11 45 8 15 57 92

3. Name three fractions whose benchmark is ½._______ _______ ________ .

4. Name three fractions whose benchmark is 1.________ _______ _________.

5. Estimate each sum or difference, using benchmarks.

(a) + (b) –

(c) 6 + 2 (d) 11 - 3

8 9

15 16

11 12

5 6

5 6

1 9

6 7

7 9

Icy glass of Lemonade on a Hot Summer Day….

A recipe for strawberry lemonade calls for the following ingredients:2 cup lemon juice2 cup strawberry juice1 ¼ cup sugar5 ¾ cups water

6. Estimate the amount of lemonade that can be made. (hint: add all liquid parts)

7. Estimate the difference between the ingredient that is needed most and ingredient that is needed least.

1 3 3 8

We learned and measured an awful lot….Let’s Recap!

We learned that benchmarks are used to replace fractions that are less than 1.

The benchmarks 0, ½ and 1 are used to estimate sums and differences of fractions.

Our Guidelines for selecting benchmarks

Numerator much smaller than denominator 0 Numerator almost half of denominator ½ Numerator almost same as denominator 1

To estimate sums and differences of mixed numbers, round to the nearest whole number.

If mixed number has a fraction of ½ or greater round up to next whole number.

If mixed number has a fraction less than ½ leave whole number the same!

Congratulations on a job that really “measures” up GREAT!