Lesson: Estimate with fractions and mixed numbers

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Lesson Objective

SWBAT estimate sums, differences, products, and quotients using mixed numbers and fractions, 6.NSO-E.18, Estimate

Lesson Plan

10 minutes

Daily Math Review (Warm-Up/ Do Now)

Compare using <, >, or =.

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5 minutes

Math Vocabulary

Benchmark: a convenient number used to replace fractions that are less than 1.

 5 minutes

Engage

We can estimate fractions using benchmarks we will focus on three benchmarks, 0, 1, and ½

 

0: when numerator is small compared to denominator

½ : when the numerator is about half the denominator.

1: when the numerator and the denominator are nearly equal.

Give a few examples of each

15 minutes

Explore (Conceptual Development)

Ex 1: Using benchmarks wit fractions

Estimate 7/8 + 4/9

Have students synthesize steps while we complete the problem

Step 1: use the benchmarks to estimate each fraction.

Step 2: add

1 ½ is the correct estimate

Have students use benchmarks to estimate the following 5/12 + 1/15    and 3/5 – 1/8 independently then review as a class.

 

Ex 2: Estimating with Mixed numbers:

When using mixed numbers we can make a reasonable estimate by rounding to the nearest whole number.

In one week, Paulo practices by swimming 8 1/5 miles. Allen swims 4 ¾ miles. About how many more miles does Paulo Swim?

Have students synthesize steps as we complete the problem.

Step 1: round each fraction to the nearest whole number (use benchmarks 0 and 1)

Step 2: subtract the whole numbers

Paulo swims about 3 miles farther.]

Have students try the following problem on their own

You buy a pupy that weighs 8 ¼ lb. a month later the puppy weighs 11 7/8 lb. About how much weight did the puppy gain?

 

Example 3: Estimating products: 2 2/5 ∙ 6 1/10

(very similar to estimating with mixed numbers, you simply estimate to the nearest whole number if the numerator is at least half of the denominator the whole number goes up one if it is not the whole number remains the same)

Have students synthesize steps as we complete the problem

step 1: round each mixed number and rewrite them

step 2: multiply

Have students complete these independently then review them as a class

Estimate 3 5/6 ∙ 5 1/8

 

Example 4: Estimating with compatible numbers estimate 43 ¼ ÷ 5 7/8

(when dividing we need to find compatible numbers or numbers that are easy to divide)

Have students synthesize steps as we complete the problem

Step 1: round each mixed number and rewrite

Step 2: determine compatible numbers close

Step 3: divide

Have students complete these independently then review them as a class.

Estimate 35 ¾ ÷ 5 11/12

 

15 minutes

Explain

(Guided Practice)

We use these skills when the problem asks us to estimate or tells us it is about some number.

(ask students before each question how we know to estimate or round expect them to reply with it said estimate or about)

 

Now we will have a race to see who can estimate adding, subtracting, multiplying, and dividing fractions and mixed numbers the fastest. You have 10 problems when I say go you will flip your paper over and attempt to answer those ten questions. Once finished flip your paper back over and read until I can come check your work. When you are reading I will know you are finished. Those that finish in 10 minutes and are 100% correct will receive a ticket for the raffle.

(worksheet in guided notes)

5 minutes is left to review questions the entire class had difficulty with. Students can explain how they got their answer or the teacher can explain how to get the right answer.

 

 

 

20 minutes

Extend (Independent Practice)

Students will complete 20 more problems independently. When they are finished they should get out their book and read. When the students finish I will check their work. The first two students finished and 90% correct will become the grader and they will grade the other students papers.

5 minutes

Evaluate

(Assessment/ Closure)

Exit slip is attached on guided ntoes.

Lesson Resources

6 NSO E 18mixednumberfractionsGN   Activity
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