Estimating Fraction Sums

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Objective

SWBAT estimate fraction sums.

Big Idea

Students will learn about overestimating and underestimating.

Do Now

10 minutes

Prior to this lesson, students learned about Estimating Fractions.  The Do Now is a review of the lesson and an introduction to the lesson of estimating fraction sums.

 

Estimate each fraction using a benchmark.

1.      2/9

2.      1  3/5

3.      11/20

4.      2  7/10

 

After about 5 minutes we will review the answers.  I will randomly select students to come up to the board to explain and show how they estimated each fraction.  I am looking for students to explain the benchmark they used and why.

Hook

5 minutes

As an introduction to the lesson, I will share a story with students.

Every Sunday I go grocery shopping for the week.  I am on a budget, which I have estimated the amount of money that I will spend throughout the week.  For example, I've estimated that I will spend $40 this week on gas.  Last Sunday before I went grocery shopping, I went to the bank to take out the $100 cash I budgeted for groceries.  After, I went to the supermarket and found all the items on my list.  When I checked out, my total came to $127.  I didn't have enough money on me.  I hadn't estimated enough money to pay for my groceries that week.

Vocabulary Review

5 minutes

 

Students may already be familiar with the terms overestimate and underestimate.  Before revealing the definitions, I will ask students to share their thoughts of what it means to overestimate and underestimate and when they may be useful.

What does it mean to overestimate?  

Students may give answers like:  

  • to round up
  • to estimate high
  • to estimate over what the answer is

After several students have shared their thoughts, I will give them the formal definition. 

Overestimate - to give an estimate that is larger than the actual value 

What are some situations where you might overestimate?

 Students may give answers like:

  • when you're buying supplies
  • when you need money for shopping
  • food for a party

 

What does it mean to underestimate?  

Students may give answers like:  

  • to round down
  • to estimate too low
  • to estimate below what the answer is

After several students have shared their thoughts, I will give them the formal definition. 

Underestimate - to give an estimate that is smaller than the actual value

What are some situations where you might underestimate?

 Students may give answers like:

  • when guessing someone's age or weight
  • someone's abilities

 

 

Mini Lesson

10 minutes

I will work through a few examples with students.

Ex. 1 - Estimate 1  5/6 + 1  7/8

How can we estimate the sum without finding the actual sum? What benchmarks should you use? Is this an overestimate or an underestimate?

Once students have estimated the sum, I want them to think about the type of situations we discussed.  What if you were buying fencing for a garden with these lengths, would you want to overestimate or underestimate?

 

Ex. 2 - Estimate 5  1/11 + 23  2/8 + 4/17

 Is this an overestimate or an underestimate?

 

Independent Practice

10 minutes

Students will have 5 minutes to estimate the sums of the fractions below.They will determine if the sum is an overestimate or an underestimate.  After 5 minutes, students will discuss their strategies and answers with their group.  

As students work I will circulate throughout the room assessing students for understanding and answering their questions.  If a student is struggling, I will suggest that they look back at the number lines we created in the Estimating Fractions lesson.

 

Estimate the sum using whole numbers.  Explain if it is an overestimate or underestimate.

1.     

678 
1
2
  –  
621 
1
2

 

2.     

46 
2
9
  +  
15 
4
9

 

3.  

91 
1
8
  +  
825 
5
8

4.

938 
1
6
  –  
10 
5
6

Lesson Review

5 minutes

I will complete the lesson by reviewing the concepts of overestimation and underestimation with students.  I will randomly select students to share their thoughts.

How do you know if you have an overestimate or an underestimate?  What information does it give you?