Is Your Answer Reasonable?

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Objective

SWBAT check for reasonableness by using estimation to make sure they used the correct calculations.

Big Idea

Using estimation can help you check to see if your answer is reasonable.

Opener

5 minutes

The students have already learned how to estimate by rounding  In today's lesson, they learn to use estimation to help determine if their answers are reasonable(4.OA.A3). This is very important because when a student is multiplying sometimes their answers could be way off.  If they would use estimation, this will ensure that they are calculating their answers correctly.  

To get the students started and excited about the lesson, I start with asking the students to think of an item that they would like to receive for their birthdays. (I want the students to get excited about the lesson.  Most students enjoy receiving gifts for their birthdays.) I let some of the students share their responses.  Some student responses:  a new bike, Xbox 360, and Jordan tennis shoes.  Now, that I have their attention, I tell them that today we will figure out how much it would cost to buy 3 brand new watches for a birthday gift. 

 

 

 

Direct Instruction

10 minutes

The Is Your answer reasonable power point is displayed on the Smart board.

At the beginning of each lesson, I like to review skills that we have learned that will help with the new skill.  In this lesson, we review the steps of rounding.

Review:

—1.  Underline the place to be rounded.
2.  Â—If the place behind the underlined digit is 5 or more, the underlined digit goes up by 1 and everything behind it become zeros.
3.  If the place behind the underlined digit is 4 or less, the underlined digit stays the same and everything behind it become zeros.
To help lead the students to the concept, we will work a problem together.   I like for my students to interact with me during our whole group discussion.  I like to ask questions of them to make sure they are understanding the skill.  So, throughout the instruction, the students can interact by answering questions or asking questions.
Problem:

Mrs. Thomas has triplets,  Jerry, James, and Jack.  They each want a new watch for their birthday.  If the watch costs $125 each, how much money will Mrs. Thomas spend?

Let’s find out.  

 

—First, estimate your answer.  This will help you determine if your exact answer is correct.
—
—To estimate, round your problem.
—

125 rounds down to 100 because there is a 2 behind the 1.

$100 x 3 = $300 

Mrs. Thomas will need about $300.00

 

 Â—Now that we have our estimate, it is time to find the exact answer.

—

125

x   3

 375

 

The exact amount of money that Mrs. Thomas needs is $375.00.

 

—The estimate was for $300, and the exact answer was $375.  Is the exact answer reasonable?
—
—Yes, the answer is reasonable.  125 rounded down to 100, therefore, your exact answer would be higher than $300. 

 

•The exact answer is not much over $300, so this tells you that your answer is not way off.  It is a reasonable answer.
•What if you round up when you estimate?  How will that compare to your exact answer? (Your exact answer will be less than the estimate.)

 

Group or Partner Activity

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others (MP3).

For this activity, I put the students in pairs.  I give each group an  Group Activity Is your answer reasonable activity sheet of word problems.  The students must work together to solve word problems by finding an estimate, then the exact answer.  The students must tell if their exact answers are reasonable based upon their estimation.  The students must decontextualize the problem and represent them symbolically (MP2).  The students must work together to find the product and tell if the answer is reasonable by using estimation. They must communicate precisely to others within their groups (MP6).  They must justify their answers, as well as critique the reasoning of their partner (MP3).

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students.  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1.  What is this problem asking you to find? 

2. Is this an exact answer or an estimate? Why?

3. Is your exact answer reasonable? How do you know?

 

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing:http://www.mathnook.com/math/mathmanrounding.html


Independent Activity

10 minutes

To give me a clear understanding of what each student knows, the students will do an independent assignment (Independent Activity Is your answer reasonable).  Group activities are great, but as a teacher I need to assess students independently to make sure they are all receiving the help they need.  I will put a problem on the Smart board for the students to work (see attached resource).  The students will use paper and pencil to solve the problem.  I will walk around to visually assess the students understanding, keeping track of all students who I will work with in small group for remediation.

 

Problem:

78 students are going on  a field trip to the zoo.  The cost to get in the zoo is $3.00.  What is the total cost for all of the students to get in the zoo?

Estimate:  _______

Exact answer:  _______

Is your answer reasonable?  __________   Explain.

Closure

10 minutes

To close the lesson, I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples, as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during student independent and partner sharing will be addressed whole class.