Estimating Sums and Differences of Whole Numbers

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Objective

SWBAT round whole numbers to estimate sums and differences.

Big Idea

If students do not need an exact answer, they will use place value to round numbers to find sums and differences.

Opener

5 minutes

In this Estimating Sums and Differences Video, I introduce the lesson for today.

In today's lesson, the students learn to estimate numbers.  This aligns with 4.NBT.A3 because the students use place value understanding to round numbers to any given place.

To begin the lesson, I ask the students a question that will gain their full attention.  "Who wants to see a magic trick?"  The majority of the hands are raised.  I let the students know that today, they are going to learn how to estimate sums and differences of whole numbers.  I knew that this question was coming!  A student asks, "What does that have to do with magic?"  I tell them, "Let's find out."

 

Direct Instruction

10 minutes

Usually, if I am doing direct instruction from my Smart Board, I call the students to the carpet so that they will be close to me, and I know that I have all of their attention.  In today's direct instruction lesson, I want the students at their desk because they will be working along with me.  The students should have out a sheet of paper, a pencil, and a ruler.  The skill that the students are working on is estimating sums and differences of whole numbers.  The students have had practice with rounding in previous lessons using place value charts.  In this lesson, the students learn to use a number line to help round numbers.  I feel that this will give them a more conceptual understanding of rounding if they can see the numbers on the number line.  I use the following site to teach the skill:

 http://studyjams.scholastic.com/studyjams/jams/math/numbers/nestimate-whole-numbers.htm

We follow along with the interactive site to round a number using the number line.  The students round 234 to the nearest tens.  This will prepare them to estimate as they add or subtract for this lesson.  The students are rounding to the nearest tens, so have them count by tens beginning with 200: 200, 210, 220, 230, 240, etc. all the way to 300.  I ask, "Which two numbers would 234 fall between?"  The students tell me that 234 falls between 230 and 240.  "This means that if you round 234 to the nearest tens, your answer must either be 230 or 240."

The next step in the process is to draw the number line.  The students draw a number line using their ruler.  They should put 230 on the left end of the number line and 240 on the right end of the number line.  All numbers in between these two numbers will be added in.  I have the students circle 234.  This should give the students a visual of how to round 234.  They should see that 234 rounds to 230.  (This is a good time to tell them that they just saw magic.  In rounding, the number 234 "magically" became 230.)  I remind the students of the rules that they have already learned about rounding.   Underline the place to be rounded.  If the number behind the underlined place is 5 or more, the underlined place goes up by 1 and everything behind it becomes zeros.  If the digit behind the underlined place is 4 or less, the underlined place stays the same and everything behind it becomes zeros.  I let them know that these rules apply whether you are using a place value chart or a number line.

For this lesson, the students use rounding to find the sum or difference of two numbers. I let the students know that we can estimate by rounding when we do not need an exact answer to a problem.  I practice this with the students before they work in groups.  We have been working on adding and subtracting in previous lessons.  I write the following problem on the board:  234 - 127= ____.  I tell the students that we will estimate to find out approximately the difference between these two numbers.  I remind them that we just rounded 234 to 230, so now we need to round 127 to the nearest tens.  I have the students draw a number line and put 120 on the left end and 130 on the right end.  I tell them to write all of the numbers that fall between these two numbers on the number line.  Next, circle the number 127.  I ask, "Does 127 round to 120 or 130?"  They me that 127 rounds to 130.

I let the students know that now they will get a chance to practice with their classmates.

 

Group or Partner Activity

20 minutes

I put the students in pairs.  When the students work in small groups, it makes it easier for all students to share their voices.  Sometimes in larger groups, the quiet student gets forgotten or they hide behind the other voices.  For this activity, the students estimate numbers in order to find the sum or differences.  I really like for my students to have fun in my class, so this activity is played as a game. Each group receives Number LinesEstimate Sums and Differences, and Estimating Sums or Differences Score Sheet.   As the students work in pairs, I walk around to monitor and listen in on the students conversation.  Even though they are playing a game, my goal is for all students to master the skill.  Therefore, I ask questions to help lead the students to mastery of the skill.

Possible Questions:

1.  What place are you rounding to?

2.  What two numbers does this number fall between when counting by tens?

3.  By looking at the number line, is this number closer to the number on the left or on the right?

4.  What do the rules of rounding tell you to do?

5.  When you round the underlined digit, what happens to the numbers behind it?

 

Activity:

Whoever's last name comes first in the alphabet goes first.  The first person works problem 1, the second person works problem 2, etc.  The students must round and find the sum or differences.  Their partner must check the answer to see if it is correct.  If they have the answer correct, then they get a point.  If they have the answer wrong, then they lose a point.  The students keep taking turns until all of the time is up or all the problems are gone.  

Independent Activity

10 minutes

To give the students practice on their own, I have the students estimate the sum of two numbers.  The students must use a number line to help with the rounding.    Individual practice gives the teacher the opportunity to make sure that all students master the skill.  Each student receive the handout with an addition sentence.  The students must use the the number line to help with the rounding.  The students can round the number to either the tens place or hundreds place.  Based upon the results of the independent assignment, I plan for further instruction in small group for the students who need it.

This is a sample of Student work - Estimating.  In this student work, you can see how the student used the number line to help with rounding.

Closure

15 minutes

To close the lesson, I bring the class back together as a whole for a review. I call on a few students to summarize how you can use a number line to help you round.  Also, I let some students tell the rules of rounding.  If they can tell me, then they should know how to use it.  I like to have students summarize for me because that lets me know if the student was listening.