Adding and Subtracting Decimals

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Objective

SWBAT add or subtract decimals to the hundredths.

Big Idea

A decimal place value chart can assist students with adding and subtracting decimals.

Whole Class Discussion

10 minutes

Today's lesson is adding and subtracting decimals to the hundredths place.  I remind students that we have already learned how to add and subtract whole numbers.  To review, I write a 6-digit number on the board.  The students call out the places beginning with the ones place all the way to the hundred thousands place.  I remind the students that we have also learned place value to the right of the decimal. I write the number 43.24 on the board.  I refresh the students memory that a decimal is part of a whole, just like a fraction.  In this number, what place is the 2 in?  Students' response:  tenths.  That is correct, because it is one digit to the right of the decimal.  "What money do we associate with the tenths place?" Students' response:  Dimes.  "What place is the 4 in?"  Hundredths.  "What money do we associate with the hundredths place?"  Pennies.  

 On the Smart board, I have a Decimals Place Value Chart1.  I remind students that each place has its own value.  It is very important that numbers are lined up in their correct place value in order to be added or subtracted.  

The students are sitting at their desks.  I instruct them to draw a decimal place value chart on their papers.  They work the practice problems at their desk, while I work them on the Smart board.  

On the Smart board, I display:

Mom spent $12.93 at the corner store.  She spent another $5.38 at Walgreens.  How much did she spend in all?

I read the word problem aloud to the students.  I ask the students to tell me what clue word or words tells which operation to use.  Students' response:  in all.  "What operation should be use?"  Students' response:  add.

The students place the numbers in the decimal place value chart.  I remind them that the decimal points should be lined up, and this will help line the other numbers up correctly.  Also, when we add or subtract, we begin to the far right.  Together we add 8 plus 3 to get 11.  We place 1 in the answer, then regroup the other 1.  I remind the students about a lesson we had previously where we regrouped using place value blocks (http://cc.betterlesson.com/lesson/502655/adding-whole-numbers?from=owner_view) .  I tell them that we can only write 1 digit in each place.  Therefore, for 2 digit numbers, we must regroup.  The one that we regroup here is like having 10 pennies.  We trade the ten pennies for 1 dime.  That is why the 1 is regrouped to the tenths place.  Next, we add 9 + 3 + 1 to get 13.  We place the 3 in the answer, then regroup the 1 to the ones place.  I ask, "How many dimes did we trade in for the 1?"  Students' response:  10.  I let the students know that they are correct because 10 dimes is equal to 1 dollar.  The students then add 5 + 2 + 1 to get 8.  Last, the students bring down the 1 in the tens place.  The answer is $18.31.

To give the students more practice, we work another problem.  Problem 2 is displayed on the Smart board:
The teacher showed two short films in class about weather.  The first film was 47.37 minutes long.  The second film was 15.29 minutes long.  How much longer was the first film than the second film?

As we did with the first problem, the students and I work together to solve this problem.  As we do so, I continually question the students to make sure that they understand the skill.  I work on the Smart board, as the students work the problems on their paper using a decimal place value chart. Because this is a subtraction problem, I require the students to use the inverse operation to check their answers.  (This is important because most students do better with addition than with subtraction.)

 

Skill Building/Exploration

20 minutes

For this activity, I let the students work independently first, then share with a partner after they have had time to work on the concept.  (By doing this, it allows me to see what each student is doing on their own.  Also,  the students have a chance to hear their classmates thinking on the skill.)  

I give each student an activity sheet.  The students must add and subtract decimals to the hundredths.  The students use the decimal place value chart to help them with the skill.  By using the decimal place value chart, the students get a conceptual understanding of the skill because they must line up the numbers according to their place value.  The chart shows the value of the tenths (dimes) and hundredths (pennies) to help the students connect the skill to something that they are familiar with - money.

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

1. What clue word tells you the operation?

2.  What does it mean to regroup?

3.  What can you do to tell that your subtraction problem is correct?

As I walk around the classroom, I am questioning the students and looking for common misconceptions among the students.  Any misconceptions are addressed at the point, as well as whole class at the end of the activity.

 Any student that finishes the assignment early, can go to the computer to practice fractions  at the following site until we are ready for the whole group sharing: http://www.math-play.com/soccer-math-adding-decimals-game/adding-decimals-game.html

Closure

15 minutes

To close the lesson, I bring the students back together as a whole class.  I feel that it is very important to let the students share their answers as a whole class.  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  (Student Work) (Student Work -Adding and Subtracting Decimals.jpg), 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 the activity will be addressed whole class. 

I collect all papers from the students.  All struggling students identified as I monitored during their independent activity will receive further instruction in small group.

Misconception(s):

I noticed that a few students were making mistakes on the subtraction problems.  The students were regrouping by putting a 1 in front of the number.  What they failed to do is subtract 1 from the place in front of it.  Because the students were working independently first, it allowed me to pull those students to the back table to work in a small group.  I gave each student a manipulative kit.  Each student used money to display the problem.  As we subtracted on paper, the students regrouped by exchanging the dimes for pennies, and the dollars for dimes.  This helped those students understand the concept better.