##
* *Reflection: Developing a Conceptual Understanding
Adding and Subtracting Decimals - Section 2: Skill Building/Exploration

Using a place value chart helps the students to gain conceptual understanding. As my students worked on this assignment, I walked around to monitor and assess their understanding. I noticed how much easier it was for the students to keep the numbers lined up according to place. Also, I feel, that it gave the students a better understanding of adding and subtracting decimals because the students know the value of each number as they add or subtract. They know that hundredths are like pennies, and tenths are like dimes.

*Decimal Place Value Chart*

*Developing a Conceptual Understanding: Decimal Place Value Chart*

# Adding and Subtracting Decimals

Lesson 6 of 8

## Objective: SWBAT add or subtract decimals to the hundredths.

*45 minutes*

#### Whole Class Discussion

*10 min*

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.

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#### Skill Building/Exploration

*20 min*

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

#### Resources

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#### Closure

*15 min*

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.

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##### Similar Lessons

Environment: Urban

Environment: Urban

###### Revisiting Day

*Favorites(9)*

*Resources(20)*

Environment: Suburban

- UNIT 1: Fractions
- UNIT 2: Skills Review
- UNIT 3: Algebra
- UNIT 4: Geometry
- UNIT 5: Patterns & Expressions
- UNIT 6: Problem-Solving Strategies
- UNIT 7: Decimals
- UNIT 8: Measurement and Data
- UNIT 9: Multiplication and Division Meanings
- UNIT 10: Place Value
- UNIT 11: Adding and Subtracting Whole Numbers
- UNIT 12: Multiplying and Dividing

- LESSON 1: Using Money to Understand Decimal Place Value
- LESSON 2: Comparing and Ordering Decimals using Money
- LESSON 3: Fractions and Decimals
- LESSON 4: Comparing and Ordering Fractions and Decimals Task
- LESSON 5: Fractions and Decimals on a Number Line
- LESSON 6: Adding and Subtracting Decimals
- LESSON 7: Multiply a Whole Number by a Decimal
- LESSON 8: Dividing a Decimal by a Whole Number