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* *Reflection: Developing a Conceptual Understanding
Fractions and Decimals on a Number Line - Section 2: Skill Building/Exploration

As I reflect on this lesson, I realize that independent work is very important. I know that Math Practice 3 says that the students must critique and analyze the reasoning of others. I agree completely with MP3. However, I feel that before they can critique and analyze, they must first work independently to have something to discuss.

Earlier this year, a lot of my activities began with group work. I have come to the realization that beginning with group activites does not allow some of my students to contribute to the conversation because they have not had time to think it through. Therefore, I am now giving them independent time before they discuss in groups.

*Independent Work*

*Developing a Conceptual Understanding: Independent Work*

# Fractions and Decimals on a Number Line

Lesson 5 of 8

## Objective: SWBAT name fractions and decimals on a number line.

*50 minutes*

#### Whole Class Discussion

*15 min*

I let the students know that today's lesson is identifying fractions and decimals on a number line. I remind the students that we have already had a lesson on fractions and decimals. On the board, I draw a number line. On the left end of the number line, a label it with a 0. On the right end, I label it with a 1. I divide the number line into pieces. I ask the students, "Will this number line have fractions or mixed numbers?" I give the students a few minutes to think about the question. (I always encourage my students to think before they speak.) The majority of the students yell out that the number line will have fractions. I always ask my students "why" because I want to know if they really understand or if they guessed upon the answer. Student response: You count fractions before you get to a whole number. I ask another student to add on or clarify what the first student is saying. Student response: You cannot put a mixed number on the number line because you will be past 1. I go on to explain to the students that you cannot have a mixed number on this number line because the number line ends with 1. This number lines goes from zero to one.

I model for the students how to figure out the missing numbers on the number line. I let them know that I start with the first whole number and count to the next whole number to find the number of pieces. On the board, I begin with the zero and go to the first tick mark on the number line. I count that as one. From there, I continue on to the next mark and count that as two. The students continue to count with me until we discover that there are 6 pieces on the number line. I ask, "I wonder what my denominator will be?" Student response: 6. It is easy to find a denominator on a number line because all you have to do is go from whole number to whole number and count the pieces. If you do that, you will have your denominator. Together, we fill in the number line beginning with 1/6, 2/6, 3/6 (1/2 simplified), 4/6, and 5/6. I then ask, "Where is the 6/6?" Student response: 1 whole. "Why is 6/6 my 1 whole?" Student response: 6/6 is equivalent to 1 whole. I remind the students that any number over itself in a fraction equals to 1 whole.

To give the students additional practice, I draw another number line. This time we work with decimals. I draw a number line with 1 and 2 as the whole numbers. I remind the students to always pay attention to the whole numbers on a number line. I divide the number line into 10 equal pieces. I label 1.5 on the number line. Together, we count the number of pieces on the number line. The students know that there are 10 even pieces on the number line. The students count out loud as I label 1.1., 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, then 2. One of my lower students asked the question, "Why is it not 1.10?" I was really glad that she asked that question. I wanted to see if the students remembered what they learned in the previous fraction and decimal lesson. I tell the students that we can write this in a different way. "Can we write decimals as fractions?" Student response: yes.

Let's see if we can figure out why we did not label 2 as 1.10. If this is 1.1, how can I write this as a fraction? (Some of them didn't quite remember, so I had to ask another question.) "How many pieces was the number line cut into? 10. What is our denimator? 10. I remind the students that we learned that the denominator represents the total number of pieces. At this point, I wanted the students to say the word name for 1.1 aloud so that it would help them with the fraction. The students read the mixed number as one and one tenth. I remind them that the 1 is in the tenths place. From there, we could name the mixed numbers for the number line. When we got to 1 9/10, we stopped. "Now, let's answer the question about 1.10. The next number would be 1 10/10. Why do we not write it this way?" Student response: Because 10/10 equals 1 whole. I point to the 1 in the ones place and say, "This is one whole." Next, I point to the 10/10 and say, "This equals 1 whole. One plus one equals two. This is why we do not write 1.10."

#### Resources

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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 a Fractions and Decimals on a Number Line.** ** The students must change the fractions to decimals and the decimals to fractions. The students use the place value chart to help them with the skill.

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

1. How do you say the word name of the number?

2. How many pieces was the number line divided into?

3. What is the denominator? How do you know?

4. Will it be a mixed number or a fraction? How do you know?

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.arcademics.com/games/puppy-chase/puppy-chase.html

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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), as well as work that may have incorrect information. More than one student may have had the same misconception. In the Video - Fractions and Decimals, a student shares their work. 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):

In one of my classes, the students were confused on question number 1 on the activity sheet. This is my struggling class. Even though the students knew that the first number line was divided into fourths, some of them did not realize that 1/2 was 2/4. They tried to put the 2/4 on the number line at the next tick mark behind the 1/2. Therefore, they did not have 3/4 on the number line. I called the whole class back together again to address this misconception because I saw it on several papers.

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##### Similar Lessons

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###### Decimal Introduction

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Environment: Urban

- 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