I let the students know that in today's lesson, they learn to find fraction and decimal equivalencies. To begin, we review what we have learned. We know that a fraction has a numerator and a denominator. I ask, "What does the denominator tell you?" Student response: The total number of pieces. "What does the numerator tell us?" A student tells me that it is the amount that they ask us about. I share examples of a numerator with the students. I tell them that the numerator could refer to the number of pieces shaded or the number of students who wore blue pants.
I remind the students that we have worked on decimals for a few lessons now. On the Smart board, I draw a decimals place value chart. To the right of the decimal is what place? Student response: tenths. The money that we associate with tenths place is what? Student response: dimes. I continue to question the students by asking, "Two places to the right of the decimals is what place?" Student response: hundredths. "What do we money do we associate with the hundredths place?" pennies. I remind the students that the first place to the left of the decimal is where the whole number begins. You do not have a whole unless you have a number in that place or to the left of the ones place. We have already learned the place value to the left of the decimals. Ones, tens, hundreds, thousands, etc. Today, we are talking about writing a fraction as a decimal or writing a decimal as a fraction. Fractions and decimals are named the same way. You write them differently, but you say them the same.
On the Smart board, I write .25 in the decimal place value chart. I point out to the students that the 2 is in the tenths place and the 5 is in the hundredths place. The last place value that we name must be included in the word name. Therefore, .25 is twenty-five hundredths. I ask, "If this is twenty-five hundredths, how many pieces was the whole cut into?" Student response: 100. If the whole is cut into 100 pieces, I can write my fraction as 25/100. Remember, the denominator tells us the total number of pieces in the whole. To connect this to a model, I show a hundreds chart on the board. I shade 25 pieces out of 100.
To give the students more practice, I write 7.4 on the board. I remind the students that when we see a decimal, we say the word "and." Together we say, 7 and 4 tenths. I ask the students, "Will this be a fraction or a mixed number?" Student response: It will be a mixed number because the 7 is a whole number. The mixed number is 7 4/10. It was cut into 10 pieces; therefore, 10 is the denominator. We say the decimal name and mixed number in the same way: seven and four tenths.
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, hundreds chart, and decimal place value chart. 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. The hundreds chart is used to help the students with the concept.
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 whole divided into?
3. Where do you place the number on the place value chart?
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 any misconceptions among the students. Any misconceptions are addressed on the spot, 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
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 - Fractions and 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.
As the students were working on the activity, I saw a few students write more than one digit in a place on the place value chart. In particular, the students were writing the number 100 in the hundredths place. This is because when they said the word name, it ended with hundredths. For example, .25 is twenty-five hundredths. I worked with these students to correct this misconception. I used questioning to guide the students to the correct way to write the number in the place value chart.