In today's lesson, the students practice finding equivalent fractions by using division and visual models. This aligns with 4.NF.A1 because the students use visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.
I remind students that an equivalent fraction names the same part of the whole. In the previous lessons, the students learned to draw models and use number lines to help find equivalent fractions. Also, the students learned that equivalent fractions can be determined by multiplying or dividing the numerator and denominator by the same number. The model gives the students a conceptual understanding of the multiplication or division.
We review the Equivalent Fractions power point that is displayed on the Smart board. I show the students fraction strips of 1/2 and 2/4. The students see from the fraction strips that these two fractions are equivalent. (This is another visual for the students to see that 1/2 and 2/4 are equivalent.) Beneath those two fractions, I have 6 fraction boxes. I remind the students that we would shade 3 out of the 6 to have an equivalent fraction for 1/2 and 2/4.
I explain to the students that we can also find equivalent fractions by using multiplication or division. If my fraction is 1/2, I can find an equivalent fraction by multiplying the top number and the bottom number by the same number (which is the same as multiplying by 1). You can use any number other than 1. "What property tells use that any number multiplied by 1 is that same number?" The students remember that the property of one tells us this. "This is why we cannot use the number 1 to multiply or divide because we will end up with the same number." I can multiply 1 x 2 to get 2. I can multiply the denominator of 2 x 2 that gives me 4. This shows you that 1/2 is equivalent to 2/4. When you do this, you must make sure you use the same number for the numerator and denominator. (I point out to the students in the model that it takes two 1/4 fractions to equal 1/2. This connects to the multiplication problem and gives them a visual.)
I reinforce to the students that in equivalent fractions, we must refer to the same whole. If you have 1/2 of something, I have 2/4, and another person has 3/6, we all have the same amount if we are talking about the same whole. "If I have 1/2 of a large pie and you have 1/2 of a small pie, then my fraction is larger than yours. The whole has to be the same size and the same shape.
Before the students work in collaborative groups, I want them to take a few minutes to work on the activity independently. This will allow me the opportunity to walk around and see how much the students remember from the previous lesson. After a few minutes of independent work time, I allow the students to work together on the skill. I find that collaborative learning is vital to the success of students. Students learn from each other by justifying their answers and critiquing the reasoning of others.
For this activity, I put the students in pairs. I give each pair a What's Another Name For Me activity sheet. The students must work together to draw models (MP4) and identify the equivalent fractions. An example of student work (Student Work - Equivalent Fractions) can be found in the resources.
Each pair must draw out models to find the correct equivalent fraction. Also, they can use division along with their models (Student Work - Equivalent Fractions). They must be able to identify the connection between the division problem and model. They must write the letter or symbol for the fraction selected on the line. If they have all of the answers correct, the letters spell "Yes." If not, the letters spell, "No!" This activity gives the students another chance to draw models correctly. If their models are not exact, then it leads to incorrect answers. As well as with this activity, the students gain conceptual understanding through a visual model.
As they work in groups, the students are guided to the conceptual understanding through questioning by their classmates, as well as by me. The students communicate with each other and must agree upon the answer to the problem. Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students. As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill. As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.
As they work, I monitor and assess their progression of understanding through questioning.
1. What is the denominator?
2. How many pieces should you divide the whole into?
3. How many pieces will you shade?
4. Which fractions are equivalent?
5. What division problem is evident in the model?
Any pairs that finish the assignment early can go to the computer to practice the skill at the following site until we are ready for the whole group sharing.
To close the lesson, I have one or two students share their answers. 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, 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 group activity will be addressed whole class.
I noticed that a few of the students were drawing the fractions, but they were drawing different size wholes. I explained to them again that their wholes have to be the same. I referred back to the power point that was still displayed on the board. "My models for 1/2 and 2/4 are the same size." I let them know that you must draw your boxes that represent the whole the same size. If not, the answer will not be correct.