Materials: Construction paper, rulers, yard sticks, measuring tapes, computer paper, adding machine rolled paper, "hair" colored yarn, liquid glue, glue sticks,crayons or colored pencils.
I knew this lesson would take the whole hour for my students so we jumped right in to our project.Measuring Me Teacher Notebook Resource is a file I created to teach this lesson. It is a long lesson, so today we focused on the face only. Students who completed their faces early, could move on to measuring the other portions of their bodies.
We began our lesson by examining a ruler and going through the first two pages of the SB file.Measuring Me Classroom File. I asked if ruler's have mixed numbers. The answer from the class was an immediate yes! I am supporting MP 2 by getting students to connect their learning and looking critically at a standard ruler to reason how mixed numbers are used in this tool. I took it one step further and asked if there were improper fractions shown on a ruler? I heard the majority say "no!". Then, one lone voice said, "Yes, there is. If there are mixed numbers there has to be." I questioned the rest of the class by asking them to think about that if you used 1/8 and kept measuring to 12/8, what kind of fraction would that be? Are there 12/8 on a ruler? We turned to the SB page with the ruler and counted the eighths. We discovered it was also 1 1/2 inches. The discussion turned toward equivalency since 8/8 equals 1 whole and 1/2 equals 4/8. To hear this conversation generated by my class makes me thrilled to witness because I think that teaching CCSS is responsible.
To push their thinking just a little further: I asked my students if they thought that we should measure an object at 1 1/2 inches or 12/8? Which would be correct? Most of my students thought that either would work. I explained that it not wrong count the eighths and measure 12/8, but as a rule, always decompose the improper fraction to communicate the measurement in simplest form. I also told them that equivalent fractions were important because it was best to consider the lowest terms of the fraction. But for now, we would focus on playing with fractions on a ruler through a special measurement activity.
I told them that all measuring today would be to the nearest 1/4 of an inch.
I turned to the third page of the Measuring Me Teacher Notebook Resource to discuss what unit we would be using and explicitly direct students how to measure their faces. I told them that the difficult part would be to accurately draw their face using the measurements, but if they followed directions carefully and used what they learned about multiplying fractions, they would be able to accurately draw their face on the white sheet of paper. I explained that we would multiply by 1/2 to find the middle point of the measurement of the width and length of their faces. So if their face was 8 1/2 inches long, we would make an improper fraction using decomposition skills, and then multiply that improper fraction by 1/2 to arrive at the middle. It would be the same thing as dividing the measurement by two!
I told them that they needed to get their faces measured first. They could measure the rest of their bodies, but I would be stopping them as soon as everyone's face was measured to teach them the steps of finding the midpoint and drawing their face. Our goal was to get faces all done today.
I partnered them up by considering who would work well together and support each other. I also considered skill levels and tried to partner students with less ability with those with more skill.
After partnering, I told them to use their notebooks to record their measurements in. The fun began! It was great to watch and help students measure. Good notebook sample shows how this student recorded their work and measurements.
I had been roving the classroom looking for students to help and monitoring their measurement recording. Students were working hard. Eyes and mouths are a bit challenging to measure. I told them to smile because it would be nice to have a full smile on their faces. Besides, the corners of the mouth are stretched out and easier to measure that way.
I stopped them when I saw that everyone had face measurements recorded. Some were working on measuring hands and feet at this point, but I asked them to stop all work. Using the SB Measuring Me Classroom File, I turned to page 4. I explained that the midpoint needed to be found in order to draw their oval face as accurately as possible. I asked them to tell me what they thought the midpoint was? I continued to explain that we would use an equation by multiplying by 1/2. We calculated page four together. They could see that dividing 8 by 2 could give them the same result.
I told them the standard expects 4th graders to multiply fractions by whole numbers. I asked them what they thought would happen if their measurements were mixed numbers? Dividing mixed numbers in two could be complicated. I asked a student to measure the length and width of my face as directed on our SB page. My face measured 7 1/4".
Opportunity to think more deeply: I asked them what I needed to do? Would I simply ignore the 1/4" and round it to 7? One student suggested that I make an improper fraction and divide it in two. I said that dividing a fraction by two is the same as multiplying by 1/2. I showed them why on the whiteboard. I didn't leave room for much discussion about the reciprocal concept for fear they would be very confused at this developmental stage. So I smoothly worked right into the algorithm and we calculated the midpoint of the measurement. I explained that they should multiply both numerator and denominator and then decompose the improper fraction. I explained we needed to to the same thing with the width of my face. My face measured 5 inches across. I asked a student to come to the board and figure out the midpoint of that measurement. They got it!
I instructed them further by folding a paper as in the instructions, found the midpoint with the ruler by using the calculations, showed them how to use the midpoints and then connected the lines to create a rhombus. Then, I drew an oval using the points and lines as my guide. We talked about the placement of the eyes and how they are in the middle of our faces. I explained that they could use the folded lines of the paper as they began to find the midpoint of their paper. They would start the corner of their eyes 1/2" either side of the middle point in the paper. I measured my eyes and drew them in front of them. I also did the same with my nose and mouth so they could completely see step by step how to create their faces. I cut our the oval and explained that they should turn it over and draw the features on that side of the paper.
After we were done, I asked students for questions. They returned to their desks to begin their calculations. I roved the classroom to see their progress. Finding the midpoint using calculations shows a student calculating the midpoint in their notebook. After finding the midpoint, these boys measured and created face frame as I had demonstrated. From there, they drew the oval for their faces and cut it out. Soon, they worked on placement of features. When features were drawn, colored and yarn was glued on the face was completed. Completed faces looked a lot like their owners!
Closure: I roved the classroom and looked at some more cute faces before I delivered the bad news it was time to stop. A cute square smile. I couldn't believe how much they looked like my students! None of my students were completely done with measuring the height yet, nor putting themselves together. I stopped them even though they whined about it. This was exhausting today!
I wanted them to explain why multiplying by 1/2 created the midpoint or the middle of the number. I drew a number line on the board and labeled it 1-4, and then wrote the algorithm 4 x 1/2. I asked to the whole class: Where is the middle or midpoint of this line?Hands shot up. The student I called on said, "2". I asked how they could prove that 4 x 1/2 was 2?
"I just divided it by 2."
I replied, " You need to mulitiply by 1/2" Can you draw it?
He came to the board and drew 1/2 four times and added it. He then decomposed it by adding 2/2 + 2/2 arriving at 2.
I turned to the class and explained that 1/2 x 4 is the same thing as dividing 4 by 2 wholes. I heard many "OHHHHH!" Through CCSS they could see the relationship that I avoided explaining by using the word reciprocal earlier when the concept started to surface. This CCSS decomposition standard explains why. They will need more exposure to this concept before they learn to divide fractions.
I asked them to pick up and told them we would finish our "Me's" tomorrow.