In order to fulfill the standard of students being able to demonstrate their ability to find all factor pairs from 1-100, I have allowed daily work and drill in this area to help with mastering this standard. Once a week, they are given a test of random numbers between 1-100 to find factor pairs for. This test then reveals their fluency in those facts. This test occurs on Wednesdays. I keep track of their progress by using a spreadsheet. To master the goal, my team and I decided that 80% overall was proficient.
In addition to that goal, however, between weekly assessments of factor pairs, all students who didn't achieve 100% on the last assessment practice finding factor pairs by writing a given product down in their math notebook and write out the factor pairs of each. I check their answers and ask them to check the online factor pair calculator to be sure they have found all of them.
I have numbered note cards 20-100. I throw them up in the air and they land around the room. Students choose one they haven't worked on before and begin to factor the number.
They list the number in their notebook like this: They have chosen a card with 35 on it.
I check them and if they have found all of them, I ask them to check their findings on their factor pair calculator ( this makes them take responsibility for being sure they have completed all the factor pairs).
As people finish, I allow them to log onto a math ap on their iPad and work for a few minutes.
As soon as everyone is finished, I begin the core lesson.
Materials: I set up for groups of 3-4 students.
Sinks in the science lab, or a water source, 1 liter graduated cylinders, 100 ml cylinders, eye droppers, 250 ml measuring cup, 1 styrofoam coffee cup, 1 12 oz plastic beverage cup and any other common container that might interest them in knowing how many ml it contains. I also used small pill containers. They will pour and explore capacity using the provided containers. I also used 1 2 liter pop bottle and 2 500ml water bottles for a sample of labeled containers they commonly see. I stapled together a four page flipbook out of two pieces of blue paper for each child. I had cut 8.5 x 11 blue sheets of paper for our liter flip book. I chose the color blue for water so they would connect it to liters. The flipbook would be used as it had been when we studied meters and grams, but they would be filling it out independently and drawing objects at the end of the lesson and for homework.
I started the lesson today in the science lab, by writing the sentences on the white board with blanks to fill in:
I can use meters to measure _____________.
I can use grams to measure _____________.
We talked about what words we could use to fill in the blanks. Quickly students said "length" for meters and "weight" for grams. One student said that he thought that "mass" for grams was a better word. So, I erased weight and wrote in mass. I coached my students to think about width as well as length and suggested that distance was a good word too. I explained that meters measure a length, width or distance of a line or line segment.
Under the sentences, I wrote as I asked: What is left to measure? Liquid! And then I continued: So what metric unit do we measure liquid ? Everyone shouted "Liters!"
I opened up my SB file to the first page and we discussed each question on the first page. I used this SB file as a lesson guide. What's a Liter SB File
I asked my students what they thought a liter looked like? Students mentioned pop bottles and water bottles. I told them that they would use the containers on the counter in front of me to measure and discover what a liter looks like. I told them that I wanted them to think about the shape of the containers and use their estimation skills to predict what container would hold one liter. I told them that they would be pouring and measuring water in the graduated cylinders and other containers to find a liter. I randomly grouped students in groups of 3.
I wrote instructions on the whiteboard: For now, you will use millilters as your unit. You are looking for a liter. Think: How many milliliters is in a liter? Instructional Note: Remember that students have not been told that 1000 ml equals a liter. I am hoping they figure this out using their prior knowledge from studying and converting meters.
Take turns sharing responsibilities without arguing!
1. Choose a container in your station that your group thinks is about a liter.
2. From the faucet, fill the container.
3. Pour the water into the larger 1000 ml graduated cylinder and record the measurement in your notebook.
4. When you have found the container that is a liter, sketch it on the first page of your flipbook. Fill out your flipbook from liter, deciliter, centiliter and milliliter with kiloliter on the back.
Extra: When you have found your liter, for fun, use the eyedropper to measure a ml. Count how many drops of water you need to make it to the ml mark on the smallest graduated cylinder. Are you surprised by your finding? Why or why not?
I finished by explaining that deciliter and centiliters would be blank on their flipbooks because it was an uncommon unit as it was with meters and grams. With that, the "learning chatter" started as teams played with the containers. I could see they were engaged and that there was discussion about how to measure, which container to use first and that they guessed the large graduated cylinder was the liter. I roved the classroom, listening for insightful comments and remarks that I could use to guide them to mastery of the standard and math practice standards for accuracy and using the right tools the right way. I heard one student say they thought the large graduated cylinder was too big to be liter. I later would use this to get them to understand that containers were deceiving when it came to measuring liquids. To master this standard, students need to understand that relative sizes includes things that may not look like what they think the unit should be. This is demonstrated in liquid measurement very easily.
Students started to figure out how and why the large graduated cylinder was a liter because they made the choice to start with the largest container. I said nothing to lead them to this decision because I wanted to see if their critical thinking skills and logic would kick in gear. I noticed they were using their math reasoning and understanding of reading units on a measuring tool well. Understanding what a liter looks like. I had hoped that they would use prior knowledge learned in the other two labs: So What's a Meter Look Like ? and Finding a Gram because it had been a little bit more structured and directive. I wanted them to be freer this time around to make logical decisions on what tool they would use first and how they could find that liter. (I used the SB to guide their thinking in the prior section.) Some continued to measure and work. Measuring Some students needed clarification of how much water to put in the green cup when measuring. Clarifying the Expectations
I continued to rove and see them start to experiment with the eyedroppers and I stopped to ask questions about how effective an eyedropper would be filling up a larger container. This led to discussions about choice of measuring tools. In the end, most groups had discovered that 1000 ml was a liter or they understood it from another group's discovery.
As I visited each group of students I could see most were ready to wrap up and discuss what they had found. I wanted to really focus on helping them understand that volume is sometimes deceiving so I had them return to their seats as I brought out a filled 2L pop bottle and the smaller water bottle that measures 1.5 liters. Using the large 1000ml graduated cylinder, I asked them how many times I could pour the water from cylinder into the pop bottle?
Everyone had confirmed earlier that they knew that the cylinder was one liter and drew it on their flipbook, yet everyone thought that the cylinder would pour just once into my pop bottle. Me Holding a Liter. They were amazed to see it went twice. Then when I held up the half liters, they knew the bottles were 500 ml. They knew both bottles would fill the cylinder, but didn't believe four of them would fill the pop bottle. We talked more about how containers is very deceiving. Deceived by size. This gives me a clear understanding that relative size in metric liquid measurement is still difficult for them to perceive.
As I moved toward closure, I reiterated being careful about choosing our measuring tool.Logic to Measuring Things I asked for "aha" moments: Aha! Liters!: This student realizes what a liter is and explains. Aha moment with the green party cup shows a student who realized that the green party cup was not a liter. Another group was talking about how the styrofoam coffee cup held more water than they thought.Comparing the cups.
The final wrap up, I wanted students to show me using the final page on the SB file what objects would fit in the right place on the T chart. Choosing the right unit.
For their homework assignment, I asked them to complete their flipbook by drawing 3-5 examples of a liter, ml and kl. I wanted them to look around the house with the help of an adult ( since more than likely they would have to look in medicine cabinets, pantries and possibly under the sink ).