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. Once a week, they are given a test of various numbers between 1-100 for which they need to find factor pairs. 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 (35, for example):
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 students 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.
After our warm up, we got right to the heart of the core lesson. I started by drawing the stair step model on the board and labeling it from millimeters to meters, explaining that we were going to learn to measure using decimeters. After we measure, we will convert from decimeters to centimeters. I asked students to get out their meter stick measuring tapes and get ready to measure!
I asked this question to help satisfy understanding of relative measurement as expected by the standard: What kinds of things could be measured in units of decimeters?
We decided together in our dialogue that a decimeter is something that would be just under the need of measuring with a meter. One student asked why we don't see things labeled in decimeters like we do with kilometers meters, and millimeters? To get them to think a little bit more, I asked them to think about what would be measured in decimeters? I told them if we answered that question, maybe the first question would be answered.
I went to the white board and started a list. Students offered up their ideas. The list grew as we talked.
desks, white board, Ringo's tank ( Ringo is our tortoise), a large book cover, our feet, hands...
The list went on.
I returned to my student's question about why we don't see decimeters as often. Can we answer the question yet? No one could. I suggested that maybe we needed to actually measure in decimeters to reveal the answer to the question. I let students choose their partners for this activity. I counted to 10 and we were ready to rock and roll.
I passed out their measuring and conversion homework sheets to go over now instead of waiting until it was time to assign homework. I wanted them to see what the end expectation was before we started to measure. That way, they knew that they needed to think about their learning in order to apply it to their homework. I read the directions aloud. I told them to fill out the first section and show how they multiplied by ten by writing an equation. They could consult their partners and work on the first from cm to mm. After they were finished, they were to find four objects to measure in decimeters and write the measurement down along with what they measured next to it in the chart. I told them I wanted them to convert later.
About the worksheet: This sheet has three components; cm to mm, dm to cm, and m to dm. It also has a writing component that helps me understand if they notice the patterns of multiplying by 10. It also exercises skills in writing about math and gets them used to having to think and explain, because P.A.R.C.C and Smarter Balance Tests will demand writing and explanation in math.
They busily set to work and soon most partners had solved the top chart. I roved about the classroom assessing their work.It looked good! Most people didn't create any stairstep model or equation to solve. Some created the equation right into the chart.
Soon the room was buzzing with chatter about what to measure in decimeters. Partners moved through the room, choosing objects to measure. They were to measure the object to the nearest centimeter in order to produce a number to the tenth place only. As students started to read their rulers, the issue of accuracy came up, so I gathered everyone together to measure a student. One student laid on the floor as the other student measured him ( I didn't tell them that they should probably use the wall to be more accurate, because I didn't want to interfere in their decisions on what and how to measure their objects. I was more concerned about them counting the decimeters.) We discovered that we were turning the tape measure the wrong way as we were going. Two other people realized that they had done the same thing. Measuring Using Decimeters Accurately & Getting it right shows engaged students working hard to measure correctly. When we were finished measuring, I stopped to talk with everyone about accurately measuring and not including millimeters. I showed them by holding the measuring tape up and pointing to the centimeters explaining that we needed to round up to produce only one place value to the right.
Students went back to work busily measuring and finishing up their work.
When it seemed that everyone had finished up measuring in decimeters, I asked them to join me on the floor again for a discussion about what they had learned. I asked for anyone to share something they realized while they were measuring. One student shared that she thought "decimeters were kind of weird." When I asked why she replied that they seem like they don't fit. She said " I don't think decimeters do anything that centimeters can't measure. What difference did it make if we had 7.5 decimeters or 75 centimeters?" I simply explained that she was returning to the question about why we don't see decimeters as often as centimeters. I wanted to know what they thought.
One student said that decimeters "helped him speed up measuring." I think he got to the heart of understanding relative measurement concepts of the standard with that one sentence. I interceded by saying " You are right! Using the right unit speeds up the measurement, makes the numbers easier to manage and helps us be accurate." Making connections to patterns was an important way to wrap up the lesson because I wanted them to connect the multiplication of one power of 10 and the pattern. I lead them to the question of how they might think we could convert from larger to smaller units if we go down two units. Another student said they would multiply by 10 and then 10 again.
I assigned the rest of the worksheet explaining that they needed to write about what patterns and what they noticed when they convert from a larger unit to a smaller unit. I want them to write so that they put their reasoning into words. It helps them internalize the " how you do it" to "why they do it."