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 (35, for example):
I check 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.
Rationale and Preparation:
I wanted to use a map that was scaled in kilometers so students apply metric measurement to the real world and integrate some history at the same time. The Education Place website for maps from Hougthon Mifflin is a great resource for maps.
I chose the map of Lewis and Clark's Expedition as a base for us to practice map scale reading using Kilometers to tie into our American history study. I copied off a map for each student, but added my own two column table with measuring requirements to the bottom of the map. This made a great worksheet for "practice in class" assignment as we continued to practice conversions of larger to smaller units to fully satisfy the standard. (I have inserted the link so you can modify it.) I also have included mine as a resource.Lewis and Clark Improved Worksheet
I made sure learning goals were written on the large white board in my classroom for all to see before I began the core lesson. I always try to begin learning goals with an "I can" statement and tell them that they should be able to check themselves for these goals when the lesson is done. The closing will be drawn back to these learning goals.
*Understand what a kilometer is and envision what it looks like compared to a meter.
*Use a map scale to measure kilometers on a map about a real life event.
*Convert from Kilometers to Meters using a two column table, a stairstep model, and an equation that multiplies powers of ten.
Opening the Core Lesson: Setting the Stage for Understanding the Map
I used this short movie from the History Channel about Lewis and Clark to open the lesson to help students understand who Lewis and Clark were. I also wanted students to understand that in our early U.S. History, we didn't know the Pacific Ocean existed on the other side of our nation. This also helped in introducing my students to the importance of a direct trade route to China. I pulled down my world map and showed students the location of China and told them that Thomas Jefferson was looking for an easy way there...so he hired some special people to find a route. We talked about the items that Americans would have used from China. I told them that Lewis and Clark drew maps as they explored, helping us to understand the western portion of the U.S.
After the movie, I answered questions they had about the route and showed them the U.S. map I had pulled down. We also discussed the nature that Lewis and Clark brought back with them and why that was of interest.
To draw the discussion back to math, I asked: How far did Lewis and Clark travel? One student answered : 8 thousand miles. The movie had stated the distance in miles. I wanted them to work with kilometers and understand that we generally use miles as our distance unit in the United States.
To help them realize this, my next question was: In what units did Lewis and Clark measure their trip? I explained that even though we had won the Revolutionary War and the War of 1812, that the U.S. kept the English or Customary system. Lewis and Clark made their maps scaled in miles. This was a fun discussion. Note the student who says " When we threw the English out, we didn't throw their measurement system out!"
After a good chuckle, I clarified to them that we were going to read a map about their exploration route, but we were going to read it in kilometers.
It was easy to teach the whole class sitting right on the floor in front of the Smart Board where the movie was shown moments before. A student passed out the worksheet/maps.
I asked students to look over the Lewis and Clark Map and asked them to locate the important features to review map features. We found the compass rose, pronounced names of significant places, and located the key, noticing that there were three routes on this map. We determined that Lewis and Clark must have split up during their trip back. I explained that while the Rocky Mountains covered a long span, we would use their marked routes to determine our measurements when it was time to measure.
I asked them to find the scale on the map. When that was located by everyone pointing to it on their sheet, I asked what units of measurement were noted? One student said kilometers and meters, explaining that the km was kilometers and the mi was meters. Another student piped up and corrected him saying that the mi was for miles. I explained that while we do not cross over to another system, that often map scales will show both kilometers and miles giving the reader an option to use either. I told them we would be reading only in kilometers. I told them I would show them how to make a useful tool using the scale and a sticky note. This tool would be used to measure the distances we needed to know.
I pulled off a sticky note and carefully showed them how to butt up the edge of the sticky note and draw the scale on the edge using tick marks. I showed them how to continue the scale, making use of the whole edge of the sticky note as we counted by 500 to make a scale to 1500 km across the edge of the sticky note.
I showed them where their directions were at the bottom in the two column chart and explained by pointing to each one so there was no confusion about what to measure. I told them that the next step after measuring would be to convert in the other column.
I demonstrated the first one and measured the distance between St. Louis and Fort Mandan. It is 1500 km and wrote it on my sheet in the proper place. I also related it back the equation 3 x 500 = 1500 km to continually address the concept that we need to think in terms of equations for every problem.
I turned to the Smart Board where I displayed a stair step model. I asked them to copy it in their notebooks using meters as their base unit. I asked them to ignore the grams and liters and drew the abbreviations on the steps. I also drew arrows as we counted from kilometers to meters.
I wrote x10 for every step we went down as we moved to the meter "step". I stopped there and asked: How many powers of ten did we multiply by to go from km to m? They all answered 3 powers of 10 and someone said: That's a thousand times! ( Yay!)
I wrote 1 km = 1000 meters. To make sure the concept was solid, I asked them how many meters would be in 5 mm? Most answered 5000 immediately.
To continue with guiding them toward equation development, I wrote the equation on the board 5km x 1000 = 5000 m.I asked them how many powers of ten do we multiply to get 5000? The reply was 3 powers of 10. I turned to the stair step model and used it to multiply and model a visual of the powers of 10. Together we went from km to meters, multiplying by 10 on each step, saying the product aloud and moving to the next step until we landed on meters. We all said aloud: 5000 meters. I used three concepts to help them understand how we convert from kilometers to meters. We used the equation, a visual model and talked about powers of ten.
I asked for them to show me thumbs if they understood. All thumbs pointed up.
To be sure that they understood their assignment I stopped and went over exactly what they were to do.
1. Make a measuring tool with the sticky note.
2. Measure each distance that was noted in their chart.
3. After each measurement, convert using the stair step model in their notebook, or multiply by 1000 or 3 powers of ten. Label the product with M for Meters.Stair Step Model
I partnered up students by partnering an above grade level achieving student with my below grade level achieving students for optimum learning and support. This allows an opportunity for leadership from one and the feeling of support by a peer to another. They set to work.
The guide by the side: This was my opportunity to serve as their support person as they worked in partners to find distances on a map and solve and strengthen their conversion skills.
My students were partnered up and started to work. I sat awhile with one student to help get him going. This student needed me for direct instruction and support. The Scale & Measuring with the sticky shows how he and I worked together to understand how to use the sticky and the scale. He easily figured out and just needed that little boost.
Then, after he settled in, I roved about the room and spotted some misconceptions.Confusion shows how the scale itself confused the students. There were two pairs of students who thought that the scale was one kilometer even though it was marked 500. They measured the times they used the section and both came up with 3km. It was because they had scaled it as one tick equaling one kilometer and they knew they measured three times. They needed to re- measure and try again. To support the standard and get their relative size understanding, we discussed how far 3 km is. I related back to running a cross country race because several of my students' parents run in 5 K's. This conversation helped a lot with understanding relative size of a km!
I continued to move on and students soon wanted to know if they were correct and approached me with completed papers. I watched one partner group figure out that they needed to divide the 500 km in half and add it in to calculate 750 km. Measuring- Figuring it out
I conferred with students when they were finished to see if they could share what they had learned from the activity.Are we right? From looking at their work, I felt that they were ready for a quiz on conversions of meters in the next lesson.
I roved about the classroom checking students as they worked and cleared up any misconceptions.
When everyone was finished, I stopped them and we shared our "Ah Ha! " moments to close our lesson.
My aha moment: This student shares as I prod him for more explanation of his understanding. He finished his explanation off camera by telling me after I coached him into saying he multiplied by three powers of ten or one thousand.
More "Aha!" moments. This clip shows how students embraced conversions and kilometers and that they understand the stair step model.
I returned to the goals on the board and asked if they had achieved each of the goals. They showed their thumbs up if they mastered each goal. I noticed that everyone's thumbs were up for each goal. I collected their papers to assess their understanding.