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 Needed for the Lesson: Gram balance scale. Gram weights. Rice: 2-3 tablespoons of it in little viles ( old pill bottles work well). Random small items to measure. A paper clip, pencils, erasers, etc. Green paper to create a flipbook. ( I prepare and staple flip books for my students ahead of time to save time. Take a look at the short video.) There are two sheets to make 4 pages. Using this visual, What's a Gram? and flipbooks ready on their desks, I set the stage for the lesson.
Today, I was able to use the science lab and set up stations with gram scales and items to weigh at each station. Each station had a little vile of rice, a pencil and other random objects to measure. It is best to set up this lesson in stations or on desks pushed together.
Supporting Vocabulary: This is the first time my students studied anything about grams and so to master this concept, I knew it was important to front load with content vocabulary.
Mass: Prior to starting the lesson I had written "MASS" on the whiteboard in a Frayer Model. Around the word, clockwise, I listed in the model: My own words of what it is, Formal Definition, and What it isn't.The fourth area was labeled Measuring tool looks like... This little vocabulary strategy helps students personalize their vocabulary, making it more meaningful and fun. I use the Frayer Model for most of my vocabulary study in all subjects. I like to adjust the outside categories to fit the subject. The resource on the website is nice because it gives you paper models you can copy.
After students were seated and ready, I opened the lesson by pointing to the word "mass" on the whiteboard and prompting students to write the word in their math journal at the top of a page and also create a Frayer Model in their notebook if they wanted. I asked them to help me fill in the model as we discussed the term.
We discussed "mass" and its relationship to weight and defined the word in our own words. One student had mentioned that he had heard that we weigh less on the moon, but our mass is the same. I explained that what we are made of doesn't change, but gravity affects our weight or weightlessness as on the moon. I explained it as lightly as possible. Our definition in our own words was student friendly; " How much stuff something is made of." I guided them with this definition carefully. I explained that "stuff" means that it has weight. I think the concept of "weight" is more applicable to their developmental level and for our purposes of mastering understanding of relative sizes as the standard demands. In this lesson we will focus on this connection. We lightly talked about the difference between weight and mass and how hard it is to really think about at this point. We listed that "It isn't, length, width or height" We continued and created a more formal definition by looking it up in the dictionary as they wrote it in their notes. Gram I drew a balance scale in the "tools" section. The last time we used a balance scale was when we had studied the meaning of equals earlier in the year. So, they were familiar with the scale but didn't know that the units measured were grams.
Gram: I asked them to write gram on the cover page of their flipbook. I opened the SB file to the first page and we went through the next four pages together as I taught the lesson whole class. We discussed questions one by one. We then drew the stair step model without the units ( just the steps) in our notebooks, and discussed that we usually see units of grams, kilograms and milligrams more so than the others, I asked the question: How is the term "gram" like "meter" in metric units? Where does it fall on the stair step model?"
One student raised his hand and said: A gram is like a meter, but measures mass. It is the base unit. I didn't expect this understanding but as I work through CCSS, I see better connective thinking in mathematics. I labeled the steps with the correct prefixes and we filled in our stair step model. I explained that grams measure dry weight or mass. One student asked after looking at his stair step model, if we multiply by ten when we go down a step. Again, this is an example of how CCSS supports students' connections and thinking process.
I asked the question: What does a gram look like in the real world? Students gave me all kinds of answers. One boy said it looks like a kilometer. One boy said he thought it was as big as a book. One girl said that she knows that a pencil is about 5 grams. So, I had her come up to the beam scale and helped her weigh her pencil. She read it as 6.2. I was happy to see her transfer her knowledge of decimal points in smaller units and I explained that the smaller units were decigrams. I asked everyone to sketch a drawing of the pencil on the first page of their flipbook. I assessed that they really did not have any idea of what a gram was. They cannot master the standard without having a solid concept of a gram.
I told them that today they would discover what a gram looked like, just like they did with meters, as I grabbed one of the viles of rice to put on the gram scale. The rice is a good model because it can be adjusted until it weighs exactly one gram.
I started by adjusting the beam scale so that the beam lined up with the line on the end and I explained that this was important in order to have accurate measurements. I showed them the cups of rice I had prepared and demonstrated that we could pour the rice directly on the top of the scale. As I weighed the rice, they could see right away that I had put too much on the scale and they would need much less for a gram.
I then explained that they needed to measure exactly one gram of rice. After students placed exactly one gram of rice poured from the vile, they were to count the grains and draw that on the first page of their flipbook labeled "gram" near the pencil they had sketched earlier. Using rice was a way for students to use their quantitative reasoning as they figured out if they should put more rice on the scale or take it off. When they arrived at one gram, partners worked together, as one counted the grams, another chose another item to weigh so the activity kept moving along. I told them that I wanted them to be sure and weigh the paper clip before the class was over. A paper clip is a good solid example of an object that weighs one gram.
Students began their work and I watched and collected these little clips. They were engaged and working together well. Teamwork and counting shows students working to count the grains of rice. Note that I remind them of teamwork. Gram? Got it! shows students arriving at their gram and I push them to get another item to measure.Measuring dilemma! shows that students had to cooperate and think about how much rice should be on the scale.
When students finished weighing items, they were busy getting more items to measure. They measured paper clips and found that they were precisely one gram. I asked them to draw each item they measured on the cover of their booklet and label the weight.
Time to Share: I stopped students after about 20 minutes of working to check and see if they had 3-5 items weighed and drawn on the cover of their booklets. All had a paper clip! So, I asked how much the paper clip weighed. They told me 1 gram.
Pushing them to think: To fully fulfill Math Practice Standards 4 & 5, I asked how many grains of rice were in one gram?: They told me 36 - 45 grains. I asked why there was a range of numbers? Students offered up explanations that grains of rice might be different sizes. One students mentioned that the scale may have been "off". I was happy to see the math reasoning of why and the thinking as they demonstrated proper use of tools, strategic methods of weighing items and modeling as expected in Math Practice 4 & 5.
I continued to extend their thinking by talking about gram units that we usually use in the real world. I told them that kilograms and milligrams are other units that are common. The others are less common for every day use, but that scientists perhaps would use those units commonly. We need to know decigrams, centigrams, Dekagrams, Hectograms to think about how many powers of ten we use when we convert units. I pointed back to the stair step model we had created on the board. Many raised hands to say that nothing was different about grams and meters as far as converting was concerned. There was a lot of chatter about that, so I could tell they were connecting the understanding well. (Gram Lesson Board.jpg This photo helps you see what had been written in class as the lesson was taught and what our stair step model looks like. I avoid the stair step models with the decimal numbers since it doesn't apply to what is expected in our standard.)
We continued our discussion as I showed them the slide about what would we do if we needed to measure a larger item? Then I slid the slide down so they could see the whale on the scale. One student raised his hand and explained that kilograms would be measuring larger things. I told them that they would be weighed in kilograms. I had them turn their flip book over and write kilograms on the back. I also had them write milligrams on the very bottom of the last page. Then, they filled in decigrams and centigrams on their flipbook.
As we finished our discussion, I moved the pages on the SB file to the page where we could choose what picture went in the T chart. We took turns filling this in and no one had a problem with identifying what would be weighed in grams vs kilograms. Choosing the right unit on the SB
Wrap Up: I asked for one last closing remark: I wanted a clarifying sentence that would tell everyone how what we use grams for versus kilograms. One student answered eloquently and I had each student repeat his statement. Explanation Wrap up.mov
After our closing, I assigned students the task of finding and drawing items we would measure in kilograms and milligrams. I asked them to ask their parent for help with milligram examples so that they didn't go into the medicine cabinet or to their vitamins on their own. We did not discuss medicines or vitamins, but I simply said that chemicals are sometimes measured in milligrams and that they would need help with finding items measured in milligrams.
I told them that even though they may not have a gram scale at home to actually weigh in kilograms, that they could research what, for example, an elephant would weigh in kilograms. I told them that they should give me 3-5 drawings with labels for each of these units for their homework this evening.
This homework then extends their thinking in the smallest and largest unit and will help segue into the liter lesson for tomorrow and for another flip book. See the reflection for student samples of the flipbooks they made.