To reinforce the concepts students learned yesterday and to help support the two students who were still developing a deeper understanding of the relationship between a gram and kilogram, I decided to begin this lesson by reviewing.
For comparison purposes I showed students a gram of gravel and a kilogram of gravel: Kilogram & Gram. I first held up a gram and asked: Does this seem about right... one gram? Students agreed, "Because a gram isn't very big." Then, I once again, showed them a kilogram of gravel in a bag. I continued, But how do you know how many grams are in a kilogram? Students responded, "You can get a platform scale!" "You can use the weight set." I purposefully placed a platform scale on a particular student's desk. This student was one of the students who incorrectly answered the question, "How many grams are in three kilograms?" on yesterday's exit slip. I wanted to make sure he received another layer of instruction. Then, I pulled out five 20 gram weights and placed the weights one at a time on the scale. Count with me... 20...40....60...80...100. One hundred what? "Grams!" I then showed students the scale and asked, What is the scale telling us? "That you have 100 grams." Turn & Talk: How many grams would be in a thousand? During this time, I conferenced with this student: Counting by 100. The student successfully explained the number of grams in a kilogram!
Prior to this lesson, I created a T-chart comparing grams to kilograms. I alternated back and forth between giving the number of grams and giving the number of kilograms: Lesson Template. When creating this sequence of tasks, I started off with what students know (1,000 g. = 1 kg.). Then I built upon this concept by asking students to convert 8,000 g and 12,000 g. to kilograms as well as 3 kg. to grams. Then, to push their thinking one step further, I included fractional parts and decimal numbers.
To begin, I introduced the lesson's goal: I can record measurement equivalents in a two-column table. Students wrote the goal on a new page in their math journals. We discussed the meaning of the goal in detail by circling higher level words and writing the meaning next to them on the chart. What does record mean? "To write down." "To take notes." What does equivalents mean? Students struggled with explaining this! We finally came up with "Equal." What does a two-column table mean? "A t-chart. Okay then, let's make a T-chart to compare grams to kilograms! Please draw a T-chart in your journal. I modeled this while giving directions. At the top of one column, write... I paused for a moment to see if any students could fill in the blank. I do this often to encourage active listening and engagement. I was so proud when I heard a student say, "Grams!" And at the top of the next column, we are going to write... I paused... "Kilograms!" You got it!
I then revealed the first task on the chart (1,000 g. = _____ kg.) and asked: A thousand grams is equal to how many kilograms? All student saids, "One kilogram!" I modeled how to write the "equivalent conversion" in the second column. I used higher level vocabulary often to help support Math Practice 3: Construct viable arguments. Part of constructing viable arguments is becoming familiar with appropriate math language. We continued on to each of the other tasks, Revealing one at a Time. With each task, I asked students to Turn & Talk to explain their thinking. Then, we would come back together as a class. To hold students accountable and to make sure I was calling on a all students, I chose students randomly using popsicle sticks with names. To further support any students who seemed apprehensive, I asked if they wanted to ask another student to help them at the board. Students' excitement began to grow more and more with each reveal of a new task.
At first, students were quite successful with 12,000 g and 3 kg. When we got to Half a Kilogram, I asked as student to model 1/2 a kilogram on the number line at the top of the paper. The task, 1.5 kg = ____g, is where this activity become challenging for students! This video sequence is my favorite part of this lesson. At first, Collaborating Part 1, two students were stumped on this tasks. Other students began to provide feedback and support. One student said, "1,500!" Others responded with "What?!" This was a perfect opportunity to discuss how we should respond to each other when we disagree. If I had thought of it at the time, I would have reminded students of our prompt, "I disagree with respect because...." Next, Collaborating Part 2, the student who shouted out, "1,500!" came up to the board to explain his thinking. One student caught on and began to write 500 grams. Then, with the help of the student helping, she realized the answer would be 1,500 grams instead. At this point, the helping student told me that the third student "didn't get it." I asked them to explain it further using the number line model: Collaborating Part 3. The helper student turned out to be right, even though several of his classmates originally responded to him with a, "What?!" What a great learning opportunity for many reasons!
We then moved on to the last two tasks: 2,500 g. = _____kg and ____g. = 1/4 kg. In order to support student learning, I slowed the lesson and encouraged student collaboration, as well as the use of models. Here's a conversation I had with a student during this time: 2,500 Grams. You can hear other students collaborating and sharing their thinking in the background. When students explained One Fourth of a Kilogram to me, I encouraged the drawing of a model. After our math lesson, I noticed this student was successful at drawing a model on the side of his paper: Student Journal.
To check for understanding, I asked students to complete an exit slip task. I handed out a 1/2 sheet of paper to each student and asked the following questions. I also wrote them on the board to help support students in need of extra processing time and for students who are more successful if they hear the questions and see the questions: Exit Slip Questions.
1. How many grams equals 1 1/2 kg?
2. How many grams is 2.5 kg?
The majority of students were proficient at this task. Here's an example of a Proficient Student.