Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation.
Task 1: 3 x 2
For today's Number Talk, I asked team leaders to pass out the Number Line Model to help students show their thinking later on. For the first task, 3 x 2, students took three jumps of two, two jumps of three, and Decomposing 3 x 2. One student showed how to Double 2 & Halve the Product. Shortly after, another student wanted to share how to Double 3 & Halve the Product!
Task 2: 7 x 3
When we moved on to 7 x 3, students eagerly shared the following strategies: seven jumps of three, 3 Jumps of 7, and Decomposing 7x3 into (7x2) + (7x1). Other students took three umps of seven or seven jumps of three. Sometimes students mixed up concepts (such as doubling and halving). The best way for them to figure out that a strategy doesn't work is to try it!! For example, in this video, a student tries to solve 7x3 by doubling the seven AND the three: This Isn't Always Easy!.
Task 3: 6 x 7
During the final task, we discussed 6 x7. I loved hearing the various strategies students used. One student decomposed 6 x 7 into 2 x (3x7).
You can see that each of the number talks involve multiples of seven and three. By working with common multiples, students will be able to connect and apply the learning from one task to the next task. In addition, I'm hoping students will discover patterns between the given tasks. For example, 7 x 3 is double 3 x 2 + 4 x 3. This will help students develop Math Practice 8: Look for and express regularity in repeated reasoning.
My favorite part of today's Number Talk was the level of student engagement. I heard students say, "Mrs. Nelson! I have a good strategy!" "Can we do more than three strategies?" "I did three jumps of seven, but I have another strategy!" "Mrs. Nelson, can I pleeeeeeaaaassssse share my strategy?" At one point, I asked, Who would like to share another strategy? Student engagement was so amazing, I had to stop and record their excitement: Excited Students!.
I began by reviewing the goal listed on the Anchor Chart from the previous lesson, Day 1: What's a Gram? Yesterday, we investigated the size of a gram. Who can tell me something you learned about a gram yesterday? Students looked the chart and said, "One gram is about one noodle." "One gram is about a paperclip." To push their thinking further and to solidify students' understanding of the relative size of grams, I asked: What would you measure with a gram? Would you measure a heavy or light object? Students said, "A light object!" So what can we add to the "Grams" side of our t-chart? "Used to measure _____" Students said, "Light objects!"
I then held up a bag of gravel that weighed one kilogram from yesterday's lesson. Does anyone remember how much this bag of gavel weighed? "One Kilogram!" I walked the room with the 1-gram bag and the 1-kilogram bags of gravel (Kilogram & Gram), just as I had done the day before, placing the bags in students hands and asking, Which weighs more? One gram or one kilogram? I purposefully targeted students who are hands-on learners, struggle with math, or were absent yesterday.
I gave purpose to lesson by connecting the activity with the goal: In order to reach our goal of being able to compare grams to kilograms, we need to learn more about kilograms! Instead of using a balance scale today, you are going to use a platform scale. A platform scale is a weighing machine with a flat platform on which objects are weighed. I showed students how to calibrate their scale and reminded them to adjust the arrow back to zero anytime they removed or added the top tray. I asked team leaders to get out the platform scales for each group and asked groups to work together to calibrate their scales. Then, I asked students, Can you find 0 kg on the platform scale? Point to the "kg." I waited until all groups were successful. Now, can you find 1 kg? I checked on students. How about 2 kg? How about 3 kg? How about 4 kg? How about 5 kg? When asked to find 6 kg, students responded with, "No!" Well, why not?! "Because the scale only goes to 5 kg!"
I modeled how to use the scale using the 1 kilogram bag of gravel. How much does this bag weigh again? "One kilogram!" I showed students what happens when you place the bag to the front or back of the tray (the measurement changes) and then I modeled what happens when you place the bag in the center (the scale reads 1 kg).
I wrote on the board, "Items that Weigh About 1 Kg" followed by a numbered list and asked students to write the same on a new page in their journals. Holding up the bag of gravel, I asked,What do we already know weighs about one kilogram? Students responded, "A baggie of gravel!" After writing "a baggie of gravel" on number on our list, students brought up that we should be more precise by saying a quart size bag of gravel that was 3/4 full. I loved this conversation as it supported Math Practice 6: Attend to Precision. To lead into the day's investigation, I wonder what else weighs one kilogram in the classroom! Students immediately began chatting and looking around without any prompting. After giving students a few minutes to visit, I explained: Today, I'd like for you to measure different items using the platform scale. I'd like you to really understand the size of a kilogram! Please continue this list and try to come up with some more items that weigh about a kilogram. I also asked students to be very careful with the scales and to use good judgement when choosing which items are probably too heavy to place on the scale. Students went right to work, weighing shoes, whiteboards, notebook journals, markers, and books. Here, students are counting the number of markers in a kilogram by placing them on the platform scale: Markers. Here's a Student Journal Example.
During this time, I walked around from group to group with the 1 kilogram bag of gravel: Weighing One Kilogram. I asked students guiding questions to lead them to the discovery that one kilogram is equal to 1000 grams. I first modeled the inquiry process by stating: I wonder how many grams are inside a kilogram. I then asked various questions: How many grams do you think are in one kilogram? How do you know? What can you use to help you? Can you show me your thinking? So are you saying _____? Does everyone agree? It was sooooo great to see students finding the relationship between grams and kilograms instead of just telling them! In previous years, I would have just written on the board: 1000 grams = 1 kilogram. However, since the implementation of Common Core standards, I feel that I now have the freedom to teach concepts like this in more depth by allowing students the time to truly investigate mathematical ideas.
Group A: In this video, 1000 Grams = 1 Kilogram, one student begins by saying, "I don't know how much a gram weighs." Then a student grabs a yellow gram weight. She places it on the platform scale and the arrow barely moves. Then a student says, "900 grams." He is making a common mistake. He sees that the larger mark before 1 kg reads "800 grams" so he thinks the scale counts by 100. To help this student realize the mistake, I called attention to the scale increments.
Group B: Prior to this video, Counting by 200s, a student told me that he learned last year that 1000 grams = 1 kilogram. I then asked, How do you know? Can you prove it to me? In the video, you'll hear this particular student in the background say, "I was right! 1000!" This experience further solidified what he already knew and also gave him a way to prove this thinking instead of just saying, "My teacher told me last year!"
Group C: I loved how this group tried to prove to me that the 100 on the scale is equivalent to 100 grams by placing 100 grams worth of weights on the scale: Comparing Grams to Kilograms. Later on, I came back and they had a stack of weights totaling 200 grams: 200 Grams vs 1 Kilogram.
After students had found several items that weighed about one kilogram, we cleaned up and came back together as a class. Going back to the Anchor Chart, I asked students, What did you learn about a kilogram today? Students raised their hands and shared, "A kilogram is equal to 3 spiral notebooks!" "We found that 6 kilograms equals one kilogram." "I know that 1,000 grams (weights) equals one kilogram!" "That means that 1,000 paperclips equals one kg." I then asked, Are kilograms used to weigh light objects or heavier objects? Many students responded, "Heavier!" At the bottom of the Anchor Chart, under the kilogram column, we added "used to measure heavy objects." This was a great opportunity to ask students to Turn & Talk: What is the difference between a gram and a kilogram? Student conversations were filled with evidence from their investigations! This is an important part of developing Math Practice 3: Construct viable arguments and critique the reasoning of others. For example, students were able to say, "A gram is a smaller unit of measurement than a kilogram because a gram is the same weight of a paperclip. It would take 1000 paperclips, or grams, to get to a kilogram."
To check for understanding, I handed out a half sheet of lined paper to each student and asked them three questions. I wrote each question on the board to ensure students were given the processing time needed and sometimes students are more successful when they can see the question written out.
1. Which is bigger... a kilogram or a gram?
2. How many grams equal 3 kilograms?
3. How many grams equals a 1/2 kilogram?
All students, but two demonstrated proficiency on this quiz, answering all three questions correctly: Proficient.
Here's an example of a student Working Toward Proficient. There's confusion on the number of grams per kilogram. Tomorrow, I'll make sure to provide further support for this student.