Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation.
Task 1: 3 x 5
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 5, students took three jumps of five, five jumps of three, decomposed 3 x 5 into (2x5)+(1x5), and multiplied 3 x 10 and then divided by 2. In this video, a student models the strategy, Doubling & Halving.
Task 2: 5 x 6
When we moved on to 5 x 6, students eagerly shared the following strategies: five jumps of six, six Jumps of Five, multiply 10x6.JPG and then divide by two. The student in this video shows how he found that five jumps of six = six jumps of five. Here, we drew a picture to show the doubling and halving strategy on the number line: 5 x 6 = 10x3.
Task 3: 8 x 5
During the final task, we discussed 8 x 5. I loved hearing the various strategies students used. Some students started by taking 8 jumps of 5. One student turned the 8 into a 10 and then decomposed 10 x 5 into (8x5) +(2x5). After this, she took two fives away: (8x5) +(2x5) = (10x5) - (2 x 5). In this picture, (6 x 8) -8, the student went to far and then came back. Another student solved (4x5) and then doubled it: Decomposing 5 x 8. Students then came up with several other ways of decomposing:
You can see that each of the tasks involve multiples of five. By working with a common multiple, 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, 5 x 6 is double 3 x 5 minus a 5. 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 when a student proved the Commutative Property through experiential learning. Instead of my telling students that 5 x 6 = 6 x 5. Students are discovering this concept. This is the heart of Common Core: guiding students to discover and truly understand key concepts in math instead of just telling them!
As always, I began by introducing the instructional goal for the lesson. I wanted students to understand the underlying purpose of the lesson today. By the end of today's lesson, I want you to be able to say: I know the difference between a gram and a kilogram. I then wrote the goal on the Anchor Chart while many students automatically wrote it at the top of a new page in their journals. I celebrated the students and within seconds, every student was fully participating!
I went on to explain the definition of mass. Instead of going into a long and carried out conversation about the difference between mass and weight, I simply explained: Mass is the amount of matter (or stuff) in an object. I paused to let students process. It is commonly measured by how much something weighs. As I spoke, I emphasized the bold words to help with comprehension.
Turn and Talk: How do you you measure mass? Most students were able to explain, "You look at how much the object weighs." Next, I pointed out: What you need to know about a gram and a kilogram is that they are both measurements of mass. A gram is a measurement of how much something weighs and a kilogram is a measurement of... I paused and let my students finished the sentence, "how much something weighs." I'll often let students fill in words while I'm teaching to encourage active listening and student engagement.
Turn & Talk: How are grams and kilograms similar? Many students turned and explained, "A gram and kilogram are both measurements of how much something weighs." Conversations naturally continued as students tried to apply these concepts to their own lives, "I could measure this book or this pencil."
This was a great place in the lesson to ask, Which unit do you think is bigger? A gram or a kilogram? I paused to let students think. Some were silent while others were already explaining their thoughts to classmates. Who thinks a gram is bigger? I was surprised to see almost every hand raised! Who thinks a kilogram is bigger? Only a few hands were raised. I thought to myself: Good thing I'm teaching this lesson! I explained: Today, you are going to be investigating a gram using a balance scale. I held up the balance scale and kids were immediately excited about the lesson! Today, I want you to find the answer to this question, "How big is a gram?" I paused and let students process the question. How many paperclips are equal to a gram? I held up a bag of paperclips. How many drips of water are equal to a gram? I showed students an eye dropper and explained how to use it.
I held up an unbalanced balance scale. One side was up and the other side was down. Let's talk about using a balance scale as a tool to measure mass. Does anyone notice that something is wrong here? Students responded, "It's not even." "Both sides have to be equal." Good! You're right! We need to calibrate the scale before we use it! When we calibrate the scale, we adjust the scale to make sure it's fair. We want both sides to be equal before we begin comparing objects. I showed students how to line the white arrow up with the middle point. Then, I asked team leaders to get out their balance scales and their bag of weights (I showed them an example). At each group of desks, I have a supply center to help organize all of our math materials. This way, students can have access to a variety of math tools at all times. I purposefully organized my classroom this way to support Math Practice 5. I want students to students consider the available tools when solving a mathematical problem.
Students immediately began calibrating their scales. I went to each group and checked to make sure their scales were balanced. Then I asked students to look in the bag of weights to find a gram. It didn't take long for students to find the small yellow tile. I asked: How do you know this is a gram? One student said, "It says 1 g." What do you think g means? "Gram!" Good! Today, you will be investigating a gram and trying to find what weighs about a gram. First, let's start with coffee beans! I modeled and explained to students how to make a t-chart to record their observations. We placed Items at the top of the first column and Number of Items at the top of the second column. I also modeled how to place the yellow gram into one tray of the balance scale. Students anxiously watched the scale become unbalanced. Let's see how many coffee beans are equal to a gram! One coffee bean... two coffee beans... Students continued counting for me. We got to four coffee beans and the scale moved a bit, but wasn't equal. I stopped and said, Okay! Four coffee beans! One gram is equal to four coffee beans. I even went as far as writing it in the chart. Students were quite upset, "The scale isn't balanced!" "You have to keep adding coffee beans until it's balanced!" I giggled a bit and said, So the scale has to be balanced? We continued on, adding coffee beans until the scale was balanced with 6 beans. We recorded this measurement in the t-chart: Student Journal Example. Students were ready to begin investigating!
I showed students Items to Weigh at the back table: candy corn, paperclips, Craisins, pasta noodles, flour, sugar, drops of water, and grains of rice. With each item I asked, I wonder how many _____ will be equal to a gram?!
Prior to students completing their own investigation, we went over expectations. I didn't want to take too much time on this so I simply asked, When should a group move on to another item? Students discussed and agreed: The group can move on if all students have recorded their findings. Who should get to weigh each item. Again, students discussed and agreed to include everyone and to take turns. Okay! Team leaders can choose an item from the back table. Specifically asking team leaders to get an item saves students from spending five minutes deciding which item they should start with, which takes away from instructional time!
While Students Investigated, I went from group to group, conversing with students and asking probing questions: About how many pieces of rice are equal to a gram? How do you know? Does everyone agree? What are you doing to make sure your measurement is accurate? Are you taking turns? Some students came across a few problems: a whole candy corn weighs more than a gram. Instead of providing students with solutions, I asked, What are you going to do to solve that problem? When you let kids solve their own problems, you are supporting the development of Math Practice 1: Make sense of problems and persevere in solving them. Instead of using whole candy corn pieces, students used fractional pieces. Instead of using the measuring spoons to measure sugar, students began using a pinch of sugar at a time.
Here, you'll see a group who needs to be more Careful with Calibration. When they place too much flour on the balance scale, they try to balance the scale by moving the calibrating tool instead of taking flour off. I stopped the video and discussed how to calibrate the scale correctly.
In this video, How many drops of water?, you'll see students trying to figure out how many drops of water are in one gram. Correctly counting was sometimes an issue with groups! You'll also hear a group in the background (the same one that struggled with calibrating the scale) discover, "Just the [cupcake] wrapper equals one gram!"
In this clip, a group explains What equals one gram?. You can really tell that they are beginning to understand the relative size of a gram.
After investigating for as long as time would allow, we cleaned up the supplies. Team leaders put the balance scale and weights back while other students returned the items to the back table. During this time, I wanted students to discuss what they knew about a gram: Tell me what you have learned about a gram! I created a t-chart on our anchor chart: Gram vs. Kilogram and added student observations under the gram column: "about 35 grains of rice = 1 gram, about 20 drops of water = 1 gram, one noodle = 1 gram, one paperclip = 1 gram." At times, students reported different findings. We discussed the factors that could have impacted their investigation: not wiping all of the water out of the tray afterwards, not calibrating the scale correctly, not taking into account the weight of the cupcake wrapper when using it as a cup for the flour. Even though investigation results varied, I knew students were working toward meeting a 4th grade standard: "Know relative sizes of measurement units within one system of units."
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 showed them a kilogram of gravel. As we passed the two around, student reactions were priceless! They were surprised at the weight difference. I explained: Tomorrow, we will delve in even deeper so we can truly say we understand the difference between a gram and a kilogram!
As a final check of understanding, I said, Think about a gram and a kilogram. Who thinks a gram is bigger? No hands were raised! Who thinks a kilogram is bigger? Every hand went up! In my head, I couldn't help but think, "SUCCESS!"