Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation.
Task 1: 2 x 8
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, 2 x 8, students took two jumps of eight, eight jumps of two, and Decomposing into 2x4 + 2x4. This student used Doubling & Halving. He really surprised me. I can tell that some strategies are really starting to make sense for him.
Task 2: 5 x 8
When we moved on to 5 x 8, students eagerly shared the following strategies: five jumps of eight, eight jumps of two, and decomposing 5 x 8 into 3 x 8 + 2 x 8.
You can see that each of the number talks involve multiples of eight. 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 8 is 3 x (2 x 8) - (1 x 8). This will help students develop Math Practice 8: Look for and express regularity in repeated reasoning. By the time we were finished with this task, most students' number lines were full of Multiple Strategies.
My favorite part of today's Number Talk was when two students successfully used the distributive property without any help from me!!! I was so proud of them: Independent Success!!.
Prior to the lesson, I created an anchor chart using the Lesson Template. Here's what the chart would have looked like before the lesson: Anchor Chart Before Lesson. As I explained the goal for the day, students wrote the goal at the top of a new page in their journals: Here's our goal for today! I can record measurement equivalents in a two-column table. Remember that record means to write down and equivalent means equal. Making it simpler, I explained: So today, we want to write down equal measurements in a t-chart.
I then asked students to recreate the t-chart in their math journals (ounces on one side, pounds on the other). They also filled in the given measurements, prewritten on the Anchor Chart Before Lesson. I gave plenty of time for students to complete this task. Early finishers began finding the equivalent conversions for each of the given measurements.
I also took the time to work with an individual student. We began by discussing the number of ounces in a pound. I brought the One Ounce vs One Pound bags to help model this concept. It didn't take him long to figure out 16 oz clay balls = 1 lb. To provide him with an opportunity to construct and present a viable argument (Math Practice 3), I decided to ask him to show his thinking to the rest of the class. Sometimes the students who are still developing an understanding of math lose out on the valuable opportunity to share.
Claaaaaassssss! Students responded, "Yeeessssss!" Let's begin filling this chart in together. I'm going to ask students to come up to the board and share their thinking. Let's start with Ben! This was the student who I had just conferenced with: 16 oz. = 1 lb. In the video, you'll hear silence in the background. This is because all the other students are so engaged in finding the next converstions, they're hardly making a peep! Before sending this student back to his desk to continue working on his own, I tried to prepare him for the next conversion: If you know that one pound equals 16 ounces, what are you going to do to find 2 pounds?
At this time, I asked students to continue completing the conversion chart in their journals. Students naturally enjoyed finding the missing numbers. It was almost like a game! Some students chose to work with others while others worked on their own. I went from student to student, providing support as needed.
Here, Problems with Doubling, is one of may favorite moments of this lesson. This student discovered how to use the doubling strategy, but applied the strategy incorrectly, doubling 32 ounces to solve the conversion for 3 pounds. When students look for and make use of structure (such as doubling and halving), they are developing Math Practice 7! In this video, you'll notice that my first attempt to guide this student to recognize her mistake doesn't work! So then, I tried again! Here, Now I Understand Doubling!, you'll see she makes the connection with time and support. I was so proud of her and proud of myself for finding a way to develop her understanding of in and out tables.
After giving students about 20 minutes to work through each conversion independently, with a partner, or with my guidance, I asked for volunteers to help fill in the Anchor Chart. One by one, we discussed each problem. Here, a student explains 32 oz. = 2 lbs. Each time students shared, I always tried to ask: How do you know? How did you get this? I wanted to make sure students were focused on mathematical reasoning and justifying answers (Math Practice 3), instead of just finding the answers.
Next, a student began to explain how he found 16 lbs. = 96 oz?. It's clear to me that he found 6 pounds x 16 ounces = 96 ounces and forgot to find how many ounces is equal to 10 pounds more. This turned out to be a more difficult problem that the fractional conversions later on! Here, Using 4 lbs. to Find 16 lbs, I asked students: If you multiply by four on this side, what will you need to do on this side? We moved on while the two students worked together to solve the conversion. After the lesson, during recess time, one of the students successfully explained her thinking: 16 lbs. = ? oz.
Students then went on to explain the number of pounds equal to 1 oz., 2 oz., 3 oz., 4 oz. 8 oz. and 24 oz. Including fractional parts of a pound was a bit of an experiment. I was unsure if students would be able to identify the number of ounces equal to fractional parts of a pound or not. Either way, I knew that whatever conversation resulted, all students would develop a deeper understanding of the relative sizes of ounces and pounds.
I was surprised to see this student, 1 oz. = ? lbs, find that 1 ounce is equal to 1/16 of a pound. Now looking back, I wish I would have asked him to share how he found this!
Another student, 2 oz. = ? lbs, surprised me even more when she explained that 2 ounces is equal to 1/8 of a pound! Next, students explained the equivalent conversions for 3 oz, 4 oz, 8 oz = ? lbs. Unbelievably, one student said that 4 oz. = 1/4 lb. and 8 oz. = 1/2 lb.
Once a few students began sharing, many others began to see the conversions as well!
Finally, the moment that astonished me the most was when a student found how she solved for the number of pounds equal to 24 ounces. At first, she wrote: 16 oz. + 16 oz. is 32 oz. Then she said: 32 oz. - some number = 24 ounces. In the end, she decided that 32 ounces = 2 lbs., minus 8 ounces (which is 1/2 a pound) equals 1 1/2 pounds: 24 oz. = ? lbs. Also, you'll noticed this student replaced her question mark with the variable, T (an unknown number). This goes to show that introducing variables at the beginning of the year encourages algebraic thinking and abstract reasoning (Math Practice 2) throughout the year.
After teaching this lesson and experimenting with exposing students to fractions prior to a unit on fractions, I'm a believer that fraction concepts should be integrated with all other math units throughout the year. So amazing!!
As an exit slip today, I asked students to answer the following questions on a half sheet of paper.
1. How many ounces are in a pound?
I wanted to see if students understood the relationship between a pound and an ounce.
2. 1 pound - 3 ounces = ?
I asked this question to see which students could apply their understandig of ounces and pounds to solve a multi-step problem.
3. 8 ounces = X pounds
I felt that this problem would show me who was able to connect the relationship between ounces and pounds with fraction concepts as well as abstract thinking.