Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation.
Task 1: 2 x 4
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 4, students took two jumps of four, four jumps of three, and tried Decomposing 2 x 4.
Task 2: 4 x 8
During the next task, we discussed 4 x 8. I loved hearing the various strategies students used. One student solved 4 x 8 by solving (4 x 5) -4. Another student decomposed 4 x 8 into (2x8)+(2x8). Another student began Experimenting with Decompsing and the Distributive Property. She struggled a bit and began working with a partner. Then, she came back up to me with the correct calculations: Now I've Got It!.
You can see that each of the number talks involve multiples of four. 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, 4 x 2 = one fourth of 4 x 8. This will help students develop Math Practice 8: Look for and express regularity in repeated reasoning.
Without any guidance, one student made the doubling/halving connection with the Commutative Property: 4 x 8 = 8 x 4, Doubling & Halving Connection. You can double the 4 and then halve the 8 to get the same answer. This understanding will help this student solve a more difficult problem such as 5 x 464 = 10 (double 5) x 232 (halve 464).
I began by explaining the difference between the Metric System and US Customary System using an Anchor Chart. Here are the Anchor Chart Pictures I used to construct the chart. The purpose of this chart was to help students connect new knowledge to previously learned information. I began by saying: Fourth graders, there are two basic systems of measurement. One is the Metric System and the other is the US Customary System. What you need to know is that they are both systems of measurement. The Metric System is used world-wide whereas the US Customary System is primarily used in the United States. On the Anchor Chart, I glued the apple, a bunch of apples, and a slug bug car. I asked: Using the Metric System, what measuring unit would we use to weigh an apple? "Grams!" What was the abbreviation for grams again? "You write a g with a dot after it." How about a bunch of apples? Do you remember placing a bunch of apples on our platform scales? "Yeah!" "We would measure using kilograms!" What was the abbreviation for kilograms again? "It's a lowercase kg!" That was when a student said, "Would we use a metric ton to measure the slug bug?" I asked him to "Google it" while the rest of us moved on. I always encourage students to search for the answers to their questions. This is an important College and Career Readiness skill that supports Math Practice 1, Making sense of problems. I want to encourage my students to be thinkers and to ask, "Does this make sense?" in a variety of contexts.
Then, I explained: With the Customary System, we would use ounces to measure the weight of an apple. Does anyone know the abbreviation for ounces? One student said, "It's oz!" At this point, I was getting ready to move on, thinking that we could further discuss pounds later on. That was when a student said, "Mrs. Nelson! Wouldn't we use pounds to measure a bunch of apples?" I couldn't help but acknowledge the readiness of students and complete the chart: You're right! Before I could ask if anyone knew the abbreviation, another student shouted out, "I know the abbreviation for pounds! It's lbs!" Another student piped in, "Yeah... l and then b... then an s on the end!" At this point, the student who was curious about a metric ton had found the definition online, "a unit of weight equal to 1,000 kilograms." So what you're saying is that a metric ton is 1,000 kg? What would we weigh with a metric ton then? The slug bug! Before I could even take note of this on the anchor chart, another student said, "And I know what we would measure a car with using the Customary System! A ton!" I completed the chart as students busily discussed their thoughts, "A ton is really heavy." "A ton is the same thing as a metric ton." I heard this last comment and stated: I just want to clarify. A gram is not equal to an ounce. A kilogram is not equal to a pound. And a metric ton isn't equal to a ton. However, you could use both a gram and an ounce to weigh an... I waited for students to respond. "Apple!" And you could use either a kilogram and a pound to weigh a... "Bunch of apples!" Finally, a Slug Bug car could be weighed with either a metric ton or a "Ton!"
Note: This lesson was inspired by the Georgia CCGPS 4th Grade Measurement Unit, p. 53.
At this point, I felt students were ready to move on to the heart of the lesson. I wanted students to learn the relative size of an ounce and the number of ounces in a pound. In past years, I would have written on the board: 1 pound = 16 oz. Now that I have less standards and am able to teach content with greater depth, I wanted students to discover this on their own! Prior to our math time, I purposefully cut clay into pieces that were just over an ounce or just under. I passed these pieces of clay out to each student and said: I wonder how big an ounce really is! Don't you!? Students couldn't wait to hear what we were doing with the clay! Today, I have set out three digital scales set around the room. I'd like for you to create a ball out of your clay that weighs exactly 1.0 ounces. When you're using the scale, make sure you are measuring using ounces. See how you can click the mode button to get either ounces or grams? I demonstrated this, clicking back and forth between the two measurements for each group of students. When you think you have a clay ball that is a perfect ounce, you can weigh your ball using one of the three scales. Some of you will have to add clay using the extra amount at each group while some of you will have to take away clay. Each student eagerly shaped their clay into balls and practiced Weighing a Clay Ball using one of the digital scales placed around the room. In this video, you'll see students Finding an Ounce. I took this time to question students and support learning: What do you think 0.85 means? Do you think it's similar to money... Like having 85 cents? Do you think you should add clay or take away clay to get to one whole? Here, Relating to Money, I scaffold the activity for a student by relating 1.05 to $1.05. Soon, all students successfully had a perfect one-ounce ball: Exactly an Ounce.
To bring closure to the lesson, I brought everyone back together. Sometimes I use a call and response to get the attention of students: Have a seat! Students repeat: "Have a seat!" Eyes are up! Students repeat: "Eyes are up!" Once everyone was ready to learn, I explained: I have a book here that is one pound. If we place this one pound book on one side of this balance scale, what would we do to see how many ounces are in a pound? Turn and Talk. I gave students a minute to talk and then asked for their thoughts: "Put the clay balls on the other side." "See how many it takes to make it even on both sides." One, by one, I asked students to bring their clay balls up to the front of the room and set them on the balance scale, opposite from the book. With prompting, students began to count: Students Counted. They watched excitedly to see what would happen. We got to 16 clay balls (each weighing one ounce), and nothing happened! With some minor adjustments (moving the book and clay balls around in the trays), I was able to balance the scale: Relating Ounces to Pounds. It was at this moment that students discovered the number of ounces in a pound! Turn and Talk: How many ounces are in a pound and how do you know? "16 ounces" "Yeah, because the book is one pound and it took 16 balls on the other side to make it balanced." "And each ball equals one ounce... so 16 ounces." I placed one clay ball in a bag and labeled it "1 ounce" and placed 16 clay balls in another bag and labeled it "16 ounces" so that I could refer to these models later on: One Ounce vs One Pound.
To check for understanding, I asked students to complete an exit slip on a half sheet of notebook paper. I asked two questions:
1. Name one item you would measure using ounces.
2. Name one item you wouldn't ever measure using ounces.