Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using an array model.
Task 1: 9 x 12
For the first task, 9 x 12, students experimented with decomposing the multiplicands: 9 x 12 = (3x3)x(2+5+5) and 9 x 12 = (10+2) x (5+4). Other students experimented with doubling and halving: 9 x 12 = 18 x 6. This student doubled and halved twice: 9 x 12 = 6 x 18 = 3 x 36.
Task 2: 18 x 12
To begin today's lesson, I reviewed this unit's goal: I can round multi-digit whole numbers. Pointing to the Rounding Anchor Chart, I revisited key concepts (rounding, benchmark numbers, midpoint, and "going to the nearest gas station when out of gas") that were covered in previous lessons. For each concept, I asked students to turn and talk: What is a benchmark number again? Then, we reviewed the Rounding Song to help students remember the rounding procedures.
At this point, we moved on to guided practice with rounding.
I began by asking each student to get out the Student Bent Number Line that they created yesterday. Today, I wanted to introduce students to a vertical number line model. I asked, Do number lines always have to be horizontal? Can a number line also be vertical? Later on in the lesson, we will discuss this further. I passed out a plain sheet of paper and modeled how to make a Student Vertical Number Line. Students then placed the vertical number line inside their sheet protectors so that a bent number line from yesterday was on one side and the vertical number line was on the other side.
Rounding in the Real World
Once students were ready to go, I used a powerpoint presentation (Rounding to the Nearest 1,000) to model actual circumstances in which rounding would be helpful. I also wanted to engage students in Math Practice 4: Model with mathematics.
I explained: Let's say that our principal was interested in buying some new playground equipment and she wanted us to make some recommendations and provide estimated costs. For the first part of this presentation, we will be shopping for new playground equipment.
Rounding to the Nearest 1,000
For the first rounding task, I showed students a Playground Ant $2,143 and modeled how to use the Bent Number Line and the Vertical Number Line to round 2,143 to the nearest thousand. At first, some students thought we should round to 2,140. Others thought we should round to 2,100. This was a great opportunity to discuss how we should determine the closest thousands to 2,140. I pulled out play money to model 2,000 and 3,000. I then asked, Can we count by thousands and land on 2,140? Would we land on 2,100? How about 2,000? Students immediately began discussing these ideas with peers while naturally engaging in Math Practice 3: Construct Viable Arguments.
Next, we moved onto rounding $4,390 to the nearest thousand. Here, a student is Rounding 4,390 using both a bent number line and a vertical number line. After each new task (including 6,439, 7,581, and 9,877) students rounded the number to the nearest thousand using both the bent and vertical number lines. Then students volunteered to model their thinking on the board: Rounding 9,877.
Rounding to the Nearest 10,000
Next, we moved on to rounding to the nearest 10,000. In order to provide students with real-life examples of products that cost even larger amounts, I researched and presented the costs of vehicles using the second half of the Rounding to the Nearest 10,000. I explained: Let's say that we did just a good job recommending playground equipment to our principal that she now wants our help finding the estimated costs of new vehicles!
I showed students the first slide, Chevrolet Cruze Sedan and we discussed how we would round to the nearest ten thousand using the Bent Number Line and Vertical Number Line. Again, students modeled using their own number lines (Student Model A and Studnet Model B) and volunteered to Model on the Board.
During independent practice time, students worked on two practice pages on their own. I loved how the first practice page required students to identify the benchmark numbers (which required much more of students that remembering the procedure of rounding). On the next page, students practiced rounding numbers 4-digit and 5-digit numbers to the nearest thousand without having to identify the benchmark numbers.
As students finished, they checked answers with each other, which gave them the opportunity to construct viable arguments (Math Practice 3) when answers differed.