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: 6 x 28
For the first task, students successfully used the array model to solve this problem in a variety of ways. Some students decomposed both multiplicands: 6 x 28. Other students decomposed one multiplicand: 6 x 28 = 6(10+10+8) and 6 x 28 = 4(10+10+8) + 2(10+10+8).
Task 2: 12 x 28
During the next task, we discussed 12 x 28. Students caught on quickly to the pattern and announced that we would "just double" the product of 6 x 28. Here, a student decomposed both multiplicands evenly: 12 x 28 = 6(14+14) + 6(14 +14). In this video, I work with a student on Catching Mistakes 12 x 28 while other students are busy solving the problem on their white boards or Doubling Checking Work 12 x 28.
Task 3: 24 x 28
Here's an example of a student sharing his work with the rest of the class using the iPad (connected wirelessly to the projector): Sharing Work. In order to connect wirelessly, I downloaded the AirServer application for $11.99. I was then able to download the application on two other coworker's computers.
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 asked students: Do you remember yesterday when we first started talking about rounding? Let's review some of the key concepts that are important to know! I then revisited key concepts (rounding, benchmark numbers, midpoint, and "going to the nearest gas station when out of gas") that were covered in yesterday's lesson, Introduction to Rounding. 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.
Before moving on with today's lesson, wanted to see what would happen if I asked student to round to the nearest 1. With constructing my lessons for this unit, I wanted to make sure students could round to the nearest 10, 100, 1,000, 10,000, and 100,000, but then I began thinking about it... why not 1? Here's what happened!
I showed students the number, 21, and asked, What is 21 rounded to the nearest one? They looked a bit confused at first!
I wrote the number 21 on the Rounding to the Nearest One Poster. Then, I asked students to turn and talk: Please round 21 to the nearest one! Such a powerful conversation resulted: Round 21 to the Nearest One.
At this point, we moved on to guided practice with rounding.
Making Bent Number Lines
After yesterday's lesson, I noticed many students had to repeatedly redraw their bent number lines on their white boards each time they were given a new rounding task. This was great practice drawing the number line model. However, I wanted to find a way to save time today, so I asked students to create bent number lines and to place them in sheet protectors: Student Number Line Model. Here, students are Creating Bent Number Lines. This will save time and provide students with more practice rounding. I have found that dry erase markers wipe off the easiest.
Rounding in the Real World
Once students were ready to go, I used a powerpoint presentation (Rounding to the Nearest Ten) to model actual circumstances in which rounding would be helpful. I explained: Sometimes after I go shopping, I go home and tell my husband about some of the items that I would like to purchase. Instead of saying, "The dress is $48" I'll say, "The dress is about $50." Today, we are going shopping for sporting gear at Sports Authority! Immediately, students lit up!
Rounding to the Nearest 10
For the First Rounding Task, I showed students a pair of roller skates that were $21. I shared, Let's say you want to buy this pair of roller skates. Instead of telling your parents the exact price, you decide to round to the nearest ten! I flipped to the next page, featuring a Horizontal Number Line. I asked students, What would the benchmark numbers be for 21 if we are rounding to the nearest ten? Students responded, "20 and 30." I modeled how to write the benchmarks on the horizontal number line. What would the midpoint be? "25!" Again, I modeled how to write the midpoint on the line and then asked, Where does 21 fall on this number line? I asked for a student volunteer to help place 21 on the horizontal number line: Round 21 to the Nearest 10. I then asked, Would we round up or round down? "20!" Which benchmark is 21 closest to? "20!"
Next, I showed students the Bent Number Line. I asked students to turn and talk: What do you notice is similar between the horizontal number line and the bent number line? Thereafter, a student eagerly came up to explain his "ah-ha" moment: A bent number line is the same as a straight number line.
We then moved on to the Second Rounding Task. While students came up to the board to model their thinking using the horizontal and bent number line, Round 43 to the Nearest, other students Practiced Using their Own Bent Number Line. We continued in this same fashion, rounding two-digit numbers (64, 75, 98) to the nearest ten. Here a student uses her number line model to show Student Rounds 98 to 100.
Rounding to the Nearest 100
After students had practiced rounding to the nearest 10 in the "real world," I wanted students to practice rounding to the nearest 100. Using the Rounding to the Nearest Hundred powerpoint, I slowly guided students as they practicing rounding numbers the costs of other items at a sporting goods store ($214, $439, $643, $758, $987) to the nearest 100. Here, a student models how to Round 750 to the Nearest 100. We discuss how 758 is "past the midpoint" and is "closer to" the benchmark number, 800.
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 than remembering the procedure of rounding). On the next page, students practiced rounding numbers 3-digit and 4-digit numbers to the nearest hundred 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. Here's an example of Students Checking Each Other.