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: 18 x 24
For the first task, 18 x 24, students decomposed one or both multiplicands. Others doubled and halved: 18 x 24 = 9 x 48.
Task 2: 36 x 24
When students got to 36 x 24, many made the connection, "just double the product of 18 x 24: 36 x 24 = 2(18x12). Again, other students decomposed in a variety of ways: 36 x 24 = (3x10+6) x (2 x10+4), 36 x 24 = (6x6) x (6x4), and 36 x 24 = (30+6) x (20x4). This is such a powerful activity that truly aids the development of number sense!
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 and the Student Vertical Number Line (created by students in previous lessons). Both the bent and vertical number lines were still inside sheet protectors back to back so that both tools were accessible to students.
Rounding in the Real World
Once students were ready to go, I used a powerpoint presentation, Rounding to the Nearest 100,000, 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 a new family moved to the area and the family wanted us to make some housing recommendations and provide estimated costs. For today's lesson, we will be rounding the prices of actual homes in the Bozeman area to the nearest hundred thousand.
Rounding to the Nearest 100,000
For the first rounding task, I showed students the First House and modeled how to use the Bent Number Line and the Vertical Number Line to round $214,360 to the nearest hundred thousand. Here are students Rounding 214,360 on a Bent Number Line and Rounding 214,360 on a Vertical Number Line.. Just as we had done in previous lessons, a Student Volunteered to Model how he/she rounded 214,360 on the board.
Next, we moved onto rounding the Second House, Third House, Fourth House, and Fifth House. The price of each house gradually increased to provide students with a staircase of complexity. I just loved listening students develop a deeper understanding of rounding: Student Models how to Round 643,900. Instead of saying, "I rounded down to 600,000 because the digit next door is 4 or less," students were able to provide a more in-depth explanation, "I rounded down because this hundred thousand is the nearest" or "I rounded down because this number fell below the midpoint."
During independent practice time, students worked on two practice pages from commoncoresheets.com on their own. I actually provided students with the choice: work independently or work with others in your group. Either way, I asked students to check each answer with a student next to them. This way, students not only got immediate feedback, but also caught mistakes before completing the entire page.
I loved how both practice pages randomly asked students to round to all place values and would often require students to round a 5-digit number to the nearest ten (instead of a two-digit number to the nearest ten).
Also, I modeled how to use a highlighter to select important information, such as the place being rounded to. This action supports Math Practice 6: Attend to Precision.