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 32
For the first task, students solved 9 x 32. Here, some students decomposed both multiplicands: 9 x 32 = (7+2) x (8x4).jpg, 9 x 32 = 9 x (10+10+10+2), and 9 x 32 = (3x3) + (10+20+2). I loved watching students use multiple strategies: 9 x 32 Multiple Strategies.jpg. One of my favorite moments was when a student explained how the used doubling and halving: 9 x 32, Halving & Doubling. Many students were inspired!
Task 2: 18 x 32
During the next task, we discussed 18 x 32. Again, many students decomposed: 18 x 32 = (20+10+2) x (10+8). Here, an inspired student used doubling and halving: 18 x 32, Doubling & Halving. Impressively, this student even used a decimal number, 4.5 x 128: 18 x 32, Decimal Numbers, Doubling & Halving.
Today, I provided students with more time to complete their State Population Growth projects from yesterday's lesson, Estimating State Population Growth Part 1. To begin, I we reviewed the Goal: I can round multi-digit whole numbers.
We also reviewed the project expectations. To make sure all students were successful, I explained that I wanted to check their calculations on each slide before they moved on to the next state. I also reminded students that I was also looking for them to show their calculations on their white boards. Students also liked being able to check their work using the calculator on the computer. We discussed when a calculator is an appropriate tool to use (Math Practice 5) and then students agreed to only use the calculator after completing their work on their white boards.
During this time, I conferenced with every pair of Students. Whenever students made mistakes, I always tried to restrain myself from immediately correcting. More often than not, students either self-correct with time or are able to correct their mistake when simply asked to repeat their thinking.
Other times, students made simple mistakes and I would help them catch the mistakes on their own through questioning: Catching Simple Mistakes.
I loved watching these two students discuss their calculations after Getting two Different Estimates. Both estimates were correct but one estimate provided them with an answer that was closer to the exact population growth.
Often times, students grappled with Determining the Digit to Round to. Many times, students had to adjust the place being rounded to in order to get a more reasonable solution.
While this video was taken at the very end of the day when students were starting to get ready to go home, it is a good example of supporting a full understanding of place value and rounding: Estimating Kentucky's Population Growth. He then went on and was able to successfully calculate the estimated difference on his white board without any help: Calculating on Whiteboards. During this student conference and all others, I always encouraged Math Practice 6: Attend to Precision by asking students to clarify the operation being used, by adding in commas, labeling, and lining up the digits when calculating.
Finally, many students arrived at the final and most complicated slide: the United States of America. I loved hearing one of these boys tell his partner that he went ahead and completed this slide yesterday because he couldn't wait. That's always a great sign of student engagement! Even more exciting is how one student discovered a mistake by working with his partner.