Clip 5/29: Day 1: Decimal Math Talk
Erika Isomura engages her 4th and 5th graders in a mental math talk, inviting multiple iterations of dividing by 10, e.g., 8,000/10, 800/10, 80/10, 8/10, (8/10)/10. She asks students to justify and revise their answers if needed. She reviews norms for whole-class participation, and asks students to evaluate the reasonableness of their results. Erika then presents multiple iterations of dividing 8 by multiples of 10 (e.g., 8/10, 8/100, 8/1,000, 8/10,000), noting similarities and patterns.
The number talks were to give 4th graders a touch on moving towards decimals but not necessarily expect them to produce anything, just to get it in their heads. The 5th graders then turn around and use it. At first, I thought, “Decimals are a nonissue if they know fractions really well and if they can understand the patterns in place value." My idea was to really open up this series of lessons using a bunch of number talks.
The number strings are a series of equations that are all related to each other. Typically, when I do them they tend to be related to place value. The ones I'm most comfortable with are times 10, 100, 1,000. I've done them with fractions where you do something like 1/2, 1/4, 1/8, but I'm personally most comfortable when I'm using the base 10 number system in the talk because I think that gives them a lot of understanding of why the numbers are turning out the way they are and how the number system that we work with really is helpful. This particular number string strategy helped them see how the numbers are growing in those relationships. The day before this they had started doing some decimal work on their calculators. We hadn't really named them, so I still heard them calling them 0 point whatever.
How do we think about the ones place, and how is it different from the tens place, or the hundreds, and so on? They talked about each time you move over, it's ten times bigger. Then, we talked about here's this decimal. What's this place called? They were able to tell me, because we've played with it. They named it as the tenths and the hundredths. Then, I asked what would be next. Thousandths. They were able to name it, and they wanted to go keep going. Then, we wrote it out. They were more familiar still with the fraction notation, so we went with that. The tenth, the hundredth. How do we go this direction? They said, "If you're dividing by ten each time you go, you're going ten parts smaller."
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