Zero is amazing in some other ways! Check out Howie Hua’s TikTok explanations of how “adding zero” (the property a + 0 = a) is a great strategy for computations and why 0 × a = 0 shows why a negative times a negative equals a positive. From Ben Orlin ( Why Can’t You Divide By Zero? Illustrated (of course), including using pizza for division.Two great posts about why you can’t divide by zero: On the TI-84+ family, use Transformation Graphing to change the values in the slope fraction.ĭividing with zero… nothing to be afraid of! This version of the student lab handout has specific instructions for TI-84+ and TI-Nspire calculators, including accessing the fraction templates.
#TI 84 CALCULATOR ONLINE GEOGEBRA HOW TO#
This student lab handout What is Zero All About? can be used to guide the exploration on any of the platforms, and concludes by prompting students to make some “notes to my future self” 3 about how to handle fractions involving zeros, and the slopes, equations, and graphs of the various types of lines. In Desmos Activity Builder: What is Zero All About? Here is the slope exploration in Geogebra: Zero & Slope Fractions Instead, I emphasize the slope triangle showing a positive or negative move in the X direction, and a positive or negative move in the Y direction. I try to use phrasing and terminology that supports mathematical sense-making, so I say “slope equals zero” or “slope is undefined” rather than the ambiguous “zero slope” or “no slope.” I also avoid the phrase “rise over run” because it isn’t clear which way the line “runs,” and “rise” can seem contradictory for a negative slope. A graph grid and optional “slope triangle” enable students to make mathematical sense of slope, and to understand slope = 0, undefined slope, and negative values for either or. A common point of confusion for Algebra 1 students is the slopes of horizontal and vertical lines, and how these relate to the fraction used for slope.īy graphing the line and changing the numerator and denominator values, we can visualize how slope is impacted when either number is zero. Slopes of lines give another window into how zero operates in a fraction. Students can also observe how the fraction’s value decreases when the numerator decreases, but the denominator has the opposite impact: the fraction’s value increases when the denominator decreases. When 0 is in the denominator, the fraction’s value is undefined. This numerical investigation demonstrates that when 0 is in the numerator, the fraction’s value = 0. What happens as the denominator gets smaller? 2ĭividing by zero results in an “undefined” message in Desmos, the TI-84+ family, and TI-Nspire, while GeoGebra displays the symbol for infinity. As you decrease the numerator down to 0 what do you notice? Begin with these fractions on your calculator or computer technology. Now, let’s look at fractions numerically by finding decimal equivalents. = undefined Looking at Fractions Numerically It doesn’t make sense: it is “undefined.” If we were dividing money, $10 divided into a certain number of piles (10 piles, 5 piles, 2 piles, or 1 pile, for example) can all be done, but we cannot divide $10 into ZERO piles. But if the pizza delivery doesn’t show up, we have 0 pizzas divided among the 4 people in my house, so we each get 0: With pizzas, we can divide 1 pizza into 4 pieces, 10 pieces, or 1 piece, so those fractions can all be calculated.
If you have $10, you can share that among 5 people: $10 5 = $2 each.īut if you have no money, zero dollars divided by 5 people means everyone gets $0.ĭisappointing, but mathematically sensible, and we can carry out the division. I like to use the idea of money or pizzas with my students. We can interpret a fraction as division of two numbers with a sharing metaphor 1. Let’s take a quick look at the “sharing” interpretation of division, then turn to technology for numerical and graphical representations of the amazing ZERO.
How might we help students make sense of fractions containing zeros? The difference between and can be confusing.Įveryone knows from elementary school that you “can’t divide by zero” but that rule might not be enough to help learners interpret fractions and slopes that include a zero in the numerator or denominator. Understanding Zeros in Fractions & Slopes
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