Ti 84 calculator online geogebra how to#

( of people much smarter than me have shared videos on why we canвЂ™t divide by zero, and other uncertainties/indeterminate forms involving zero. HowieвЂ™s Adding Zero TikTok and HowieвЂ™s Multiplying by Zero TikTok. Zero is amazing in some other ways! Check out Howie HuaвЂ™s TikTok explanations of how вЂњadding zeroвЂќ (the property a + 0 = a) is a great strategy for computations and why 0 Г— a = 0 shows why a negative times a negative equals a positive. From Ben Orlin ( Why CanвЂ™t You Divide By Zero? Illustrated (of course), including using pizza for division.Two great posts about why you canвЂ™t divide by zero: On the TI-84+ family, use Transformation Graphing to change the values in the slope fraction.Дividing with zeroвЂ¦ 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 вЂњnotes to my future selfвЂќ 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 вЂњslope equals zeroвЂќ or вЂњslope is undefinedвЂќ rather than the ambiguous вЂњzero slopeвЂќ or вЂњno slope.вЂќ I also avoid the phrase вЂњrise over runвЂќ because it isnвЂ™t clear which way the line вЂњruns,вЂќ and вЂњriseвЂќ can seem contradictory for a negative slope. A graph grid and optional вЂњslope triangleвЂќ 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.Д«y 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 fractionвЂ™s value decreases when the numerator decreases, but the denominator has the opposite impact: the fractionвЂ™s value increases when the denominator decreases. When 0 is in the denominator, the fractionвЂ™s value is undefined. This numerical investigation demonstrates that when 0 is in the numerator, the fractionвЂ™s value = 0. What happens as the denominator gets smaller? 2Дividing by zero results in an вЂњundefinedвЂќ 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, letвЂ™s look at fractions numerically by finding decimal equivalents.

= undefined Looking at Fractions Numerically It doesnвЂ™t make sense: it is вЂњundefined.вЂќ 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 doesnвЂ™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.Д«ut if you have no money, zero dollars divided by 5 people means everyone gets $0.Дisappointing, 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. LetвЂ™s take a quick look at the вЂњsharingвЂќ 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.Д®veryone knows from elementary school that you вЂњcanвЂ™t divide by zeroвЂќ 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