Number Line (used with an Absolute Values presentation)

Number Line (used with an Absolute Values presentation)

• 1.
  ∞ ∞ Whole Numbers-2 -1 0 1 2 Decimals -2 -1.75 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Fractions -2/1 -1 3/4 -1 1/2 -1 1/4 -1/1 -3/4 -1/2 -1/4 0/1 1/4 1/2 3/4 1/1 1 1/4 1 1/2 1 3/4 2/1 Percentages -200% -175% -150% -125% -100% -75% -50% -25% 0% 25% 50% 75% 100% 125% 150% 175% 200% Odds 0:0 1:3 1:1 3:1 1:0 Symbols … Words … or Combination … A Review of the Number Line and Representations of Number-Based Values "Absolute numbers" are positive whole numbers . These are expressed to the right side of 0 on the number line. "Fractions" are comprised of numerators (top) and denominators (bottom). They can represent parts in a more precise manner than just whole numbers. Fractions are more "granular." By comparison, whole numbers are less granular (less precise). If a cashier wants to round up to the next closest dollar and donate the difference to charity (on your and their behalf), they are moving up in the number line to the next whole dollar value. "Integers" include both positive AND negative whole numbers. These are on the left and the right sides of zero on the number line. What is <, >, ≤, ≥ on the number line? ≅ ≈ ... As you move right on the number line, the numbers get bigger. As you move left on the number line, the numbers get smaller. This is true for both negative and positive numbers. Positive numbers are on the right side of the zero on the number line. Negative numbers are on the left side of the zero on the number line. Positive numbers indicate gains, and negative numbers indicate losses. To calculate odds from probabilities, start with the fraction of the probability. So, say there is 75% probability expressed as 3/4. Take the "numerator / (denominator minus numerator)" for
• 2.
  1/1 and 200/200both = 1 (value). But why do most people just expressthe value as 1/1. Similarly, 1/4 and 250/1000both equal 25% or .25. Why is 1/4 preferred? The math concept is to be as reductionist and simple as possible. A "rational number" is any number that can be expressed as a fraction numerator / denominator where the numerator and denominator are whole numbers including negative numbers and zero (except not in the denominator). One cannot divide by zero. A rational number can also be said to be expressedas a quotient (a dividend divided by a divisor) (dividend ÷ divisor). A rational number is one that can be expressed as a "ratio" or a fraction. One way to remember this is to pronounce it a "ratio" + "nal" number. Integers,commonfractions,terminating decimals(those that don't go on forever), and some repeatingnon-terminaldecimalsthat can be convertedto fractions...AREALL rationalnumbers. "Pi" is not considereda rational number because it is a non-terminatingand non-repeatingdecimalnumberwith an ≈ approximated value. Pi is an "irrational number." π (pi) is also a mathematical constant with a set value. Different ways of representing the same values--whether by whole numbers, integers, decimals, fractions, percentages,odds, symbols, words, or mixed alpha numeric combinations...give people flexibility in representationand exploration. To calculate odds from probabilities, start with the fraction of the probability. So, say there is 75% probability expressed as 3/4. Take the "numerator / (denominator minus numerator)" for the odds. 3/(4-3)= 3:1. "3:1" or "three to one odds" is the same as the 75% probability. Odds cannot go above 1 (which is certainty).