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Statistics can be used to gain information about agroup. Everyone who is a member of the group beingstudied is part of the population. Sometimes the population of a group is simply too large to studyeveryone. When this happens, a sample is taken anddata is collected from this smaller group. For thesample to give correct information, the sample needsto represent or be like the entire group or population. Usually larger, random samples tend to be better.To be random, everyone in the population must have an equal chance of being chosen. Everyone who is a member of the group beingstudied is part of the . Sometimes, I make questions where all they have to do to answer correctly is read. The interval range for this data is . Sometimes, I make questions where all they have to do to answer correctly is read. Each interval must have the same range. When we subtract the low from the high, we must have the same range. Complete the chart below. 10 - 14 15 - 19 20 - 24 5 - 9 0 - 4 The interval range is the high of any row minus the low of the same row. Sometimes I will give several informational slides prior to asking a question slide. See the next several slides. RATIONAL NUMBERS INCLUDE THE FOLLOWING: Natural numbers are the counting numbers 1, 2, 3, ... Whole numbers are the counting numbers plus zero 0, 1, 2, 3... Integers include whole numbers and their opposite (adds negative whole numbers)-3, -2, -1, 0, 1, 2, 3,... The last set of rational numbers are all fractions of twointegers. These can be converted to a repeating orterminating decimal.½ = 0.5 ⅓ = 0.333... ⅜ = 0.375 ⅔ = 0.666... IRRATIONAL NUMBERS INCLUDE... Irrational Rational The roots that can not be simplified to terminate. If theysimplify to terminate, they are rational. Pi = π 7 25 = 5 NOT REAL NUMBERS INCLUDE... Negative even roots. We can not multiply any number byitself an even number of times and get a negative answer.This is not possible. Any number divided by zero is not real either. -4 4 0 not real not real The number below is best classified as... Real but rational only (fraction/repeating or terminating decimal) Real, rational, and an integer Real, rational, integer, and a whole number Real, rational, integer, whole number, and natural Real but irrational (can't be written as a fraction of two integers Not real ⅞ In the following slides, replace x with the given value from the chart and solve for y. y = 2x + 1 y = 2(2) + 1 y = 2(1) + 1 y = 2(-1) + 1 y = 2(0) + 1 y = 2(-2) + 1 Complete the following chart for x y-2 -3-1 0 1 2 Complete the following chart for Notice: For the last three slides, less and less help is given. y = 3x - 5 x y-2-1 0 1 2 Sometimes I use drag and drop to have students match up choices. Drag and drop your answers. (0, 0) ? y axis ? x axis ? (x, y) →(x - 3, y + 2) (x, y) →(x, -y) Drag and drop your answers. (x, y) →(-x, -y) (x, y) →(x + 3, y - 2) (x, y) →(y, -x) (x, y) →(-x, y) translation 3 to the left and two up ? translation 3 to the right and two down ? 90 degrees clockwise rotation about the origin ? 180 degrees rotation about the origin ? reflection over the y-axis ? reflection over the x-axis ? Sometimes problems have multiple fill-in-the-blanks as follows. Fill in the missing equivalent. = 0 = 40% Fill in the missing equivalent. 1 2 = 0 = % Some problems have students show all of the work as follows. 5x - 3 = 2 Reverse any addition or subtraction first. 5x = 5 x = + + Then reverse multiplication or division. Change to slope-intercept form (y=mx + b) by solving for y. +3x -3x + 2y = 9 y = x 2y = + 9 2 + At other times I use a combination of multiple choice and fill-in-the-blank 3: sum-of-the-digits divisble by 3? (Add up the digits before deciding. 3 + 5 = Is it divisible by 3? Yes, it totals to 3, 6, 9, 12, 15... No, its sum is not a multiple of 3 35 |