Vocabulary California Assessment of Student Performance and Progress
SUBMIT BY FRIDAY:Write down the two assignments that are due by Friday in your planner All Schoology Assignments All Schoology Assignments Home work:
MONDAY 5/8/23 & TUESDAY 5/9/23
Lesson: FF.10 Identify lines of best fit
Probability Share lesson:
Probability is how likely something is to happen. Probability is measured using numbers from 0 to 1. A probability that's close to 0 means something is unlikely to happen, such as correctly guessing a stranger's birthday. In fact, you're much more likely to guess a stranger's birthday incorrectly. The probability of guessing the birthday incorrectly is close to 1. When determining probabilities, the possible results of an action are called outcomes. For example, if you roll a six-sided die, there are six possible outcomes. The die can land on 1, 2, 3, 4, 5, or 6. Anevent is a set of those outcomes. If you roll a six-sided die, the outcomes of rolling a 4, 5, or 6 make up the event of rolling a number greater than 3. The probability of an event happening, written as P(event), is the number of favorableoutcomes divided by the total possible outcomes. Favorable outcomes are the outcomes that make up the event. You can write P(event) as a fraction: P(event) = number of favorable outcomes number of possible outcomes For example, the probability of rolling a six-sided die and having it land on 1 can be written as P(1).
There are 6 possible outcomes: 1, 2, 3, 4, 5, or 6.
There is 1 favorable outcome: 1.
So,P(1)=6. The probability of rolling a six-sided die and having it land on a number greater than 3 can be written as P(>3).
There are 6 possible outcomes: 1, 2, 3, 4, 5, or 6.
There are 3 favorable outcomes: 4, 5, and 6.
So,P(>3)=36=12. Probabilities can also be written as percentages. Since P(>3)=12, you could also say that P(>3)=50% . Tip Youcantellhowlikelyaneventistooccurbasedonitsprobability:
Calculatingprobabilities Let's try calculating some other probabilities. Find the probability of drawing a heart from a standard deck of 52 cards. You can write this as P(heart). To find P(heart), write a fraction with the number of favorable outcomes over the number of possible outcomes. There are 13 favorable outcomes because there are 13 hearts in a deck. There are 52 possible outcomes because there are 52 total cards in a deck. P(heart)=1352=14So,P(heart)=14, or 25%.The probability of choosing a heart is between 0 and 12. So, you are less likely to draw a heart than you are to draw a card that is not a heart. Anotherexample Let's try another example. Find the probability of drawing a heart or a diamond from a standard deck of 52 cards. You can write this as P(heart or diamond). There are 13 diamonds and 13 hearts in a deck. So, there are 26 favorable outcomes. There are 52 possible outcomes. P(heart or diamond)=13+1352=2652=12 So,P(heart or diamond)=12,or 50%. Since the probability of drawing a heart or a diamond is 12, you are equally likely to draw a heart or diamond as you are to draw a card that is not a heart or diamond. Onemoreexample Let's try one more example. Find the probability of drawing any card that is not a heart from a standard deck of 52 cards. You can write this as P(not heart). There are 13 spades, 13 clubs, and 13 diamonds in a deck. So, there are 39 favorable outcomes. There are 52 possible outcomes. P(not heart)=13+13+1352=3952=34So,P(not heart)=34, or 75%. The probability of drawing any card that is not a heart is between 12 and 1. So, you are more likely to draw a card that is not a heart than you are to draw a card that is a heart. Tip
GG.4 Find probabilities using two-way frequency tables
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> DUE BY END OF CLASS: https://www.ixl.com/math/grade-8/find-probabilities-using-two-way-frequency-tables?signInRedirect=https%3A%2F%2Fwww.ixl.com%2Fsignin%2Fteachacademy >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> missing assignments
Homework; finish all Schoology assignments
WEDNESDAY 5/10/23
Review?Assessment Day
Lesson Review
alternate interior/exterior angles
line of best fit
Probability
CORE STANDARDS
8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
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Learning Objectives define circumference and diameter. calculate pi and identify it as 3.14. measure circumference and diameter of circular objects. STANDARD Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres. Y.5 Circumference of circles
Pi is the ratio of the circumference of a circle to its diameter. If you divide the circumference of any circle by its diameter, you will get pi! You can use the symbol 𝜋 to show pi. Pi is an irrational number. Irrational numbers written as decimals never repeat or end. Since pi is an irrational number, it cannot be written out fully. Here is how it starts: … You'll often see or used as approximations for pi. Calculating circumference If you know the diameter or radius of a circle, you can use pi to find the circumference. circumference diameter = 𝜋 3.1415926535 3.14 22 7
Fun Fact Have you ever heard of Pi Day? It is March 14, or 3/14! People often celebrate by baking and eating pie, or by holding contests for people to recite as many digits of pi as they can. In countries that use the day/month format instead of month/day, some people celebrate Pi Approximation Day on July 22, or 22/7. Pi Calculating circumference using diameter To find the circumference of a circle, you can multiply pi by the diameter of the circle. In the formula below, d is the diameter. Let's try it! Find the circumference of the circle below. The diameter of the circle is 12 units. Use 3.14 as an approximation for pi. The symbol ≈ means approximately equal to. So, the circumference of the circle is about 37.68 units. Calculating circumference using radius If you have the radius instead of the diameter, you can still calculat
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