Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Everyday language is full of chance words: impossible, unlikely, a toss-up, probable, certain. Seventh graders learn to replace those fuzzy words with a single number on a scale from 0 to 1. A probability of 0 means the event cannot happen, 1 means it is certain, and every other event sits somewhere in between. The closer the number is to 1, the more likely the event.
The midpoint matters as much as the ends. A probability of about 1/2 describes an event that is as likely to happen as not, like a fair coin landing heads. Values close to 0, such as 0.03, describe events that rarely happen; values such as 0.9 describe events that usually do. Students learn to read and write probabilities as fractions, decimals and percents (1/4, 0.25 and 25% all name the same likelihood) and to place them on a number line labelled from impossible to certain.
This is the vocabulary for the rest of the probability cluster. Before students can build models (7.SP.C.7) or work with compound events (7.SP.C.8), they need a firm sense that a probability can never be negative or larger than 1, and that its size tells them how surprised to be when the event happens.
Some students write a probability of 3 when an event has 3 favorable outcomes. A probability is a part of the whole, so it is always between 0 and 1 inclusive.
An event with probability 0.05 is unlikely but can still happen. Only a probability of exactly 0 means it cannot happen at all.
Students sometimes argue that any event either happens or it does not, so its probability must be 1/2. Two possible results are not automatically equally likely; a spinner with a tiny red slice shows why.
Writing 0.7 as 7% hides a much less likely event. Remind students that 0.7 = 70%, and 7% = 0.07.
A bag holds 2 red, 3 blue and 15 green counters. One counter is drawn at random. Find the probability of each color and say whether each event is unlikely, about even or likely.
Answer: P(red) = 0.1 (unlikely), P(blue) = 0.15 (unlikely), P(green) = 0.75 (likely).
A washing line or floor number line from 0 to 1 works well: students hang event cards (snow in July where you live, the sun rising tomorrow, a coin landing tails) and justify where they put them, then refine positions once they compute exact values for spinners and bags.
Assessment items usually give a probability and ask for a description, or describe an event and ask which value fits it best. Watch for answers that accept 1.2 or a negative number; asking 'could that be a probability?' is a quick self-check worth building as a habit.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: C) 1.25
Probabilities run from 0 to 1. The value 1.25 is greater than 1, so it cannot be a probability.
Answer: B) Likely
0.9 is close to 1, so rain is likely, though not certain.
Answer: 0.25 (also accepted: .25, 1/4, 25%)
2 of the 8 equal sections are yellow, so P(yellow) = 2/8 = 1/4 = 0.25.
Answer: D) A fair coin landing heads
Heads and tails are equally likely for a fair coin, so P(heads) = 1/2. Rolling a 7 is impossible (0), the blue marble has probability 1/10, and the sun setting is certain (1).
Answer: 0.35 (also accepted: .35)
Percent means per hundred, so 35% = 35/100 = 0.35.
Answer: 0.85 (also accepted: .85, 85%)
The bus is either late or not late, so the two probabilities add to 1: 1 - 0.15 = 0.85.
A full lesson with slides, activities and an exit ticket on probability as a number from 0 to 1, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 7.SP.C.5 with an answer key, ready in about a minute.
Make a worksheet βTurn probability as a number from 0 to 1 into a quiz students answer online that marks itself, with a class summary for you.
Build a test βYes. Fractions, decimals and percents are all fine: 3/4, 0.75 and 75% describe the same chance. The value must still lie between 0 and 1, or between 0% and 100%.
No. It means that over many trials the event happens about half the time. Short runs can look very uneven, which is the focus of 7.SP.C.6.