Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A probability model is a list of every possible outcome together with a probability for each one, where the probabilities add up to 1. Seventh graders build two kinds. In a uniform model every outcome gets the same probability: if one of 25 students is chosen at random, each student has a 1/25 chance, and if 14 of them are girls, the chance of choosing a girl is 14/25.
Not every situation is that tidy. A spun penny, a rolled bottle cap or a tossed paper cup may favor some outcomes over others, and nobody can work out the probabilities by symmetry alone. Here students build a model from data: they run the process many times and use the observed relative frequencies as the model's probabilities. Spinning a penny 100 times and seeing 38 heads suggests that heads and tails may not be equally likely for spinning, even though they are for flipping.
The second half of the standard is testing. Students compare what a model predicts with what actually happens and, when the agreement is poor, suggest reasons: too few trials, a biased object, a process that was not truly random, or a model built on a wrong assumption.
Students often give each outcome an equal share without checking. A thumbtack has two outcomes, but data quickly show they are not equally likely.
A model that gives 0.5, 0.3 and 0.3 to three outcomes is broken. Checking the total catches counting errors before they spread.
Getting 46 heads in 100 fair flips is not evidence of bias. Small gaps are expected; large, persistent gaps over many trials are what call a model into question.
A class has 28 students: 12 boys and 16 girls. One name is drawn at random. Find the probability that Jane is chosen and that a girl is chosen. Over the term, 40 draws were made and a girl was chosen 30 times. Compare this with the model.
Answer: P(Jane) = 1/28 and P(girl) = 4/7 (about 0.57). The observed 30 girls in 40 draws (0.75) is higher than the model predicts, which might be chance or a draw that was not truly random.
Pair a symmetric object with a lopsided one: number cubes alongside bottle caps, or flipped pennies alongside spun pennies. Students predict, collect data, and decide which objects deserve a uniform model. The contrast makes the reason for experimental models obvious.
Assessment often presents a frequency table and a proposed model, then asks whether they agree and why they might not. Push students past 'it was random' toward specific explanations such as sample size or a flaw in how the experiment was carried out.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 0.6 (also accepted: .6, 3/5, 18/30, 60%)
In a uniform model each student is equally likely, so P(walks) = 18/30 = 0.6.
Answer: D) 0.2, 0.45, 0.35
The probabilities in a model must add to 1. Only 0.2 + 0.45 + 0.35 = 1.
Answer: 0.37 (also accepted: .37, 37%)
The experimental probability is 74 ÷ 200 = 0.37.
Answer: B) The result could be chance, but more rolls are needed to judge the cube
The model predicts about 10 ones, so 4 is low, but 60 rolls is a small sample. Rolling many more times would show whether the cube is biased.
Answer: 45
Expected count = 0.3 × 150 = 45.
Answer: D) Data show heads and tails do not occur equally often when spinning
A spun penny tends to favor one side because of its uneven weight, so the observed frequencies are not equal. A model built from data fits better.
A full lesson with slides, activities and an exit ticket on building and testing probability models, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.SP.C.7 with an answer key, ready in about a minute.
Make a worksheet →Turn building and testing probability models into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Part a covers uniform models, where all outcomes are equally likely by design. Part b covers models built from data, which may not be uniform.
Grade 7 judgments are informal. Students should expect some gap and become suspicious only when a large difference persists over many trials.