Mathematics
Grade 7
15 min
Make predictions
Make predictions
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1
Introduction & Learning Objectives
Learning Objectives
Define what a prediction is in a mathematical context.
Use ratios and proportions to make predictions about a population based on a sample.
Calculate experimental probability and use it to make predictions for future trials.
Calculate theoretical probability and use it to make predictions for future events.
Determine the expected number of outcomes for a given event.
Evaluate the reasonableness and limitations of a prediction based on the data provided.
Ever wonder if it will rain tomorrow ☔ or if your favorite team will win the next game 🏆? That's making a prediction!
In this lesson, you'll learn how to use mathematical tools like probability and proportions to make educated guesses about future events or unknown quantities. Understanding ho...
2
Key Concepts & Vocabulary
TermDefinitionExample
PredictionAn educated guess or forecast about a future event or an unknown quantity, based on available data, patterns, or probability.Predicting that a coin will land on heads 50 times if flipped 100 times.
SampleA smaller, representative group selected from a larger population, used to gather data and make inferences about the entire population.Surveying 100 students from a school of 1000 students to find out their favorite lunch.
PopulationThe entire group of individuals, objects, or events that a study is interested in, from which a sample is drawn.All 1000 students in a school.
ProportionAn equation stating that two ratios are equivalent. It is often used to scale up findings from a sample to make predictions about a larger population.If 2 out of 10 students pre...
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Core Formulas
Proportion for Population Prediction
$\frac{\text{Part in Sample}}{\text{Total in Sample}} = \frac{\text{Part in Population}}{\text{Total in Population}}$
Use this rule when you have data from a smaller sample and want to predict a quantity for the entire larger population.
Experimental Probability
$P(\text{event}) = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}$
Calculate this probability from observed data or experiments. It helps predict future outcomes based on past results.
Theoretical Probability
$P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
Use this for events where all outcomes are equally likely (e.g., rolling a fair die, flipping a fair coin) to predict outcomes without c...
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Challenging
Two students predict the number of the 2,000 students in their high school who will attend a football game. Student A randomly surveys 25 students in the hallway and finds 10 will attend. Student B gets a list of all 2,000 students and randomly surveys 150 of them, finding 63 will attend. Which statement is the most accurate?
A.Student A's prediction is more reliable because the math is easier (10/25 = 40%).
B.Student B's prediction is more reliable because the sample size is larger and it was randomly selected from the entire population.
C.Both predictions are equally reliable because they both used random sampling.
D.Neither prediction is reliable because they should have surveyed everyone.
Challenging
A biologist uses a 'capture-recapture' method to predict a fish population. She catches and tags 80 fish, then releases them. Later, she catches 300 fish, and 12 of them have tags. She sets up the proportion 80/T = 12/300 to predict the total population (T). What is the most critical assumption she is making for this prediction to be accurate?
A.The lake has exactly 300 fish.
B.The tagged fish have mixed evenly throughout the population and are just as likely to be caught again.
C.No new fish were born and no fish died between captures.
D.The tagged fish are easier to catch than non-tagged fish.
Challenging
A car dealership tracks its sales. In a sample of 150 vehicle sales, 75 were trucks, 45 were SUVs, and the rest were sedans. The dealership has 1,200 vehicles in its total inventory across all lots. The sales manager has a budget to detail 250 vehicles for a special promotion. Based on the sales data, what is the best prediction for how many sedans they should detail?
A.30
B.50
C.75
D.90
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