7.SP.C.6Common CoreMathStatistics and ProbabilityGrade 7
7.SP.C.6: Estimating Probability from Relative Frequency
In plain English: 7.SP.C.6 is the Common Core grade 7 math standard that asks students to estimate the probability of a chance event by repeating the process many times and finding the relative frequency: the fraction of trials in which the event happened. Students also work the other way. Given a probability, they predict about how often the event will happen, knowing the real count is usually close but not exact.
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Common Core State Standards for Mathematics · Domain: Statistics and Probability (SP) · Cluster: Investigate chance processes and develop, use, and evaluate probability models. Also written as 7.SP.6 · Official standard
Students find out how likely something is by trying it many times. They toss bottle caps, roll number cubes and draw cubes from bags, count how often an event happens, and turn the count into a relative frequency: the number of times the event happened divided by the number of tries. After many tries, the relative frequency settles down and becomes a good estimate of the probability. Students also go the other way: when the probability is known, they multiply it by the number of tries to predict about how often the event will happen.
The official example sets the tone: roll a number cube 600 times, and a 3 or a 6 should come up roughly 200 times, but probably not exactly 200 times. Students learn to expect results that are close to a prediction without matching it, and to trust estimates from many trials more than estimates from a few. All data sets on this page are invented for teaching, and were made by a computer simulation (a program that imitates the chance process) so that they vary the way real results do.
Learning Objectives
By the end of this lesson, students will be able to:
Collect data on a chance process and find the relative frequency of an event as a fraction, a decimal and a percent
Explain why an estimate from many trials is more trustworthy than an estimate from a few trials
Use the long-run relative frequency to estimate the probability of an event
Predict about how many times an event will happen in a number of trials, given its probability
Explain why a real count is usually close to a prediction but probably not exactly equal to it
Prior Knowledge Required
Students should already be comfortable with:
Probability as a number from 0 to 1 that tells how likely an event is 7.SP.C.5
Writing a fraction as a decimal 7.NS.A.2 and as a percent 6.RP.A.3
A fraction as division, for example 3/4 = 3 ÷ 4 5.NF.B.3
Finding a percent or a fraction of a number, for example 25% of 80 7.RP.A.3
Hold up a plastic bottle cap. Show the two ways it can land: top up (the flat top faces the ceiling) or top down (the open side faces the ceiling).
Warm-Up Prompt
"Maya says the chance that a bottle cap lands top up is 1/2, because there are only two ways it can land. Do you agree? How could we find out without guessing?"
Take a quick vote, then toss the cap 10 times in front of the class and tally the results on the board. Ask: "Are 10 tosses enough to decide?" Students usually say no, which sets up the lesson: we need a way to use many tosses. Point out that two outcomes do not have to be equally likely. A cap is not shaped the same on both sides, so there is no reason to expect 1/2.
Direct Instruction20 minutes
Introduce the words students need, one at a time, with the bottle cap as the example:
A chance process is an action whose result you cannot know ahead of time, like tossing a cap or rolling a number cube (a cube with the numbers 1 to 6 on its faces).
Each time you do it is a trial. The result of one trial is an outcome, such as top up. An event is one outcome or a group of outcomes, such as "rolling a 3 or a 6".
The frequency of an event is the number of trials in which it happened. The relative frequency is the frequency divided by the number of trials. Write it as a fraction, a decimal or a percent.
The long-run relative frequency is the relative frequency after a large number of trials. It levels off near the probability, so it is a good estimate (a careful approximate value) of the probability.
To predict a count, multiply: probability × number of trials. Say "about", because chance results vary from the prediction.
Estimate a probability from data
A class tossed the same bottle cap 200 times. It landed top up 77 times (invented data). Estimate the probability that the cap lands top up.
Equation: Relative frequency = 77/200 = 0.385, or 38.5%. The probability of top up is about 0.39, so top up is a little less likely than top down. Maya's guess of 1/2 does not fit the data.
Why many trials matter
The same class kept a running total. After 10 tosses the cap had landed top up 3 times, and after 20 tosses, 9 times.
Equation: 3/10 = 0.30 and 9/20 = 0.45: the value jumps a lot with few trials. After 120 tosses it was 49/120 ≈ 0.41, and after 200 tosses 0.385. With many trials the value stays near 0.4, so use the estimate from the most trials.
Predict a count, the official example
A fair number cube (one whose 6 faces are equally likely) is rolled 600 times. About how many times will it land on a 3 or a 6?
Equation: The 6 faces are equally likely, and 2 of them are a 3 or a 6, so the probability is 2/6 = 1/3. Prediction: (1/3)(600) = 200 times. The real count will probably not be exactly 200. One class got 195 (invented data), which is close.
Predict from a known probability
A spinner is split into 4 equal parts, and one part is red. Kai will spin it 120 times. About how many times should it land on red?
Equation: P(red) = 1/4, and (1/4)(120) = 30. Kai should get about 30 reds. A result such as 26 or 34 would not be surprising.
Estimate first, then predict
At a school fair, 18 of the first 150 players won the ring toss game (invented data). About how many of the next 500 players will win?
Equation: Estimate: 18/150 = 0.12. Prediction: 0.12 × 500 = 60. About 60 of the next 500 players should win.
Running totals for the bottle cap (invented class data)
Tosses so far
Top up so far
Relative frequency
10
3
0.30
20
9
0.45
40
15
0.375
80
31
0.3875
120
49
0.408
160
64
0.40
200
77
0.385
Diagram 1 graphs the running relative frequency. Ask: "Where does the line jump the most? Where does it level off?" Then show Diagram 2, one class's 600 rolls of a number cube. Every face was predicted to come up 100 times, but no two bars are the same height, and the event "3 or 6" came up 195 times instead of 200. Stress the official example's words: roughly 200, but probably not exactly 200.
Guided Practice15 minutes
Pairs solve these four problems. One partner writes the relative frequency or the prediction, and the other says in a sentence what it means. Then they switch roles.
Guided practice problems with answers
Problem
Answer
A basketball player made 34 of her last 40 free throws. Estimate the probability that she makes her next free throw.
34/40 = 0.85, about 85%
A coin was flipped 50 times and landed heads 28 times. What is the relative frequency of heads? Is 50 flips enough to say the coin favors heads?
28/50 = 0.56. No: 0.56 is close to 0.5, and 50 flips is not many trials
A spinner lands on blue with probability 0.3. Predict the number of blue results in 250 spins.
0.3 × 250 = 75, so about 75
A number cube is rolled 90 times. Predict how many rolls show a number greater than 4.
5 and 6 are 2 of 6 faces: (2/6)(90) = 30, so about 30
Listen for students who divide by the wrong total, for example 28 heads ÷ 22 tails. The relative frequency always divides by the number of trials. Also listen for "exactly 75": push for "about 75".
Independent Practice10 minutes
Students work alone on five problems, then check with a partner.
Independent practice problems with answers
Problem
Answer
45 of 60 bean seeds in a test sprouted. Estimate the probability that a seed sprouts, then predict how many of 200 seeds will sprout.
45/60 = 0.75; 0.75 × 200 = 150 seeds
A number cube is rolled 300 times. Predict the number of 1s.
(1/6)(300) = 50
A spinner lands on green with probability 2/5. Predict the number of greens in 80 spins.
(2/5)(80) = 32
A game says the chance of a rare card in a pack is 5%. About how many rare cards are in 400 packs?
0.05 × 400 = 20
Class A tossed a cap 30 times and got top up 12 times. Class B tossed the same kind of cap 200 times and got top up 81 times. Which estimate is more trustworthy?
Class B: 81/200 = 0.405 comes from many more trials (Class A: 12/30 = 0.4)
Closure5 minutes
Exit ticket: (1) A marble is drawn from a bag and put back 50 times. It is green 14 times. Estimate the probability of green. (Answer: 14/50 = 0.28.) (2) An event has probability 0.6. Predict how many times it happens in 150 trials. (Answer: about 90.) (3) In one sentence, explain why the real count in question 2 will probably not be exactly 90.
Differentiation Strategies
For Struggling Students
Give a recording sheet with columns already labeled: trials so far, times the event happened, relative frequency
Start with 10, 20 and 50 trials so the division is easy, then use a calculator for totals such as 77/200
Use a percent bar (a strip from 0% to 100%) to show where a relative frequency such as 0.385 falls
For Advanced Students
Ask students to use Diagram 1 to find the number of tosses after which the relative frequency always stays between 0.38 and 0.42
Have students design an experiment for a new object, such as a paper tent, and decide how many trials they need before they trust the estimate
Ask: a cap landed top up 40% of the time in 1,000 tosses. How many top ups in a row would surprise you, and why?
Assessment Guidance
What to Look For
Check that students divide the frequency by the total number of trials, not by the number of times the event did not happen. Listen for the words "about" or "roughly" in every prediction. Students should be able to say which of two estimates is more trustworthy and give the reason: more trials. When a result differs from a prediction, a strong answer says the difference is normal for chance results, unless it is very large.
02
Classroom Activities
3 Activities
1
Bottle Cap Toss
20 minPairs
Pairs collect real data on a chance process whose probability nobody knows ahead of time. The class pools (combines) its tosses and watches the relative frequency settle, as in Diagram 1.
Procedure
Each pair tosses the same kind of plastic bottle cap 25 times from the same height (about 30 cm) onto a desk and tallies top up and top down
Each pair finds its own relative frequency of top up, for example 9/25 = 0.36
On the board, the class keeps a running total: after pair 1, after pairs 1 and 2, and so on, with the relative frequency each time
Each student graphs the running relative frequency on grid paper, with the number of tosses on the horizontal axis
Recording Sheet
Columns: Pair number, Top up (our pair), Tosses so far (class), Top up so far (class), Relative frequency so far. With 8 pairs, the class reaches 200 tosses.
Discussion Questions
Which pair's relative frequency was farthest from the class value? Why can one pair's 25 tosses be far off?
Where does the class graph jump the most, and where does it level off?
Does the class data support Maya's warm-up claim that top up has probability 1/2?
Would a larger cap, or a cap from a different bottle, give the same estimate? How could you find out?
Modification for Distance Learning
Each student tosses a cap at home 25 times and types the result into a shared spreadsheet that keeps the running total and graph.
2
Predict, Then Roll
15 minPairs
Pairs make predictions from known probabilities before they roll, then compare the predictions with what happens.
Procedure
Before rolling, each pair predicts how many times each event will happen in 60 rolls of one number cube: E1 "a 6", E2 "a 1 or a 2", E3 "an even number", E4 "a number less than 6"
Pairs roll 60 times, tally each roll, and write the real count next to each prediction
The class adds all pairs' counts and finds the pooled relative frequency of each event
Prediction Key
E1: (1/6)(60) = 10
E2: (2/6)(60) = 20
E3: (3/6)(60) = 30
E4: (5/6)(60) = 50
Discussion Questions
Did any pair get exactly its prediction for every event? For any event?
How far from the prediction would a count need to be before you suspect the cube is not fair?
Was the pooled class relative frequency for E3 closer to 1/2 than most single pairs' values?
3
Mystery Bag
15 minGroups of 3
Each group gets a closed paper bag with 10 connecting cubes. The teacher has put 7 red and 3 blue cubes in every bag, but students do not know this. Groups estimate the probability of red from their draws, then guess what is in the bag.
Procedure
Without looking, one student draws a cube, another records its color, and the cube goes back in the bag (this is called drawing with replacement). Shake the bag and repeat
Each group makes 40 draws and finds the relative frequency of red
Each group guesses how many of the 10 cubes are red, then the class pools all draws
Sample Class Results (invented)
Red draws out of 40 for 8 groups: 30, 26, 29, 24, 31, 27, 25, 27. The pooled result is 219 red in 320 draws, a relative frequency of about 0.68, so the class guesses 7 red cubes. Open a bag to check.
Discussion Questions
In the sample results, no group got exactly 28 red, the count predicted by 7 red cubes out of 10. Why not?
The group with 24 red would guess 6 red cubes. Why is the pooled estimate more trustworthy?
In the sample results, the pooled value 0.68 is closer to 0.7 than any single group's value. Will that always happen?
Challenge Variation
The teacher changes the bags to 4 red and 6 blue cubes without telling the class. How many draws does a group need before it can tell that the bag changed?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: The Running Relative Frequency Settles Down
Invented data for 200 tosses of one bottle cap, graphed every 10 tosses. After 10 tosses the relative frequency of top up is 0.30 and after 20 it is 0.45. From 30 tosses on, it stays between 0.37 and 0.42, ending at 77/200 = 0.385 (dashed line). Drawn to scale.
Diagram 2: 600 Rolls of a Number Cube
Invented class data for the official example. Each face was predicted to come up (1/6)(600) = 100 times, and the counts scatter around 100. The event "3 or 6" (dark bars) came up 100 + 95 = 195 times: roughly 200, but not exactly 200. Drawn to scale.
04
Homework Assignment
~30 min
7.SP.C.6 Homework: Estimating and Predicting with Relative Frequency
Directions: Show your work. Write every relative frequency as a fraction and as a decimal. Write every prediction with the word "about" and explain in a sentence what it means.
Part 1: Estimating Probability from Data (Problems 1-2)
A game booth spinner has parts of different sizes, and nobody has measured them. In 160 spins it landed on "Prize" 24 times. (a) Estimate the probability of "Prize" as a fraction in lowest terms, a decimal and a percent. (b) About how many prizes should the booth expect in the next 1,200 spins?
Ana flips a coin 20 times and gets 13 heads. Ben flips the same coin 400 times and gets 206 heads. (a) Find each relative frequency of heads. (b) Whose result gives the better estimate of the probability of heads? Explain.
Part 2: Predicting from a Probability (Problems 3-4)
A number cube is rolled 420 times. Predict about how many times it will show (a) a 5, (b) an odd number, (c) a number less than 3.
Over the whole season, a basketball player made her free throws with a relative frequency of 0.7. (a) About how many of her next 30 free throws should she make? (b) If she makes 19, is that surprising? (c) Could she make all 30? Is it likely? Explain.
Part 3: The Long Run (Problems 5-6)
A class spun one spinner and kept a running total of blue results (invented data). After 20 spins: 8 blue. After 50 spins: 18 blue. After 100 spins: 34 blue. After 200 spins: 65 blue. After 400 spins: 132 blue. (a) Find the relative frequency of blue at each point, as a decimal. (b) Give your best estimate of the probability of blue, and say why you chose it. (c) Predict the number of blue results in 1,000 spins.
Lily says: "If I roll a number cube 900 times, a 2 or a 5 will come up exactly 300 times." (a) What is right about her prediction, and what is wrong with it? (b) Her class then rolled a number cube 900 times and got a 2 or a 5 in 312 rolls (invented data). Find the relative frequency to the nearest hundredth and compare it with 1/3.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Relative Frequency
Frequency divided by the number of trials, written as a fraction and a decimal
Correct fraction with a division or rounding error
Divides by the wrong total or is missing
Predictions
Probability times the number of trials, stated as "about"
Correct product but stated as exact
Wrong operation or missing
Long-Run Reasoning
Chooses the estimate from the most trials and explains why
Chooses correctly without a reason
Chooses the estimate from few trials
Explaining Variation
Says real counts are close to predictions but vary, and judges when a result is surprising
Says counts vary but gives no judgment
Expects exact matches
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A spinner is spun 50 times and lands on yellow 12 times. What is the relative frequency of yellow?
Answer: B
Divide the frequency by the number of trials: 12/50 = 0.24. Choice A divides 12 by 100 instead of by 50. Choice C divides by the 38 spins that were not yellow: 12/38 ≈ 0.32. Choice D is the relative frequency of not yellow, 38/50.
Question 2 of 20 · Multiple Choice
Four groups tossed the same plastic spoon and counted how often it landed face up. Which group's result gives the best estimate of the probability that the spoon lands face up?
Answer: D
The estimate from the most trials is the most trustworthy, and 250 tosses is the most: 118/250 ≈ 0.47. Choice A has the largest relative frequency (0.6), but 5 tosses is far too few to trust. Choices B and C use more tosses than A but still far fewer than D.
Question 3 of 20 · Multiple Choice
A number cube is rolled 240 times. About how many times should it land on a 4?
Answer: C
Each of the 6 faces has probability 1/6, and (1/6)(240) = 40. Choice A divides by 4, the number on the face, instead of by 6. Choice B divides by 5, comparing the 4 with the other five faces. Choice D divides by 10.
Question 4 of 20 · Multiple Choice
The probability of getting a red gumball from a machine is 0.35. About how many red gumballs should you expect in 80 gumballs?
Answer: A
Multiply the probability by the number of trials: 0.35 × 80 = 28. Choice B uses the 35 in 0.35 as if it were the count. Choice C subtracts: 80 - 35 = 45. Choice D predicts the gumballs that are not red: 0.65 × 80 = 52.
Question 5 of 20 · Multiple Choice
A fair coin (one that is equally likely to land heads or tails) is flipped 500 times. Which statement is true?
Answer: B
The prediction is (1/2)(500) = 250, but chance results vary, so the real count is usually close to 250 and not exactly 250. Choice A treats the prediction as exact. Choice C forgets to multiply by the probability 1/2. Choice D ignores that long-run results are predictable even though one flip is not.
Question 6 of 20 · Multiple Choice
As the number of trials grows, what usually happens to the relative frequency of an event?
Answer: C
With many trials, the relative frequency settles near the probability, as in Diagram 1. Choice B describes a small number of trials, when the value jumps the most. Choice D is too strong: the value gets close to the probability but usually does not equal it exactly.
Question 7 of 20 · Multiple Choice
A claw machine gave a prize in 20 of its last 250 plays. About how many prizes should it give in the next 1,000 plays?
Answer: D
Estimate the probability: 20/250 = 0.08. Predict: 0.08 × 1,000 = 80. Choice A keeps the old count. Choice B divides 1,000 by 8 instead of multiplying by 0.08. Choice C reads 20 as 20% and finds 0.20 × 1,000 = 200.
Question 8 of 20 · Multiple Choice
A spinner landed on green 45 times in 180 spins. Estimate the probability of green as a percent.
Answer: A
45/180 = 0.25 = 25%. Choice B uses the count 45 as if it were a percent. Choice C divides 45 by the 135 spins that were not green. Choice D is the percent of spins that were not green.
Question 9 of 20 · Multiple Choice
Which event would you predict to happen about 150 times in 450 rolls of a number cube?
Answer: C
A 1 or a 2 is 2 of the 6 faces: (2/6)(450) = 150. Choice A gives (1/6)(450) = 75. Choice B gives (3/6)(450) = 225. Choice D gives (4/6)(450) = 300.
Question 10 of 20 · Multiple Choice
Over a whole season, a player made free throws with a relative frequency of 0.8. About how many of her next 25 free throws should she make?
Answer: B
0.8 × 25 = 20. Choice A reads 0.8 as the count 8. Choice C predicts the misses, 0.2 × 25 = 5. Choice D assumes she makes every shot, which the data does not support.
Question 11 of 20 · Multiple Choice
Kai predicts about 75 blue results in 300 spins of a spinner. What probability of blue did he use?
Answer: D
75/300 = 1/4. Choice A reads 75 as 75%. Choice B divides 75 by the 225 results that are not blue. Choice C assumes blue and not blue are equally likely.
Question 12 of 20 · Multiple Choice
Ella tosses a bottle cap 10 times and it lands top up 7 times. She says the probability of top up is 0.7. What is the best response?
Answer: C
Ten trials give a rough value that can jump around, as in Diagram 1, so she should collect many more tosses. Choice A trusts too few trials. Choice B assumes the two outcomes are equally likely, which a cap does not have to be. Choice D wrongly thinks the cap remembers earlier tosses.
Question 13 of 20 · Multiple Choice
A fair number cube is rolled 1,200 times. Which number of sixes would be the most surprising?
Answer: A
The prediction is (1/6)(1,200) = 200 sixes. Counts such as 196, 207 and 188 are within about a dozen of 200, which is normal for chance results. A count of 300 is 100 more than predicted, which would make you suspect the cube is not fair.
Question 14 of 20 · Multiple Choice
In 200 spins, a spinner landed on red 62 times, blue 88 times and green 50 times (invented data). Estimate the probability of blue.
Answer: B
88/200 = 0.44. Choice A divides 88 by 100 instead of by 200. Choice C is red, 62/200 = 0.31. Choice D is green, 50/200 = 0.25.
Question 15 of 20 · Short Answer
A spinner landed on purple 27 times in 90 spins. Estimate the probability of purple as a decimal, then predict the number of purple results in 400 spins.
A number cube is rolled 360 times. Predict how many rolls will show a number greater than 2, and explain why the real count will probably be different.
3, 4, 5 and 6 are 4 of the 6 faces: (4/6)(360) = about 240. Each roll is a chance result, so the total usually lands near 240, a little above or below, rather than exactly on it.
Question 17 of 20 · Short Answer
A game spinner lands on "Lose a turn" with an unknown probability. In 250 spins it landed on "Lose a turn" 35 times. (a) Estimate the probability as a fraction in lowest terms. (b) About how many times will it land on "Lose a turn" in the next 50 spins?
In a video game, the probability of finding a gem in a treasure chest is 1/8. (a) How many gems should a player expect in 96 chests? (b) Mia opened 96 chests and found 15 gems. Does this mean the game's probability is wrong? Explain.
(a) (1/8)(96) = about 12 gems. (b) No. 15 is only 3 more than the prediction, and chance results often differ from a prediction by that much. Many more chests would be needed to show the probability is wrong.
Question 19 of 20 · Short Answer
What is the difference between the probability of an event and its relative frequency? Use a coin in your example.
The probability is the number that tells how likely the event is; for heads on a fair coin it is 1/2. The relative frequency comes from data: if 23 of 40 flips are heads, it is 23/40 = 0.575. The relative frequency changes from experiment to experiment, and with many flips it gets close to the probability.
Question 20 of 20 · Short Answer
Describe how you would estimate the probability that a wooden clothespin tossed in the air lands on its side. Then suppose it landed on its side in 141 of 300 tosses. Give your estimate.
Toss the clothespin many times (a few hundred) in the same way, count the times it lands on its side, and divide by the number of tosses. With 141 of 300: 141/300 = 0.47, so the probability is about 0.47, a little less than 1/2.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 7.SP.C.6 mean?
7.SP.C.6 means students estimate a probability by running an experiment many times and finding the relative frequency. If a bottle cap lands top up 77 times in 200 tosses, the probability of top up is about 77/200, or 0.385. The standard also asks students to predict: if an event has probability 1/3, it should happen in about 1/3 of the trials.
What grade is 7.SP.C.6, and what comes next?
7.SP.C.6 is a grade 7 standard in the Statistics and Probability domain. It follows 7.SP.C.5, which introduces probability as a number from 0 to 1, and it sits beside 7.SP.C.7, where students build probability models and compare them with data. Compound events come next in 7.SP.C.8. In high school, students decide whether a model fits data from a simulation (HSS.IC.A.2).
What is relative frequency in 7th grade math?
Relative frequency is the number of times an event happened divided by the number of trials. If a spinner lands on red 21 times in 60 spins, the relative frequency of red is 21/60 = 0.35, or 35%. It can be written as a fraction, a decimal or a percent.
Is experimental probability the same as relative frequency?
Yes, many textbooks call the relative frequency from an experiment the experimental probability. The probability that comes from reasoning about equally likely outcomes, such as 1/6 for each face of a number cube, is often called the theoretical probability. The standard itself uses the words relative frequency and probability.
Why doesn't the count match the prediction exactly?
Because each trial is a chance result, the total wanders a little above or below the prediction. The official example says a number cube rolled 600 times should show a 3 or a 6 roughly 200 times, but probably not exactly 200 times. A result such as 195 or 206 is normal. A result such as 260 would be a reason to check whether the cube is fair.
How many trials are enough to estimate a probability?
There is no single number, but more trials give a more trustworthy estimate. With 10 or 20 trials, the relative frequency can jump a lot. Pooling a whole class's data, often a few hundred trials, usually gives a value that stays steady as more trials are added. Students can see this by graphing the running relative frequency, as in Diagram 1.
What objects work well for 7.SP.C.6 experiments?
Objects with an unknown probability work best, because students cannot know the answer ahead of time. Bottle caps, paper cups, clothespins and paper tents all land in ways that are not equally likely. Number cubes, coins and bags of colored cubes work well for predictions, because their probabilities are known.
How is 7.SP.C.6 tested?
Typical test questions give a table of experiment results and ask for an estimate of a probability, or give a probability and ask for a prediction. Many also ask which of two estimates is more reliable, or whether a result is surprising. Students should show the division or multiplication and use the word "about" in predictions.
What mistakes should teachers watch for?
A common mistake is dividing by the wrong total, such as heads divided by tails instead of heads divided by all flips. Other frequent errors are trusting an estimate from very few trials, expecting a count to match a prediction exactly, and assuming two outcomes must each have probability 1/2.
How can parents help with 7.SP.C.6 at home?
Parents can run a quick experiment with their child. Drop a spoon or a bottle cap 50 times, count how it lands, and find the relative frequency. Then ask: "If we did 100 more drops, about how many would land this way?" Talk about why the answer is "about" and not an exact number.
07
Related Standards
6 standards
These standards connect to 7.SP.C.6: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.RP.A.3Prerequisite
Use ratio and rate reasoning, including percents, to solve real-world problems
