In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Statistics
Samples
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2 - Understand (Statistics)
3 - Use (Statistics)
3 - Examine (Samples)
2 - Understand (Random sampling)
2 - Infer (From samples)
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2 - I understand that I can use statistics to gain information from random sampling.
3 - I can use statistics to gain information about a population.
3 - I can examine a sample of the population.
2 - I understand that my sampling must be random.
2 - I can make inferences from random sampling about a population.
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A. One can use random sampling of a population to produce and support valid inferences about that population.
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A.1 How does one collect a random sample?
A.2 How does one examine that sample to make inferences about the population?
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Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Sample
Predictions
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3 - Use (Date from sample)
2 - Infer (From sample about population)
6 - Generate (Samples)
5 - Gauge (Variation)
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3 - I can use date from a random sample to draw inferences about a population.
2 - I can make inferences about a population from a random sample.
6 - I can generate multiple samples of the same size from a population.
5 - I can gauge how far off the estimate or prediction might be.
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A. One can make predictions about a population from a random sample and can generate multiple random samples of the same size to gauge the variation of the prediction.
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A.1 What is a random sample?
A.2 How do you draw inferences about a population from random samples?
A.3 How do you gauge variation in your prediction by gathering multiple samples of the same size?
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Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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5 - Assess (Visual overlap)
2 - Measure (Deviation)
2 - Expressing (Measure of variability)
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5 - I can informally assess the degree of visual overlap of two data distributions with similar variability.
2 - I can measure the difference between the centers of the data distributions.
2 - I can express the difference between the centers of the data distributions as a multiple of a measure of variability.
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A. One can assess the degree of visual overlap of two numerical data distributions with similar variabilities by measuring the difference between the centers and expressing it as a multiple of a measure of variability.
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A.1 What is a data distribution?
A.2 What does similar variabilities mean?
A.3 How do you assess the degree of visual overlap?
A.4 How do you measure the difference between the centers of the data distributions?
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Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Measures
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3 - Use (Measures of center and variability)
2 - Infer (Informal comparison between two populations)
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3 - I can use measures of center and measures of variability for numerical data from random samples.
2 - I can make inferences about two populations from the measures of center and variability.
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A. One can make informal comparative inferences about two populations by using the measures of center and variability.
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A.1 What is a measure of center?
A.2 What is a measure of variability?
A.3 How do you use the measure of center and the measure of variability to draw comparative inferences about two populations?
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Investigate chance processes and develop, use, and evaluate probability models.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Probability
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2 - Understand (Probability)
2 - Express (Likelihood)
1 - Indicate (Likelihood)
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2 - I understand that the probability of a chance even is a number between 0 and 1.
2 - I can express the likelihood of an event occurring as being between 0 and1.
1 - I can indicate the likelihood of an even occurring by comparing the probability to 0, 1/2 and 1.
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A. The probability of an event occurring is between 0 and 1 which can then be inspected to determine the liklihood of the event occurring.
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A.1 How does one compute the probability of an event?
A.2 Why is probability always between 0 and 1?
A.3 Why does a probability near 0 indicate an unlikely event?
A.4 Why does a probability near ½ indicate that an event is neither likely nor unlikely?
A.5 Why does a probability near 1 indicate that an event is likely?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Chance event
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2 - Approximate (Probability)
3 - Collect (Data)
4 - Observe (Relative frequency)
3 - Predict (Relative frequency)
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2 - I can approximate the probability of a chance event.
3 - I can collect data on the chance even process that produces it.
4 - I can observe a chance event’s relative frequency.
3 - I can predict the approximate relative frequency given the probability.
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A. One can approximate the probability of a chance event by observing its long-run relative frequency and can also predict the approximate relative frequency given the probability.
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A.1 What is probability?
A.2 What is a chance event?
A.3 What is a chance process?
A.4 What is relative frequency?
A.5 How can you predict the relative frequency given the probability of an event?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Agreement
Discrepancy
Outcomes [a]
Probability [b]
Data [b]
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6 - Develop (Probability model)
3 - Use (Probability model)
2 - Compare (Probability and Frequency)
4 - Explain (Discrepancies)
6 - Develop (Uniform probability model [a])
3 - a Use (Uniform probability model [a])
4 - a Determine (Probability [a])
6 - Develop (Probability model [b])
4 - Observe (Data frequency [b])
6 - Generate (Data [b])
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6 - I can develop a probability model.
3 - I can use a probability model to find probabilities of events.
2 - I can compare probabilities from a model to observed frequencies.
4 - I can explain possible sources of discrepancies if the probability and observed frequencies are not close.
6 - I can develop a uniform probability model. [a]
1 - I can assign equal probability to all outcomes. [a]
3 - I can use a probability model. [a]
4 - I can determine the probability of events from a probability model. [a]
6 - I can develop a probability model. [b]
4 - I can observe data frequency of an event. [b]
6 - I can generate data from a chance process. [b]
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A. One should compare the probability from a model to observed frequencies and should explain any discrepancies.
B. One can develop and use a probability model to find the probability of an event.
C. One can develop and use a probability model to find the probability of a chance process that may not be uniform.
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A.1 What is probability?
A.2 What is a probability model?
A.3 What is the frequency of an event?
A.4 What is considered a good agreement between the probability and frequency of an event?
A.5 What are some possible sources of discrepancies if the probability and frequency of an event are not in agreement?
A.5 How do you develop a uniform probability model?
A.6 How do you use a probability model?
A.7 How do you generate data from a chance process?
B.1 What is a probability model?
B.2 What is the frequency of an event?
B.3 What is considered a good agreement between the probability and frequency of an event?
C.1 How do you develop a uniform probability model?
C.2 How do you use a probability model?
C.3 How do you generate data from a chance process?
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Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Probability
Probability e.g.
Probability [a]
Compound event [b]
Methods [b]
Compound Event [c]
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3 - Find (Probabilities)
3 - Use (Organized lists)
3 - Use (Tables)
3 - Use (Tree diagrams)
3 - Use (Simulation)
2 - Understand (Compound probability [a])
4 - Represent (Sample space [b])
3 - Use (Organized lists [b])
3 - Use (Tables [b])
3 - Use (Tree diagrams [b])
1 - Identify (Outcomes [b])
6 - Design (Simulation [c])
3 - Use (Simulation [c])
6 - Generate (Frequencies [c])
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3 - I can find the probability of compound events.
3 - I can use an organized list to find probabilities of compound events.
3 - I can use a table to find probabilities of compound events.
3 - I can use a tree diagram to find probabilities of compound events.
3 - I can use simulation to find probabilities of compound events.
2 - I can understand that the probability of a compound event is a fraction of outcomes in the sample space for which the compound event occurs. [a]
4 - I can represent sample spaces for compound events using various methods. [b]
3 - I can use an organized list to find probabilities of compound events. [b]
3 - I can use a table to find probabilities of compound events. [b]
3 - I can use a tree diagram to find probabilities of compound events. [b]
3 - I can use simulation to find probabilities of compound events. [b]
6 - I can design a simulation. [c]
3 - I can use a simulation to generate frequencies for compound events. [c]
6 - I can generate frequencies for compound events. [c]
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A. One can find probabilities of compound events.
B. The probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
C. Sample spaces for compound events can be represented by using organized lists, tables and tree diagrams.
D. One can design and use simulation to generate frequencies for compound events.
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A.1 What is probability?
A.2 What is a compound event?
B.1 What is a compound event?
C.1 How does one make an organized list to find probability?
C.2 How does one use a table to find probability?
C.3 How does one use a tree diagram to find probability?
C.4 How does one design a simulation to generate frequencies for compound events when finding probability?
C.5 How does one set up the fraction for probability?
D.1 How does one design a simulation to generate frequencies for compound events when finding probability?
D.2 How does one set up the fraction for probability?
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