Statistics and Probability Grade 7
Hook 1 7.SP.A.1
Prompt: Which survey approach is the best? Why?
The idea of sampling populations to gather valid data is new for most seventh graders and worthy of the time needed for a full discussion. Although we can't say what biases all green or tall women might have, we can say to our students that because they are all alike in this one way, we are not getting a representative voice for all women. Only random sampling, choosing every fifth woman, allows us to hear from the entire range of the population.
Video: America's Changing Population (4:10)
Hook 1 7.SP.A.2
Prompt: What percent of states would you expect Democrats to win?
There's intentionally a lot of gray to this hook both literally and figuratively. Of course, certain states' proclivity to vote for one party or another is not determined by the results of others. However, for the sake of the standard, students can use the early results to make prediction to the final count of states. Questions that students bring up about the political realities of the country's election history and system are great opportunities to discuss the limits and pitfalls of statistical predictions.
Hook 1 7.SP.B.3 and 7.SP.B.4
Prompt: Who is the better runner?
This hook, which covers two standards, ask students to consider two different measures of data, mean and MAD. Most seventh graders are familiar with the mean and from that measurement will assume Ashley is the better runner. However, some students may point out Ashely's inconsistency compared to Michelle's. Students do not need to know MAD to have a discussion of how to measure "consistency" nor do they need to come up with the formula. But we can expect them to spitball ideas about this measurement to deepen their understanding of its need and purpose. If students engage in this thought process the MAD formula can be an "Aha!" moment that they won't forget.
Hook 1 7.SP.C.5
Prompt: Assign each event a measure of likelihood for today's weather.
There'll be some haze in this hook depending on the day and your students' grasp of weather events and their causes. However, the conversations your students have around the weather should illuminate their understanding of probability and how we measure it. The moon picture is meant to be "night time" as an example of an event that has a certain probability. Of course, night is not weather so it's a bit confusing. Students may interpret it as a clear night sky or you can define it for them. In any case, students have the opportunity to work with the scale of probability and think of it both in terms of numerical values and levels of likelihood.
Video: Fear and Probability (2:04)
Hook 1 7.SP.C.6 and 7.SP.C.7
Prompt: Design rules to play the game.
This hook ask students to design rules to the game using data collected from experimental. If students haven't worked with random generators such as dice, spinners or choosing cards you may want to review these tools to help them get started. Watch to see if students are using the data to create their rules. For those who are not, ask them to discuss the likelihood of each event and then ask them how they could ensure these likelihoods are part of their game design.
Video: Thinking Outside the Box (2:03)
Hook 1 7.SP.C.8
Prompt: Explain how to find probability by using the area of a square.
Students who complete the area model may find probability by using the model as a simple listing tool and identify each event as having a one in nine chance of occurring. This is correct but it does not address the use of area to find probability. Therefore, it may be necessary to ask leading questions to get them thinking geometrically. Ask them what shapes they see. Ask them how the shapes are related. Ask them how the shapes are created. Ask them how it would be different if there were four boys instead of only three. What would the area diagram look like then? Would the addition of a boy change the probability of each pair of dancers? Ask them to explain in terms of the rectangle created and the area of that rectangle. In short, this hook asks students to interpret an area model, a probability model that most will not have see before. Focusing their attention on the geometric foundation of the model will help them to see how area models can be excellent tools to calculate the probability of compound events.