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Pair-Alysis (Updated!)

How many options are too many options?

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Pair-Alysis (Updated!)

How many options are too many options?

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Check it out! This lesson was just updated in September 2024, and we hope you love the new and improved version. If you've already prepped an earlier version, fear not, you can still find those here through Thursday December 5, 2024.

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Pairalysis - Student Handout.pdf
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Pairalysis - Teacher Guide.pdf
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2023-2024 Versions

In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.

You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.

How many different shoes can you design on NIKEiD? NikeID allows users to customize a pair of shoes before buying them. While some people think technologies like this allow shoppers to find the perfect shoe, others aren’t so sure.

Students use tree diagrams to determine the total number of design combinations that are possible on NikeID and discuss the psychological impact of having billions of options to choose from.

REAL WORLD TAKEAWAYS

  • There are both advantages and disadvantages of having so many options. The “paradox of choice” is the phenomenon by which more choice – often assumed to always be better than less choice in western societies – can lead to less happiness, less satisfaction, and a harder time making a decision in the first place.
  • Traditional retail stores limit the amount of options that are available to customers. For instance, if a shopper wants a specific type of shoe from Foot Locker (e.g. a Nike Air Force 1), they only have a few options for colors.
  • New online services like Nike By You allow users to customize shoes before they purchase them. In some cases, there may be billions of different options for a customer to choose from.

MATH OBJECTIVES

  • Apply the fundamental counting principle to determine the total number of outcomes in a real-world context (i.e. tree diagrams)
Appropriate most times as students are developing conceptual understanding.
Grade 7
Probability & Statistics
Grade 7
Probability & Statistics
Content Standards 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. (a) Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. (b) Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. (c) Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Mathematical Practices MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Other Grade 7 Lessons

Big Foot Conspiracy (Updated!)

Should people with small feet pay less for shoes?

Grade 7
Ratios & Proportions
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Common Cents (Updated!)

Should the United States get rid of the penny?

Grade 7
Rational Numbers
Appropriate most times as students are developing conceptual understanding.

To Have and to Hold (Updated!)

Is renting a storage unit a good idea?

Grade 7
Equations & Expressions
Appropriate most times as students are developing conceptual understanding.

Axle Roads (Updated!)

How do vehicles turn so smoothly?

Grade 7
Measuring Circles
Appropriate most times as students are developing conceptual understanding.

Grading Scales of Justice (Updated!)

What’s the best grading policy?

Grade 7
Percents & Proportions
Appropriate most times as students are developing conceptual understanding.

Big Foot Conspiracy (Updated!)

Should people with small feet pay less for shoes?

Grade 7
Ratios & Proportions
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Common Cents (Updated!)

Should the United States get rid of the penny?

Grade 7
Rational Numbers
Appropriate most times as students are developing conceptual understanding.

To Have and to Hold (Updated!)

Is renting a storage unit a good idea?

Grade 7
Equations & Expressions
Appropriate most times as students are developing conceptual understanding.

Axle Roads (Updated!)

How do vehicles turn so smoothly?

Grade 7
Measuring Circles
Appropriate most times as students are developing conceptual understanding.

Grading Scales of Justice (Updated!)

What’s the best grading policy?

Grade 7
Percents & Proportions
Appropriate most times as students are developing conceptual understanding.