Who’s No. 1? Investigating the Mathematics of Rankings

By PATRICK HONNER and HOLLY EPSTEIN OJALVO

Jay Pickthorn/Associated PressThe No. 13 N.C.A.A. seed, Oakland, with Travis Bader and Coach Greg Kampe, makes a tempting pick against No. 4, Texas, in the second round.Go to related FiveThirtyEight blog post » | Go to related article »

Overview | Rankings and ratings can have considerable, and serious, implications. How do we determine that a student, team, school, teacher or policy is better than another? And what does “better” mean? In this lesson, students explore the use of quantitative ratings by examining how Division I college basketball teams are ranked, and how specific mathematical decisions can have significant consequences.

Materials | Computers with Internet access; Simple Spreadsheet software (optional)

Warm-up | Tell students to pair up and work with their partners to answer the following questions:

How can we determine the top student in school? Would you use a single variable, like grade point average? Or would you create a ranking system based on multiple variables, like G.P.A. and standardized test scores, activity participation and perhaps other factors? How might you begin to create a fair composite ranking system using quantifiable measures?

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Maths Card Game - More / less / the same - Place value

Thankyou to Michael Ymer for this great game suitable for students from Prep to Year 6.

Card game for groups of four. Remove picture cards and jokers. Deal each child 6 cards. Cards left placed in the middle and turn the top one over.

Taking turns the children place a card down according to

* same number. * one more or one less. * two more or two less. * double the number

* half the number

The child must verbalise the choice they have made to discard and why. If a card cannot be discarded then a card is picked up from the deck.

First to discard all their cards wins the game.

Variations

Discard two or more cards that add up to the card displayed.                                  

Include the Joker with the value of zero.

Include the picture cards with the values   Jack  11     Queen 12      King  13



Maths Card Game 10 in a row - Choosing and using operations

Thanks to Michael Ymer for another great game suitable for students from Prep to Year 6.

Children play game in pairs. All picture cards removed leaving numbers 1 – 10.

Place 10 cards face up in a row. The remainder of the deck kept together face down. Students take it in turn rolling a ten sided dice [ Can use a six sided dice ]. Using the number that is displayed the student is challenged to use combinations of cards to equal the number. Cards used to make the answer are collected and kept by each student and then replaced from the deck. The game continues until all cards have been used. Young children will use addition / subtraction to make answers using two cards. Older or more able students can use any combination of operations, decimals, negative numbers, fractions, order of operations etc and use up to five cards. Students need to articulate how they make the answer, trying to gather more cards than their partner.

Variations

Use six sided dice. Offer counters that can be added to total collection of cards at end of game for using operations and signs other than addition or subtraction.

Roll two dice making a two digit number as the target.