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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Target 100 - Maths Card Game from Michael Ymer

Thanks to Michael Ymer for this great game

Introduction / objectives

This is a card game that provides the students with the opportunity to investigate a variety of mental computation strategies when adding and multiplying numbers. It is quick and easy to organise and is lots of fun, even for adults who play it. The less able student can win, as there is an element of chance involved. A terrific number sense game to use as a warm up activity, or a focus lesson for young children.

Equipment [for each pair of students]

100 number board, 10 x 10 tables chart and two counters.

Deck of cards. All number cards have face value. Ace = 1. 2 = 2 etc.

Picture cards = 10

Joker = wild [can have the value of any other card in the deck].

1	2	3	4	5	6	7	8	9	10
11	12	13	14	15	16	17	18	19	20
21	22	23	24	25	26	27	28	29	30

Procedure

Two students compete against each other to see who can get closest to 100 without busting. One student deals cards out to his/her opponent who adds or multiplies the cards. This continues until the student decides to stop.

Example Player A is going first and having cards dealt by partner.

Card 5 is dealt first so player A moves counter to 5 on number board. Card 6 is the next card dealt. This could be 5+6 and the counter is moved to 11 or it could be 5x6 and counter is moved to 30. Let’s assume that Player A decides to move to 30. The next card is a KING so the student adds 10 and moves the counter to 40. Next card is 2. Student decides to multiply and moves to 80. Next card is Ace. Student decides to multiply and stay on 80, hoping that the next two cards are 10’s and he/she can hit exactly 100. Next card is a 5. Student adds and moves to 85. Next card is 9. Student moves to 94 and decides to stop fearing that the next card flipped will be bigger than a 6and she / he would bust.

Player B now has the cards dealt to him / her and tries to better 94 without busting. Once this game is completed, play again but player B goes first.

Teacher tips

• Card familiarisation activities are a good idea if students haven’t been exposed to decks of cards before. Perhaps alder students could tell you the value of a deck of cards based on the values listed in this game. Younger students should do sorting activities to help them discover that there are four of each card. How many cards in the deck?

• Transparent counters help students see the numbers on the board.
• Children find shuffling cards difficult so keep working through the deck of cards until you run out. Then shuffle or ask the teacher to help.
• Children only deal a card out when the partner says, ‘Card please ‘. This eliminates the problem of students dealing the card while the other student is still deciding their move. If the card is flipped without being asked for the receiver has the option of using it or having a fresh one dealt out.
• Try modelling the game to students using an overhead, transparency of 100 number board, transparent counters and overhead miniature playing cards. A very effective way to demonstrate the game and strategies that you need to discuss.
• Vary the game if needed. Perhaps only add for young children or play hit exactly 100 for older students. For this game students can use any operation with winner being the student who hits 100 in the least amount of cards.
• Vary the game by making it more challenging. Use any operation to hit exactly 100 in fewer cards than your partner.
• When introducing the game, tell the children that while the game is lots of fun, the point of the game is to make decisions and become a smarter mathematician by taking short cuts when adding or multiplying. The overhead gives you the opportunity to discuss some of the strategies listed later in the article.



Maths Card Game - High Card - Addition

A game suitable for students from Prep to Year 6 from Michael Ymer.

Two students place a deck of cards in front of them face down. Remove the Kings, Jacks, and Jokers. The Ace represents the number one and the Queen represents a zero. All other cards are face value. 

Chn share out all the cards and place their cards in front of them in one pile.

Player one turns over his/her top two cards and adds them up ie. 7 and 10 = 17. Player two then turns over his/her top two cards hoping to get a higher score than player one. Whoever has the higher score takes all 4 cards and places them at the bottom of their pack. Play continues until teacher says stop or all cards are used. Player with most cards wins.

Variations

Turn over three cards, Subtract, turn over three cards and add and subtract between cards to make greatest total. Make the largest two/three digit number, multiply

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



Math Card Game - Cover Up – Choosing and using operations

Thanks to Michael Ymer for this game suitable for students from Year 1 to Year 6.

Children play the game in pairs. A deck of cards with all pictures removed. Game board with the numbers 0 -20 displayed in a grid.

Each child has 7 counters of the same colour. Their partner has a different colour.

Children take it in turns taking two cards at a time from the top of the deck and add or subtract the numbers to make an answer from 0 - 20. One of their seven counters is placed on that number. The objective is to get rid of all counters first. If a student lands on top of number that has their partner’s counter on it they take the place and send the counter back to their partner. Students can have more than one counter of their own on the same number but if their opponent lands on that number all counters are sent back.

Variations....use three cards, use dice instead of cards, allow any operation, simplify the game by using a 0 – 12 board and a cards 1 to 6 or a six sided dice.