# 'Roll the die and win the cards. Solve the equation before your partner does!'

Unless you have scientific or engineering parents you may never have seen Quadratic equations outside of the mathematics classroom. Even if you have seen them, you may have struggled to understand why/how/what on earth? such symbols can represent anything “real”! The youtube clip below hopefully provides a first insight into how quadratics (and equations generally) were an amazing invention by the Frenchmen, Descartes, for defining position in space perfectly. The motion of projectiles, rockets, any object falling under the influence of gravity, can be described perfectly by quadratics. If gravity did not exist, it is possible that you wouldn’t be learning about quadratic equations!

The below video shows a rocket launch and how quadratic equations might help to define perfectly its motion:

### Resources

Print and cut out these cards Quadratic Substitution, or use the pre-prepared laminated cards your teacher gives you.

The pictures below show how a winning hand for each of the games described at the bottom of this page: Die Card Snap, Connect 3 and Matching Pairs. Viewing these photos before reading the rules for each game should help clarify how they can be played:

### Description

Die Card Snap

• Students play the game in pairs, threes or fours.
• Each player has a pile of the quadratic expression cards face down in front of them. One of the players rolls a die and then they each turn one of their cards face up.
• Each player uses the number on the die as the value for "x" in their equation (the teacher can decide if students are allowed to use calculators or not). The player whose expression is equal to 0 wins that hand.
• When all the cards are gone, the player with the most winning piles is the overall winner.

There are many games that can be played using these cards. Why not get students to create their own gameplay or set of cards? Below are two further examples:

Connect 4

• Students lay the cards out in a rectangle, face up. Each player can turn over one card at time by saying what "x" value will make the expression = 0. The first to get 3 or 4 in a row wins (Connect 3 or 4!).

Matching Pairs

• Students play in groups of four. All cards are dealt out. If two cards have the same "x" root then the student lays these on the table as a matching pair. When students have got rid of all their matching pairs, they take it in turns, starting from the dealers right and going round the table clockwise, to pick a card at random from their partner. If the new card makes a pair, they add it to their winning pile before offering their cards, blind, to the next player. When there are no cards left the player with the most matching pairs wins.