Quadratic Factorisation with 'Wrecks Factor'
CURRICULUM AREAS COVERED
Ages 14-17
- Factorising Standard Form Quadratics (ax² + bx + c = 0)
- Quadratic factorisation like (x + 2)(x + 3), (x – 3)(x + 2), (2x + 1)(x – 3), s(3x – 1)(x + 3)
HOW TO PLAY
Use your factoring skills to 'draw' a search area for the rescue chopper. The side lengths of the search area represents the linear factors for the quadratic.
In this maths game you are the chief of rescue operations for the Bermuda Rectangle. Your task is to protect the ships crossing this notorious body of water, keeping watch for any vessels that fall prey to its strange and terrifying phenomena. Stricken ships will transmit their search area coordinates encoded as a quadratic expression. You must decipher the code before the ship sinks, and dispatch a rescue chopper to locate life rafts and save the crew.
- Point and hold down your mouse button then drag across the sinking ship to form a rectangular search area. Ensure that the search area encompasses the sinking ship you are trying to 'rescue'.
- Release your mouse button when the side lengths of the rectangle corresponds to the quadratic's factors.
- The direction in which you drag the mouse determine whether the number terms are positive, negative or both
- Correctly factorised quadratic will:
- dispatch a rescue helicopter to scour the search area for life rafts and rescue survivors
- add point to your score
- add extra time to the timer
- add a life-ring to the 'Multiplier bar' (top left hand corner of the screen). The Multiplier is applied to any points you earn.
- Incorrect answers will:
- sound a warning, and ship continues sinking
- have seconds deducted from the timer
- have three life-rings deducted from the 'Multiplier bar' (If the bar drops to or beyond empty then your Multiplier decreases.
SCORING INFORMATION
There are 4 modes to this game. Complete the relevant mode and beat the Target Score to earn a medal (Bronze, Silver, Gold).
- Mode 1: Quadratic factorising like (x + 2)(x + 3) >> Target Score >>> 175,000 (B), 375,000 (S), 800,000 (G)
- Mode 2: Quadratic factorising like (x - 3)(x + 2) >> Target Score >>> 150,000 (B), 325,000 (S), 700,000 (G)
- Mode 3: Quadratic factorising like (2x + 1)(x - 3) >> Target Score >>> 125,000 (B), 275,000 (S), 600,000 (G)
- Mode 4: Quadratic factorising like 2(3x - 1)(x + 2) >> Target Score >>> 100,000 (B), 225,000 (S), 500,000 (G)
SCORING INFORMATION
The total number of points earned for each rescued ship is calculated as:
Total Score = Base Score × Difficulty) + Link Score
- Base Score - there are four different types of ship sailing the Bermuda Rectangle. Each moves at a different speed and sinks at a different rate, and so is worth a different ‘base score’ if rescued:
- Difficulty - there are 4 difficulty levels. Getting three correct answers in a row makes you go up a difficulty level, two incorrect answers in a row makes you go down.
- Link Bonus. After correctly answering a question the cells in that selection light up for 8 seconds. If within that time you get another correct answer, and the selection includes any of those cells, you get an extra 100 points.
MATHS STRATEGIES
- If the number term is positive and the coefficient of x is also positive, for example in the quadratic x² + 5x + 6, then the number terms in the factorisation are both positive, e.g. (x + 3)(x + 2). Start drawing your search area below and to the left of the ship.
- If the number term is positive and the coefficient of x negative, like in x² – 5x + 6, then the number terms in the factorisation are both negative, e.g. (x – 3)(x – 2). Start drawing your search area above and to the right of the ship.
- If the number term is negative then one of the number terms in the factorisation is positive and the other is negative. You need to think more carefully about these cases; take your time and try to get it right first time. Start drawing your search area above and to the left or below and to the right of the ship.
- To be good at The Wrecks Factor you need to be able to spot quickly pairs of numbers that multiply to give a particular number. For example: these pairs – 1 and 12, 2 and 6, 3 and 4 – all multiply together to give 12.
- In Mode 4, if the quadratic has a common factor then make sure you pull out the largest common factor. For example: 2 is a common factor of the numbers in the quadratic 4x² + 12x + 8. But so is 4, which is a bigger number. As 4 is the largest common factor, pull out the factor of 4 and not 2.
OTHER BASIC STRATEGIES
- Where to place the cursor:
- If the correct factorisation is (x + 3)(x + 2) then place the cursor to the bottom left of the ship, as dragging up and to the right will create the search area.
- If the correct factorisation is (x – 3)(x – 2) then place the cursor to the top right of the ship, as the search area will be created by dragging down and left
- If the correct factorisation is (x + 3)(x – 2) then place the cursor to the top left or bottom right of the ship, as the search area will be created by dragging up and left or down and right
- Count squares:
- The bigger the number terms, the bigger the search area. Ensure the search area fits the grid from the chosen start point.
- The smaller the number terms, the smaller the search area. Ensure your start point is close enough to the ship that the search area contains the ship.
- Look out for special cases. The search areas for factorisations like x² - 9 = (x + 3)(x - 3) are especially easy to draw: it’s square and you drag either down and right or up and left.
- Choose carefully which ship to save next. For each ship you need to figure out how long it’s been waiting for rescue, and how difficult its factorisation is. You should be able to decide quickly how difficult a factorisation is by looking at the numbers in the quadratic. Sometimes it’s worth leaving an ‘easy’ factorisation (even if the ship has been waiting for longer) and focus on a difficult one. Once you save the difficult ship, you can return to the easier one.
- Each ship type is worth a different amount of points and sinks at a different rate. Focus on saving the fastest sinking ship types first for the biggest scores.
- Once you save a ship, it will stop sinking. Use this fact to wait until you have a lot of ships sinking in the same area, then save them all as quickly as possible while ensuring their search areas overlap – this can generate huge bonus points!
