Reflection questions and Theoretical probability Cane Toads: Leg it! Reflection questions and Theoretical probability

Did humans have any effects on the lives or travel of your toads? Reflection Questions Which animals or food did your toads eat? How did this affect other animals? Did any animals eat your toads on your journey? How did this affect them? Did humans have any effects on the lives or travel of your toads? Ask students to categorise the cards into groups, on the basis of these questions, or on the basis of whatever group they like! Any answer is correct if they can explain it!

Theoretical Probability: “What’s the chance I get to roll?” 1 4 ACTIVE Roll dice! INACTIVE Miss a turn p(roll) = number of wanted outcomes total possible outcomes ACTIVE Roll dice! ACTIVE Roll dice! 3 4 = Now, let’s discuss probability and how it affected our game. First we will find the probability of an event where you have spun your spinner. Looking at this in terms of mathematics involves what we call theoretical probability. We need to think about the number of possible outcomes we can get from spinning the spinner. So if we did spin out spinner, how many outcomes can we get? There are four. That means all of our probabilities for exploring the spinner will be out of four. What’s the probability of rolling “roll dice”? Three of the four parts of the circle have “roll dice”, so our answer is three in four. 3 2 Activity Wheel

Theoretical Probability: “What’s the chance I get to roll?” don’t 1 4 ACTIVE Roll dice! INACTIVE Miss a turn p(roll) = number of wanted outcomes total possible outcomes ACTIVE Roll dice! ACTIVE Roll dice! 3 4 = What’s the probability of spinning “miss”? How many miss a turn parts of the circle are there? There is 1, so the probability is 1 in four. 3 2 Activity Wheel p(miss) =

Theoretical Probability: Why did the different dice allow some toads in the game to move further? 1 2 3 4 5 6 6 1 2 3 4 5 6 7 8 8 Now let’s discuss probability and how it affected the movement of our toad if we had different dice. We again need to consider the number of possible outcomes we can get from a six sided dice. If we roll, how many outcomes can we get? 1,2,3,4,5,6. That means all of our probability questions here will be out of 6. For an eight sided dice, out of eight For a ten sided dice, out of ten. 1 2 3 4 5 6 7 8 9 10 10

We can explore probabilities on different dice as probabilities in a pie chart, or on a spinner too. See if you can colour the pie charts on your worksheet to represent probabilities of different dice rolls as a fraction.

“What’s the chance of rolling a 6?” 1 2 3 4 5 6 1 6 p(roll) = number of wanted outcomes total possible outcomes 1 2 3 4 5 6 7 1 8 8 Because 6 is the “best” roll usually when we play games with dice, let’s explore the probability of rolling a 6 on each of the dice. Probability of getting a six gets smaller as we increase the number of sides on the dice. 1 2 3 4 5 6 7 8 9 1 10 10

“What’s the chance of rolling a six or higher?” 1 2 3 4 5 6 1 6 p(roll) = number of wanted outcomes total possible outcomes 1 8 1 8 1 8 1 2 3 4 5 6 7 8 3 8 1 10 1 10 1 10 1 10 1 10 But there are other good numbers. Let’s look at the possibility of getting a 6 or higher! It gets bigger as the number of sides on a dice go up! 1 2 3 4 5 6 7 8 9 10 5 10

“What’s the chance of rolling a 3 or lower?” 1 2 3 4 5 6 3 6 p(roll) = number of wanted outcomes total possible outcomes 1 2 3 4 5 6 7 3 8 8 What about if we think about the low numbers? Yup, the possibility of getting a number of 3 or less also goes down each time we increases the sides on a dice. So theoretical probability suggests that over many rolls, we’re likely to get more high numbers and less low numbers! 1 2 3 4 5 6 7 8 9 3 10 10

Further Exploration of Probability What can you see on the game board that we could explore in terms of probability? The 100 square grid gives students an opportunity to explore probability in terms of decimals\percentage\etc!

Reflection Questions How did your predictions about how far the different toads would travel compare to what actually happened in the game?   Did the toads always move further in the game if they had dice that could roll higher? Why or why not? Can you think about a reason why some toads might be able to move further than others? EXPLAIN! Students have predicted, observed. Now can they explain what has happened? P.O.E! Extension opportunity: Probability of power-ups/events

Toads are moving faster every year across the Australian landscape Distance from starting place in Qld. [kilometres per year (km/y)] 1945-1954 10 1955-1964 1965-1974 20 1980-1984 25 2001-2008 60 Invasion front 10 10 20 25 60 Every year, cane toads are spreading across Australia faster and faster. Estimated spread? 1974 1935 – First released 1954 1964 1984 2008 Where cane toads have been found

Longer-legged toads are spreading the fastest Toads at the invasion front have the longest legs. Longer legged toads don’t always move further than regular toads. If toads CAN move further, then that changes the probability of them moving further. Invasion front Scientists have found that toads at the invasion front move the fastest (and have the longest legs of all the toads). Living things have structural features and adaptations that help them to survive and flourish in their environment. The toad invasion is not a race. Toads don't have to make giant leaps. However, if they can then that affects the probability of them moving further. Just as not everyone’s toad invasions didn’t move as far as each others, (even if they rolled the same dice), when we look at the general trend, toads with “longer legs” typically moved further. Just like it was different for your toads, it is different in real life! Different groups of toads do move different amounts. However, th general trend is that toads with longer legs move further. Maybe, the reason some travel further than others is just because of the possibility to do so. Maybe it’s a matter of mathematical probability? Because it’s possible, in the end, by chance, it does? Nonetheless, scientists have found that toads at the invasion front have longer legs. 10 8 6