Odds and Order and Probability are very important foundational concepts at this age. Carlo should be able to create and interpret more complicated graphs, including graphs based on statistics and probability. With his firm understanding of how to read data, there will be a natural progression to using and manipulating the Cartesian coordinate system (graphs with an x and y axis) which involves plotting data points to create number lines. Carlo should be able to both plot and interpret each data point, and use basic graphing formulas to calculate attributes like the slope of a number line. The more concrete these skills can be, the better Carlo’s understanding of more complex graphs and 3D models. It will help Carlo stay focused to relate these graphs to real world scenarios, using examples that involve politics, business advertising, or sales to reinforce concrete skills and deductive reasoning. Having him create the data through experiments will also help him apply and retain the information.
Playing probability-based games like Yahtzee is a great way for Carlo to apply the likelihood of a specific roll. For example, the likelihood of a player rolling a Yahtzee on the first roll is 1/1296. Discussing this with other game play like carnival games or the lottery will increase Carlo’s interest. Having students create their own fair and unfair games is an interesting addition to the practice. At the end of 8th grade, Carlo should be able to solve these odds and order problem: 1. 11 people are racing. What are the odds of being 1st, 2nd or 3rd? 2. A bag contains 3 red, 4 green and 3 yellow marbles. Three marbles are randomly drawn from the bag. What is the probability that they are all (i) the same color? (ii) different colors (one of each color)?