Today we met on Teams. We started a new chapter on Algebraic Expressions. We will go back and review ratios, percents, and proportions a bit later.
Aiden had an excellent class. We reviewed a problem where an automatic dog feeder, which holds 20 cups of food, dispenses the food at 2/5 cup per day. First, we came up with an expression for the amount of food dispensed for d days. We determined after, say 2 days, the amount dispensed would be 2/5+2/5 or 2/5(2). After 3 days, it would be 2/5+2/5+2/5 or 2/5(3). We noticed regardless of the number of days d, we could get the amount dispensed with the expression 2/5d. Then we considered the expression for the amount remaining in the bowl after d days. We started with the original amount of 20 cups and then subtracted the amount dispensed 2/5d, to get 20-2/5d. Aiden had no trouble making these connections. To confirm, I gave him a hypothetical question, to come up with an expression for the total cost. We let Apples cost $3 per pound and Bananas cost $2 per pound. We let "A" represent the amount (in pounds) of apples you buy, and "B" represent the amount of bananas you buy. Aiden was able to determine expression 3A+2B would represent the total cost.