Update: This Lesson Is Part of Book 1 of Doodles Do Algebra: “Starting Out With Mental Algebra” available on Amazon.
Today’s lesson continues the same ideas as lessons 2 and 3, but begins to think more about using the concept of an unknown, or “x” as a placeholder. DoodleCat begins by reinforcing the idea that 2x is two x’s and 3x is three x’s and so on. The questions that follow in the Doodle Dailies rely on using that idea.
Available in the book, “Starting Out With Mental Algebra, Book 1 of Doodles Do Algebra”
- Have your child think of the number of lemons and oranges as “x”, which we can do since Kendra bought an equal number of lemons and oranges. If this is hard, you can equate the concept of “x” to fruit as a general class. So Kendra bought 2x plus 3x dollars, or 5x, worth of fruit for a total of 30 dollars. Then the number of each type of fruit was 30 divided by 5, or six. So Kendra bought 6 lemons and 6 oranges.
- This is the classic train problem, only we use a Dad and a Gpa instead. Dad and Gpa are moving at the same speed towards each other, which means we can say that they are both 4x miles (miles per hour times the unknown hours) away from the middle where they will meet. That means they are a total of 4x miles plus 4x miles away from each other, or 8x miles which is equal to 40 miles (the distance given in the problem). This means that x is 40 divided by 8, or 5 – so Dad and Gpa will meet in 5 hours.
- This last problem is maybe the most practical. It is in some senses like problem one, but the two pipes that are emptying the cistern are doing it at different rates (one discharges four times faster that the other). So one pipe discharges at a rate of 4x gal/hour and the other at a rate of x gal/hour and when you add the two together, you empty the 100 gallon cistern in 2 hours. So 4x gal/hour plus x gal/hour equals 100/2 gallons/hour (see how we used the capacity of the cistern and the total time to empty it to calculate the constant that equals the overall rate of discharge? That is because rate means the number of units changed per time elapsed and in our case we have gallons and hours.) So 4x + x = 100/2, or 5x =50, and x =10. That means that one pipe has a flow of 10 gallons/hour and the other pipe has a flow of 40 gallons/hour (since one pipe discharged at a rate 4 times the other).
If this seems a bit daunting, not to worry just lead your child through it and don’t worry – we will come back to it again in future lessons. Your child should not get discouraged – the main point is to expose him (or her) to algebra-type thinking at this stage.
Please give me any feedback you have (good or bad) in the comments below!