Update: This Lesson Is Part of Book 1 of Doodles Do Algebra: “Starting Out With Mental Algebra” available on Amazon.
Today DoodlePoodle gets in on the action and we add more complexity to the problems covered in previous lessons. The underlying goal is for your child to start thinking in terms of “x” as a placeholder for some unknown quantity.
Available in the book, “Starting Out With Mental Algebra, Book 1 of Doodles Do Algebra”
1. This problem takes your child step by step through the process of figuring out how many boys and how many girls there are in the Smith family. We choose the unknown, x, to represent the number of girls (because there are 3 more boys than girls, thus the smallest number is the number of girls). Based on that the number of boys is x+3 (or three more boys than girls). Then the total (boys and girls together) is (x+3) + x = 13 (the total number of kids). Solving for x means adding x + 3 + x to get 2x + 3. Then to solve for x, you follow along the example given by DoodlePoodle. So 2x + 3 = 13 is the same as 2x = 13 – 3 (you can explain this with the idea that if you take (or add) something from one side of an equation, you have to do the same to the other side of the equation for the equation to stay the same). This is one of those steps where your child just needs to take it on faith right now and learn how to solve these types of problems. The deeper understanding of why it is so comes later. So back to the problem. 2x = 10 (since 13-3 is 10), and then 1x = 5 (when you divide both sides of an equation by the same number the unknown keeps the same value). And finally, x=5. So there are 5 girls (x) and 8 boys (x+3) in the Smith family.
2. This problem is completely abstract. Point out to your child the similarity with the first problem, and things will become clear. The sum of the two numbers in this problem is just like The Smiths having 13 children. They are both talking about the total, when you add up both kinds of unknowns (numbers in this case, and children in the previous problem). So Number One + Number Two = 35. Now, the problem also states that the difference between those two numbers is 5. That is the same thing as saying that one number is 5 more than the other, and that is just like the previous problem where there were 3 more boys than girls. So let’s pick Number One = x (this will be the smaller number). Then Number Two = x+5. So Number One + Number Two = The Total, or x + (x+5) = 35. Now we simplify (add in this case) to get 2x + 5 = 35. Then we subtract 5 from both sides, 2x = 30. And finally we divide both sides by 2 (the coefficient of the unknown – a good concept to start embedding in your child’s mind now) and x=15. So One Number is 15 and the Second Number is 20.
So you can see that we are slowly shifting your child away from a simple conceptual understanding of algebra and towards a practical ability to solve more complex, and sometimes abstract, problems. The goal is for your child to be familiar with how algebra basically works, and then to take a trip through a series of vocabulary and definitions (in order to start using Algebra-speak) before returning to Algebra in a more abstract fashion.
Please give me any feedback you have (good or bad) in the comments below!