Doodles Do Algebra – Lesson 3


Update: This Lesson Is Part of Book 1 of Doodles Do Algebra: “Starting Out With Mental Algebra” available on Amazon.


Teacher’s Notes:

DoodlePoodle explains today’s lesson, Lesson 3, which builds most especially on Lesson 2, in which your child learned how to mentally calculate the division of something (like money or apples or books) between two people knowing only the total amount and the relative amounts of the total held by each person.

Today your child expands that concept to division of something between three people. As always, the concepts are not really hard and can easily be done mentally. They are a really good way to get your child thinking about the concepts of algebra before facing the added complexity of working out the steps on paper. And practically speaking, these are very helpful skills to have throughout life.



Available in the book, “Starting Out With Mental Algebra, Book 1 of Doodles Do Algebra”



  1. The “people” in this problem are numbers that add up to (like people share out money or apples) a total number, in this case 30. You are told that the second number is twice the first and the third is three times the first. You can think of it as one part for the first number, two parts for the second number, and three parts for the third number for a total of 1+2+3 or 6 parts. DoodlePoodle explains this concept on the sheet by guiding your kid to start thinking of an unknown and calling it “x”, but you can explain it to your kid (if they are having trouble getting the concept) in terms of parts (like apples, or money, or forks, or whatever you have around the house since showing sometimes works where explaining doesn’t). So if there are 6 total parts and the overall number we need to divide out is 30, then each part takes 5 of the total (30 divided by 6 is 5). So the first number is 5, the second is twice 5 or 10, and the last number is thrice 5 or 15. First number: 5, Second number: 10, Third number: 15.
  2. In this problem, the 3 days are each like a person dividing apples. The total distance, 63 miles, is divided three unequal ways. The first day is one part, or distance. The distance on the second day is twice the first day, or two parts. And the distance on the third day is (here is where it is different) twice the distance on the second, not the first, day – so it is twice the two parts, or 4 parts. So the total number of parts is one (first day), two (second day), and four (third day), for a total of 7 parts. And the distance of each part is 63 miles (the total) divided by the 7 parts, or 9 miles per part. So, Day one Daddy travels 9 miles, Day two he travels 18 miles, and Day three he travels 27 miles.
  3. Here you can get out a jar of pennies or raisins or jellybeans (I have found my kids really learn best when there is an edible manipulative for some reason). You make three piles (or just say aloud) “one x” and “two x’s” and “3 times 2 x’s, that makes 6 x’s” are “one plus two plus 6, or 9 x’s”. Answer: 9x
  4. You can do the same thing as in #3 above, but you have “two times two x’s” plus “three times three x’s”, or “4 x’s” plus “9 x’s”, or a total of “13 x’s”. Answer: 13x

Please give me any feedback you have (good or bad) in the comments below!