Doodles Do Algebra – Lesson 2

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

Teacher’s Notes:

Day 2 of “Doodles Do Algebra” is taught by my boy (DoodleTwo).

The types of mental “algebra” problems your child will learn today are focused on solving the typical type of “so-and-so has twice as many apples as his friend, if together they have such-many apples, how many does each person have?” problems.

The key here is to mentally count up how many “units” there are in total.

In the example taught by DoodleTwo,

My sister and I have 18 cents, and I have twice as many as my sister; how many cents do each of us have.

So you need to help your kid think about it like this:

• There are 18 cents total
• You are dividing that 18 cents a total of 3 ways. DoodleTwo gets 2 of those parts (or ways) and DoodleOne (his sister) gets the last 1 part.
• So if you are dividing 18 into 3 equal parts, then each part is 6 cents because 18/6 is 3.
• That means that DoodleOne (sister) gets one part, or 3 cents
• and DoodleTwo gets two parts, or 2×3 cents, or 6 cents.
• Now if you think of dividing the 18 cents “x” ways instead of using the word “parts”, you are now doing mental algebra!

It is really easy unless you had a traumatic middle school algebra experience and then fear, uncertainty, and doubt creep in at odd moments.

Don’t worry, your kids will have a much easier time with this than you think.

Worksheet:

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

Answers:

1. DoodlePoodle is 10, and DoodlePig is 5. (again there are 3 parts and 15 divided by 3 is 5. DoodlePoodle gets 2 parts, or 10 years and DoodlePig gets one part, or 5 years).
2. Part One is 7 and Part Two is 28 (this time there are 5 parts total and 35 divided by 5 is 7. One part is 7 and the other is 7 times 4 or 28). Note that here it is just as correct to say Part One is 28 and Part Two is 7, since the question was worded ambiguously.
3. First number is 4 and Second number is 36 (now there are 10 parts and 40 divided by 10 is 4 so the smaller number, which is just one part is 4 and the larger number, which is 9 parts, is 4 times 9 or 36.) Also here the first number could by 36 and the second number could by 4, it doesn’t matter which way you write it.
4. 3x (here we are reviewing the ‘one x and two x’s make a total of 3 x’s’ concept. If your kid has trouble abstracting you can sit down with a pile of pennies, or apples, or teaspoons, or raisins and show them how you add with a tangible thing and then tell them that the penny or raisin or apple can be an ‘x’ just as easily as a ‘real thing’)
5. 4x
6. 5x

Once again, please give me any feedback you have (good or bad) in the comments below!