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.

Worksheet:

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

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.

• 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”

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

Doodles Do Algebra – Lesson 1

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

Teacher’s Notes:

The first section of the algebra book (Doodles Do Algebra) starts your kid out with a series of mental math exercises. Before your kids learns about unknowns and how to simplify polynomials, it is really really helpful to give your kids familiarity and confidence “mentally” solving problems that usually are taught as algebra problems with written steps.

I discovered, after fielding years and years of repeated forms of the “why do I have to know how to do this?” questions, that my kids just took to algebra straight away when I took them through a number of mental math problems first. It was also quite surprising how easily they (and I) could do the problems without pencil and paper.

Day One (or Lesson 1) is taught by my darling daughter doodle who tells us how she solves the problem of dividing out tshirts from her uncle between her and her twin brother. Those of  you with twins will know how important it is to keep track of who gets more and how to make things equal when you have twins. I have even learned how to count out the raisins in their snack and measure the milk so that both glasses are poured equally. But today it begins with tshirts.

Then each day there are a few problems for your kid to try (called Doodle Dailies). The book is designed for minimal parent teaching. Most everything comes from the Doodle Cartoon explaining the lesson of the day. As a side note, my kids like to color in the Doodle Cartoon character each day and give them hats and crazy facial expressions.

Worksheet:

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

The answers for today’s sheet are:

1. Mary and John are 11. (yes, the twin theme is strong)
2. You each get \$15, which is quite a lot in my family.
3. x + x is 2x (I always say “one x plus one x is two x’es” to drive the point home that x could be apples or pears or chocolate bars)
4. 3x
5. 4x