Doodles Do Algebra – Lesson 23

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today we teach your child the difference between known and unknown quantities as we continue the process of learning the vocabulary you need to understand algebra.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

Doodles Do Algebra – Lesson 22

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today’s lesson teaches the difference between a theorem and a problem.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

Doodles Do Algebra – Lesson 21

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today’s lesson teaches the difference between concrete and unencumbered numbers… in a small poem.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

 

Doodles Do Algebra – Lesson 20

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today’s lesson teaches the next two articles, or definitions. This time all she has to do is understand the definition and use that to draw a line from the term to quantity it measures. That may not make much sense until you look at the worksheet, and then it is crystal clear.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

Doodles Do Algebra – Lesson 19

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today’s lesson is more vocabulary learning – and today it is learning the difference between multitude and magnitude. DoodlePoodle explains it best, so I will leave the worksheet to explain for itself.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

Doodles Do Algebra – Lesson 18

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

The first 17 lessons were designed to get your child thinking about algebra and doing problems, mostly in their head instead of on paper. This idea is much like having a child learn to play piano first by playing a scale, or a small memorized tune, without having to manage reading notes, counting, and playing all at once. It will give your child a sense of accomplishment to jump straight into solving problems successfully by doing the first 17 lessons before backing up to learn the theory and vocabulary.

And now we begin the second section of this program – learning the vocabulary of algebra. Understanding the terms used in algebra is important so that your child can speak the language of algebra math and understand others as well – much like it is helpful to understand basic vocabulary and phrases in French when you travel to France. (this explanation worked really well for the child of mine who counters every new lesson or idea with “why do I have to learn that?”)

Today’s activity is one of memorizing the first two definitions, or articles of algebra – at least long enough to come recite the rhymes to you. Don’t worry too much, your child will be exposed to these terms over and over so he will learn it over time, even if he cannot remember the rhyme tomorrow.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

 

Please leave any feedback you have, as always,

Doodles Do Algebra – Lesson 17

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today’s lesson is continued practice in manipulating numbers in algebraic equations, with the aim of solving for an unknown. The only new bit today is understanding that all the rules governing fractions apply when those fractions contain an unknown quantity, or “x”. The “x” just goes along for the ride!

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

 

Challenge Question Answers:

  1. 9x/7 = 18, so 9x=18*7 and x=18*7/9, or x=2*7=14
  2. 2x + 3x/7 = 14x/7 + 3x/7 = 17x/7 (this is just to show your child that the same rules of fractions apply, even when there is an unknown in the problem)

Doodle Dailies Answers:

  1. x/2
  2. x=2
  3. x=15
  4. 2x/3 = 8, so 2x=3*8=24, then x=12
  5. Here you have to recognize that Eliza is the older of the sisters, so her age is x. Ruth’s age is 3x/5 (or three fifths that of Eliza’s age). Then the sum of the ages of the sisters is x (Eliza) + 3x/5 (Ruth) and that sum is 24 years. So x + 3x/5 = 24. Then you need to change both fractions so they have a common denominator before you can add them, so 5x/5 + 3x/5 = 24. And then you can add to get 8x/5 = 24, and then 8x=24*5, x=24*5/8=3*5=15 So Eliza is 15 and Ruth is 6 (or 3/5 of 15).

As always, please leave comments when you have them.

Thanks

doodlemom

 

Doodles Do Algebra – Lesson 16

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today is a trick day – I had one child who never read instructions and so every so often I planted a lesson with an easy and quick way out of doing problems. Today is such a day: If your child reads what DoodleTwo is saying in the speech bubble, then she will know to do the one, pretty easy problem and write it above DoodleTwo’s head on the paper. If however, your child is like one of mine was, she will skip the reading and do all the problems below. Don’t get me wrong, my kids like math a lot and enjoyed the problems, but it was good to check and see if she was reading every once in a while.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

 

Answers:

main problem:(x+5)*2 = 3x, so x+5 = 3/2x, and 5=3/2x – x = 1/2x, so x=10

decoy problems:

1. 5x=3x+6, so 2x=6, and x=3

2. 5x=2x+15, so 3x=15, and x=3

3. 8x=3x+15, so 5x=15, and x=3….seeing a pattern here?

4. 10x=4x+24, so 6x=24, and x=4 (this problem is also on purpose so if you have smart kids who always look for patterns instead of doing the math, like I do, then you will be able to tell)

Please leave any feedback you have.

Thanks,

 doodlemom

Doodles Do Algebra – Lesson 15

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today DoodlePig walks your child through calculating something practical – how much money each of three boys gets from their father. The first half of the problem helps your child extract the mathematical relationships between the money each boy received and set up the problem to be solved. Then the second half of the main problem walks your child through solving the problem. At this point, the process of solving simple problems should be getting pretty easy for your child.

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

 

Answers:

1. first boy got x cents, second boy got x + 2 cents, third boy got x + 2 + 3 cents (since the third boy got 3 more cents than the second boy who got 2 more cents than the first boy), and all together the boys got 25 cents. So 3x + 7 = 25, and then 3x = 25 – 7, [intermediate steps here are first to subtract 7 from 25 to get 18, and then divide both sides of the equation by 3] and finally x=6. (just for completeness, boy 1 got 6 cents, boy 2 got 8 cents, and boy 3 got 11 cents).

2. 4 times 2x + 3 is 4 times 2x plus 4 times 3, as described a few lessons back. So the answer is 8x + 12.

3. This problem takes your child through the process of solving 5x-3 = 17. First you add three to both sides, and 5x = 20. Then you divide both sides by 5 and x=4.

 Please leave feedback, if you have any.

doodlemom

Doodles Do Algebra – Lesson 14

unknowns-and-the-29-articles-of-algebra

Update: This Lesson Is Part of Book 2 of Doodles Do Algebra: “Unknowns And The 29 Articles of Algebra” available on Amazon.

 

Teacher’s Notes:

Today’s lesson is very self-explanatory. The idea is to walk your child through the process of solving a problem, much like the ones he did over the last few lessons.

 

Worksheet:

Available in the book, “Unknowns And The 29 Articles of Algebra, Book 2 of Doodles Do Algebra

 

Answers:

number=x

add 4 to number = x+4

x+4 = 3x

and x=2.

 

As always, I appreciate feedback.

doodlemom