Multiplication Table!

Make your own multiplication table after listening to all these songs. You could memorize the whole thing in one day. I promise!

You should scan the products on a multiplication table and see how many factors it has.

Hint: Factors are highlighted in green. Products are not.

For example, find all the instances of 20 in the table noting that 2x10, 4x5, 5x4 and 10x2 all equal 20. Therefore 20 has 4 factors shown on the table:  2, 4, 5 and 10. What about 48? 32? Do some numbers have more factors than others? Yes! Do they also appear more frequently on the table? Maybe not...

Memorizing the chart as a whole ... as a picture (ie by recalling the spots of all the numbers ... ie where '20' appears ..." can be an abacus in your brain! Remember we are doing an INTENSE REVIEW. Our aim is to really learn this stuff... permanently! We are using SQR3 for this .. Survey, Question, Read, Recite, Review.

As a further exercise, you could make a frequency chart that plots each product in the table and the number of times it appears. Print out the table, Cut out the numbers and rearrange them on your frequency table.

After you finish this first day of work I want you to spend 5 minutes 3 times a day doing the Math Trainer game. It is designed to help you memorize and it's fun. By the end of our Intense Review week you will finally know your times tables. Hooray!

Challenge Problem

By the end of this course you will know how to use the Pythagorean Theorem. It is useful for determining the dimensions of some solid shapes. You will also study Integers and Measurement. When you are confident in your work I want you to consider this unsolved math problem known as the Integer Brick (or Euler's Brick): 

"Is it possible to construct a rectangular solid such that the dimensions of all sides and all diagonals including the interior diagonal through the center are integers?" 

See here for a fuller explanation http://www.durangobill.com/IntegerBrick.html. There is no youtube video for this. It's an obscure issue that very few people explore.

Please know that great mathematicians have pondered the Integer Brick. No solution has been found to date. As it happens, a person such as yourself who is new to the topic is sometimes capable of "thinking outside the box" and ends up with the right answer. It's happened before...

A 16-year-old Indian origin schoolboy in Germany has managed to crack puzzles that baffled the world of maths for more than 350 years...

COURSE OUTLINE

11 Units of Study

(Blog Usage Note: Mouseover the text on the following list to learn brief definitions for key vocabulary words.)

1. Numbers, Variables and Equations,

2. Applications of Ratio, Rate and Percent

3. Geometry and Measurement

4. Fractions and Decimals

5. Data Management

6. Circles

7. Geometry

8. Square Roots and Pythagoras

9. Integers

10. Algebra

11. Probability

Our 5 Week Study Program

Week One: Intense Review

Week Two: Units 1, 2 and 3

Week Three: Units 4, 5 and 6

Week Four: Units 7, 8 and 9

Week Five: Units 10 and 11.

You are working full time on this 5 week long course (not 4 hours a week for 10 months like a classroom+homework routine). The course requires 6 hours a day of work for 150 hours total.

Please note that Grade 6 and 7 review exercises will accompany each new Unit.

There is a daily vocabulary list to learn. This is a key component of the course. Each vocabulary word will have its definition in mouse over text as a way to identifying it for committal to your long term memory. You are responsible for looking up the definitions of vocabulary words yourself to help you learn their meanings. You should review all the vocabulary words every day.

There are daily quizzes, 15 tests, a mid-term exam and a final exam. These are designed to help you review what you recently learned and recall it a few days and then weeks later. Testing of this nature helps to move information into your long term memory so you never forget it.

Good Luck!

INTENSE REVIEW: 6 DAYS

The first six days of our 5 week math course are about reviewing math topics to prepare you to study Grade 8 material.

We will use "Complete MathSmart 4" as our working text during this review period. This doesn't mean we will focus exclusively on Grade 4 topics. In fact we will be using a junior workbook to "anchor" our review but will reach back to Grade 2 and ahead to Grades 6 and 7 as we work.

YOU CANNOT SUCCEED OR PROCEED TO OUR GRADE 8 TEXTBOOK WITHOUT DOING THIS INTENSE REVIEW. THIS STEP IS CRUCIAL.

To begin:

Open the MathSmart4 Workbook and start doing the exercises.
Google topics you don't know.
Use your calculator.
In the Intense Review blog posts I'll challenge you to reach backwards and forwards ... from Grade 2 to Grade 7.

MATHSMART4 - Section 1, Parts 1 - 7

1. Multiplication and Division Fact Families

• Note: A 'fact family' isn't a real thing: it's a teaching meme. Just learn as many facts about "x" and "/" as you can and don't worry too much about grouping them into 'families'.
• Make a Multiplication Table.
• Read Quandaries and Queries for a Grade 8 student's question about the origin of the division symbol.
• Play this game.

2. Multiplying by 10, 100 or 1000

3. Multiplication Facts to 81

4. Division Facts to 81

5. Multiplying 2-digit numbers by 1-digit numbers

6. Multiplying 3-digit numbers by 1-digit numbers

7. Multiplying 2-digit numbers by 2-digit numbers

DAY 1 VOCABULARY

NUMBER

VARIABLE

EQUATION

RATIO

RATE

PERCENT

GEOMETRY

MEASUREMENT

FRACTION

DECIMAL

DATA MANAGEMENT

CIRCLE

SQUARE ROOTS

PYTHAGORAS

INTEGER

ALGEBRA

PROBABILITY