Unit 1

1. Unit 1 Patterns & Relations

2. Answering questions from last class…

3. What is the Big bang theory? • Story of the creation of the universe. • Most astronomers believe the Universe began in a Big Bang about 14 billion years ago. • At that time, the entire Universe was inside a bubble that was thousands of times smaller than a pinhead. • It was hotter and denser than anything we can imagine. • Then it suddenly exploded. The Universe that we know was born.

5. Time, space and matter all began with the Big Bang. • In a fraction of a second, the Universe grew from smaller than a single atom to bigger than a galaxy. • And it kept on growing at a fantastic rate. It is still expanding today. • Extension Activity Big Bang Theory

6. How are Math and big bang theory connected? • The universe has a natural mathematicality. • The universe is mathematically consistent. • The natural phenomena physics seeks to describe and explain, are the results of the natural mathematicality. • To put it more simply… math is used to check physics!

7. Why do we use the decimal (10) system? • Not an “accident”. There is no mistaking the influence of our “10 fingers” on the selection of the base of our number system. • Called the “anthropomorphic nature” of our counting scheme. • Anthropomorphic: crediting human form or characteristics/attributes to something not human.

8. Math experts state that almost any other base (other than 10), with the possible exception of 9, would have done at least as well as 10, and some much better. • The reason is a base with the greatest number of divisors (such as 12), or a prime number (7,11, 13) would be “easier” or more effective. • Math is supposed to make the complicated, simple & understandable. • It is interesting that CULTURALLY, we chose something that is near & dear to us (10 fingers) over what works best.

9. Why pi is (actually) important • 3.14 • Pi (π) is the ratio of the circumference of a circle to its diameter. It doesn't matter how big or small the circle is - the ratio stays the same. Properties like this that stay the same when you change other attributes are called constants. • Because it's so easily observed (you can measure it with a piece of string!), Pi has been popular for centuries.

10. It turns out pi is an "irrational number," meaning its exact value is inherently unknowable. • Computer scientists have calculated billions of digits of pi, starting with 3.14159265358979323…, but because no recognizable pattern emerges in the succession of its digits, we could continue calculating the next digit, and the next, and the next, for millennia, and we'd still have no idea which digit might emerge next. • The digits of pi continue their senseless procession all the way to infinity.

11. Ancient mathematicians apparently found the concept of irrationality completely maddening. • It struck them as an affront to the omniscience of God, for how could the Almighty know everything if numbers exist that are inherently unknowable?

12. What are we doing today?

13. Key Terms, page 5 • Divisibility rules • Algebraic expression • Numerical coefficient • Constant term • Relation • Linear Relation • Unit tile • Variable tile • Algebra tiles

14. Questions to answer in groups • What do you THINK the term means? • Definition • Why or why not? Is it important? • Do you UNDERSTAND the term/concept?

15. This powerpoint is on virtual classroom, but do YOU still need to take notes? • How do you use an “index”?

16. Divisibility rules (pages 6-12) • These rules let you test if one number is divisible by another, without having to do too much calculation! • Help us to find the factors of a number. • Factors are the numbers you multiply to get another number: 2 (factor) x3 (factor) = 6 • Extension Exercise Divisibility Rules

17. Algebraic expression • 3x^2 - 2xy + c is an algebraic expression. • 6x – 4 is an algebraic expression. • An algebraic expression is a mathematical expression containing a variable. • A variable in math is a symbol for a number we don't know yet. It is usually a letter like x or y. • Example: in x+ 2, x is the variable. If it is not a variable it is called a Constant.

18. Numerical coefficient • A number used to multiply a variable. • Example: 6x means 6 times x, and ”x" is a variable, so 6 is a coefficient. • Could use any letter for a variable in the same algebraic expression, and the answer would be the same! • 6x – 4 • 6z – 4 • 6a – 4 • 6m – 4

19. Constant term • 4x + 3, 3 is the constant term. • The number in the expression that does not change. • A constant is a fixed value. • In Algebra, a constant is a number on its own (or sometimes a letter such as a, b or c to stand for a fixed number)

20. So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"

21. relation • When we compare or “relate” a variable to an expression that contains the variable, we have a RELATION. • 10 + 6n is related to n • You will experience the term “relation” as having several different meanings in math.

22. Linear relation • You will hear this term when you are graphing relations (so… you’re going to need graph paper in this unit!! Check your course outline to see what kind of graph paper you need and make sure you have some asap!) • When graphed, a set of points that lie on a straight line have a linear relation.

24. Algebra Tiles • We can use tiles to represent an expression visually. • Together, unit tiles and variable tiles are algebra tiles

25. Unit tile • A tile that represents -1 or +1

26. Variable tile • A tile that represents x • Can be called an “x” tile, or a variable tile. • Unit and Variable Tiles

27. Read Independently • Math Makes Sense… pages 5-8 • Practice, pages 8 & 9, #s 1-7