# Advanced Math Chapter 1: Exploring and Communicating Mathematics.

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Advanced Math Chapter 1: Exploring and Communicating Mathematics

Section 1.2: Investigating Patterns A variable is a letter used to represent one or more numbers.

Sample 1 Peter earns \$12 an hour. Write a variable expression for the amount he earns in h hours. Look for pattern… 12 (1) = 12 12 (2) = 24 12 (3) = 36 Increasing each time by 12…. 12h Try this one on your own… Hitesh walks 3 miles in 1 hour. Write a variable expression for the number of miles he walks in h hours. 3h

Sample 2 A row of triangles is built with toothpicks. Write a variable expression of the perimeter of Shape N. Try this one on your own… A row of squares is built with toothpicks. Write a variable expression for the perimeter of Shape N.

Sample 3: Evaluating Variable Expressions Suppose a kudzo vine grows 12 inches a day. How long is the vine after each number of days? 7 : 12 (7) = 84 inches 30 : 12 (30) = 360 inches 365 : 12 (365) = 4380 inches Try this one on your own… Hector works 8 hours each day. How many hours does he work for the given number of days? 8 90 1000 64 hours 720 hours 8000 hours

Section 1.3: Patterns with Powers Numbers multiplied together are called factors. When the same number is repeated as a factor, you can rewrite the product as a power of that number. The repeated factor is the base, and the number of times it appears as a factor is the exponent.

Sample 1 Write the product as a power. Then write how to say it – in words. 2x2x2x2x2x2x2x2 6x6x6x6x6 Try these on your own… 3x3x3x3x3x3x3 three to the seventh power 8x8x8x8x8x8x8x8x8x8 eight to the tenth power

Sample 2 Write an expression for the area covered by the tiles. Evaluate your expression for each value of x. X = 5 X = 10

Try this one on your own… Write an expression for the area covered by the tiles. Evaluate your expression for each value of x. X = 4 29 X = 8 89

Counterexamples A counterexample is an example that shows that a statement is false. Conjectures about Powers of Ten A conjecture is a guess based on your past experiences. Make a conjecture about the number of zeros you need to write out 10 to the 9 th power.

Sample 3 Larry makes a conjecture that x squared is greater than x for all values of x. Find a counterexample. You only need to find 1 example that makes it a false statement. Start at 0. Try this one on your own… Nina makes a conjecture that x cubed is greater than x squared for all values of x. Find a counterexample. X = 1

Section 1.4: Writing and Evaluating Expressions The order of operations are a set of rules people agree to use so an expression has only one answer. P.E.M.D.A.S. – Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Sample 1 Calculate according to the order of operations. Try this one on your own… 11

Sample 2 Insert parentheses to make each statement true. 4 + 16 / 2 + 3 x 5 = 20 4 + 16 / 2 + 3 x 5 = 59 Try these on your own… 2 + 8 / 4 + 6 x 3 = 22 2 + (8 / 4) + (6 x 3) = 22 2 + 8 /4 + 6 x 3 = 3 (2 + 8) / (4 + 6) x 3 = 3

Sample 3 Write an expression for the area covered by the tiles. Evaluate the expression when x = 5.

Try this one on your own… Write an expression for the area covered by the tiles. Evaluate the expression when x = 4. 55 square units

Section 1.5: Modeling the Distributive Property Sample 1 Find each product using mental math. 7(108) 7 x 100 + 7 x 8 700 + 56 756 15(98) 15 x 100 – 15 x 2 1500 – 30 1470 Try these on your own… 9 (999) 9 x 1000 – 9 x 1 9000 – 9 8991 12 (1003) 12 x 1000 + 12 x 3 12000 + 36 12036

Sample 2 Illustrate expression 3 (x + 2) using algebra tiles. Rewrite the expression without parentheses. 3x + 6

Try this one on your own… Illustrate the expression 4(x + 1) using algebra tiles. Then, rewrite the expression without parentheses. 4x + 1

Combining Like Terms The numerical part of a variable term is called a coefficient. Terms with the same variable part are called like terms. You use the distributive property in reverse to combine like terms.

Sample 3 Simplify… 5 ( x + 4) – 3x 5x + 20 – 3x 2x + 20 Try this one on your own… Simplify… 4 ( x + 3) – 2x 4x + 12 – 2x 2x + 12

Section 1.6: Working Together on Congruent Polygons Two figures that have the same size and shape are called congruent. Slide = Translation Turn = Rotation Flip = Reflection Vertex = Corner Two sides that have the same length are called congruent sides.

Exploration 1 How many different ways can you divide a square into four identical pieces? Use only straight lines. Square can only use 25 dots. 5 Minute Time Limit

Exploration 2 Can you work with others to find new ways to divide the square? 4 people in a group 10 Minute Time Limit

Section 1.7: Exploring Quadrilaterals and Symmetry