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Order of Operations & Expressions

+, -, x, / Integers

Coordinate Planes

Patterns Vocabulary

Order of Operations and expressions for $100

What does PEMDAS stand for?

Answer

ParenthesisExponentsMultiplicationDivisionAdditionSubtraction

Back

Order of Operations and expressions for $200

Does Multiplication always come before Division? How are they solved?

Answer

No, they are solved from left to right.

Back

Order of Operations and expressions for $300

Write and expression to represent the following:

Joe has 5 less than three times the number of pencils that Jean has.

Answer

Let x = the number of pencils that Jean has, then the number that Joe has is:

3x - 5Back

Order of Operations and expressions for $400

What is the difference between an expression and an equation?

Answer

An expression does not have an equal sign, an equation does.

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Order of Operations and expressions for $500

Use order of operations to simplify:

3*|-4 +2| - 5*(-3 + 1) + 32

Answer

3*|-4 +2| - 5*(-3 + 1) + 32

= 3*|-2| - 5*(-2) + 32

= 3*2 – 5*-2 + 9

= 6 - -10 + 9

= 6 + 10 + 9

= 25

Back

+, -, x, / Integers for $100

Simplify:

(-6) – (-3)

Answer

(-6) – (-3) = -6 + 3 = -3

Back

+, -, x, / Integers for $200

Simplify:

(12) / (-3)

Answer

(12) / (-3) = -4

Back

+, -, x, / Integers for $300

Simplify:

(-7) * (4) / (-2)

Answer

(-7) * (4) / (-2) = -28/-2 = 14

Back

+, -, x, / Integers for $400

Simplify:

(-7 - 4) * (2 - -6)

Answer

Back

(-7 - 4) * (2 - -6) = -11 * 8 = -88

+, -, x, / Integers for $500

Simplify:

(22)/ (-2) * (4) / (-11) + -5

Answer

(22)/ (-2) * (4) / (-11) + -5

= -11*4/-11 + -5

= -44/-11 + -5

= 4 + -5

= -1

Back

Patterns for $100

What are the next two numbers in the following pattern?

2, -6, 18, -54…

Answer

The pattern is multiply by -3 every time, so the next two numbers in the pattern are:

-54*-3 = 162 and162*-3 = -486

Back

Patterns for $200

Are answers found using inductive reasoning always correct? Why or why not?

Answer

No, answers based on inductive reasoning are simply guesses based on perceived patterns. In actuality, there could be multiple correct patterns, or no pattern at all.

Back

Patterns for $300

Write a rule for the following pattern:

3, 5, 8, 12, …

Answer

Start with 3, then add 2. Add 3 the second time, 4 the 3rd time, etc. In other words increase the number you are adding by one each time.

Back

Patterns for $400

How many black triangles are going to be in the fifth (5th) picture?

Answer

The pattern is multiply by three:

1 x 3 = 3

3 x 3 = 9

9 x 3 = 27

27 x 3 = 81Back

Patterns for $500

The Fibonacci sequence was first published in 1202 by a man named Leonardo of Pisa. The first terms of the sequence are given below. Find the next three terms.

1, 1, 2, 3, 5, 8, 13, 21….

Answer

The pattern is that the next number equals the sum of the two numbers that come directly before it.

1+1 = 2, 1+2 = 3, 3+3 = 5, etc.So, 13+21 = 34, 21+34 = 55, and

34 + 55 = 89

Back

Vocabulary for $100

Define the following word:

Constant

Answer

Constant- Any quantity or value that does NOT change

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Vocabulary for $200

Define the following word:

Expression

Answer

Expression – A mathematical phrase that represents a quantity that may contain variables, numbers, and/or operators, but NO statement of equality.

Back

Vocabulary for $300

Define the following word:

Variable

Answer

Variable – A quantity that can change or take on different values

Back

Vocabulary for $400

Define the following word:

Quadrants

Answer

Quadrants – The four sections into which the x-y plane is divided by the x and y axes.

Back

Vocabulary for $500

Define the following word:

Origin

Answer

Origin – The intersection of the x and y axis in a coordinate plane. Labeled as the point (0, 0)

Back

Coordinate Planes for $100

Write the ordered pair for point B:

Answer

(-2, -4)

Back

Coordinate Planes for $200

Draw and label the quadrants on a coordinate plane.

Answer

Back

Coordinate Planes for $300

Graph the points (-2, 4) and (3, -2) on a coordinate plane.

Answer

Back

Coordinate Planes for $400

What information must be on every coordinate plane?

Answer

1) x and y axis (labeled)

2) Arrows on the ends of the axes

3) Evenly spaced tick marks (correctly numbered)

Back

Coordinate Planes for $500

Graph the following points and connect them to form a shape. Label each point correctly.

A:(-1, -2); B:(-1, 4); C:(4, 4); D:(4, -2)

Answer

Back

B C

A D