NOVA: Math & Tech Workbook

MATH & TECH WORKBOOK

Core camp activity manual

NOVA CAMP Grade Level

6

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Copyright Š2020 by NOVA

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ISBN: 978-0-447-49429-5 Printed in the United States of America

First Edition 1 3 5 7 9 10 8 6 4 2

Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . .

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EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . .

8 8 9 10

Equations. . . . . . . . . . . . . . . . . . . . . . .

Evaluations . . . . . . . . . . . . . . . . . . . . .

Solving for variables . . . . . . . . . . . . . .

ACTIVITY . . . . . . . . . . . . . . . . . . . . . . . . . . .

Escape the room!. . . . . . . . . . . . . . . . .

Map . . . . . . . . . . . . . . . . . . . . . . . . . . .

12 12 14

Glossary/Index . . . . . . . . . . . . . . . . . . . . . .

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Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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MAT

TH &TECH When trying to find a secret number, we must do what is called “solve for the unknown,” or “solve for x.” Solving an equation or inequality is like asking, “Which value makes this statement true?”

Math & Tech

EQUATIONS

Finding the missing numbers Example:

Equation

Is x = 8 the solution for x + 12 = 20?

8 + 12 = 20 (Rewrite the equation and substitute 8 for x.)

20 = 20 Both sides are the same, so the solution (x = 8) makes the sentence true.

An equation is a mathematical sentence with an equal sign. To solve an equation, we find the missing number, or variable, that makes the sentence true. This number is called the solution.

Example: Is −6 the solution to 3x = 18?

3(−6) = 18 -18 = 18 Both sides are NOT the same, so −6 is NOT the solution!

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THE CORE CAMP WORKBOOK

Hi! I'm your substitute for this equation.

Great!

I really need a day off!

Evaluation It’s is the process of simplifying a mathematical expression by first substituting (replacing) a variable with a number, and then solving the expression using order of operations-kind of like when you have a substitute teacher. Your teacher is replaced by somebody else who does the same function.

Example: Evaluate x + 1 when x = 3.

3 + 1 = 4 (Because we know x = 3, we can take the x out and replace it with 3.)

Example: Evaluate 3y - 6 when y = 8.

3 • 8 - 6 (Because we know y = 8, we substitute y with 8. Then, we follow order of operations: In this case, we multiply first.)

24 - 6 = 18

Math & Tech

9

SOLVING FOR VARIABLES

A Balancing Act Often, we are not given a number to substitute for the variable.

This is when we must “solve for the unknown,” or “solve for x.” In order to do so, we must Isolate the variable on one side of the equal sign.

Example: x + 7 = 13 In order to isolate the variable (x) on one side of the equal sign, we must: 1. Think of an equation as a scale, with the = sign as the middle. You must keep the scale balanced at all times.

2. Ask yourself, “What is happening to this variable?” In this case, 7 is being added to the variable.

3. So, how do we get the variable alone? We use inverse operations on both sides of the equation. What is the inverse of adding 7? Subtracting 7.

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x + 7 = 13 x + 7 − 7 = 13 − 7 x=6 (We subtract 7 from both sides to keep the equation balanced.)

Inverse Inverse is just another word for opposite. Here’s a quick rundown of all the operations and their inverse operations: Addition / Subtraction Multiplication / Division Squaring / Square root Cubing / Cube root 3

KATHERINE JOHNSON was a gifted NASA mathematician. She helped calculate the trajectory of Alan Shepherd’s first trip into space in 1953.

Math & Tech

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ACTIVITY

Escape the room!

Rules

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You may use pen, paper and your knowledge of equations No phones No calculators You have two hours to escape three rooms You may ask for 3 additional clues

THE CORE CAMP WORKBOOK

The Challenge

A team of scientists has found a time capsule of secret experiments that could be vital to mankind. However, in order to open the capsule, you and your team must solve a series of puzzles to demonstrate your understanding of equations. Can you do it in time, or will the secrets stay locked in the capsule forever?

Tip Don’t be afraid to look under desks, inside boxes or behind paintings!

Math & Tech

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ACTIVITY

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Math & Tech

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GLOSSARY

D Denominator The part of a fraction that is below the line and that functions as the divisor of the number above.

Dependent variable A dependent variable represents a quantity whose value depends on how the independent variable is manipulated.

Y is often the variable used to represent the dependent variable in an equation.

Example: Let’s use the same context.

You are doing chores to earn your allowance. For each chore you do, you earn $3. What is the dependent variable? The dependent variable is the amount of money you earn because the amount of money you earn depends on how many chores you do.

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THE CORE CAMP WORKBOOK

E

I

Exponent

Independent Variable

Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the equals sign in (5)(5)(5) = 53. The exponent, being 3 in this example, stands for however many times the value is being multiplied.

The thing that’s being multiplied, being 5 in this example, is called the base. This process of using exponents is called “raising to a power”, where the exponent is the “power”. The expression “53” is pronounced as “five, raised to the third power” or “five to the third”.

An independent variable is a variable that represents a quantity that is being manipulated in an experiment.

X is often the variable used to represent the independent variable in an equation.

Example: You are doing chores to earn your allowance. For each chore you do, you earn $3. What is the independent variable? The independent variable is the amount of chores you do because this is the variable you have control over.

Isolate Expression A mathematical Expression is a combination of symbols that can designate numbers (constants), variables, operations, symbols of grouping and other punctuation.

Isolating a variable in Math means rearranging an algebraic equation so that a different variable is on its own. The goal is to choose a sequence of operations that will leave the variable of interest on one side and put all other terms on the other side of the equal sign.

N Numerator The part of a fraction that is above the line and signifies the number to be divided by the one below.

P Parenthesis One or both of the curved marks ( ) used in writing and printing to enclose a parenthetical expression or to group a symbolic unit in a logical or mathematical expression.

R Root Roots (or radicals) are the opposite operation of applying exponents; we can undo a power with a radical, and we can undo a radical with a power.

For instance, if we square 2, we get 4, and if we “take the square root of 4”, we get 2; if we square 3, we get 9, and if we “take the square root of 9”, we get 3. The symbol used is called the radical symbol. (Technically, just the “check mark” part of the symbol is the radical; the line across the top is called the vinculum.) These expressions are read as “root nine”, “radical nine”, or “the square root of nine”.

Math & Tech

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NOTES

Write notes here

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Notes

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