IMPORTANT WORDS TO KNOW UNIT 1

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IMPORTANT WORDS TO KNOW UNIT READ THESE WORDS ALOUD THREE TIMES WITH YOUR TEACHER! Chapter. equation. integer 3. greater than 4. positive 5. negative 6. operation 7. solution 8. variable Chapter.

1 IMPORTANT WORDS TO KNOW UNIT READ THESE WORDS ALOUD THREE TIMES WITH YOUR TEACHER! Chapter. equation. integer 3. greater than 4. positive 5. negative 6. operation 7. solution 8. variable Chapter. ordered pair. parentheses 3. coordinate plane 4. axis 5. horizontal 6. vertical 7. quadrant Chapter 4. value. diagonal 3. column 4. important 5. solve Chapter 5. pattern. finite Chapter 6. formula. function 3. group 4. functional notation Chapter 3. location. coordinate 3. infinite Illegal to copy

Algebra is part of real life. REAL LIFE UNIT Do you like to go places? Do you like to play games like Battleship? Do you like to draw? Do you like to go to the mall? Do you like to make money?

2 Algebra is part of real life. REAL LIFE UNIT Do you like to go places? Do you like to play games like Battleship? Do you like to draw? Do you like to go to the mall? Do you like to make money? Do you like to be outside? Do you like to know if it is going to rain or be sunny? All these things have to do with algebra. The Game: Check (3) the things that you have done. looked at a map played Battleship played baseball sat on a brick wall sat on a deck saw a weather report on TV crossed a road mowed a yard played football played Checkers Illegal to copy

3 START WITH NUMBER LINES Use number lines to compare integers, do operations, and graph solutions to equations with one variable. UNIT The numbers on the number line are called integers. Zero is in the middle. Positive numbers are to the right of zero. Negative numbers are to the left of zero. Graph 5 To graph 5, start at zero and move left to find 5. Place a dot there. The Game: Graph the integers on the number lines. Graph 7 Graph 0 Graph 5 and 8 Illegal to copy 3

4 COMPARE Integers to the right are greater than those to the left. UNIT Use these symbols to compare numbers: > means greater than means greater than or equal to < means less than means less than or equal to Compare 8 and The number line shows 8 to the right of on the positive side. This means the integer 8 is greater than. 8 > Math fact: The small part of the arrow points to the smaller integer: 8 >. Use a number line to compare positive and negative integers. Compare < 3 On the number line, 3 is to the left of 3, so 3 is less than 3. Math fact: A positive integer is always greater than a negative integer! The Game: Compare these integers. Look at a number line. Write > or < in the blanks Illegal to copy 4

GRAPH THE ANSWERS Graph solutions to equations with one variable. x = 3 x > 3 x 3 UNIT Use a letter instead of a number! A variable is a letter that you can use for a number.

5 GRAPH THE ANSWERS Graph solutions to equations with one variable. x = 3 x > 3 x 3 UNIT Use a letter instead of a number! A variable is a letter that you can use for a number. x = 3 The only solution is 3. Use a dot to graph 3 on the number line. x > 3 This means that x is greater than 3. It can have many answers! Anything greater than 3 is part of the solution. Is 3 part of the solution? Use an open dot to show that 3 is not part of the solution. x 3 This means that x is equal to or greater than 3. Is 3 part of the solution? Use a closed dot to show that 3 is part of the solution. Illegal to copy 5

6 GRAPH SOLUTIONS Graph solutions to equations with one variable. x = x > x x UNIT If the only solution is, use a dot to graph. x = If the solution is anything greater than, use an open dot to show that is not part of the solution. x > If the solution is and anything greater than, use a closed dot. x If the solution is and anything less than, use a closed dot. x The Game: Graph the solutions. x = x > x x Illegal to copy 6

7 COORDINATE GRAPHS A coordinate graph is a fancy name for a drawing. It is a way to plot numbers to know more about what is going on. Coordinates are numbers that show where a point is on a graph or map. UNIT Lunch! You plan to meet your friend for lunch. You will meet at Street 3 and Lane 4. Lane Street Start at 0. Move right to Street 3. Then move up to the spot where Street 3 crosses Lane 4. You will meet your friend here. Put a dot. The coordinates are 3 and 4. The Game: You will meet your friend at Street and Lane 4. Put a dot where you will meet your friend. Lane Street What are the coordinates? What are numbers called that show where a point is on a graph? Illegal to copy 7

FIND THE SLOPE Builders, artists, and wallpaper hangers need to know if lines are perpendicular. The slopes of perpendicular lines are the negative reciprocals of each other.

8 FIND THE SLOPE Builders, artists, and wallpaper hangers need to know if lines are perpendicular. The slopes of perpendicular lines are the negative reciprocals of each other. Flip and change the sign of a number to get the negative reciprocal. Write the equation for Line A to find out if Line A is perpendicular to Line B, y = x + 3. Line A includes the y-intercept 3. First find the negative reciprocal of. Flip and change! p _ or y = mx + b Plug in the slope. p y = x + b Plug in the y-intercept. p y = x +3 Line A, y = x +3, is perpendicular to Line B, y = x + 3. TRUE? Line B Line A UNIT 3 The Game: Fill in the blanks. Find out if Line A is perpendicular to Line B, y = 4x + 0. Line A includes the y-intercept 0. First find the negative reciprocal of 4. Flip and change! p or 4 y = mx + b Plug in the slope. p y = x + b Plug in the y-intercept. p y = 4x + Line A, y = 4x +0, is perpendicular to Line B, y = x + 0. TRUE? Line B Line A Illegal to copy 90

USE THE POINT Plug in the ordered pair to find out if the point is the solution to the system. Plug in the coordinates of the ordered pair. (, ) Line A p x = Line B p y = x + 0 Plug in x and y.

9 USE THE POINT Plug in the ordered pair to find out if the point is the solution to the system. Plug in the coordinates of the ordered pair. (, ) Line A p x = Line B p y = x + 0 Plug in x and y. p = () + 0 Plug in x and y. p = () + 0 Work it! p = + 0 Work it! p = + 0 Simplify. p = TRUE Simplify. p = TRUE Each equation is true. (, ) is the solution. Is (, ) the solution to the system? The Game: Fill in the blanks. Plug in the coordinates of the ordered pair. (, ) UNIT 4 Line A p y = 3x Line B p y = x + Plug in x and y. p = 3( ) Plug in x and y. p = () + Work it! p = 3 Work it! p = + Simplify. p = TRUE! Simplify. p = TRUE! Is each equation true? Is (, ) the solution to the system? Illegal to copy

BE SMART It is smart to look at data. You can make decisions that help you get what you want in life. Liz buys snacks Monday through Friday. Monday $.50 Tuesday $4.00 Wednesday $3.00 Thursday $.

10 BE SMART It is smart to look at data. You can make decisions that help you get what you want in life. Liz buys snacks Monday through Friday. Monday $.50 Tuesday $4.00 Wednesday $3.00 Thursday $.50 Friday $4.00 Total $5.00 Divide by the number of days. p 5 5 = 3 The mean is $3.00. The average amount that Liz spends each day is $3.00. $3.00 x 0 days = $60.00 Liz spends an average of in a month. $60.00 x months = $70.00 She spends an average of in a year. Wow! That's a lot of money! Liz decides to bring snacks from home and save money. The Game: Fill in the blanks. Think about buying lunch at a cafe Monday through Friday. Monday $ 5.00 Tuesday $0.00 Wednesday $ 5.00 Thursday $ 5.00 Friday $0.00 Total $ Divide by the number of days. p 5 = 7 The mean is. The average amount spent each day is $7.00. UNIT 5 $7.00 x 0 days = $ You spend in a month. $40.00 x months = $ You spend in a year. If you brought lunch from home, you would save $, in one year. What would you do with that money? Illegal to copy 9

Show off with fancy math words! BIG WORDS Statistics is a fancy math word. It means to gather and study information. Example: The U.S. government has a record of every baby born in the U.S. That data is grouped in many ways.

11 Show off with fancy math words! BIG WORDS Statistics is a fancy math word. It means to gather and study information. Example: The U.S. government has a record of every baby born in the U.S. That data is grouped in many ways. One way is by year, sex, and name. The results are reported. In the 990s, the most popular name for a boy was Michael. The most popular name for a girl was Jessica. In the 890s, the most popular name for a boy was John. The most popular name for a girl was Mary. You can be a statistician! There are four easy steps:. Get data.. Organize the data. 3. Study it. 4. Report what you learned. The Game: Match the word with the meaning. mean median organize data information the regular average of a set of numbers middle value of a set of numbers to put in order UNIT 5 range statistics mode statistician most frequent number in a set of numbers the difference between the values (highest minus lowest) collecting, organizing, studying, and telling about data person who collects, organizes, studies, and reports about data Illegal to copy 46

TELLING THE FUTURE Look at trends to predict the future. You can predict the future! Not really, but you can have an idea about what might happen. 5" 4" 3" " " Example: It began to rain at noon. By p.

12 TELLING THE FUTURE Look at trends to predict the future. You can predict the future! Not really, but you can have an idea about what might happen. 5" 4" 3" " " Example: It began to rain at noon. By p.m., it had rained one inch. By p.m., it had rained two inches. p.m. p.m. 3p.m. 4p.m. 5p.m. If it keeps raining at the same rate, how much rainfall will there be by 3 p.m.? The Game: Plot the rainfall, graph the line, and fill in the blanks. It began to rain at noon. By p.m., it had rained one inch. By p.m., it had rained two inches. By 4 p.m., it had rained a total of four inches. Plot the rainfall. Draw a line through the points. 5" 4" 3" " " It keeps raining! What do you think the total rainfall will be at 5 p.m.? What do you think the total rainfall will be at 6 p.m.? p.m. p.m. 3p.m. 4p.m. 5p.m. UNIT 5 Do you predict that there is a chance of a flood? What is another word for guess or foretell? Illegal to copy 50

Show data on a stem-and-leaf plot. STEM AND LEAF A stem-and-leaf plot is one way to read data. Think about people swimming in a pool. Their ages are, 8,, 30, and.

13 Show data on a stem-and-leaf plot. STEM AND LEAF A stem-and-leaf plot is one way to read data. Think about people swimming in a pool. Their ages are, 8,, 30, and. The digits in the tens place are the stems. The digits in the ones place are the leaves. List the numbers in order. p, 8,,, 30 List the tens-place digits under STEM. List the ones-place digits under LEAVES. STEM LEAVES, 8, 3 0 The Game: Fill in the blanks. Five people are playing basketball. Their ages are 6, 4, 0, 33, and. STEM LEAVES List the numbers in order. p 4, 6, 0,, List the tens-place digits under STEM. List the ones-place digits under LEAVES. 4, 6 0, 3 UNIT 5 What does a stem-and-leaf plot show? Illegal to copy 5

Section Graphs and Lines

Section Graphs and Lines Section 1.1 - Graphs and Lines The first chapter of this text is a review of College Algebra skills that you will need as you move through the course. This is a review, so you should have some familiarity