MATH AND ASTRONAUTS WRITING ALGEBRAIC EXPRESSIONS SOME NOTABLE

MATH AND ASTRONAUTS WRITING ALGEBRAIC EXPRESSIONS

SOME NOTABLE ASTRONAUTS IN SPACE Neil Armstrong Guion S. Bluford, Jr. ele Mae Carol Jemison Franklin Chang-Diaz John B. Herrington

EATING FOOD WITHOUT GRAVITY… Food and drink are packaged in containers that are easy to hold. Astronauts can drink the fluids and eat from the packages easily.

THEY CAN ALSO HAVE WHOLE SOLID FOODS, BUT THEY SOMETIMES FLOAT AWAY! Astronauts need to use problem-solving skills to solve problems. So do we! Today, we will learn how to write algebraic expressions.

FOR OUR MATH LESSON TODAY, YOU’LL NEED TO BE ABLE TO. . . Find the value of each expression. Take a moment to copy each problem into your notebook. Then solve. 1. 40 – 16 ÷ 2 2. 3 X 5 + 12 ÷ 3 3. 7 X (9. 5 – 3. 2) 4. 48 ÷ (5. 8 + 6. 2)

FOR OUR MATH LESSON TODAY, YOU’LL NEED TO BE ABLE TO. . . Find the value of each expression 1. 40 – 16 ÷ 2 32 2. 3 X 5 + 12 ÷ 3 19 3. 7 X (9. 5 – 3. 2) 44. 1 4. 48 ÷ (5. 8 + 6. 2) 4

NEW VOCABULARY Numerical expression Algebraic expression Variable Evaluate

INVESTIGATION: PATTERNS AND ALGEBRAIC EXPRESSIONS In each diagram, segments already join point A to the points next to it on the circle. Copy each diagram. Join A to the other points.

COPY AND COMPLETE THE TABLE USING YOUR DRAWINGS FROM PART 1. Number of points on circle Number of segments drawn to other points 4 5 6 ? ? ? Extend you table to include 7 points and 8 points on a circle. How many segments would you draw for n points on a circle?

INVESTIGATION: PATTERNS AND ALGEBRAIC EXPRESSIONS In each diagram, segments already join point A to the points next to it on the circle. Copy each diagram. Join A to the other points. 4 points Lines Drawn 1 5 points 6 points 2 3

COPY AND COMPLETE THE TABLE USING YOUR DRAWINGS FROM PART 1. Number of points on circle Number of segments drawn to other points 4 5 6 1 2 3 Extend you table to include 7 points and 8 points on a circle. How many segments would you draw for n points on a circle?

COPY AND COMPLETE THE TABLE USING YOUR DRAWINGS FROM PART 1. Number of points on circle Number of segments drawn to other points 4 5 6 1 2 3 Extend you table to include 7 points and 8 points on a circle. How many segments would you draw for n points on a circle? 4; 5 n– 3

NEW VOCABULARY Numerical expression: a mathematical phrase with only numbers and operation symbols (+, -, X, ÷). Here are some examples of numerical expressions: 8+5– 2 25 X 4 – 9² X 13 (7 – 6 ÷ 3) X 12

THE FOLLOWING MATHEMATICAL EXPRESSIONS HAVE SYMBOLS THAT REPRESENT UNKNOWN NUMBERS: n+2 5 d 7 b – 2 12 x ÷ 3 In the expressions above, n, d, b, and x are variables. A variable is a symbol that represents one or more numbers. A mathematical expression with one or more variables is an algebraic expression.

You can model algebraic expressions using algebra tiles. A yellow tile represents 1. A green tile represents a variable.

From Expressions to Algebra Tiles Model the expression 5 x + 3 with algebra tiles. 5 green tiles represent 5 x, and 3 yellow tiles represents 3 1. Draw algebra tiles to model each expression. a. 3 x b. x ÷ 2 c. 4 x + 3

1. Draw algebra tiles to model each expression. a. 3 x b. x + 2 c. 4 x + 3

To evaluate an algebraic expression, you replace each variable with a number. Use the order of operations to simplify the expression. Example: Evaluating Algebraic Expressions Evaluate 2 x – 8 for x = 11 2 x – 8 = 2(11) – 8 Replace x with 11 = 22 – 8 Multiply 2 and 11 = 14 Subtract 8 from 22

Check for Understanding: Evaluate each expression for x = 7. a. 3 x + 15 b. 5 x ÷ 7 c. 56 – 4 x d. Reasoning Explain how you used the order of operations to evaluate the expression in part (c).

Check for Understanding: Evaluate each expression for x = 7. a. 3 x + 15 b. 5 x ÷ 7 c. 56 – 4 x 36 5 28 d. Reasoning Explain how you used the order of operations to evaluate the expression in part (c). x was replaced by 7; 7 was multiplied by 4; 28 was subtracted from 56

REAL WORLD PROBLEM SOLVING Imagine an astronaut went to space. For each day in space, the astronaut had 3 packets of food per day. The expression 3 p represents the amount of packets used per day. Complete the table for the given number of days in space. Number of Days in Space 1 15 40 60 Number of Food Packets Eaten 3 p Substitute each number of days for s 3 x 15 = 45 3 x 40 = 120 3 x 65 = 195

CHECK FOR UNDERSTANDING… • How much will the club earn if they sell 85 subscriptions?

CHECK FOR UNDERSTANDING… • How much will the club earn if they sell 85 subscriptions? $255

MORE THAN ONE WAY…. • Recently, NASA placed a device on Mars called the Curiosity Rover which takes ground samples. The Rover began taking samples 10 feet away from where it landed. Then it moved 4. 5 feet per every minute and took another sample. How far from the landing site did the Rover move in all, if it moved 10 feet, and then 4. 5 feet per minute, and traveled for 8 minutes?

FIRST WAY: To find the number of feet in 8 minutes, use the algebraic expression 10 + 4. 5 m, with m representing the number of minutes. Then, evaluate the expression for m = 8. 10 + 4. 5 m = 10 + 4. 5(8) = 10 + 36 = 46 Replace m with 8 Multiply 4. 5 and 8 Add 10 and 36 The Curiosity Rover traveled 46 feet.

SECOND WAY: If the Curiosity Rover traveled 4. 5 feet in one minute, then in two minutes, it will travel 9 feet. After four minutes, it will have traveled 18 feet. After eight minutes, it will have traveled 36 feet. I also need to add the 10 feet it traveled from where it landed to where it began taking samples. So the total number of feet would be 36 + 10 = 46 ft.

YOU TRY IT… Choose a Method The Curiosity Rover will take samples on the other side of the landing site. This time, it moves only 5 feet from the landing site, and then begins taking samples every 4 feet per minute. Find how many feet it will travel in 10 minutes. Explain why you chose this method.

YOU TRY IT… Choose a Method The Curiosity Rover will take samples on the other side of the landing site. This time, it moves only 5 feet from the landing site, and then begins taking samples every 4 feet per minute. Find how many feet it will travel in 10 minutes. 45 feet Explain why you chose this method. Share out

Turn to Page 71 in your math text. Complete problems: 1 and 2 9 through 12 17 18 through 23 28 through 30