Name Period Date UNIT : EXPRESSIONS AND EQUATIONS WEEK 10: Student Packet 10.1 Algebraic Expressions and Equations Solve problems with money and decimals. Use variables in expressions and equations. Use the distributive property and the conventions for order of operations to evaluate expressions. Find a value that makes an equation true. Write verbal statements symbolically. 10.2 Balance Puzzles 1 Emphasize that the equal sign is a relational symbol, not a to do symbol. Establish a foundation for the concept of balance and the rules of equality prior to solving equations by symbol manipulation. Understand and use concept of a variable. 10. Fractions: Addition and Subtraction Add and subtract proper fractions using pictures and using numerical procedures. Review math concepts in prior lessons. Demonstrate competency in place value, rounding, and expanded form of decimals (highlighted review). 1 9 1 Unit 2: Rational Number Concepts (Student Packet) Week 10 SP
FOCUS ON VOCABULARY 10 Match the word(s) to the clues. Words 1. variable Clues a. A combination of numbers, variables, and operation symbols. 2. expression b. To find the number(s) or expression(s) that makes the equation true.. evaluate an expression c. Rational numbers greater than one can be written as these. 4. equation 5. solve an equation d. A number that can be written in the form a, where a and b are numbers and b b 0. e. Rational numbers between zero and one can be written as these. 6. equal sign f. 5 4 and 16 2 are examples of these. 7. rational number g. A quantity, often represented by a symbol, that may vary. 8. proper fraction h. A mathematical symbol to indicate equality. 9. improper fraction i. To replace each variable in an expression with a number and then calculate the value of the expression. 10. mixed number j. A mathematical statement that shows the equality of two expressions. Unit : Expressions and Equations (Teacher Packet) Week 10 SP0
10.1 Algebraic Expressions and Equations ALGEBRAIC EXPRESSIONS AND EQUATIONS Ready (Summary) We will write and evaluate expressions that represent the costs of items on a menu. We will find values that make equations true. Set (Goals) Solve problems with money and decimals. Use variables in expressions and equations. Use the distributive property and the conventions for order of operations to evaluate expressions. Find a value that makes an equation true. Write verbal statements symbolically. Go (Warmup) Use exactly one 4 and one -2 to make as many different expressions as you can, and find the value of each. Then, write your expression and its value as an equation. Expression Equation Example: 4 + (-2) 2 = 4 + (-2) Week 10 SP1
10.1 Algebraic Expressions and Equations PIZZA PLACE VARIABLES AND EXPRESSIONS Pizza by the slice: Cheese... Pepperoni... Deluxe... $1.00 $1.25 $1.75 Drinks: Small... Medium... Large... Extra large... $0.95 $1.20 $1.60 $1.90 Your teacher will read some orders aloud. Define your variables. Use the variables that you recorded to write expressions that match each order. Then evaluate each expression. 1. Expression: c + p Evaluate: 2. Expression: Evaluate:. Expression: Evaluate: Week 10 SP2
10.1 Algebraic Expressions and Equations PIZZA PLACE VARIABLES AND EXPRESSIONS (continued) Pizza by the slice: Cheese... Pepperoni... Deluxe... $1.00 $1.25 $1.75 Drinks: Small... Medium... Large... Extra large... $0.95 $1.20 $1.60 $1.90 Your teacher will read some orders aloud. Define your variables. Use the variables that you recorded to write expressions that match each order. Then evaluate each expression. 4. Expression: Evaluate: 5. Expression: Evaluate: 6. Expression: Evaluate: Week 10 SP
10.1 Algebraic Expressions and Equations PIZZA PLACE ORDERS You and your classmates wrote pizza orders on cards. Use the front of the card to write an expression for the cost of the order using variables. Evaluate the expression. Use the back of the card to check the solution. 1. 2.. 4. Week 10 SP4
10.1 Algebraic Expressions and Equations PIZZA PLACE EQUATIONS Pizza by the slice: Cheese... Pepperoni... Deluxe... c = $1.00 p = $1.25 d = $1.75 Drinks: Small... Medium... Large... Extra large... Find a menu item with a cost that makes the following equations true. In different s = $0.95 m = $1.20 L = $1.60 x = $1.90 problems, the need not represent the same menu item. 1. p + = c Menu item: Cost of menu item = 2. 2s = Menu item: Cost of menu item =. 2m + L = p + + c Menu item: Cost of menu item = Week 10 SP5
10.1 Algebraic Expressions and Equations PIZZA PLACE EQUATIONS (continued) Pizza by the slice: Cheese... Pepperoni... Deluxe... c = $1.00 p = $1.25 d = $1.75 Drinks: Small... Medium... Large... Extra large... Find a menu item with a cost that makes the following equations true. In different s = $0.95 m = $1.20 L = $1.60 x = $1.90 problems, the need not represent the same menu item. 4. m + 2 = 4p Menu item: Cost of menu item = 5. 4p = 5 Menu item: Cost of menu item = 6. 5s + = 2 + 2d Menu item: Cost of menu item = Week 10 SP6
10.1 Algebraic Expressions and Equations MY MENU Use a menu from a local take-out restaurant or create a menu with your own favorite foods. Identify the costs of some food items on the menu with variables. Be sure to use different letters to represent the costs of different items. Write in words at least two different orders. Write an algebraic expression to represent the cost of each of the orders. Evaluate each expression to find the cost of each order. Write two equations (using the same variables you identified) that show that the cost of the items is equal to the total cost (in dollars) for each order. Write an expression for the cost of both orders together. Evaluate the new expression to find the total cost. Write an equation (using the same variables you identified) that shows that the cost of the items is equal to the total cost (in dollars) for the combined orders. **Make a poster that creatively displays your menu and all your work.** Week 10 SP7
10.1 Algebraic Expressions and Equations FROM WORDS TO SYMBOLS Write an expression or equation to match the words. 1. The number of puppies is p and the number of kittens is k. a. Write an expression for the total number of puppies and kittens: b. Write an equation to show that there are 14 animals in all: 2. KC had x trading cards and gave away y of them. a. Write an expression for the number of trading cards she has now: b. Write an equation to show that she has 144 trading cards now:. Sarah has x ribbons. Connie has times as many ribbons as Sarah. a. Write an expression for the number of Connie s ribbons: b. Write an equation to show that Connie has a total of 51 ribbons: 4. Salim has m crackers. He puts them into 5 equal groups. a. Write an expression for the number of crackers in each group: b. Write an equation to show that each group has 4 crackers: Week 10 SP8
10.2 Balance Puzzles 1 BALANCE PUZZLES 1 Ready (Summary) We will use the concept of balance to understand the meaning of the equal sign and solve balance puzzles. Set (Goals) Emphasize that the equal sign is a relational symbol, not a to do symbol. Establish a foundation for the concept of balance and the rules of equality prior to solving equations by symbol manipulation. Understand and use concept of a variable. Go (Warmup) Find values for the circle and square that make each equation true. The shapes may have different values in different problems. 1. 4+ 6 40 = 2 2. = (19 7). 10 + = 5 4. = 4(12) 6 Week 10 SP9
10.2 Balance Puzzles 1 FIND EACH WEIGHT 1 For each puzzle: The same shapes have the same weight. Different shapes have different weights. A horizontal bar shows balance. Each problem has only one correct solution. Use the clues for help. 1. Total weight = 8 = 1 = = Verify the solution by writing a numerical equation to show that the scale is balanced: 2. Total weight = 40 = = Verify the solution by writing a numerical equation to show that the scale is balanced. Week 10 SP10
10.2 Balance Puzzles 1 FIND EACH WEIGHT 2 For each puzzle: The same shapes have the same weight. Different shapes have different weights. A horizontal bar shows balance. Each problem has only one correct solution. Use the clues for help. 1. Total weight = 64 = = = = Verify the solution by writing a numerical equation to show that the scale is balanced. 2 Total weight = 54 = 20 = = Verify the solution. Write a numerical equation to show that the scale is balanced. Week 10 SP11
10.2 Balance Puzzles 1 FIND EACH WEIGHT For the puzzle below: The same shapes have the same weight. Different shapes have different weights. A horizontal bar shows balance. Each problem has only one correct solution. Use the clues for help. 1. Total weight = 80 + = 8 + + + = = = = = = Verify the solution by writing a numerical equation to show that the scale is balanced. Week 10 SP12
10. Fractions: Addition and Subtraction SKILL BUILDER 1A Shade the appropriate portions in each problem. Then record the numbers. Words Picture Numbers 1. You have two and one-third protein bars. Shade the picture to show this amount. 1 2 = 2 + 1 2. Your friend has one and two-thirds protein bars. Shade the picture to show this amount.. You have two and one-third protein bars. Your friend gives you another one and twothirds protein bars. Shade the picture to help figure out how many protein bars you have total? 4. There are two protein bars. You eat threefifths of a protein bar. How many protein bars are left? = 2 1 = 1 + 2 1 2 2 + 1 1 2 2+ + 1+ = 2 + 1 + 1 + 2 = + = 2 5 = 1 Compute. Then place the result on the number line. (Hint: rules for integer subtraction apply.) 5. 1 1 6. 5 5-4 0-1 0 Week 10 SP1
10. Fractions: Addition and Subtraction SKILL BUILDER 1B Use pictures, if needed, to make sense of each operation. 1 1 1 7. + + 8. 9. 2 8 2 2 1 4 4 Compute each operation mentally. 1 5 10. + + 11. 8 8 1 12. 4 1 5 5 1. 1 1 2 + 1 + 2 14. 9 4 4 2 6 15. 2 7 7 16. 1 1 4 4 + 2 + 17. 5 8 5 4 9 18. 7 2 5 9 9 Week 10 SP14
10. Fractions: Addition and Subtraction SKILL BUILDER 1C Write each number as the sum or difference of an integer and of a fraction. Then label the number lines and place each number on the lines. Ex: 1 = 1+ 4 4 0 1 2 4 Ex: 1 1 1-2 = -2 + - or -2 - -2-1 0 1 19. 1 2 20. -1 1 5 5 21. - 2 5 1 22. - Week 10 SP15
10. Fractions: Addition and Subtraction SKILL BUILDER 2 Perform each operation mentally. 2 2 1 1. + + 1 2. 5 5 5 1. 8 1 2 4. 5 5. 6 1 6+ 4 + 6. 8 8 5 11 11 7. What does the 4 represent in 26.045? 8. Write 26.045 in words. Write each number in an expanded form. 9. 16.85 10. 0.024 Compute. 11. (-8 2) (-14 7) + 12. -8 1. (-16 + 8) ( 6 + (-4)) Week 10 SP16
10. Fractions: Addition and Subtraction SKILL BUILDER Perform each operation mentally. 4 1. 1 2. 8 2 4. 6 6 2 2 + 4+ 1 4. 4 2 + 1 5. 5 5 4 8 6. 9 9 7 8 9 Round to the nearest hundredth. 7. 48.02 8..6172 9. 56.748 Write in expanded form. 10. 0.7 + 0.01 11. 0.4 + 0.0 + 0.001 12. Order these numbers from least to greatest. 0.75, 7, 8, 0.25, 1,,,, 1. Circle the composite numbers. 2 11 6 9 21 14. Circle the prime numbers. 7 14 60 169 Week 10 SP17
10. Fractions: Addition and Subtraction TEST PREPARATION 10 Show your work on a separate sheet of paper and choose the best answer. 1. Evaluate 2x + 6x + 17 for x = -4. A. -15 B. -1 C. 1 D. 15 2. What is the weight of each circle if the total weight is 80? E. 40 F. 20 G. 10 H. 5. Compute 4 5. 7 A. 1 7 B. 1 6 C. 5 7 D. 4 7 4. What is the place value of the underlined digit in 82.194? E. tens F. tenths G. hundreds H. hundredths 5. Which of these numbers has the greatest value? A. 2 - B. 2 - C. -0.6 D. -0.6 6. Which one of these is the prime factorization of 48? E. 4 8 F. 2 2 2 2 G. 6 8 H. 2 2 2 Week 10 SP18
10. Fractions: Addition and Subtraction This page is left intentionally blank for notes. Week 10 SP19
10. Fractions: Addition and Subtraction This page is left intentionally blank for notes. Week 10 SP20
10. Fractions: Addition and Subtraction KNOWLEDGE CHECK 10 Show your work on a separate sheet of paper and write your answers on this page. 10.1 Algebraic Expressions and Equations 1. Evaluate 4x 6 for x = 5. 2. Solve for x: 4x = 21 + x 10.2 Balance Puzzles 1 Find the weight of each shape. Then write a numerical equation to show that each scale is balanced.. 4. Total weight = 24 = 8 = = Total weight = 68 = 10 = = 10. Fractions: Addition and Subtraction Compute each sum or difference mentally. 5. 1 5 + 2 6. 7 7 2 7. 7 6 8 9 9 Highlighted Review: Decimals: Place Value, Rounding, and Expanded Form 8. Round 68.245 to the nearest tenth. 9. Write 12.07 in three different expanded forms. Week 10 SP21
10. Fractions: Addition and Subtraction Home-School Connection 10 Here are some questions from this week s lessons to review with your young mathematician. 1. Evaluate 7 + 12(x 4) for x = 5. 2. Compute 1 mentally. 5. Find the weight of each shape. Then write a numerical equation to show the scale is balanced. Total weight = 16 = 7 = = Parent (or Guardian) signature Selected California Mathematics Content Standards NS 6.2.1 AF 4.2.1 AF 4.1.1 AF 6.1.0 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Know and understand that equals added to equals are equal. Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable). Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. Week 10 SP22