Apply and extend previous understandings of arithmetic to algebraic expressions. Draft

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1 6th Grade - Expressions and Equations 1 Standard: 6.EE.1 No Calculator: Write and evaluate numerical expressions involving whole-number exponents The population of fruit flies increases by a factor of 200 each week. Write an expression to represent this situation. How many fruit flies will there be after five weeks if you start with 50 fruit flies?

2 6th Grade - Expressions and Equations 2 Standard: 6.EE.1 Difficulty: Easy Write and evaluate numerical expressions involving whole-number exponents. Evaluate:

3 6th Grade - Expressions and Equations 3 Standard: 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. Evaluate the numerical expression

4 6th Grade - Expressions and Equations 4 Standard: 6.EE.2.a Difficulty: Easy Write, read, and evaluate expressions in which letters stand for numbers. A. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. Write the numerical expression for the written expression: The sum of twenty-five and a number, divided by 3.

5 6th Grade - Expressions and Equations 5 Standard: 6.EE.2.a Difficulty: Easy Write, read, and evaluate expressions in which letters stand for numbers. A. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. Write the numerical expression for the written expression: The quotient of 10 and 3 added to 25.

6 6th Grade - Expressions and Equations 6 Standard: 6.EE.2.a Difficulty: Easy Write, read, and evaluate expressions in which letters stand for numbers. A. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. Write the numerical expression for the written expression: Ten less than a number, summed to 15.

7 6th Grade - Expressions and Equations 7 Standard: 6.EE.2.a Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. Write an algebraic expression for the following: A piece of yarn that is x inches in length is cut into 8 equal pieces. How long is each piece of string?

8 6th Grade - Expressions and Equations 8 Standard: 6.EE.2.a Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. Jake collected 85 cans in a food drive. He is going to sort the cans into n bags with an equal number of cans in each bag. Write an expression to show how many cans will be in each bag.

9 6th Grade - Expressions and Equations 9 Standard: 6.EE.2.a Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. Write an algebraic expression for the written expression. Nine less than the product of negative five and x.

10 6th Grade - Expressions and Equations 10 Standard: 6.EE.2.a Difficulty: Easy Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. Michael is 12 years old and Kent is p years old. Write an expression to represent the sum of their ages.

11 6th Grade - Expressions and Equations 11 Standard: 6.EE.2.a Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. Write an algebraic expression for the following: A box of an unknown weight is added to a box whose weight is 15 kilograms. What is the total weight of the two boxes?

12 6th Grade - Expressions and Equations 12 Standard: 6.EE.2.a Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. Write an algebraic expression for the following: A sporting goods store as f footballs for sale. John buys 10 footballs. How many footballs does the store have left?

13 6th Grade - Expressions and Equations 13 Standard: 6.EE.2.a Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5-y. Write an algebraic expression for the following: There are 4 classrooms, each classroom has n students. How many students are there all together?

14 6th Grade - Expressions and Equations 14 Standard: 6.EE.2.b Difficulty: Hard Write, read, and evaluate expressions in which letters stand for numbers. B. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. Write a sentence to represent the following numerical expression: 2(n + 8) 3

15 6th Grade - Expressions and Equations 15 Standard: 6.EE.2.b Difficulty: Hard Write, read, and evaluate expressions in which letters stand for numbers. B. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. Write a sentence to represent the following numerical expression: 3 + (4 + 11) x

16 6th Grade - Expressions and Equations 16 Standard: 6.EE.2.b Difficulty: Easy Depth of Knowledge: 1 Write, read, and evaluate expressions in which letters stand for numbers. B. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. Identify the coefficient in the following expression: 7 + 3x 8/3

17 6th Grade - Expressions and Equations 17 Standard: 6.EE.2.b Difficulty: Easy Depth of Knowledge: 1 Write, read, and evaluate expressions in which letters stand for numbers. B. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. Identify the factor in the following expression: x 6

18 6th Grade - Expressions and Equations 18 Standard: 6.EE.2.b Write, read, and evaluate expressions in which letters stand for numbers. B. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. Identify the resulting product in the following expression:

19 6th Grade - Expressions and Equations 19 Standard: 6.EE.2.b Depth of Knowledge: 1 Write, read, and evaluate expressions in which letters stand for numbers. B. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. Identify the number of factors in the following expression: 2 (8 + 3) 9

20 6th Grade - Expressions and Equations 20 Standard: 6.EE.2.b Difficulty: Easy Write, read and evaluate expression in which letters stand for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) view one or more parts of an expression as a single entity. For example, describe the expression 2(8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. 10x + 5y + 3z + 9 Which of the following is a true statement of the expression above? a) The expression is a product of 4 terms. b) The expression has 2 variables c) The expression has coefficients of 10, 5, 3, and 9 d) The expression has one constant term, 9.

21 6th Grade - Expressions and Equations 21 Standard: 6.EE.2.b Difficulty: Easy Depth of Knowledge: 1 Write, read and evaluate expression in which letters stand for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) view one or more parts of an expression as a single entity. For example, describe the expression 2(8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. List the coefficients in the expression 9x 2 + 3x + 5y + 8

22 6th Grade - Expressions and Equations 22 Standard: 6.EE.2.b Difficulty: Easy Depth of Knowledge: 1 Write, read and evaluate expression in which letters stand for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) view one or more parts of an expression as a single entity. For example, describe the expression 2(8+7) as a product of two factors; view (8+7) as both a single entity and a sum of two terms. Apply and extend previous understandings of arithmetic to algebra expressions. The expression 5(4+9) can be described as a product of two factors. State the two factors used to determine the product.

23 6th Grade - Expressions and Equations 23 Standard: 6.EE.2.c Difficulty: Easy No Calculator: Write, read, and evaluate expressions in which letters stand for numbers. C. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = ½. You measure the side of a cube to be ½ cm. What is the volume of the cube and the surface area of the cube if V = s 3 and A = 6s 2?

24 6th Grade - Expressions and Equations 24 Standard: 6.EE.2.c No Calculator: Write, read, and evaluate expressions in which letters stand for numbers. C. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = ½. Your family needs to purchase a rectangular tent for an upcoming camping trip. You would like to get the best deal possibly so your research tents online. The following list represents your choices. You want to get the best price per square foot. Which tent would you select? Name Length Width Price Odyssey 6 8 $49.99 Wrangler 5 11 $52.87 Saddleback 7 7 $47.14

25 6th Grade - Expressions and Equations 25 Standard: 6.EE.2.c Difficulty: Easy No Calculator: Write, read, and evaluate expressions in which letters stand for numbers. C. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = ½. Evaluate the following expression for t = t

26 6th Grade - Expressions and Equations 26 Standard: 6.EE.2.c Difficulty: Hard No Calculator: Write, read, and evaluate expression in which letters stand for numbers. C) Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations) The figure shows an equilateral triangle. 4x 4x 4x Use the formula P=3s to find the perimeter of an equilateral triangle if s=4x and x=3.

27 6th Grade - Expressions and Equations 27 Standard: 6.EE.2.c No Calculator: Write, read, and evaluate expression in which letters stand for numbers. C) Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations) Evaluate the product of a 5 and 3 b when a=2 and b=4.

28 6th Grade - Expressions and Equations 28 Standard: 6.EE.3 No Calculator: Depth of Knowledge: 3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. A farmer sells asparagus for $3.75 per bundle, and broccoli for $2.25 per bundle. Elizabeth and Reece want to buy 6 bundles of each. a. Elizabeth says she can find the total cost by multiplying the number of bundles of each food by its price, and then adding the costs. Write and evaluate an expression Elizabeth would use to find the total cost. b. Reece says he can find the total cost by first adding the costs of one bundle of each food and then multiplying that sum by 6. Write and evaluate the expression Reece would use to find the total cost. c. Compare the costs using Elizabeth s and Reece s methods. What does that tell you about the expressions you wrote?

29 6th Grade - Expressions and Equations 29 Standard: 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Write an expression for the perimeter of the trapezoid. Then, simplify the expression. 2a x y 2a

30 6th Grade - Expressions and Equations 30 Standard: 6.EE.3 Depth of Knowledge: 4 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Simplify the expression. Use a property or operation to justify each step

31 6th Grade - Expressions and Equations 31 Standard: 6.EE.3 Difficulty: Hard Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Simplify the following expression: 5(4 2x) + 7(4 + 2x)

32 6th Grade - Expressions and Equations 32 Standard: 6.EE.3 Difficulty: Easy Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Simplify the following expression: y + y + x + z + y + 2z

33 6th Grade - Expressions and Equations 33 Standard: 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Apply the distributive property to write an equivalent expression to the following: 24x + 18y

34 6th Grade - Expressions and Equations 34 Standard: 6.EE.4 Depth of Knowledge: 3 Identify when two expressions are equivalent (i.e. when the two expressions name the same number regardless of which value is substituted into them). For example, the expression y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. State whether the expressions are equivalent. Justify your answer. 4s s and 3s + 2s + 3

35 6th Grade - Expressions and Equations 35 Standard: 6.EE.4 No Calculator: Depth of Knowledge: 3 Identify when two expressions are equivalent (i.e. when the two expressions name the same number regardless of which value is substituted into them). For example, the expression y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. State whether the expressions are equivalent. Justify your answer. 4s 4s and p 4 p + 4

36 6th Grade - Expressions and Equations 36 Standard: 6.EE.4 Depth of Knowledge: 3 Identify when two expressions are equivalent (i.e. when the two expressions name the same number regardless of which value is substituted into them). For example, the expression y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. State whether the expressions are equivalent. Justify your answer. 6(x 2) and 2(x 6) + 4x

37 6th Grade - Expressions and Equations 37 Standard: 6.EE.4 Difficulty: Hard Depth of Knowledge: 4 Identify when two expressions are equivalent (i.e. when the two expressions name the same number regardless of which value is substituted into them). For example, the expression y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Why are the expressions y + y + y and 3y equivalent?

38 6th Grade - Expressions and Equations 38 Standard: 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Find five pairs of whole numbers, such that when they are inserted into the equation below, the solution of the equation is 3. X + =

39 6th Grade - Expressions and Equations 39 Standard: 6.EE.5 No Calculator: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Reason and solve one-variable equations and inequalities. Find five pairs of whole numbers, such that when they are inserted into the equation below, the solution of the equation is 2. 5 x =

40 6th Grade - Expressions and Equations 40 Standard: 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Reason and solve one-variable equations and inequalities. Find five pairs of whole numbers, such that when they are inserted into the equation below, the solution of the equation is 5. X 5 =

41 6th Grade - Expressions and Equations 41 Standard: 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Reason and solve one-variable equations and inequalities. Which values from the set of real numbers make the inequality below true? y 10 < 13

42 6th Grade - Expressions and Equations 42 Standard: 6.EE.5 Depth of Knowledge: 3 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Reason and solve one-variable equations and inequalities. Which values from the set of real numbers make the inequality below true? x

43 6th Grade - Expressions and Equations 43 Standard: 6.EE.5 Difficulty: Easy Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Reason and solve one-variable equations and inequalities. Does the value x = -15 make the following inequality true? x

44 6th Grade - Expressions and Equations 44 Standard: 6.EE.6 Depth of Knowledge: 1 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Reason and solve one-variable equations and inequalities. Which word phrase could represent the variable expression 2p + 3? a. Three more than Sam s age doubled b. Twice Sam s age times three c. Half Sam s age times three d. Three times Sam s age

45 6th Grade - Expressions and Equations 45 Standard: 6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Reason and solve one-variable equations and inequalities. Jennifer has $17 in her piggy bank. How much money does she need to buy a game that costs $68? Let x represent the amount of money Jennifer needs. Write an equation to solve the problem.

46 6th Grade - Expressions and Equations 46 Standard: 6.EE.6 Difficulty: Easy Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Reason and solve one-variable equations and inequalities. On my last birthday I weighed 125 pounds. A year later I have gained x pounds. Write an expression for my weight one year later?

47 6th Grade - Expressions and Equations 47 Standard: 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Reason and solve one-variable equations and inequalities. Suppose you have 35 DVDs. You know that you have 11 more DVDs than your friend. Write and solve an equation to find the number of DVDs your friend has.

48 6th Grade - Expressions and Equations 48 Standard: 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Reason and solve one-variable equations and inequalities. Jennifer saves $12 each month. At this rate, how many months will she need to save $132? Write an equation and solve to find how many months Jennifer will need to save $132.

49 6th Grade - Expressions and Equations 49 Standard: 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Reason and solve one-variable equations and inequalities. Marcy worked ½ the time that Jerry worked. If Marcy worked 23 hours, how much time did Jerry work? Write an equation and solve to find the solution.

50 6th Grade - Expressions and Equations 50 Standard: 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Reason and solve one-variable equations and inequalities. Together, Louisa and Jill scored more than 30 points in the basketball game. If Jill scored 12 points, how many points p did Louisa score?

51 6th Grade - Expressions and Equations 51 Standard: 6.EE.8 Difficulty: Easy Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams Reason and solve one-variable equations and inequalities. Students must score a grade of 85 or better on a placement test to take a high school math course. Write an inequality to represent this situation and make a graph.

52 6th Grade - Expressions and Equations 52 Standard: 6.EE.8 Difficulty: Easy Depth of Knowledge: 1 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams Reason and solve one-variable equations and inequalities. A road has a speed limit of 30 mi/h. Write an inequality that describes the legal speeds r for motor vehicles.

53 6th Grade - Expressions and Equations 53 Standard: 6.EE.9 Difficulty: Easy Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Represent and analyze quantitative relationships between dependent and independent variables. Identify the independent and dependent variables for each relation. Then describe what is happening in each graph. The graph represents the speed of a car as it travels to the grocery store.

54 6th Grade - Expressions and Equations 54 Standard: 6.EE.9 Difficulty: Easy No Calculator: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time Represent and analyze quantitative relationships between dependent and independent variables. The equation a = 640s gives the relationship between s square miles and a acres. Create a table and a graph to illustrate the equation.

55 6th Grade - Expressions and Equations 55 Standard: 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time Represent and analyze quantitative relationships between dependent and independent variables. James is a carpenter who makes square tables in various sizes. The table shows the side lengths, in feet, and the areas of various table tops, in square feet. Side Length (feet) Area (square feet) a. Write the values from the table as a set of ordered pairs (side length, area). b. Graph the relation

56 6th Grade - Expressions and Equations 56 Standard: 6.EE.9 No Calculator: Depth of Knowledge: 3 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time Represent and analyze quantitative relationships between dependent and independent variables. You want to have your birthday party at the local children s museum. Below is a cost grid. Time (hours) Cost (dollars) a. Graph the relation. b. Write an equation for the cost c related to the given time t.