Pacing 2 days Begin with bar models as a concrete representation (engage NY), then. inverse operations to isolate and

Transcription

1 28 Determine whether mathematical statements of equality and inequalities are true or false. Write three different equations that have a solution of 0. Write each equation and prove it is accurate by solving for the variable. Module 4 Lessons Replace variables with values that make equations and statements of inequality true. Chapter 7 Lesson 29 Solve one-step addition and subtraction equations using bar models. Solve one-step equations by using inverse operations to isolate and solve for the variable. 30 Use substitution to check the accuracy of your work. Pacing 2 days Begin with bar models as a concrete representation (engage NY), then connect this to the concept of using inverse operations to isolate and solve for the variable () Draw a bar diagram then write and solve an equation to solve the following word problem: Patsy and LaShonda together have saved up $ to buy a TV that costs $ Write and solve an equation to solve for how much more money they need to raise. Module 4 Lesson 26 Chapter 7 Lessons Solve one-step multiplication and division equations using bar models. Solve one-step equations by using inverse operations to isolate and solve for the variable. 32 Use substitution to check the accuracy of your work. Pacing 2 days Begin with bar models as a concrete representation (engage NY), then connect this to the concept of using inverse operations to isolate and solve for the variable () Use tape diagrams to find the solution of!!" = 4. Module 4 Lesson 27 Chapter 7 Lessons Page

2 33 Represent and solve real world problems using onestep equations Use substitution and tape diagrams to check the accuracy of your work In a given amount of time, Jamie drove twice as far as Rhonda. Altogether they drove 90 miles. Write an equation to find the number of miles driven by each. Module 4 Lesson 28 mathematics.org/illustr ations/07 34 Apply knowledge of simplifying expressions, order of operations and properties of equality to calculate the solution of multi-step equations. A pet store owner, Byron, needs to determine how much food he needs to feed the animals. Byron knows that he needs to order the same amount of bird food as hamster food. He needs four times as much dog food as bird food and needs half the amount of cat food as dog food. If Byron orders 600 packages of animal food, how much dog food does he buy? Let b represent the number of packages of bird food Byron purchased for the pet store. Module 4 Lesson Flex Day (Instruction Based on Data) Recommended Resources: Bake Sale Brownies Chapter 7 2 st Century Careers (Pages ) Chapter 7 Review (Pages ) Page

3 36 Given an equation with two variables, determine which is the independent variable and which is the dependent variable Determine whether or not the equation is solved for the second variable in terms of the first variable or vice versa create a table by placing the independent variable in the first row or column and the dependent variable in the second row or column. They compute entries in the table by choosing arbitrary values for the independent variable (no constraints) and then determine what the dependent variable must be. Students understand that the dependent variable changes proportionally to the changes in the independent variable. What is the relationship between the two variables shown in the table? Write an equation that illustrates the relationship. Explain your reasoning. Module 4 Lesson 3 Chapter 8 Lesson demy.org/math/cc- sixth- grade- math/cc- 6th- expressions- and- variables/cc- 6th- dependent- independent/v/depen dent- and- independent- variables- exercise- example- 37 Graph one-step equations on the coordinate plane On the four square do now, assess students ability to plot points in the first quadrant of the coordinate plane Students understand that a set of ordered pairs make the equation true and that the y value, or dependent variable, is the result of substituting numbers for the x value, or independent variable. Students understand that the relationship between two variables may be represented on a graph where the independent variable is on the x axis and the dependent variable is on the y axis and analyzed in relationship to the equation. Write about a real-world situation that can represented by the equation y = /2x. Explain what variables represent in the situation. Solve your scenario and graph it below. Module 4 Lesson 32 Chapter 8 Lesson 3 my.org/math/cc-sixthgrade-math/cc-6thexpressions-andvariables/cc-6thdependentindependent/v/depende nt-and-independentvariables-exerciseexample-2 4 Page

4 38 Represent graphs with an equation Use the graph below to answer the question: Making Sense of Graphs Circle the equation that the graph above matches: Y = 4 6x Y = 6 - (/4)x Explain how you know: A table can be used to show the relationship between the number of hours a painter works painting and the total amount the painter charges for painting. my.org/math/cc-sixthgrade-math/cc-6thexpressions-andvariables/cc-6thdependentindependent/v/depende nt-and-independentvariables-exerciseexample-3 39 Students recognize independent and dependent variables in a real world context and represent the relationship in various ways (graphs, equations, tables) 40 Pacing 2 days Additional Practice: Stephanie is helping her band collect money to fund a field trip. The band decided to sell boxes of chocolate bars. Each bar sells for $.50 and each box contains 20 bars. Below is a partial table of monies collected for different numbers of boxes sold. (a) Complete the table above The painter charges $25 per hour to paint a room. (a) Complete the table to show the relationship between h, the number of hours the painter works, and c, the total amount, in dollars, the painter charges for painting. (b) Write an equation that can be used to find c, the total charge for h hours of painting. Chapter 8 Lesson 4 Making Sense of Tables mind.com/parcc/about_ middle_3788.html h.com/common- core- standards/6.ee.9- use- variables- to- represent- two- quantities- in- a- real- world- problem- that 5 Page

5 (b) Write an equation for the amount of money, m, that will be collected if b boxes of chocolate bars are sold. Which is the independent variable and which is the dependent variable? (c) Calculate how much money will be collected if 00 boxes of chocolate bars are sold. (d) The band collected $ from chocolate bar sales. How many boxes did they sell? It took the painter 3 hours to paint a room. (c) What is the total amount, in dollars, the painter charged for painting the room? Show or explain how you got your answer. math.com/tag/6- ee- 9/ 4 Flex Day (Instruction Based on Data) Recommended Resources: Who Has Faulty Thinking? Chapter 8 Lesson 2 Chapter 8 Problem-Solving Investigation (Pages 6 63) Chapter 8 Mid-Chapter Check (Page 64) Chapter 8 Inquiry Lab (Pages 65 66) mmymath.com%2ftag%2f6-ee-9%2f&ei=gwzquswffpfjsqta0ocicq&usg=afqjcnhdjiwjfa3ujugye8u8dip23sea&bvm=bv ,d.awc 42 Determine whether a given value is a solution to an inequality. Find possible solutions to inequalities 6 Page Work with your student to distinguish between inequalities and equations. Ask your student to solve an equation like 6y - 3 = 5. Once they have found the solution, ask them to substitute the = for a > sign and ask them to solve. Discuss how the answer has changed Check out this LearnZillion video for additional ideas on how to teach this concept: Twelve is less than 3 times another number can be shown by the inequality 2 < 3n What numbers could possibly make this a true statement? Module 4 Lesson 33 Chapter 8 Lesson 5 om/common-core- standards/6.ee.5- understand-solving-anequation-or-inequalityas-a-process-ofanswering-a

6 43 Determine when a real world situation should be represented by an inequality rather than an equation. Graph the range of solutions. Tom wants to buy a pair of shoes and a t- shirt. The shoes cost $65. He has $82 to spend.. Write an inequality to represent this situation. 2. What could the cost of the t-shirt be? Explain how you know using words. When is it Not Equal? Evaluating Solutions to One-Step Equations and Inequalities Chapter 8 Lesson 6 44 Write and graph the range of solutions to an inequality. Explain why there are an infinite number of solutions to the inequality x > c or x < Key Understandings: ) Students recognize that inequalities of the form x < c and x > c, where x is a variable and c is a fixed number have infinitely many solutions when the values of x come from a set of rational numbers. Work with your students to recognize the values on a number line that will satisfy an inequality by graphing them and then inserting them and determining if the value satisfies the inequality. For additional ideas, use this LearnZillion lesson: graph-an-inequality Little Ceasar s charges $5.00 for a pizza. Kervin will spend no more than $ How many pizzas can he buy? Write an inequality to solve and graph on a number line. Module 4 Lesson 34 Chapter 8 Lesson 7 om/common-corestandards/6.ee.8-writean-inequality-of-theform-x--c-or-x--c-torepresent-a-constraint 7 Page

7 45 Determine the range of solutions that would make an inequality true in a real world problem 46 (2 days) Use these task from Illustrative Mathematics to create task-based problem-solving lessons: Task I: Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can hold at most eight people. Additionally, each boat can only carry at most 900 pounds of weight for safety reasons. (a) Let p represent the total number of people on a boat. Write an inequality to describe the number of people that a boat can hold. Draw a number line diagram that shows all possible solutions to the inequality. (b) Let w represent the total weight of a group of people wanting to rent a boat. Write an inequality that describes all total weights allowed in a single boat. Draw a number line diagram that shows all possible solutions to the inequality. Task II: A theme park has a log ride that can hold 2 people. They also have a weight limit of 500 pounds for safety reasons. If the average adult weighs 50 pounds, the average child weighs 00 pounds, and the log itself weighs 200 pounds, the ride can operate safely if the following inequality is satisfied: 50A + 00C Part I: Ana is saving to buy a bicycle that costs $35. She has saved $98 and wants to know how much more money she needs to buy the bicycle. The equation 35 = x + 98 models this situation, where x represents the additional amount of money Ana needs to buy the bicycle. (a) When substituting for x, which value(s), if any, from the set {0, 37, 98, 35, 233} will make the equation true? (b) Explain what this means in terms of the amount of money needed and the cost of the bicycle. Part II: Ana considered buying the $35 bicycle, but then she decided to shop for a different bicycle. She knows the other bicycle she likes will cost more than $50. This situation can be modeled by the inequality x + 98 > 50. (c) Which values of x, if any, from 250 to 250 will make the inequality true? If more than one value makes the inequality true, identify the least and greatest values that make the inequality true. (d) Explain what this means in terms of the amount of money needed and the cost of the bicycle. mathematics.org/illustr ations/673 h.com/common- core- standards/6.ee.8- write- an- inequality- of- the- form- x- - c- or- x- - c- to- represent- a- constraint classrooms.com/com mon_core/write_ineq uality_form_x_c_expre ssions_equations_sixt h_6th_grade_math_ma thematics.htm 8 Page

8 A is the number of adults and C is the number of children on the log ride. There are several groups of different numbers of children waiting to ride. Group A has 4 children, group B has 3 children, group C has 9 children, group D has 6 children, and group E has 5 children. If 4 adults are already seated in the log, which groups of children can safely ride with them? Which cannot? Explain your answers. 47 Flex Day (Instruction Based on Data) Recommended Resources: Want Ads Chapter 8 2 st Century Career (Pages ) Chapter 8 Review (Pages ) Unit Project (Pages ) mmymath.com%2ftag%2f6-ee-9%2f&ei=gwzquswffpfjsqta0ocicq&usg=afqjcnhdjiwjfa3ujugye8u8dip23sea&bvm=bv ,d.awc 48 MCLASS End of Unit Assessment Appendix B *Note: This assessment will be administered online 9 Page

9 Standard 6.EE. Write and evaluate numerical expressions involving whole-number exponents. Appendix A: Unpacked Standards Guide Source: Public Schools of North Carolina NCDPI Collaborative Workspace Unpacking What do these standards mean a child will know and be able to do? 6.EE. Students demonstrate the meaning of exponents to write and evaluate numerical expressions with whole number exponents. The base can be a whole number, positive decimal or a positive fraction (i.e. 5 can be written which has the same value as ). Students recognize that an expression with a variable represents the same mathematics (ie. x 5 can be written as x x x x x) and write algebraic expressions from verbal expressions. Order of operations is introduced throughout elementary grades, including the use of grouping symbols, ( ), { }, and [ ] in 5 th grade. Order of operations with exponents is the focus in 6 th grade. Example: What is the value of: Solution: Solution: Solution: 67 Example 2: What is the area of a square with a side length of 3x? Solution: 3x 3x = 9x 2 6.EE.2 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 20 Page Example 3: 4 x = 64 Solution: x = 3 because = 64 6.EE.2 Students write expressions from verbal descriptions using letters and numbers, understanding order is important in writing subtraction and division problems. Students understand that the expression 5 times any number, n could be represented with 5n and that a number and letter written together means to multiply. All rational numbers may be used in writing expressions when operations are not expected. Students use appropriate mathematical language to write verbal expressions from algebraic expressions. It is important for students to read algebraic expressions in a manner that reinforces that the variable represents a number.

10 calculation Subtract y from 5 as 5 y. Example Set : Students read algebraic expressions: r + 2 as some number plus 2 as well as r plus 2 n 6 as some number times 6 as well as n times 6 s 6 and s 6 as as some number divided by 6 as well as s divided by 6 Example Set 2: Students write algebraic expressions: 7 less than 3 times a number Solution: 3x 7 3 times the sum of a number and 5 Solution: 3 (x + 5) 7 less than the product of 2 and a number Solution: 2x 7 Twice the difference between a number and 5 Solution: 2(z 5) The quotient of the sum of x plus 4 and 2 Solution: x Students can describe expressions such as 3 (2 + 6) as the product of two factors: 3 and (2 + 6). The quantity (2 + 6) is viewed as one factor consisting of two terms. Terms are the parts of a sum. When the term is an explicit number, it is called a constant. When the term is a product of a number and a variable, the number is called the coefficient of the variable. Students should identify the parts of an algebraic expression including variables, coefficients, constants, and the names of operations (sum, difference, product, and quotient). Variables are letters that represent numbers. There are various possibilities for the number they can represent. Consider the following expression: x2 + 5y + 3x Page The variables are x and y. There are 4 terms, x2, 5y, 3x, and 6. There are 3 variable terms, x2, 5y, 3x. They have coefficients of, 5, and 3 respectively. The coefficient of x2 is, since x2 = x2. The term 5y represent 5y s or 5 y. There is one constant term, 6. The expression represents a sum of all four terms.

11 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. 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 = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = ½. Students evaluate algebraic expressions, using order of operations as needed. Problems such as example below require students to understand that multiplication is understood when numbers and variables are written together and to use the order of operations to evaluate. Order of operations is introduced throughout elementary grades, including the use of grouping symbols, ( ), { }, and [ ] in 5th grade. Order of operations with exponents is the focus in 6th grade. Example : Evaluate the expression 3x + 2y when x is equal to 4 and y is equal to 2.4. Solution: Example 2: Evaluate 5(n + 3) 7n, when n = 2. Solution: 5( 2 + 3) 7( 2 ) 7 5 (3 2 ) Note: 7( 2 ) = 2 = Students may also reason that 5 groups of 3 2 take away group of 3 2 would give 4 4 groups of 3 2. Multiply 4 times 3 2 to get Page