GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER

Transcription

1 GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER UNIT OVERVIEW This unit contains a curriculum- embedded Common Core aligned task and instructional supports. The task is embedded in a 2 3 week unit on expressions. TASK DETAILS Task Name: Grocery Shopping and The Quilt of a Math Teacher Grade: 6 Subject: Math Depth of Knowledge: 3 Task Description: There is a combination of two tasks that will be administered as this culminating assessment. The Grocery Shopping task will assess students knowledge of representing equivalent expressions and being able to justify this through the use of the distributive property. The second task is The Quilt of a Math Teacher. This task will assess students knowledge of formulating an algebraic expression based on a real- life situation, while addressing Mathematical Practice standards as well. Standards: 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. 6.EE.2b 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. 6.EE.2c 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. 6.EE.3 Apply the properties of operations to generate equivalent expressions. 6.EE.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). Standards for Mathematical Practice: MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct a viable argument and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure. 1

2 TABLE OF CONTENTS The task and instructional supports in the following pages are designed to help educators understand and implement Common Core aligned tasks that are embedded in a unit of instruction. We have learned through our pilot work that focusing instruction on units anchored in rigorous Common Core aligned assessments drives significant shifts in curriculum and pedagogy. Callout boxes and Universal Design for Learning (UDL) support are included to provide ideas around how to include multiple entry points for diverse learners. PERFORMANCE TASK: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER 3 RUBRIC...7 ANNOTATED STUDENT WORK...12 INSTRUCTIONAL SUPPORTS...25 UNIT OUTLINE INITIAL ASSESSMENT...40 FORMATIVE ASSESSEMENT Acknowledgements: This instructional unit was written by Yolette Desire, 18K211 with input from Jennifer Lewner, NYCDOE Common Core Fellow and Laginne Walker, NYCDOE Common Core Fellow. 2

3 GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER PERFORMANCE TASK 3

4 Name: Date: Class: Grocery Shopping The table below shows the prices of different items at A and B Supermarket. Items Prices Pack of Oreos $3 1 lb of ham $7 1 gallon of milk $4 1 pumpkin pie $5 24 oz. box of cereal $7 Mr. D buys 3 packs of Oreos and 3 pounds of ham. 1. Write two equivalent expressions to represent the total amount Mr. D will pay for the items he buys. Expressions: and 2. Explain how Mr. D can use the distributive property to calculate the total amount he has to pay. 4

5 Name: Date: Class: The Quilt of a Math Teacher Mrs. Mothes is making a quilt in the shape of a square for her younger sister. The border of the quilt is made of 1-foot by 1-foot patches. She asks one of her students, Maria, to use the picture of the quilt below to write an expression to illustrate the number of patches needed to border the square quilt with side length s. s 1 ft s 1 ft The square quilt has side length s. (Not drawn to scale.) Patch (Not drawn to scale.) Maria writes: (s + s + s + s) + ( ) Part A: Is Maria s expression correct? Explain your reasoning. 5

6 Part B: Mrs. Mothes asks four other students (Samantha, Jerry, Nadia, and Joseph) to generate expressions that are equivalent to Maria s expression. 1. Samantha s expression: 4s Jerry s expression: 4(s + 1) 3. Nadia says the correct expression is 4s Joseph writes: 2s + 2(s + 2) How many of the students wrote a correct or an incorrect expression? Justify your answer with a detailed explanation. 6

7 GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER RUBRIC The following section contains a rubric to assess student mastery of the targeted Common Core standards in the culminating performance task. The rubric includes both the content standards and the Mathematical Practices. 7

8 Grocery Shopping Rubric Score-Point 3 All aspects of the problem yield complete and correct responses. The responses accomplish the prompted purposes and effectively communicate the student s mathematic understanding. The student s strategy and execution meet the content demands of all parts of the task. PART 1: Equivalent Expressions: 3(7 + 3) = 3(10) = (3 x 7) + (3 x 3) = 30 A pair of any of the expressions above or an expression that is equivalent, including variables as well, will suffice. PART 2: An explanation of the distributive property and how it has been applied to represent two equivalent expressions from Part 1. Responses successfully demonstrate use of mathematical practices. Score-Point 2 Some aspects of the problem yield complete and correct responses. The student s response demonstrates adequate evidence and understanding necessary to complete the task with minor errors in execution. It is evident that the student shows some mathematical understanding and will be able to revise the work with discussion and/or feedback from peers or teachers. Errors may include: Incomplete justifications for written responses Explaining the wrong number property to justify the correct equivalent expressions Minor numerical error in the representation of the equivalent expression Responses adequately demonstrate mathematical practices. 8

9 Score-Point 1 Many aspects of the problem do not yield complete and correct responses. The student demonstrates effort to complete the task; however, there are many conceptual errors throughout the task. Student work will need to be significantly revised. It is evident that the student requires further instruction to meet the demands of the task, as well as meet the mathematical practices required to accomplish the task. Errors may include: Incomplete justifications for written responses Incorrect solutions with incomplete work Major calculation errors or mathematical misconceptions Equivalent representation, but not in the form of two expressions; the wrong number property is explained. Partially correct responses will demonstrate a limited understanding of the mathematical practices. 9

10 The Quilt of a Math Teacher Rubric Score-Point 3 All aspects of the problem yield complete and correct responses. The responses accomplish the prompted purposes and effectively communicate the student s mathematic understanding. The student s strategy and execution meet the content demands of all parts of the task. PART A: The student agrees that Maria s expression is correct. The student justifies his/her response by explaining that the s represents the side length of the quilt and the additional 4 that is added on is for the patches needed in each corner of the border. PART B: The student states that Samantha, Jerry, and Joseph are all correct, and continues to explain that the three expressions are all equivalent to 4s + 4. Nadia s response is incorrect, since that is just 4s + 1. Responses successfully demonstrate use of mathematical practices. Score-Point 2 Some aspects of the problem yield complete and correct responses. The student s response demonstrates adequate evidence and understanding necessary to complete the task with minor errors in execution. It is evident that the student shows some mathematical understanding and will be able to revise the work with discussion and/or feedback from peers or teachers. Errors may include: Incomplete justifications for written responses Incorrectly identifies 1 to 2 responses from Part B Minor conceptual error on Part A or Part B Responses adequately demonstrate mathematical practices. 10

11 Score-Point 1 Many aspects of the problem do not yield complete and correct responses. The student demonstrates effort to complete the task; however, there are many conceptual errors throughout the task. Student work will need to be significantly revised. It is evident that the student requires further instruction to meet the demands of the task, as well as meet the mathematical practices required to accomplish the task. Errors may include: Incomplete justifications for written responses Incorrect solutions with incomplete work Major calculation errors or mathematical misconceptions Only Part A or Part B shows limited understanding Partially correct responses will demonstrate a limited understanding of the mathematical practices. 11

12 GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER ANNOTATED STUDENT WORK This section contains annotated student work at a range of score points. The student work shows examples of student understandings and misunderstandings of the task. 12

13 Score Point 3 out of 3 These equivalent expressions correctly model the situation. 13

14 The student has correctly justified his/her response for the equivalent expressions and explained the distributive property. 14

15 The student has correctly justified why Maria s expression is correct and understands the representation of ( ). 15

16 The student has correctly identified the students who were correct and the one student who was incorrect. The student also demonstrates an understanding of the equivalence to Maria s expression. 16

17 Score Point 2 out of 3 The student has shown correct equivalent expressions and included the use of a variable for each item. 17

18 The student has correctly evaluated the total cost using his/her first expression from Part A. However, the student then justifies the commutative property. 18

19 The student has correctly justified why Maria s expression is correct. 19

20 The student has correctly identified only one out of the three student responses that are correct. The student has not identified Joseph as correct because he/she did not distribute the 2 outside the parentheses completely. The student has not identified Jerry as correct because he/she did not distribute the 4 outside the parentheses completely. 20

21 Score Point 1 out of 3 There is a very limited understanding of equivalency shown. The student has shown two equivalent expressions. However, the student does not correctly address the problem because he/she neglected the three pounds of ham and the three packs of Oreos. 21

22 The student demonstrates knowledge of equivalent representations through the use of number properties. However, the student has followed through with the error from Part A and justifies the commutative property. 22

23 The student shows some understanding of the diagram and expression that is being represented. The student recognizes that the quilt sides are being represented by s + s + s + s. However, the student does not understand what the represents. 23

24 The student has correctly identified one of the responses as correct. The student has demonstrated an understanding that the expression from Part A is equivalent to 4s + 4. However, the student does not address the other two responses that he/she believes are incorrect. 24

25 GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER INSTRUCTIONAL SUPPORTS The instructional supports on the following pages include a unit outline with formative assessments and suggested learning activities. Teachers may use this unit outline as it is described, integrate parts of it into a currently existing curriculum unit, or use it as a model or checklist for a currently existing unit on a different topic. 25

26 Unit Outline Grade 6 Math: Grocery Shopping and The Quilt of a Math Teacher UNIT TOPIC AND LENGTH: This unit should take approximately 2 3 weeks to complete, including all lessons and assessments. COMMON CORE CONTENT STANDARDS: Ø 6.EE.1 Write and evaluate numerical expressions involving whole- number exponents. Ø 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. Ø 6.EE2a Write expressions that record operations with numbers and with letters standing for numbers. Ø 6.EE.2b 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. Ø 6.EE.2c 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). Ø 6.EE.3 Apply the properties of operations to generate equivalent expressions. Ø 6.EE.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). STANDARDS FOR MATHEMATICAL PRACTICE: Ø MP.1 Make sense of problems and persevere in solving them. Ø MP.2 Reason abstractly and quantitatively. Ø MP.3 Construct a viable argument and critique the reasoning of others. Ø MP.4 Model with mathematics. Ø MP.6 Attend to precision. Ø MP.7 Look for and make use of structure. BIG IDEAS/E /ENDURING UNDERSTANDINGS: Ø Represent numerical relationships as expressions Ø Use algebraic expressions, inequalities, or equations to represent and solve real- world problems ESSENTIAL QUESTIONS: Ø How can relationships be expressed with symbols? Ø What are you doing when you evaluate an expression? Ø How can numerical and algebraic expressions be used to represent real- life situations? Ø How do number properties effect the creation of equivalent expressions? 26

27 CONTENT: Ø Numerical expressions involving exponents in both expanded form and exponential form Ø Parts of algebraic expressions and equations Ø Substitution and evaluation of algebraic expressions Ø Order of operations SKILLS: Ø Write a numeric and algebraic expression Ø Evaluate algebraic and numeric expressions Ø Identify equivalent expressions VOCABULARY/K /KEY TERMS: Exponent, base, expression, power, factor, evaluate, expanded form, variable, coefficient, constant, equation, twice as much, more than, less than, product, quotient, difference, increasing, decreasing, fewer than, equal to, associative property, commutative property, distributive property, additive inverse, identity element, multiplicative inverse, equivalent expressions, generate, substitute ASSESSMENT EVIDENCE AND A ACTIVITIES: INITIAL ASSESSMENT: EXPLORING EXPRESSIONS This initial assessment asks students to represent a real- life situation about comic books using variables and creating algebraic expressions. The purpose of this assessment is to allow the teacher to see students prior knowledge of this topic and determine the most effective way to proceed. FORMATIVE ASSESSMENT: MANAGE MY SAVINGS This assessment should be administered after 6.EE.1 is taught. This task also incorporates volume. It is suggested that there should be a class discussion on volume prior to this assessment. FINAL PERFORMANCE TASK: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER The culminating task is a combination of two tasks. The first task, Grocery Shopping, assesses students on their ability to create equivalent numerical expressions using number properties. The Quilt of a Math Teacher task assesses students knowledge of applying algebraic expressions to real- life situations and their ability to understand that algebraic expressions can be represented as other equivalent expressions as well. 27

28 LEARNING PLAN AND ACTIVITIES: By the end of this unit students will be able to understand that algebraic expressions can be used to represent and solve real- world mathematical problems. Standards addressed in this cluster: 6. EE.1, 6.EE.2, 6.EE.3, 6.EE.4 Connections to other clusters and domains: 6.EE.5, 6.EE9, 6.G.1, 6.G.2 Lesson 1: 6.EE.1 Skills and concepts students should know, understand, and be able to do: The exponent is the number of times the base is used as a factor. (Ex: 2 3 = 2 x 2 x 2) Exponents are sometimes called powers. The base could also be a variable (letter). Exponential notation represents multiplication in which the base stays the same (constant). Simplify and evaluate expressions with exponents. Understand and use the mathematical vocabulary in context. Vocabulary Words Used in Standard 6.EE.1 Exponent, base, expression, power, factor, evaluate, expanded form (of multiplication), exponential form Background Skills 1. Write 3 4 in repeated multiplication form. 2. Evaluate Find the area of a square computer desk with side of 18 inches. 4. Find the volume of a cube with sides of 3 inches. 5. Explain the difference between 4 3 and 3 4. Task 1: Mrs. Alexander s Offer Mrs. Alexander is offered a job with a computer company that will pay her $100,000. Represent the salary using exponential form. Answer: Task 2: Mold Growth Mr. Baily, a scientist who liked to express numbers with exponents, used a table to represent the number of mold spores in his bread experiment: 28

29 Day Number of 3 3 x 3 3 x 3 x 3 3 x 3 x 3 x 3 mold spores *Notes to teacher: Common misconceptions: Students may see 3 2 and think it means 3 x 2, and multiply the base by the exponent. Also, students may mistake 3 2 for and vice versa, or p +p +p for p 3. (Here they may realize how many of the base they need in expanded form, but they add or count by the base, rather than multiplying.) To ensure that students do not make this common mistake, it is important to encourage them to always write exponential form out in expanded form. a) Mr. Baily asked his students to write an exponential expression to represent the total number of mold spores on the fourth day. Marcus wrote the expression 3 4 and John wrote 4 3. Who was correct? Answer: b) Justify your answer with a detailed explanation. c) If the pattern continued, how many mold spores would Mr. Baily have on the fifth day? Write your answer in exponential form. Answer: Lesson 2: 6.EE.2 a c Skills and concepts students should know, understand, and be able to do: Variables are letters or symbols that take place of numbers or a range of numbers. They have different meanings, depending on whether they are being used as representations of quantities that vary or change, representations of specific unknown values, or placeholders in a generalized expression or formula. Terms are values in an expression separated by addition and/or subtraction. A coefficient is a number that multiplies a variable. Accurately translate an expression from verbal to algebraic and vice versa. Understand and use academic vocabulary in context. Vocabulary Words Used in Standard 6.EE.2 variable, coefficient, constant, expression, equation, notation for multiplication, grouping symbol such as ( ), twice as much, more than, less than, the product of, the quotient of, 29

30 difference, sum, total, increasing, decreasing, fewer than, equal to Background Skills Translate each verbal expression into an algebraic expression: a) 4 less than the product of a number and 7 b) The quotient of y and 6 c) The sum of a number and 225 d) Twice a number Task 1: Popping Off With Algebra Let h represent the number of hours Shaunda spent on homework last week. Part A Zack spent 1/2 as much time on his homework as Shaunda, plus an additional 3 hours. Write an expression for the number of hours he spent on his homework. Expression: Part B Identify the number of terms, coefficient and constant in the expression above. Number of terms: Coefficient: Constant: Part C Shauna spent 12 hours doing her homework. How many hours did it take Zack to complete his homework? Show your work. Zack: hours Task 2: Dogging Algebra Franklin, a pit bull, weighs p pounds. For Part A, write an expression for the weight in pounds of each of the dogs. Each expression should include the variable p. Part A Tatu, a pug, weighs 49 pounds less than Franklin: Mia, a Chihuahua, weighs 1/17 as much as Franklin: Lucy, a Great Dane, weighs twice as much Franklin, minus 15 pounds: 30

31 Part B Set up a chart or organizer to represent the weights of the four dogs. Part C Franklin weighs 68 pounds. How much do Tatu, Mia, and Lucy weigh? Show or explain how you found this. Tatu: pounds; Mia: pounds; Lucy: pounds Lesson 3: 6.EE.3 Note to teacher: Teach standards 6.EE.3 and 6.EE.4 simultaneously. Nature of skills and concepts students should know, understand, and be able to do: Develop a conceptual understanding of properties of operations. Understand that properties of operations and the order of operations can be used to simplify expressions and generate equivalent expressions. Know how to effectively find the common factor of two or more numbers. Generate equivalent expressions when learning properties of operations. Substitute values into expressions to make justifications. Understand that the distributive property does not apply for division. Commutative and associative property do not apply for division and subtraction: a b is different than b a, with a and b 0. Use manipulatives to represent the distributive property. Understand and use academic vocabulary words when solving problems and explaining solutions. Encourage students to use the complete names of mathematical words in class discussion. Vocabulary Words Used in Standard 6.EE.3: Equivalent equations, associative property, commutative property, distributive property, additive inverse property, identity element, multiplicative inverse, equivalent expressions, generate, substitution principle Background Skills Find an equivalent expression for each of the following: 31

32 1) 3(x 2) 2) 8x + 12y 3) p +p +p +p +p 4) 7y + 2p 5) 3x + (5m + 5p) Task 1: Distributive Property of Color Pencils Miss Bertha opens a box of pencils that contains 6 green, 8 blue, and 10 red pencils. Write two equivalent expressions to show the total number of pencils in 5 boxes. Expressions: and Explain how you know that these two expressions are equivalent. *Note to teacher: manipulatives, diagrams, or other strategies can be used to represent the distributive property. Have students show their work and explain their reasoning in writing. Lesson 4: 6.EE.4 Nature of skills and concepts students should know, understand, and be able to do: Understand that variables are letters that replace unknown values. Understand the relation between two quantities. Know that an equation is a mathematical sentence that states that two expressions are equal. Understand and use academic vocabulary words when solving problems and explaining solutions. Encourage students to use the complete names of mathematical words in class discussion. Understand that the substitution principle allows us to represent one expression by another expression that represents the same value. Use diagrams and/or manipulatives to represent equivalent expressions. Vocabulary Words Used in Standard 6.EE.4: Equivalent equations, equivalent expressions, generate, substitution principle, = Background Skills Are the following expressions equivalent? Explain your reasoning. 1) a + a = 2a + 4 2) 6(p + 3) = 6p + 6 3) 10(y x) = 10y 10x 32

33 Task 1: Equivalent? Lea says the three expressions below are equivalent to y. Is she correct? Explain your reasoning for each. 1) (1 + 3) + (4y + 20y) 2) y + 14y 3) (20 16) + (44y 20y) ADDITIONAL SUPPORT STRATEGIES: Support For Students With Disabilities The following tasks are designed to help students develop connections between concrete experiences, pictorial representations of mathematical ideas, and abstract mathematical symbols. Based on the needs of your students, you may choose to use one of the following activities to introduce students to variables, expressions, and equations. *Vocabulary words with symbols, electronic dictionaries, and manipulatives should be used throughout the unit. Marbles Expression Mrs. Desi has a large bag containing some marbles. There are 6 marbles on the floor. How many marbles are there all together? *Suggestion on how to introduce students to variables and expressions: Use one bag at a time. First method: You can draw models to show the total number of marbles if the bag contains certain numbers of marbles. Bag of marbles bag of marbles bag of marbles Second method: You can write an algebraic expression to represent the total number of marbles. 1. The number of marbles in the bag changes, so represent it with a variable, m. 2. The number of marbles on the floor stays the same, To find the number of marbles all together, add the number of marbles in the bag and the 33

34 number of marbles on the floor. 4. Let m represent the number of marbles in the bag. So m + 6 represents the total number of marbles. 5. Suppose you have 80 in the bag. Therefore, m = 80. Now you can find the total number of marbles by substituting m by 80 in the expression m + 6. * Solution (80 + 6): There are 86 marbles in the bag. RESOURCES: 1. Van De Walle, John A. Elementary and Middle School Mathematics: Teaching Developmentally, Fourth Edition. London: Longman, Singapore Math/Algebraic Reasoning on Unit_Template- 2.docx 6. Nlvm.usu.edu/en/nav/ National Library of Virtual Manipulatives via 34

35 Name: Date: Class: Student Tasks: Lesson 1 1. Mrs. Alexander s Offer Mrs. Alexander is offered a job with a computer company that will pay her $100,000. Represent the salary using exponential form. Answer: 2. Weight Loss Mr. Baily, a scientist who likes to express numbers with exponents, used a table to represent the number of pounds he lost in the past four months. Month Weight lost in 3 3 x 3 3 x 3 x 3 3 x 3 x 3 x 3 pounds a) Mr. Baily asked his students to write an exponential expression to represent the total number of pounds lost within four months. Marcus wrote the expression 3 4 and John wrote 4 3. Who was correct? Answer: b) Justify your answer with a detailed explanation. c) If the pattern continued, how many pounds would Mr. Baily lose within the fifth month? Write your answer in exponential form. Answer: 35

36 Name: Date: Class: Student Tasks: Lesson 2 Task 1: Popping Off With Algebra Let h represent the number of hours Shaunda spent on homework last week. Part A Zack spent 1/2 as much time on his homework as Shaunda plus an additional 3 hours. Write an expression to represent the number of hours Zack spent on his homework. Expression: Part B Identify the number of terms, the coefficient, and the constant in the expression you wrote above. Number of terms: Coefficient: Constant: Part C Shauna spent 12 hours doing her homework. How many hours did it take Zack to complete his homework? Show your work. hours Task 2: Dogging Algebra Franklin, a pit bull, weighs p pounds. Write an expression for the weights of the dogs in pounds for Part A. Each expression should include variable p. Part A Tatu, a pug, weighs 49 pounds less than Franklin: Mia, a Chihuahua, weighs 1/17 as much as Franklin: Lucy, a Great Dane, weighs twice as much Franklin, minus 15 pounds: Part B Set up a chart or organizer to represent Tatu, Mia, and Lucy s weights. 36

37 Part C Franklin weighs 68 pounds. How much do Tatu, Mia, and Lucy weigh? Show your work. Tatu: pounds; Mia: pounds; Lucy: pounds 37

38 Name: Date: Class: Student Tasks: Lesson 3 Distributive of Color Pencils Miss Bertha opens a box of pencils that contains 6 green, 8 blue, and 10 red pencils. Write two equivalent expressions to show the total number of pencils in 5 boxes. Expressions: and Explain how you know that these two expressions are equivalent. 38

39 Name: Date: Class: Student Tasks: Lesson 4 Equivalent? Lea says the three expressions below are equivalent to y. Is she correct? Explain your reasoning for each. 1) (1 + 3) + (4y + 20y) 2) y + 14y 3) (20 16) + (44y 20y) 39

40 Name: Date: Class: Exploring Expressions (Initial Assessment) 1) Mark has 12 comic books, Jeremy has 14 comic books, and Sam has half as many comic books as Jeremy. A. Write a numerical expression to represent how many comic books the three boys have together. B. If each comic book cost $3.50, write two equivalent expressions to represent how much the boys have spent total. and C. How do you know that these two expressions are equivalent? Justify your response. 40

41 D. If Mark lost a few of his cards, write a new expression to represent how many cards Mark has now. 2) Explain the differences between a numeric expression and an algebraic expression. 41

42 Managing My Savings Samantha wishes to save $1,024 to buy a laptop for her birthday. She does not want to save her money at any bank. She prefers to use her lovely cube money box that her godmother gave her twelve years ago. The money box is in the shape of a cube as shown below. The length of each side is a inches. a) Write an exponential expression that could be used to represent the volume of Samantha s lovely cube money box. Expression: b) Explain how you would determine the volume of Samantha s lovely cube money box if the length of one side is 9 inches. 42

43 c) Express the equation for the volume of the cube money box in exponential form. 43