**Essential Questions:**

- How many dogs do I have to walk in order to be able to buy a skateboard?

**Big Ideas:**

- Modeling with math can solve problems.

**Unit 1 instructional time is focused on these priority standards:**

**6.EE.B.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.

**6.EE.B.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.

**6.EE.C.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.

**Unit 2 instructions is supported by these standards:**

**6.EE.A.1**Write and evaluate numerical expressions involving whole-number exponents.

**6.EE.A.2**Write, read, and evaluate expressions in which letters stand for numbers.

SAMPLE assessment items

**6.EE.2**

**6.EE.A.2.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*.

**6.EE.A.2.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*.

**6.EE.A.2.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 = 1/2*.

**6.EE.A.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*.

**Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).**

6.EE.A.4

6.EE.A.4

*For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.*

**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.**

6.EE.B.5

6.EE.B.5

**6.EE.B.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.

## What to TeachUnit 2 Outline
Pre-assessment Pre-assessment Reporting Sheet Introduce Real World Experience Before starting this unit, refresh students' understandings and ability to distinguish between expressions, equations & inequalities Topic 1: Understand Relationships of the Operations (2 days) - I know and can show the relationship between addition and subtraction using identities such as w-x+x=w+x-x
- I know and can show the relationship between multiplication and division using identities such as w ÷ x • x = w • x ÷ x
- I know and can show the relationship between multiplication and addition using identities such as 4 • x = x + x + x + x
- I know and can show the relationship between division and subtraction using identities such as 15 ÷ 5 = 3 and 15 - 5 - 5 - 5=0
vocabulary: inverse operations, variable, represent, coefficient, constant, termsReal World Experience Task 1 |
## Lesson IdeasWhat are Variables-video
Factor, Expand, Combine Like Terms (teaching Channel video lesson) What are Identity Equations-video Write Equivalent Expressions Using Identities-Learnzillion video series student guided notes sheet Using Identities to Generate Equivalent Expressions-Learnzillion video series Relationship of Addition & Subtraction-EngageNY lesson Relationship of Multiplication & Division- EngageNY lesson Relationship of Multiplication & Addition-EngageNY lesson Relationship of Division & Subtraction-EngageNY lesson |
## Student PRactice |

Topic 2: Exponential Notation and the Order of Operations (2 days)
- Review the order of operations
- I can show and explain the difference between multiplying by a whole number and using the same whole number as an exponent.
- I can represent and evaluate exponential expressions or equations using the order of operations.
vocabulary: exponent, squared, cubed, order of operations, expanded notation, exponential notation, substitute, evaluate |
Write & Evaluate Exponents-Learnzillion video series
6.EE.1-4 Lesson Ideas from Newark Modified Engage NY Lessons: Topic 2 L.1 - Squared & Cubed(teacher) (student) Topic 2 L. 2 - Exponents(teacher) (student) Topic 2 L. 3 - Order of Operations (teacher) (student)Topic 2 Check for Understanding Substituting-Engage NY lesson Understanding Exponents-EngageNY lesson Order of Operations-EngageNY lesson |

Topic 3: Equivalent Expressions (4 days)
- I can expand multiplication
*expressions*into equivalent expressions. - I can factor expressions.
- I can use the distributive property with expressions.
vocabulary: value, area, volume, GCF |
Modified Engage NY Lessons:
Topic 3 L.1 - Expanded/Standard form(teacher) (student) Topic 3 L.2 - Distributing Expressions(teacher) (student) Topic 3 L.3 - Factoring Expressions(teacher) (student) Kahn Academy Lesson on GCF What is GCF? (ISBE lesson) GCF Practice Key Topic 3 Check for Understanding |

Topic 4: Write Expressions (2 days)
- I can write addition expressions.
- I can write subtraction expressions.
- I can write multiplication expressions including exponents.
- I can write division expressions.
- I can interpret situations and write an expression using various operations.
vocabulary: evaluate, expand, distributive property, factored form, standard form |
Modified Engage NY Lessons:
Topic 4 L.1 - Writing Addition and Subtraction Expressions(teacher) (student) Topic 4 L.2 - Writing Division Expressions(teacher) (student) Topic 4 L.3 - Writing Expressions with Variables(teacher) (student) Writing Evaluating Addition & Multiplication Expressions-EngageNY lesson Writing Expressions with Addition & Subtraction-EngageNY lesson Writing Expressions with Multiplication & Division-EngageNY lesson Writing Division Expressions-ENgageNY lesson Reading Expressions-EngageNY lesson Writing Expressions-EngageNY lesson Writing Expressions-EngageNY lesson Achieve the Core Exemplar lesson Toothpick Patterns I Have Who Has on Cards on expressions |

Topic 5: Write and Evaluate Expressions (4 days)
- I can evaluate expressions using addition and subtraction.
- I can evaluate expressions using multiplication and division.
- I can evaluate various expressions.
Assessment Part A & Reflection |

Topic 6: Solve Equations (8 days)
- I can write an equation to solve a real world situation.
- I can evaluate number sentences to be true and/or false.
- I can solve one-step equations using addition and subtraction by relating an equation to a diagram.
- I can solve a one-step equation algebraically using addition and subtraction.
- I can solve one-step equations using multiplication and division by relating the equation to a diagram.
- I can solve one-step equations algebraically using multiplication and division.
- I can solve two-step equations algebraically using all operations and show my understanding with tape diagrams/bar models.
- I can solve multi-step problems algebraically using all operations and show my understanding using tape diagrams/bar models.
vocabulary: evaluate, variable, coefficient, inverse operation, terms, isolateReal World Experience Task 3 |

Topic 7: Application of Equations (5 days)
- I can determine whether or not the equation is solved for the second variable in terms of the first variable or vice versa.
- I can determine which variable is the independent variable and which is the dependent variable.
- I can use tables and graphs to determine solutions to equations.
- I can write an inequality from a real world situation and solve it.
- I can graph the solution to an inequality.
Assessment Part B & Relfection |