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(STANDARD)
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What CCSS/ISBE/National Standard(s) will this unit address?
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (Integers)
 Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
 Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. (Adding
Integers)
 Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. (Subtracting Integers)
 Apply properties of operations as strategies to add and subtract rational numbers. (Number Properties)
7NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
 Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) =
1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. (Use 4 section chart to show
multiple representations - # line models of multi/div)
 Students understand that multiplication and division of integers is an extension of multiplication and division of whole numbers. Students recognize that when division of rational numbers is represented with a fraction bar, each number can have a negative sign.
 Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts. (long division)
 Apply properties of operations as strategies to multiply and divide rational numbers.
 Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
COMMON CORE STATE STANDARDS for MATHEMATICS
7NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.
 Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
 Students use order of operations from 6th grade to write and solve problem with all rational numbers.
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Applies the Power Standard to a “novel” real world situation. A statement of what students should be able to do with the standard knowledge in other contexts. Students will be able to independently use their learning on a long-term basis to…
Order of Operations provide a foundation for all other math. Every time you solve a multi-step problem, you will be using the order of operations.
Students will be able to independently use their learning of integers and operations so that in the long run they can, on their own, make responsible decisions in their daily lives when they manage money.

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What specific understandings can be predicted from the Power Standard(s)?
 Students will understand that…
 Unit 1 – A: Order of Operations o Order of operations ensures that we will get the same solution to the same problem every time.
 Unit 1 –B: Integers o We see integers in distances, sports, temperatures, lunch balances at OLHMS, money, etc. o Positive numbers increase a starting point and negative numbers decrease a starting point. o Regardless of whether numbers are whole numbers or fractions/decimals, the further right you move on a number line, the greater the number. The further left you
 move on a number line, the smaller the number.
Unit 1 – C: Coordinate Grid o Ordered pairs can be represented graphically by using the
X and Y axes. o Coordinate grids help us give directions and find locations.
 Unit 1 – D: Number Properties o Number properties explain and help us understand how numbers can be manipulated and used in different ways. o We can use number properties to simplify problems by recognizing compatible numbers and change them to make them simpler. For example 5 + 15 is simpler than
13 + 7.
 Unit 1 – E: Long Division o Multiplication and division are inverses. If in multiplication we find the product of two factors, in division we find the missing factor if the other factor and the product are known. o Terminating decimals are decimals that eventually end.
Repeating decimals have digits that either partially or completely repeats.
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What thought provoking questions would foster inquiry, understanding, and transfer of learning?
Unit 1 – A: Order of Operations o How does the order of operations provide a foundation for all other Math?
Unit 1 –B: Integers o Where do we see integers in our everyday lives? o How is it helpful to understand the difference between positive and negative numbers? o How are numbers related on the number line?
Unit 1 – C: Coordinate Grid o How can ordered pairs be represented graphically? o How do coordinate grids relate to our everyday world?
Unit 1 – D: Number Properties o Why is it important to recognize the various number properties? o How can number properties be used to make problems simpler?
Unit 1 – E: Long Division o How does my knowledge of multiplication facts help me to solve long division problems? o When dividing fractions to get decimals, what is the difference between terminating and repeating decimals?

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What should students know as a result of this unit? What can be studied? (Theory/Concepts/Mental Coordination)
 Students will know…
Numerical sequences
Exponent
Order of Operations
Properties
Power
Integers
Absolute Value
Integer
Negative Integer, Negative Number
Opposites, Additive Inverses
Positive Integer, Positive Number
Coordinates
Quadrant
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What should students be able to do as a result of this unit? What can be practiced? (Application of Theory/Concepts/Physical Coordination)
 Students will be able to…
Analyze Patterns and Relationships.
Represent, compare, and interpret numbers.
Simplify expressions using order of operations.
Solve problems involving exponents.
Explore relationships between positive and negative integers.
Develop an understanding of operations with positive and negative integers.
Model situations with integers.
Extend the coordinate grid to include negative coordinates.
Simplify problems by using the number properties.
Convert a rational number to a decimal using long division.
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Is each standard and transfer goal being assessed? An authentic assessment(s) designed to show how students demonstrate their understanding of essential questions and transfer goals when applied to a new, varied, or realistic situation. Should be written in the
GRASPS format and reflect the UbD “Six Facets of Understanding.”
Unit 1 – A: Order of Operations o 12 Questions Quiz o Some multiple choice, some open ended
Unit 1 –B: Integers o Make the Teacher Go Broke Activity o Performance Assessment focuses on integer operation in a real world context. Students need to compare amounts and determine which cards fit each situation within the game.

Unit 1 – C: Coordinate Grid o Picture Graph
Unit 1 – D: Number Properties o Three Short Response Questions
Unit 1 – E: Long Division o Solve one problem from the question bank and explain your method on a poster, in bullet form, iMovie, etc.
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What criteria will be used in each assessment to evaluate attainment of each desired result? What are the qualities by which learning is judged?
Unit 1 – A: Order of Operations o 12 Questions Quiz o Regular percentages will be applied
Unit 1 –B: Integers o Make the Teacher Go Broke o Rubric
Unit 1 – C: Coordinate Grid o Picture Graph o Rubric out of 10 points
 The number of points deducted will be based on the number of incorrectly plotted coordinates.
Unit 1 – D: Number Properties o Short Responses: 12 points
 4 points per problem: 2 points = correct answer, 2 points = explanation
Unit 1 – E: Long Division o Choice of nine problems: 3 simple, 3 medium, 3 difficult o Choice of presentation: bulleted list, poster, iMovie o Point break down: 2 points for a simpler problem, 4 points for a medium problem, 6 points for a difficult problem o Presentation points: 2 points for a bulleted list, 4 points for a decorated poster, 6 points for an iMovie or Power Point
 Partial or whole points will be deducted for missed steps o Students can earn extra points by creating an additional problem, going above and beyond, or completing a pre-approved idea
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What daily evidence has been collected to determine goal attainment? Tests, quizzes, discussions, homework, exit slips, graphic organizers, note-taking, etc…
Unit 1 – A: Order of Operations o Homework o Class responses/activities o Math Talk 6 + 2 * 4: Solve it right and wrong, asking kids which is correct. If time allows then do 20 – 2 + 4 (Partner) o Vocabulary graphic organizer on SmartBoard o Exit Slip from SmartBoard
Unit 1 –B: Integers o Homework o Class responses/activities

o Student participation in integer labs o Exit Problem: Students create a word problem where the answer is zero (additive inverse) o Math Talk: Distance from pond to a tree house – use this problem to introduce number line o Socrative formative exit slip **Use “Accentuating the Negative” – Page 86-Check Up #2 #2,3,5-8, 12, 14 o Integer Games: Spinteger, Integer War
Unit 1 – C: Coordinate Grid o Homework o Class responses/activities o Students can use interactive coordinate planes on netbooks and work with a partner to test each others’ knowledge o Students will “walk out” given coordinates on a giant floor grid
Unit 1 – D: Number Properties o Homework o Class responses/activities o Group property scrambles
Unit 1 – E: Long Division o Homework o Class responses/activities o Entrance Slip
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What will be done to determine students’ background knowledge, skill level, and possible misconceptions? (K-W-L) How will students be grouped? What opportunities for differentiation will take place?
Unit 1 – A: Order of Operations: used to split kids for entire order of operations unit o Kids who exceeded on pretest – decimals, brackets, fractions, complex/challenge o Kids who demonstrated misconceptions– small group with teacher to work on grade level problems
*Students will have the opportunity to move up or down in the groups as needed
- Unit 1 –B: Integers
Unit 1 – C: Coordinate Grid
Unit 1 – D: Number Properties
Unit 1 – E: Long Division