Learning Targets/Success Criteria: Math 700
Module 2: Rational Numbers
Priority Standards:
7.NS.A.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.
7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, 𝑎 + 0.05𝑎 = 1.05𝑎 means that “increase by 5%” is the same as “multiply by 1.05.”
7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Overarching Skills:
Add/Subtract/Multiply/Divide Rational numbers
Decimal
Percent
Solution
Variable
Equation
Coefficient
Constant
Understand/Be able to do:
Topic:
Days: 1 & 2
Adding Integers
Eureka Lessons: 1, 2, 3 & 4
Walt:
We are learning to add integers
Success Criteria:
Topic:
Day: 3
Adding Rational Numbers
Eureka Lessons: 1, 2, 3 & 4
Walt:
We are learning to add rational numbers
Success Criteria:
Topic:
Day: 4
Subtracting Integers
Eureka Lessons: 5 & 6
Walt:
We are learning to subtract integers
Success Criteria:
Topic:
Day: 5
Subtracting Rational Numbers
Eureka Lessons: 5 & 6
Walt:
We are learning to subtract rational numbers
Success Criteria:
Topic: Buffer
Day: 6
Adding & Subtracting Rational Numbers
Eureka Lesson: 7
Walt:
We are learning to apply adding and subtracting rules for rational numbers.
Success Criteria:
Topic:
Day: 7
Properties of Adding and Subtracting
Eureka Lessons: 8 & 9
Walt:
We are learning to use properties for addition and subtraction
Success Criteria:
Topic:
Day: 10
Multiplying and Dividing Integers
Eureka Lessons: 10, 11, & 12
Walt:
We are learning to multiply and divide integers
Success Criteria:
Topic:
Day: 11
Multiplying and Dividing integers using rules
Eureka Lessons: 10, 11, & 12
Walt:
We are learning multiplication and division integer rules
Success Criteria:
Topic:
Day: 12
Multiplying and Dividing Rational Numbers
Eureka Lesson: 15
Walt:
We are learning to multiply and divide rational numbers
Success Criteria:
Topic:
Days: 15 & 16
Fractions, Decimals, and Percents
Eureka Lessons: 13 & 14
Walt:
We are learning to convert between fractions, decimals, and percents
Success Criteria:
Topic:
Day: 21
Writing Equations
Eureka Lessons: 17, 22 & 23
Walt:
We are learning to write equations using algebra
Success Criteria:
Topic:
Days: 22 & 23
Solving Equations
Eureka Lessons: 17, 22, & 23
Walt:
We are learning to write equations
Success Criteria:
Topic:
Day: 25
Writing, Evaluating, and Finding Equivalent Expressions
Eureka Lessons: 18 & 19
Walt:
We are learning to find, write, and evaluate expressions
Success Criteria:
Topic:
Days: 26 & 27
Operations with Rational Numbers
Eureka Lesson: 20
Walt:
We are learning to apply operations with rational numbers
Success Criteria:
Module 2: Rational Numbers
Priority Standards:
7.NS.A.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.
- 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 𝑞𝑞 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.
- 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.
- Apply properties of operations as strategies to add and subtract rational numbers
7.NS.A.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.
- 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 𝑝𝑝 and 𝑞𝑞 are integers, then −(𝑝/𝑞) = (−𝑝)/𝑞 = 𝑝/(−𝑞). Interpret quotients of rational numbers by describing real-world contexts.
- 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.
7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, 𝑎 + 0.05𝑎 = 1.05𝑎 means that “increase by 5%” is the same as “multiply by 1.05.”
7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
- Solve word problems leading to equations of the form 𝑝 + 𝑞 = 𝑟 and 𝑝(𝑥 + 𝑞) = 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Overarching Skills:
Add/Subtract/Multiply/Divide Rational numbers
- Positive/negative whole numbers
- Positive/negative fractions
- Positive/negative decimals
Decimal
Percent
Solution
Variable
Equation
Coefficient
Constant
Understand/Be able to do:
- Add/Subtract/Multiply/Divide rational numbers
- Represent numbers visually on a number line using addition and subtraction.
- Understand rules of computation.
- Convert between fractions, decimals, and percents
- Create and solve equations to represent and solve real world problems.
- Solve equations.
- Interpret solutions to equations
Topic:
Days: 1 & 2
Adding Integers
Eureka Lessons: 1, 2, 3 & 4
Walt:
We are learning to add integers
Success Criteria:
- I can add positive integers by counting up and negative integers by counting down (using curved arrows on the number line).
- I can justify that an integer plus its opposite add to zero.
- I know the opposite of a number is called the additive inverse because the sum of the two numbers is zero.
- I can model integer addition on the number line by using horizontal arrows.
- I can recognize that the length of an arrow on the number line is the absolute value of the integer.
- I can add arrows.
- Given several arrows, students indicate the number that the arrows represent (the sum).
- Given several arrows, students indicate the number that the arrows represent (the sum).
- I understand addition of integers as putting together or counting up.
- For negative numbers “counting up” is actually counting down. Students use arrows to show the sum of two integers, 𝑝 + 𝑞, on a number line and to show that the sum is distance |𝑞| from 𝑝 to the right if 𝑞 is positive and to the left if 𝑞 is negative.
- For negative numbers “counting up” is actually counting down. Students use arrows to show the sum of two integers, 𝑝 + 𝑞, on a number line and to show that the sum is distance |𝑞| from 𝑝 to the right if 𝑞 is positive and to the left if 𝑞 is negative.
Topic:
Day: 3
Adding Rational Numbers
Eureka Lessons: 1, 2, 3 & 4
Walt:
We are learning to add rational numbers
Success Criteria:
- I can apply the rules for adding rational numbers:
- Add rational numbers with the same sign by adding the absolute values and using the common sign.
- Add rational numbers with opposite signs by subtracting the smaller absolute value from the larger absolute value and using the sign of the number with the larger absolute value.
- Add rational numbers with the same sign by adding the absolute values and using the common sign.
- I can justify the rules using arrows and a number line.
- I can extend my findings to begin to include sums of rational numbers
Topic:
Day: 4
Subtracting Integers
Eureka Lessons: 5 & 6
Walt:
We are learning to subtract integers
Success Criteria:
- I can justify the rule for subtraction: Subtracting a number is the same as adding its opposite.
- I can justify the rule for subtraction for all rational numbers from the inverse relationship between addition and subtraction; that is, subtracting a number and adding it back gets you back to where you started: (𝑚 − 𝑛) + 𝑛 = 𝑚.
- I can justify the distance formula for rational numbers on a number line.
- I know the definition of subtraction in terms of addition and use the definition of subtraction to justify the distance formula.
- I can solve word problems involving changes in distance or temperature.
Topic:
Day: 5
Subtracting Rational Numbers
Eureka Lessons: 5 & 6
Walt:
We are learning to subtract rational numbers
Success Criteria:
- I can justify the rule for subtraction: Subtracting a number is the same as adding its opposite.
- I can justify the rule for subtraction for all rational numbers from the inverse relationship between addition and subtraction; that is, subtracting a number and adding it back gets you back to where you started: (𝑚 − 𝑛) + 𝑛 = 𝑚.
- I can justify the distance formula for rational numbers on a number line.
- I know the definition of subtraction in terms of addition and use the definition of subtraction to justify the distance formula.
- I can solve word problems involving changes in distance or temperature.
Topic: Buffer
Day: 6
Adding & Subtracting Rational Numbers
Eureka Lesson: 7
Walt:
We are learning to apply adding and subtracting rules for rational numbers.
Success Criteria:
- I can recognize that the rules for adding and subtracting integers apply to rational numbers.
Topic:
Day: 7
Properties of Adding and Subtracting
Eureka Lessons: 8 & 9
Walt:
We are learning to use properties for addition and subtraction
Success Criteria:
- I can use properties of operations to add and subtract rational numbers without the use of a calculator.
- I recognize that any problem involving addition and subtraction of rational numbers can be written as a problem using addition and subtraction of positive numbers only.
- I can use the commutative and associative properties of addition to rewrite numerical expressions in different forms.
Topic:
Day: 10
Multiplying and Dividing Integers
Eureka Lessons: 10, 11, & 12
Walt:
We are learning to multiply and divide integers
Success Criteria:
- I can justify my understanding of multiplication of integers.
- I understand and can explain that multiplying by a positive integer is repeated addition and that adding a number multiple times has the same effect as removing the opposite value the same number of times.
- I can use the properties and facts of operations to extend multiplication of whole numbers to multiplication of integers.
- I understand the rules for multiplication of integers and that multiplying the absolute values of integers results in the absolute value of the product. The sign, or absolute value, of the product is positive if the factors have the same sign and negative if they have opposite signs.
- I can use the rules for multiplication of signed numbers and give real-world examples.
- I can recognize that division is the reverse process of multiplication and that integers can be divided provided the divisor is not zero.
- I understand that every quotient of integers (with non-zero divisor) is a rational number and divide signed numbers by dividing their absolute values to get the absolute value of the quotient.
- I understand that the quotient is positive if the divisor and dividend have the same signs and negative if they have opposite signs.
Topic:
Day: 11
Multiplying and Dividing integers using rules
Eureka Lessons: 10, 11, & 12
Walt:
We are learning multiplication and division integer rules
Success Criteria:
- I can use the rules for multiplication of signed numbers and give real-world examples.
- I understand that the quotient is positive if the divisor and dividend have the same signs and negative if they have opposite signs.
Topic:
Day: 12
Multiplying and Dividing Rational Numbers
Eureka Lesson: 15
Walt:
We are learning to multiply and divide rational numbers
Success Criteria:
- I can recognize that the rules for multiplying and dividing integers apply to rational numbers.
- I can interpret products and quotients of rational numbers by describing real-world contexts
Topic:
Days: 15 & 16
Fractions, Decimals, and Percents
Eureka Lessons: 13 & 14
Walt:
We are learning to convert between fractions, decimals, and percents
Success Criteria:
- I can understand that the context of a real-life situation often determines whether a rational number should be represented as a fraction or decimal.
- I understand that decimals specify points on the number line by repeatedly subdividing intervals into tenths (deci- means tenth).
- I can convert positive decimals to fractions and fractions to decimals when the denominator is a product of only factors of either 2 or 5.
- I understand that every rational number can be converted to a decimal.
- I can represent fractions as decimal numbers that either terminate in zeros or repeat.
- I can represent repeating decimals using a bar over the shortest sequence of repeating digits.
- I can interpret word problems and convert between fraction and decimal forms of rational numbers.
Topic:
Day: 21
Writing Equations
Eureka Lessons: 17, 22 & 23
Walt:
We are learning to write equations using algebra
Success Criteria:
- I can translate word problems to write and solve algebraic equations using tape diagrams to model the steps they record algebraically.
Topic:
Days: 22 & 23
Solving Equations
Eureka Lessons: 17, 22, & 23
Walt:
We are learning to write equations
Success Criteria:
- I can use tape diagrams to solve equations and identify the sequence of operations used to find the solution.
- I can use algebra to solve equations, using techniques of making zero (adding the additive inverse) and making one (multiplying by the multiplicative inverse) to solve for the variable.
- I can identify and compare the sequence of operations used to find the solution to an equation algebraically, with the sequence of operations used to solve the equation with tape diagrams.
- I can solve equations for the value of the variable using inverse operations, by making zero (adding the additive inverse) and making one (multiplying by the multiplicative inverse).
Topic:
Day: 25
Writing, Evaluating, and Finding Equivalent Expressions
Eureka Lessons: 18 & 19
Walt:
We are learning to find, write, and evaluate expressions
Success Criteria:
- I can create equivalent forms of expressions in order to see structure, reveal characteristics, and make connections to context.
- I can compare equivalent forms of expressions and recognize that there are multiple ways to represent the context of a word problem.
- I can write and evaluate expressions to represent real-world scenarios.
Topic:
Days: 26 & 27
Operations with Rational Numbers
Eureka Lesson: 20
Walt:
We are learning to apply operations with rational numbers
Success Criteria:
- I can perform various calculations involving rational numbers to solve a problem related to the change in an investment’s balance over time.
- I can recognize and use mathematics as a tool to solve real-life problems.
What to Teach
Topic 1: Order of Operations
- I can simplify an algebraic expression.
Topic 2: Like and Unlike Terms
- I can identify like terms.
- I can combine like terms.
Topic 3: Using Properties
- I know the distributive property.
- I can identify when to use the distributive property.
- I can use the distributive property to simplify an expression.
- I can distribute a whole number, fraction, and decimal.
Topic 4: Using Expressions
- I can write an algebraic expression to represent a diagram.
- I can write an algebraic expression to represent a scenario.
- I can identify equivalent algebraic expressions.
- I can generate equivalent algebraic expressions..
vocabularyassociative property
combining like terms communitive property differnce distrubutive property expression factor integer product quotient sum variable |
Unit ResourcesAssessmentPre Assessment
Real World Experience Post Assessment Formative Assessment Student Reflection and Goal Setting |
Learn the MathGeorgia 7th overview
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