enVision Mathematics Topic 1
7th Grade; August – September (5 weeks); 1st Quarter
Embedded Files
Topic Title(s):
Rational Number Operations
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
7.NS.A. The Number System: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
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. (CCSS: 7.NS.A.1)
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. (CCSS: 7.NS.A.1.a)
Demonstrate 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. (CCSS: 7.NS.A.1.b)
Demonstrate 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. (CCSS: 7.NS.A.1.c)
Apply properties of operations as strategies to add and subtract rational numbers. (CCSS: 7.NS.A.1.d)
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (CCSS: 7.NS.A.2)
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. (CCSS: 7.NS.A.2.a)
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. (CCSS: 7.NS.A.2.b)
Apply properties of operations as strategies to multiply and divide rational numbers. (CCSS: 7.NS.A.2.c)
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. (CCSS: 7.NS.A.2.d)
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.) (CCSS: 7.NS.A.3)
Solve problems with rational numbers using all four operations. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
Compute with rational numbers abstractly and interpret quantities in context. (MP2)
Justify understanding and computational accuracy of operations with rational numbers. (MP3)
Use additive inverses, absolute value, the distributive property, and properties of operations to reason with and operate on rational numbers. (MP7)
Inquiry Questions
How do operations with integers compare to and contrast with operations with whole numbers?
How can operations with negative integers be modeled visually?
How can it be determined if the decimal form of a rational number terminates or repeats?
Coherence Connections
This expectation represents major work of the grade.
In previous grades, students use the four operations with whole numbers and fractions to solve problems.
In Grade 7, this expectation connects with solving real-life and mathematical problems using numerical and algebraic expressions and equations. This expectation begins the formal study of rational numbers (a number expressible in the form a/b or –a/b for some fraction a/b; the rational numbers include the integers) as extended from their study of fractions, which in these standards always refers to non-negative numbers.
In Grade 8, students extend their study of the real number system to include irrational numbers, radical expressions, and integer exponents. In high school, students work with rational exponents and complex numbers.
Academic Vocabulary & Language Expectations:
Repeating decimal, terminating decimal, additive inverse, complex fraction, multiplicative inverse
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 1
Let's Investigate! Tasks
Let's Investigate! Can You Nail It? (TE) (relates to Lesson 1-2)
Let's Investigate! Sum Chips (TE) (relates to Lesson 1-3)
Let's Investigate! Subtraction Action (TE) (relates to Lesson 1-4)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Add Positive and Negative Integers, Add Positive and Negative Numbers, Subtract Positive and Negative Integers, Add and Subtract Positive and Negative Numbers, Multiply Positive and Negative Numbers, Divide Positive and Negative Numbers, Solve Problems with Rational Numbers, Write Fractions as Decimals
Coherence Map/Concept Progressions: 7.NS.A.1.b, 7.NS.A.1.c, 7.NS.A.1.d, 7.NS.A.2.c, 7.NS.A.2.d, 7.NS.A.3
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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