Unit 1
– Operations with Rational Numbers
Sections covered
– 1-5, 1-6, 1-8, 2-1, 2-10, 2-11, 3-1, 3-2, 3-3, 3-4, 3-5, 3-7, 3-8, 3-10
Sections to Review (if needed) - 2-2, 2-3, 2-4
Standard – MCC7.NS.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.
MCC7.NS.1a Describe situations in which opposite quantities combine to make 0.
MCC7.NS.1b 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.
MCC7.NS.1c 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.
MCC7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
MCC7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.
MCC7.NS.2a 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.
MCC7.NS.2b 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
–( 𝑝𝑞) =(− 𝑝 ) 𝑞 = 𝑝 (− 𝑞 ). Interpret quotients of rational numbers by describing real-world contexts.
MCC7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers
MCC7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.
MCC7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
Key Concept
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Relationships, Related Concepts
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Model, Quantity
Global Context
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Globalization and Sustainability
Statement of Inquiry – Different quantities can be modeled to understand relationships in our world.
Inquiry Question – How can quantities be modeled to help make educated decisions related to the world in which we live?

Vocabulary order of operations – an agreed upon method to solve problems (1-5) commutative property – states that you can add or multiply numbers in any order (1-6) associative property –when you add or multiply, group the numbers together in any combination (1-6) identity property of addition –the sum of 0 any number is always that number (1-6) identity property of multiplication – that the product of 1 and any number is that number (1-6) distributive property –if you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products (1-6) additive inverse - the sum of a number and its additive inverse is zero (1-6) zero pair – pair of numbers whose sum is zero (2-1) multiplicative inverse: if two numbers multiply to equal the identity 1, they are multiplicative inverses (1-6) opposite number–number that is the same distance from zero on a number line as the original (2-1) positive number – integer greater than zero (2-1) negative number –integer less than zero (2-1) sign – the positive or negative sign in front of a number (2-1) integers – the set of whole numbers and their opposites (2-1) absolute value – the distance from zero on a number line (2-1) repeating decimal – a decimal number that has a digit or group of digits repeating without end (2-10) terminating decimal – a decimal that contains a finite number of digits; it stops with a zero (2-10) long division - procedure for dividing multi-digit numbers (2-10) rational number – a number that can be written as a fraction with integers for its numerator and denominator. The set of numbers that can be written in the form a/b where a and b are integers and b ≠ 0.
(2-11) irrational number – a number that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal (2-11) natural numbers - the set of numbers {1, 2, 3, 4,…}. also called counting numbers (2-11) whole number – a positive integer or zero (2-11)