Additional Mathematics: Students will use addition, subtractions, multiplication, and division of rational numbers: in grade 8 when expanding their knowledge in rational to irrational numbers in algebra and geometry when they expand into real numbers and beyond Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the overarching unit standards from within the same cluster. The table also provides instructional connections to grade-level standards from outside the cluster. Overarching Unit Standards Supporting Standards within the Cluster Instructional Connections outside the Cluster 7.NS.1: and extend previous understandings of addition and subtraction to add and subtract rational numbers, and represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.1a: Describe situations in which opposite quantities combine to make 0. 7.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. 7.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. 7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers. 7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.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. 7.NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.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. 7.NS.2b:
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. 2b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with divisor) is a rational number. If p and q are integers, then: Interpret quotients of rational numbers by describing contexts. 2c: properties of operations as strategies to multiply and divide rational numbers. Ability to identity and apply the following properties: Multiplicative Inverse Commutative Property of Multiplication Associative Property of Multiplication Identity Property of Multiplication Recognize that rules for multiplying signed numbers remain the same for all rational numbers Ability to explore and to justify the result of division by 0 (zero) Ability to apply and extend knowledge of addition and subtraction of integers (i.e., two color counters, arrows on a number line) to multiplication and division Ability to use patterns and concrete models to devise a general rule for dividing integers: Ability to Identify and apply the following properties: Distributive Property Associative Properties Commutative Properties Identity Properties Ability to recognize that when rational numbers in fractional form zero
C G x D H ÷ Activity 1: Note Card Template for Concept Attainment: -- cut apart -2+2 -5+6 3.427 − 3.247 214.1 − 214.1 The highest altitude measured in the United States is Mt. McKinley, Alaska at 20,320 feet. The lowest altitude in the United States is Death Valley, California and is 282 feet below sea level. ‾ a − b a and b do not equal zero)