## Intermediate Math 1 - Number Systems

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## 1- Expressions and Equations 2- Geometry 3- Number Systems

4- Ratios and Proportions 5- Statistics and Probability

## Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

7.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.a. 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.b. 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.c. 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.d. Apply properties of operations as strategies to add and subtract rational numbers. |
7.NS.1.a I can describe rational numbers in a contextual situation.For example: The temperature dropped 5 degrees. The temperature raised 5 degrees. For example: A hydrogen atom has 0 charge because its two constituents are oppositely charged.7.NS.1.b.1 I can understand that p + q is a number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.7.NS.1.b.2 I can show that a number and its opposite have a sum of 0 (additive inverses)7.NS.1.b.3 I can interpret sums of rational numbers using contextual situations.7.NS.1.c.1 I can understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).7.NS.1.c.2 I can show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in contextual situations.7.NS.1.d I can apply properties of operations as strategies to add and subtract rational numbers.For example: 2 ¼ + 3 ½ = (2 + 3) + (¼ + ½) |

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.a. 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. b. 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.c. Apply properties of operations as strategies to multiply and divide rational numbers. d. 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.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.) |
7.NS.2.a.1 I can understand the properties used to multiply fractions extend to all rational numbers, with a particular emphasis on the distributive property and signed numbers. 7.NS.2.a.2 I can interpret products of rational numbers using contextual situations.7.NS.2.b.1 I can understand that integers can be divided, and every quotient of integers (with non-zero divisor) is a rational number.7.NS.2.b.2 I can understand that if p and q are integers, then –(p/q) = (–p)/q = p/(–q).7.NS.2.b.3 I can interpret quotients of rational numbers using contextual situations.7.NS.2.c I can apply properties of operations as strategies to multiply and divide rational numbers.7.NS.2.d.1 I can convert a rational number to a decimal using long division; 7.NS.2.d.2 I can understand that the decimal form of a rational number terminates in 0s or eventually repeats.Note: Operations with integers are NOT included in any previous grade level. 7.NS.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.) |