Blue = awareness of pre-requisite standards (pre-assess and differentiate as needed)

2. Understand

3. Understand subtraction of rational numbers as adding the additive inverse,

4. Apply properties of operations as strategies to add and subtract rational numbers.

2.

3.

4.

__UNIT 1:____Real Numbers__

5 WEEKSTest:5 WEEKS

**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.

2. 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.3. 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.4. Apply properties of operations as strategies to add and subtract rational numbers.

**7.NS.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.**2.

**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.3.

**Apply properties of operations as strategies to multiply and divide rational numbers.**4.

**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.)
**8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.**- 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., √2).
*For example, by truncating the decimal expansion of*√*2, show that*√*2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.* **8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.***For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.*- 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form
*x*² =*p*and*x*³ =*p*, where*p*is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. **8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.***For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.*- 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.