Power Skills for Honors Geometry with Data Analysis

Power Skills are those required/mandatory/vital abilities/competencies/expertise that the student should be able to demonstrate PRIOR to the course.

1. Number Sense and Operations with Fractions (Without A Calculator) (ACC 7, #1, #8)

   1. Adding and Subtracting fractions with like or unlike denominators

   2. Multiplying and Dividing Fractions

   3. Convert mixed numbers and integers to improper fractions

   4. Convert decimals to fractions and vice versa

   5. Understand the concept of reciprocal, and opposite reciprocal (For whole numbers as well as fractions)

      1. Example: the reciprocal of 3 is 13; the reciprocal of 45is 54

   6. Compare rational numbers with or without a number line.

      1. Example: 23>35

   7. Know the difference between a rational number, and an irrational number.

2. Graphing on an (x , y) coordinate plane (ACC 7, #6)

   1. Accurately plot points on the coordinate plane

   2. Know the difference between the positive and negative direction on the x and y axes

   3. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

   4. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

   5. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

3. Manipulate and Simplify expressions (ACC 7 #9, #12, #13)

   1. Simplify expressions involving integers, exponents, and/or distributive property

      1. Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.

      2. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

   2. Generate expressions in equivalent forms based on context and explain how the quantities are related.

4. Perfect Squares, Squares Roots, Perfect Cubes, Cubed Roots (ACC 7, #14, #15)

   1. Know your perfect squares up to 400 (202)

      1. For example: 122=144; 132=169; 142= 196

   2. Know your perfect cubes (up to 1000)

      1. Example: 53= 125; 73=343; 93=729

   3. Take the square root of a perfect square without a calculator (up to 400)

      1. For example: 289=17; 256=16; 16=4

   4. Take the cubed root of a perfect cube without a calculator (up to 1000)

      1. For example: 3216=6; 327=3; 3512=8

   5. Explain that the square root of a non-perfect square or non-perfect cube is irrational.

5. Evaluate expressions and solve linear equations for a specified variable (with or without a calculator) (ACC 8, #9, #22) (ACC 7, #17, #18)

   1. Evaluate variable expressions given values to input for at least one variable.

   2. Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.

   3. Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

   4. Solve systems of linear equations by graphing, substitution or addition (elimination)

   5. Use variables to represent quantities in a real-world or mathematical problem and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

      1. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.