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Pre-Algebra advanced: 8th grade What is pre-algebra?
In Volusia county we structure courses by Common Core State Standards (CCSS.) We used to use Florida's Next Generation Sunshine State Standards and associated benchmarks. YOU WILL BE TESTED THIS YEAR ACCORDING TO NGSSS.
We divide the courses by Essential Questions. The Essential Questions are then divided by Measurement Topics which are then outlined with learning targets.
Unit One: Real Numbers
Essential Question(s): In what ways can rational numbers be useful?
| MACC.8.NS.1.1 Know that numbers that are not rational are call 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. |
classify a number as a rational or irrational based on its decimal expansion. convert a repeating decimal into a rational number. |
| MACC.8.NS.1.2 (MA.912.A.1.2) 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. π2). |
use reasoning to determine between which two consecutive whole numbers a square root will fall. plot the estimated value of an irrational number on a number line. estimate the value of an irrational number by rounding to a specific place value. use estimated values to compare two or more irrational numbers. |
| MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. |
solve problems using absolute value of a number. solve problems using percents. |
Unit Two: Exponents
Essential Question(s): How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?
| MACC.8.EE.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. |
determine the properties of integer exponents by exploring patterns and applying my understanding of properties of whole number exponents. apply the properties of integer exponents to simplify expressions. |
| MACC.8.EE.1.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = 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. |
recognize taking a square root as the inverse of squaring a number. recognize taking a cube root as the inverse of cubing a number. evaluate the square root of a perfect square. evaluate the cube root of a perfect cube. justify that the square root of a non-perfect square will be irrational. |
| MACC.8.EE.1.3 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. |
write an estimation of a large quantity by expressing it as the product of a single-digit number and a positive power of ten. write an estimation of a very small quantity by expressing it as the product of a single-digit number and a negative power of ten. compare quantities written as the product of a single-digit number and a power of ten by stating their multiplicative relationships. |
| MACC.8.EE.1.4 (MA.8.A.6.1) 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. |
add and subtract two numbers written in scientific notation. multiply and divide two numbers written in scientific notation. select the appropriate units for measuring derived measurements when coMParing quantities written in scientific notation. identify and interpret the various ways scientific notation is displayed on calculators and through computer software. |
| MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems. |
solve problems using radicals. simplify real number expressions using the laws of exponents. perform operations on real numbers using multi-step and real world problems. |
Unit Three: Angles/Pythagorean Theorem
Essential Question(s): How can you convert from one measurement system to another? How can you use similar triangles to solve problems? How does geometry better describe objects?
| MA.8.G.5.1 Compare, contrast, and convert units of measure between different measurement systems (US customary or metric (SI)) and dimensions including temperature, area, volume, and derived units to solve problems. |
determine the order of measurements represented in different units. convert measurements between the metric and US customary systems. |
| MA.8.G.2.1 Use similar triangles to solve problems that include height and distances. |
use similar triangles to solve real-life problems. |
| MA.8.G.2.3 Demonstrate that the sum of the angles in a triangle is 180 degrees and apply this fact to find unknown measure of angles and the sum of angles in polygons. |
determine the unknown angle measurements of triangles. determine unknown angle measurements of polygons. |
| MACC.8.G.1.5 (MA.8.G.2.2) Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. |
prove that the sum of any triangle’s interior angles will have the same measure as a straight angle. prove that the sum of any polygon’s exterior angles will be 360-degrees. make conjectures regarding the relationships and measurements of the angles created when two parallel lines are cut by a transversal. apply proven relationships to establish minimal properties to justify similarity. |
| MACC.8.G.2.6 Explain a proof of the Pythagorean Theorem and it converse. |
demonstrate the relationship of the three side lengths of any right angle by the use of visual models. apply algebraic reasoning to relate the visual model to Pythagorean Theorem. determine if a given triangle is a right triangle using Pythagorean Theorem. |
| MACC.8.G.2.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. MA.8.G.2.4 |
apply the Pythagorean Theorem to find an unknown side length of a right triangle. draw a diagram and use the Pythagorean Theorem to solve real-world problems involving right triangles. draw a diagram to find right triangles in a three-dimensional figure and use the Pythagorean Theorem to calculate various dimensions. |
| MACC.8.G.2.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. |
connect any two points on a coordinate grid to a third point so that the three points form a right triangle. apply the Pythagorean Theorem with the characteristics of a right triangle to find the distance between the original two points. |
links on this site
Exponential notation Percent converting fractions and decimals 7th grade FCAT sample test (2.0)
pre algebra sample questions rates and proportions
greatest common factor least common multiple prime factorization
Introduction to rules for using exponent
links off-site
webmath.com aaamath.com www.mathway.com/ math.com/students/homeworkhelp.html