# 8 th Grade Pre-Integrated Math Critical Content

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1 Note: Although these are mastery objectives, pacing of content is at the discretion of the teacher. Content Standard 1: Numbers, Number Sense, and Computation Place Value Represent numbers using scientific notation in mathematical and practical situations. Powers of Ten and Scientific Notation Fractions Translate among fractions, decimals, and percents, including percents greater than 100 and percents less than 1. Explain and use the relationship among equivalent representations of rational numbers in mathematical and practical situations. Fractions, Decimals and Percents Comparing and Ordering Compare and order real numbers, including powers of whole numbers in mathematical and practical situations. Scientific Notation Comparing and Ordering Fractions Fractions and Decimals Counting (Teacher provided supplement needed for mix of all real numbers) Addressed in previous grades October 2007 Page 1 of 10 Douglas County School District

2 Facts Identify perfect square to 225 and their corresponding square roots. Square Roots and Irrational Numbers Estimating and Estimation Strategies 11-1 Use estimation strategies to determine the reasonableness of an answer in mathematical and practical situations. Computation Done throughout the book No specific section addresses this topic Calculate with real numbers to solve mathematical and practical situations. Adding Integers Subtracting Integers Multiplying and Dividing Integers Adding and Subtracting Integers Multiplying and Dividing Fractions Exponents Square Roots and Irrational Numbers Proportions and Percents Percents and Equations Percent of Change Markup and Discount Use order of operations to solve equations in the real number system. Order of Operations Solving Problems and Number Theory Identify and apply the identify property, inverse property, and the absolute value of real numbers to solve problems. Integers and Absolute Value Adding Integers Properties of Numbers Multiplying and Dividing Fractions (inverse property) October 2007 Page 2 of 10 Douglas County School District

3 Content Standard 2: Patterns Functions, and Algebra Patterns Find the missing term in a numerical sequence or a pictorial representation of a sequence. Solving 2-Step Equations Patterns and Sequences Variables and Unknowns with pictorial 13-1 Evaluate formulas and algebraic expressions using rational numbers (with and without technology). Evaluating Expressions Using Formulas Rational Numbers evaluating expressions 3-4 Formulas Solve and graphically represent equations and inequalities in one variable, including absolute value. Variables and Equations Adding or Subtracting Multiplying or Dividing Solving 1-Step Inequalities by Adding or Subtracting Solving 1-Step Inequalities by Multiplying or Dividing Adding or Subtracting Decimals Multiplying or Dividing Decimals Adding or Subtracting Fractions Multiplying Fractions Solving 2-Step Equations Solving Multi-Step Equations Multi-Step Equations with Fractions and Decimals Solving 2-Step Inequalitites October 2007 Page 3 of 10 Douglas County School District

4 Number Sentences, Expressions, and Polynomials Add and subtract binomials. Simplifying Variable Expressions Relations and Functions Identify, model, describe, and evaluate functions (with and without technology). Relations and Functions Translate among verbal descriptions, graphic, tabular, and algebraic representations of mathematical situations (with and without technology). Equations with Two Variables Slope and y-intercept Writing Rules for Linear Functions Linear Equations and Inequalities Integrated Math 1 text & teacher provided supplement needed for specific + and of binomials 8-1 Identify functions don t do domain and range Solve linear equations and represent the solution graphically. Equations with Two Variables Slope and y-intercept Algebraic Representations and Applications Describe how changes in the value of one variable affect the values of the remaining variables in a relation Teacher supplied resource needed October 2007 Page 4 of 10 Douglas County School District

5 Content Standard 3: Measurement Comparison, Estimation, and Conversion Estimate and convert units of measure for mass and capacity within the same measurement system (customary and metric). Using the Metric System Using Customary Units of Measurement Precision in Measurements Demonstrate an understanding of precision, error, and tolerance when using appropriate measurement tools. Precision and Significant Digits Formulas Math Toolbox, Page 156 Teacher supplied supplement needed for error and tolerance Identify how changes in a dimension of a figure effect changes in its perimeter, area and volume. Money Teacher supplied resource needed possibly Marilyn Burns About Teaching Mathematics Calculate percents in monetary problems. Percents and Equations Percent of Change Markup and Discount Ratios and Proportions Apply ratios and proportions to calculate rates and solve mathematical and practical problems using indirect measure. Ratios and Unit Rates Proportions Similar Figures and Scale Drawings Time Addressed in previous grades October 2007 Page 5 of 10 Douglas County School District

6 Content Standard 4: Spatial Relationships, Geometry, and Logic Two Dimensional Shapes Find and use the sum of the measure of interior angles of polygons. Angles of a Polygon Congruence, Similarity, and Transformations Apply the properties of equality and proportionality to congruent or similar shapes. Similar Figures and Scale Drawings Congruence Coordinate Geometry and Lines of Symmetry Math Toolbox p459 has find not use Teacher provided supplement needed for use 6-3 Similar figures 9-5 p466 #5-17 only for congruence Demonstrate dilation using coordinate geometry and models. Describe the relationship between an original figure and its transformation or dilation. Translations Rotations Three Dimensional Figures Integrated Math 1 text & teacher provided resource needed for dilation Integrated Math 1 text & teacher provided supplement needed for reflections Addressed in previous grades Algebraic Connections Calculate slope, midpoint, and distance using equations and formulas (with and without technology). Slope and y-intercept Distance and Midpoint Formulas October 2007 Page 6 of 10 Douglas County School District

7 Determine the x- and y- intercepts of a line. 8-2, Integrated Math 1 text & teacher provided supplement needed for x-intercept Lines, Angles, and their Properties Form generalizations and validate conclusions about geometric figures and their properties. Introduction to Geometry: Points, Lines, and Planes Angle Relationships and Parallel Lines Classifying Polygons Triangles Verify and explain the Pythagorean Theorem using variety of methods. The Pythagorean Theorem Constructions Construct geometric figures using a variety of tools. Constructions Logic Represent logical relationship using conditional statements Integrated Math 1 text & teacher provided resource needed October 2007 Page 7 of 10 Douglas County School District

8 Content Standard 5: Data Analysis Data Collection and Organization Formulate questions and design a study that guides the collection of data. Organize, display, and read data including box and whisker plots (with and without technology). Scatter Plots Circles Integrated Math 1 text & teacher provided resource needed for formulate/design , p612 stem and leaf, p618 histogram, 12-2 box and whisker, 12-1 frequency tables and line plots Central Tendency and Data Distribution Select and apply appropriate measure of data distribution, using interquartile range and central tendency. Mean, Median, and Mode Interpretation of Data Evaluate statistical arguments that are based on data analysis for accuracy and validity. Using Graphs to Persuade Permutations and Combinations Find the number of combinations possible in mathematical and practical situations. Counting Outcomes and Theoretical Probability Integrated Math 1 text & teacher provided supplement needed for interquartile range Distinguish between permutations and combinations. Permutations and Combinations October 2007 Page 8 of 10 Douglas County School District 12-6

9 Experimental and Theoretical Probability Differentiate between the probability of an event and the odds of an event. Probability Statistical Inferences Formulate reasonable inferences and predictions through interpolation and extrapolation of data to solve practical problems Teacher provided resource needed Process Standard: Problem Solving Formulate their own problems Find solutions to problems from everyday situations Develop and apply strategies to solve a variety of problems Integrate mathematical reasoning, communication and connections Generalize solutions and apply previous knowledge to new problem solving situations. Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem. Apply problem solving strategies until a solution is found it is clear that no solution exists. Interpret and solve a variety of mathematical problems by paraphrasing. Identify necessary and extraneous information. Check the reasonableness of a solution. Apply technology as a tool in problem solving situations. Process Standard: Mathematical Communication Translate information into mathematical language and symbols Process information mathematically Present results in written, oral, and visual formats Discuss and exchange ideas about mathematics as a part of learning Read a variety of fiction and nonfiction texts to learn about mathematics Use mathematical notation to communicate and explain problems Use formulas, algorithms, inquiry, and other techniques to solve mathematical problems. Evaluate written and oral presentations in mathematics. Identify and translate key words and phrases that imply mathematical operations. Model and explain mathematical relationships using oral, written, graphic, and algebraic methods. Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems. October 2007 Page 9 of 10 Douglas County School District

10 Process Standard: Mathematical Reasoning Reinforce and extend their logical reasoning abilities Reflect on, clarify, and justify their thinking Ask questions to extend their thinking Use patterns and relationships to analyze mathematical situations Determine relevant, irrelevant, and /or sufficient information to solve mathematical problems. Recognize and apply deductive and inductive reasoning. Review and refine the assumptions and steps used to derive conclusions in mathematical arguments. Justify answers and the steps taken to solve problems with and without manipulatives and physical models. Process Standard: Mathematical Connections Link new concepts to prior knowledge Identify relationships between content strands Integrate mathematics with other disciplines. Allow the flexibility to approach problems in a variety of ways within and beyond the field of mathematics. Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics. Use manipulatives and physical models to explain the relationships between concepts and procedures. Use the connections among mathematical topics to develop multiple approaches to problems. Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science. Identify, explain, and apply mathematics in everyday life. October 2007 Page 10 of 10 Douglas County School District