Essentials of Mathematics Lesson Objectives

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Bridget Reeves
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1 Essentials of Mathematics Lesson Unit 1: NUMBER SENSE Reviewing Rational Numbers Practice adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals. Practice evaluating exponents. Absolute Value and Integers Practice adding, subtracting, multiplying, and dividing absolute values and integers. Define integers and absolute value. Converting Fractions to Decimals and Percents Convert fractions, decimals, and percents. Working with Percents (1) Increase and Decrease Practice finding the percent of increase or decrease. Working with Percents (2) Applications of Percents Practice calculating discounts, markups, simple and compound interest, and commission rates. Fractions and Factoring Practice adding, subtracting, and reducing fractions with unlike denominators using the LCM and GCF. Identify prime numbers. Create factor trees to identify factors of numbers. Determine the LCM and GCF of numbers. Using Exponent Rules Add exponents when multiplying numbers with common bases. Multiply exponents when raising a number to a particular power. Subtract exponents when dividing numbers with common bases. Exponents in Scientific Notation Identify large numbers using positive exponents. Use scientific notation to translate numbers. Recognize that the multiplier in scientific notation is always equal to or greater than 1 and less than 10. Identify small numbers using negative exponents. Negative Whole-Number Exponents Multiply exponents when raising a number to a particular power. Add, subtract, multiply, and divide negative whole-number exponents. Subtract exponents when dividing numbers with common bases. Add exponents when multiplying numbers with common bases. Understand the correct order of operations. Powers and Roots Understand powers and roots. Identify perfect square roots. Recognize the approximate value of roots that are not perfect squares.

2 Essentials of Mathematics Lesson Unit 2: STATISTICS, DATA, ANALYSIS, AND PROBABILITY Measures of Central Tendency Determine the mode, or item that appears most often, in a set of data. Determine the median, or middle number, in a set of data. Determine the mean, or average, of a set of data. Evaluating Statistical Claims Recognize questions that can relate to the data. Answer questions related to data. Identify a valid claim based on data. Identify a bar graph, line graph, and a pie graph. Displaying and Comparing Data Sets Identify valid patterns and relationships of data displayed in graphs or charts. Recognize graphic representations of data. Interpret and compare sets of data. Outcomes Determine the number of ways an event can occur. Determine the total number of outcomes available in a scenario. Recognize and use graphic representations of data. Representing Probabilities Recognize probabilities as ratios that can be expressed as fractions, decimals, or percentages. Compute the probability of an event will or will not occur. Independent and Dependent Variables Recognize that variables may or may not be dependent on one another. Compute the probability of an event that is independent or dependent.

3 Essentials of Mathematics Lesson Unit 3: ALGEBRA AND FUNCTIONS Order of Operations Use the correct order of operations to evaluate expressions. Memorize 'Please Excuse My Dear Aunt Sally!' to assist in remembering the order of operations. Substitute a value for the variable and simplify the expression. Working with Exponents and Roots Add exponents when multiplying numbers with common bases. Multiply and divide numbers with exponents and common bases. Subtract exponents when dividing numbers with common bases. Calculate a power when raised to a power. Multiply and divide square roots. The Distributive Property Understand and use the distributive property to add, subtract, multiply, and divide. Distribute a negative sign correctly through the expression. Add and Subtract Polynomials Use appropriate techniques to solve word problems and simplify algebraic expressions. Add and subtract polynomials. Combine like terms in an algebraic expression. Multiply and Divide Polynomials Multiply and divide polynomials. Use appropriate techniques to solve problems. Inverse Operations Find and use the inverse operation to solve equations and inequalities. Find and use the reciprocal to solve equations and inequalities. Solving Two-Step Equations and Inequalities Solve two-step linear equations and inequalities. Interpret the solutions and judge their reasonableness. Writing Mathematical Statements Solve problems using appropriate variables and operations. Convert verbal expressions into mathematical expressions using correct symbols and procedures

4 Essentials of Mathematics Lesson Unit 4: MEASUREMENT AND GEOMETRY Measurement Systems Convert between two units of measurement, for example, pints to gallons. Convert between two systems of measurement when you are given the conversion factor, for example, miles to kilometers when one mile is approximately 1.6 kilometers. Scale Drawings and Models Read and interpret drawings and scale models. Determine the scale of a figure using the measurements that are provided. Measures of Rates and Products Analyze your answers to determine whether or not they are reasonable. Solve problems using measures expressed as rates and as products. Perimeter and Area: 2D Figures Find the volume of a rectangular prism. Surface Area and Volume: 3D Figures Find the surface area of three-dimensional figures. Find the volume of three-dimensional figures. Use analytical skills to answer multi-step questions. Identify three-dimensional figures. Converting Between Units of Measure Convert measurements from one system to another and within the same system. Complex 2D Objects Compute the area of subdivided portions of complex figures. Separate a complex figure into measurable parts. Complex 3D Objects Separate a complex figure into measurable parts. Compute the area of subdivided portions of complex figures. Compute the surface area of cubes. Geometric Shapes: Scale Factors Compute the area and volume of figures with dimensions that are increased to scale. Determine how a change in dimensions impacts area and volume. Pythagorean Theorem Use the Pythagorean Theorem to find the length of a missing side of a right triangle. Review vocabulary appropriate to understanding the Pythagorean Theorem. Coordinate Graphs Plot ordered pairs on a coordinate plane. Identify shapes created on a plane and lengths and areas related to those shapes. Transformations and Congruent Figures Determine if plotted shapes are congruent. Identify transformations in plotted figures as translation or reflection. Review vocabulary related to transformations and congruent figures.

5 Essentials of Mathematics Lesson Unit 5: MATHEMATICAL REASONING Analyzing Problems Identify the elements that will make it possible to find a solution to the problem. Analyze situations to clarify problems. Making Conjectures Justify conjectures based on the questions provided. Make conjectures based on the information. Estimation (1) Evaluate the estimations to determine whether or not they are reasonable. Estimate to find the results in computations. Estimation (2) Recognize the most accurate line of best fit through a scatter plot. Extract information from graphs using interpolation and extrapolation. Write an equation based on a graph that could solve a problem. Inductive and Deductive Reasoning Use deductive or inductive reasoning to make and test conjectures. Identify reasoning as either deductive or inductive. Solving Problems Use specific problem-solving strategies to solve problems. Understand that the problem-solving process includes reasoning, analyzing, and solving.

6 Essentials of Mathematics Lesson Unit 6: ALGEBRA I Graphs and Charts Obtain information from a given graph. Interpret the meaning of data. Represent Data Obtain information from a given graph. Produce a 2-dimensional graph for a set of data. Interpret the graph's data and its meaning. Solve direct variation problems. Graphing Linear Functions Identify the slope of a linear function. Given two coordinate points, find the slope. Graph linear functions on a coordinate plane. Parallel Lines Determine whether two lines are parallel, perpendicular, or neither. Determine the slopes of parallel linear functions. Solutions of Linear Equations Be able to interpret the solutions of the equation. Evaluate an equation at a given point. Solve linear equations algebraically. Graphing Higher Power Functions Identify graphs of linear, quadratic, and cubic equations. Solving Absolute Value Inequalities Solve absolute value inequalities algebraically. Solving Linear Equations Identify the correct steps for solving linear equations. Find solutions to linear equations. Set up linear equations from word problems. Find solution sets to linear inequalities. Produce justification for the steps and processes of the solution. Set up linear inequalities from word problems. Multi-Step Word Problems (Rate) Interpret and relate the solution with respect to the problem. Set up linear equations from word problems. Find solutions to the linear equations. Multi-Step Word Problems (Work) Be able to find solutions to the linear equations. Set up two linear equations from a word problem. Interpret relate the solution with respect to the problem. Multi-Step Word Problems (Percent Mixture) Interpret and relate the solution with respect to the problem. Set up linear equations from word problems. Find solutions to linear equations. System of Equations Solve a system of linear equations. System of Linear Inequalities Solve a system of linear inequalities graphically. Interpret and produce the graphical solution of the system.

CAHSEE Math Released Test Questions

CAHSEE Math Released Test Questions Math Released Test Questions RTQ Item Numbers by Standard (Includes CST items for Standards on ) This document references Released Test Questions from the 2008 posted Test Questions (RTQs) and the 2003