Algebra 1 Math Year at a Glance


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1 Real Operations Equations/Inequalities Relations/Graphing Systems Exponents/Polynomials Quadratics ISTEP+ Radicals Algebra 1 Math Year at a Glance KEY According to the Indiana Department of Education + = Critical Standard for ISTEP+ = Important Standard for ISTEP+ Explicitly taught CC/Learning Targets Correlating CC/Learning Targets Quarters Q1 Q2 Q3 Q4 Big Idea Indicator Bundles Read, write, compare, and solve problems using decimals in scientific notation Know that every rational number is either a terminating or repeating decimal and that every irrational number is a nonrepeating decimal Understand that computations with an irrational number and a rational number (other than zero) produce an irrational number Understand and evaluate negative integer exponents Use the laws of exponents for integer exponents Use the inverse relationship between squaring and finding the square root of a perfect square integer Calculate and find approximations of square roots Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) in multistep problems Solve problems by computing simple and compound interest Use estimation techniques to decide whether answers to computations on a calculator are reasonable Use mental arithmetic to compute with common fractions, decimals, powers, and percentages Write and solve linear equations and inequalities in one variable, interpret the solution or solutions in their context, and verify the reasonableness of the results Solve systems of two linear equations using the substitution method and identify approximate solutions graphically Interpret positive integer powers as repeated multiplication and negative integer powers as repeated division or multiplication by the multiplicative inverse Use the correct order of operations to find the values of algebraic expressions involving powers Identify and graph linear functions, and identify lines with positive and negative slope Find the slope of a linear function given the equation and write the equation of a line given the slope and any point on the line Demonstrate an understanding of rate as a measure of one quantity with respect to another quantity Demonstrate an understanding of the relationships among tables, equations, verbal expressions, and graphs of linear functions Represent simple quadratic functions using verbal descriptions, tables, graphs and formulas, and translate
2 among these representations Graph functions of the form y=nx 2 and y=nx 3 and describe the similarities and differences in the graphs Identify and describe basic properties of geometric shapes: altitudes, diagonals, angle bisectors, perpendicular bisectors, central angles, radii, diameters, and chords of circles Perform simple constructions such as bisectors of segments and angles, copies of segments and angles, and perpendicular segments. Describe and justify the constructions Identify properties of threedimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more figures intersect in a plane or in space Draw the translation (slide) rotation (turn), reflection (flip), and dilation (stretches and shrinks) of shapes Use the Pythagorean Theorem and its converse to solve problems in two and three dimensions Convert common measurements for length, area, volume, weight, capacity, and time to equivalent measurements within the same system Solve simple problems involving rates and derived measurements for such attributes as velocity and density Solve problems involving scale factors, area, and volume using ratio and proportion Use formulas for finding the perimeter and area of basic twodimensional shapes and the surface area and volume of basic threedimensional shapes, including rectangles, parallelograms, trapezoids, triangles, circles, prisms, cylinders, spheres, cones, and pyramids Estimate and compute the area of irregular twodimensional shapes and the volume of irregular threedimensional objects by breaking them down into more basic geometric shapes Identify claims based on statistical data and, in simple cases, evaluate the reasonableness of the claims. Design a study to investigate the claim Identify different methods of selecting samples, analyzing the strengths and weaknesses of each method, and the possible bias in a sample or display Understand the meaning of, and be able to identify or compute the minimum value, the lower quartile, the median, the upper quartile, the interquartile range, and the maximum value of a data set Analyze, interpret, and display single and twovariable data in appropriate bar, line and circle graphs, stemandleaf plots and boxandwhisker plots, and explain which types of display are appropriate for various data sets Represent twovariable data with a scatterplot on the coordinate plane and describe how the data points are distributed. If the pattern appears to be linear, draw a line that appears to best fit the data, and write the equation of that line Understand and recognize equally likely events Find the number of possible arrangements of several objects by using the Basic Counting Principle Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns Make and justify mathematical conjectures based on a general description of a mathematical question or problem Decide when and how to break a problem into simpler parts Apply strategies and results from simpler problems to solve more complex problems.
3 8.7.5 Make and test conjectures by using inductive reasoning Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy Select and apply appropriate methods for estimating results of rationalnumber computations Use graphing to estimate solutions and check the estimates with analytic approaches Make precise calculations and check the validity of the results in the context of the problem Decide whether a solution is reasonable in the context of the original situation Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems. A1.1.1a Evaluate real number expressions. A1.1.1b Order real number expressions. A1.1.2a Simplify square roots using factors. A1.1.2b Simplify rational expressions with square roots. + A1.1.3a Simplify expressions by using the associative and commutative properties to combine like terms. + A1.1.3b Simplify linear expressions by using the distributive property. + A1.1.3c Simplify quadratic expressions by using the distributive property. + A1.1.3d Simplify polynomial expressions by using the distributive property. A1.1.4a Identify root and power of rational exponents. A1.1.4b Simplify real number expressions with rational exponents. A1.1.4c Simplify algebraic expressions with rational exponents. A1.1.5a Use dimensional unit analysis to organize conversions and computations + A1.2.1a Determine which inverse operations should be applied and in what order to solve a given linear equation. + A1.2.1b Solve linear equations that require the use of commutative and associative properties to combine like terms. + A1.2.1c Solve linear equations that require the use of the distributive property to remove grouping symbols. + A1.2.1d Solve linear equations with the variables on both side of the equation. A1.2.2a Solve equations and formulas for a specified variable. A1.2.3 Find solution sets of linear inequalities when possible numbers are given for the variable. + A1.2.4a Solve linear inequalities that require the use of commutative and associative properties to combine like terms. Include problems where they have to reverse the inequality due to multiplying or dividing by a negative number. + A1.2.4b Solve linear inequalities that require the use of the distributive property to remove grouping symbols. Have students graph the solution to the inequality as well. + A1.2.4c Solve linear inequalities with the variables on both side of the inequality. + A1.2.4d Graph the solution set of a linear inequality in one variable (on a number line). A1.2.5a Solve compound linear inequalities.
4 A1.2.5b Graph the solution set of combined linear inequality in one variable (on a number line). + A1.2.6a Solve word problems that involve linear equations. + A1.2.6b Solve word problems that involve formulas. + A1.2.6c Solve word problems that involve linear inequalities. A1.3.1a Apply appropriate labels and intervals to each axis. A1.3.1b Sketch a reasonable graph for a given relationship. A1.3.2a Describe relationships between two measures on the horizontal and vertical axes. A1.3.2b Explain what is going on at a specific point or during a particular interval on a graph. A1.3.3a Identify the criteria for a relationship to be considered a function. A1.3.3b Determine whether a list or table of ordered pairs represents a function. A1.3.3c Determine whether a given graph represents a function. A1.3.3d Determine whether a given equation represents a function A1.3.3e Translate between a table, an equation, a graph and a verbal description, given at least of the representations. A1.3.4a Find the domain and range of a list or table of ordered pairs. A1.3.4b Find the domain and range of a given graph. A1.3.4c Find the domain and range of a given equation. + A1.4.1a Graph a linear equation given slopeintercept form. + A1.4.1b Graph a linear equation given in standard form. + A1.4.1c Graph a linear equation in any form. + A1.4.2a Find the slope of a line given its graph. + A1.4.2b Find the slope of a line given its equation. Use equations in both slopeintercept and standard forms. + A1.4.2c Find the slope of a line given two points on the line. + A1.4.2d Find the xintercept and the yintercept of a line given its graph. + A1.4.2e Find the xintercept and the yintercept of a line given its equation. Use equations in both slopeintercept and standard forms. + A1.4.2f Find the xintercept and the yintercept of a line given two points on the line. + A1.4.3a Write the equation of a line in slopeintercept form, given the slope and the yintercept. + A1.4.3b Write the equation of a line in slopeintercept form, given a graph. + A1.4.3c Demonstrate how the slope and yintercept of the graph are related to a linear equation in slopeintercept form. + A1.4.3d Write the equation of a line in slopeintercept form, given the standard form. + A1.4.3e Write the equation of a line in slopeintercept form, given a table. + A1.4.3f Write the equation of a line in slopeintercept form, given a verbal description. + A1.4.4a Write the equation of a line given two points on the line. + A1.4.4b Write the equation of a line given one point on the line and an equation of a parallel line. Be sure to discuss that parallel lines have equal slopes. + A1.4.4c Write the equation of a line given one point on the line and an equation of a perpendicular line.
5 Be sure to review that perpendicular lines have negative reciprocal slopes. + A1.4.4d Write the equation of a line, given a combination of points on the line, x or yintercepts, or the slope of the line. + A1.4.5a Write the equation of a line that models a data set. + A1.4.5b Use the equation of a line or the graph of the equation to make predictions with a given data set. + A1.4.5c Find the slope of the line described by a given data set. + A1.4.5d Determine the rate of change for a specified measure based on the equation or graph for a given set of data. This is to assess whether the student knows the rate of change is the slope. A1.4.6a Graph a linear inequality in two variables. A1.5.1a Explain that the solution of a pair of linear equations in two variables is the intersection of their graphs. This covers the possibility that the solution could be "no solution." A1.5.1b Estimate the solution of a pair of linear equations in two variables by graphing. A1.5.2a Use a graph to find the solution set of a pair of linear inequalities in two variables. A1.5.2b Shade the region of the graph that represents the solution set of a pair of linear inequalities. A1.5.2c Identify the solution set of a pair of linear inequalities in two variables given their graphs. + A1.5.3a Solve a pair of linear equations in two variables by using the substitution method. + A1.5.4a Solve a pair of linear equations in two variables by elimination using addition or subtraction. + A1.5.5a Solve a pair of linear equations in two variables by elimination using multiplication with addition or subtraction. + A1.5.6a Write a pair of linear equations from information provided in a word problem. + A1.5.6b Determine whether graphing, substitution, or elimination would be the most appropriate technique for given set of linear equations. + A1.5.6c Solve word problems involving pairs of linear equations. + A1.6.1a Define and identify monomial and polynomial. + A1.6.1b Add and subtract monomials. + A1.6.1c Add and subtract polynomials. + A1.6.2a Multiply and divide monomials. + A1.6.3a Find powers of monomials. + A1.6.3b Find roots of monomials (only when the answer has an integer exponent). + A1.6.4a Multiply monomials by binomials. + A1.6.4b Multiply monomials by polynomials. + A1.6.4c Multiply binomials by binomials. + A1.6.4d Multiply polynomials by polynomials. A1.6.5a Divide polynomials by monomials. A1.6.6a Find the greatest common monomial factor in a polynomial and rewrite the polynomial in factored form. + A1.6.7a Factor quadratics that are a difference of two squares. + A1.6.7b Factor quadratic equations. A1.6.8a Identify the xintercepts and zeros of a given quadratic graph.
6 A1.6.8b A1.6.8c A1.6.8d A1.6.8e Identify the solutions of quadratic equations. Identify the zeros of quadratic functions. Solve a quadratic equation by graphing. Describe the relationships among the xintercepts of a quadratic graph, the solutions of a quadratic equation, the zeros of a quadratic function, and the factors of a quadratic expression. Simplify algebraic ratios. Solve algebraic proportions that lead to linear equations. Solve algebraic proportions that lead to quadratic equations. Solve algebraic proportions that lead to polynomial equations. Graph quadratic equations both with positive and with negative leading coefficients. Graph cubic equations both with positive or with negative leading coefficients. Identify the basic shape of the graph of a radical function. Graph radical equations with positive or negative leading coefficients. A1.7.1a A1.7.2a A1.7.2b A1.7.2c A1.8.1a A1.8.1b A1.8.1c A1.8.1d + A1.8.2a Explain the Zero Product Rule in relation to solving factored quadratic equations. + A1.8.2b Solve quadratic equations by factoring completely and then applying the Zero Product rule. + A1.8.3a Solve quadratic equations in which a perfect square equals a constant. + A1.8.3b Solve quadratic equations in which a binomial squared equals a constant. A1.8.4a A1.8.4b A1.8.4c A1.8.4d A1.8.5a Derive the quadratic formula by completing the square. + A1.8.6a Simplify expressions that contain radicals. + A1.8.6b Determine the decimal approximation of expressions with radicals. + A1.8.6c Determine the value of a, b and c from a quadratic equation. + A1.8.6d Solve quadratic equations by using the quadratic formula. Work with both exact and decimal approximation of irrational answers. + A1.8.7a Solve word problems that involve quadratic equations. A1.8.8a A1.8.8b A1.8.9a A1.8.9b A1.9.1a A1.9.2a A1.9.3a A1.9.3b Identify perfect square trinomials Construct a perfect square trinomial by completing the square, given the first two terms of the trinomial. Factor perfect square trinomials and rewrite as a quantity squared. Complete the square to solve quadratic equations. Solve equations that contain radical expressions equal to a constant. Solve equations that contain radical expressions equal to the variable in the expression. Use graphing technology to find approximate solutions of quadratic equations. Use graphing technology to find approximate solutions of cubic equations. Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guessandcheck, solving a simpler problem, writing an equation, and working backwards. Decide whether a solution is reasonable in the context of the original situation. Use the properties of the real number system and the order of operations to justify the steps of simplifying functions. Use the properties of the real number system and the order of operations to justify the steps of solving
7 A1.9.4a A1.9.4b A1.9.4c A1.9.5a A1.9.5b A1.9.6 A1.9.7 A1.9.8 equations. Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation. Understand that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that the logic of equation solving can be extended to solving simultaneous equations. Determine whether a given linear algebraic statement is true always, sometimes, or never (include linear expressions, equations, and inequalities). Determine whether a given quadratic algebraic statement is true always, sometimes, or never (include quadratic expressions, equations, and inequalities). Distinguish between inductive and deductive reasoning, identifying and providing examples of each. Identify the hypothesis and conclusion in a logical deduction. Use counterexamples to show that statements are false, recognizing that a single counterexample is sufficient to prove a general statement false.
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