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<head>
<meta content="text/html;charset=utf-8" http-equiv="Content-Type">
<meta content="utf-8" http-equiv="encoding">
<link href="main.css" rel="stylesheet"></link>
</head>
<body>
<div class="content">
<form id="search-form" onkeydown="return event.key != 'Enter';">
<input type="text" placeholder="search"></input>
<div class="query-error"></div>
</form>
<ol style="list-style: none;">
<li data-standard-id="CCSS.Math.Content.HSA.APR.A.1">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR.A.1</h2>
</header>
<section data-field="body">
<p>Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Algebra » Arithmetic with Polynomials and Rational Expressions » Perform arithmetic operations on polynomials
Big Ideas Algebra 1 Chapters: 7.1, 7.2, 7.3
Codes: CCSS.Math.Content.HSA-APR.A.1, CCSS.Math.Content.HSA.APR.A.1, A-APR.1
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.APR.B.2">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR.B.2</h2>
</header>
<section data-field="body">
<p>Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
Algebra » Arithmetic with Polynomials and Rational Expressions » Understand the relationship between zeros and factors of polynomials
Codes: CCSS.Math.Content.HSA-APR.B.2, CCSS.Math.Content.HSA.APR.B.2, A-APR.2
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.APR.B.3">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR.B.3</h2>
</header>
<section data-field="body">
<p>Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Algebra » Arithmetic with Polynomials and Rational Expressions » Understand the relationship between zeros and factors of polynomials
Big Ideas Algebra 1 Chapters: 7.4, 8.5
Codes: CCSS.Math.Content.HSA-APR.B.3, CCSS.Math.Content.HSA.APR.B.3, A-APR.3
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.APR.C.4">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR.C.4</h2>
</header>
<section data-field="body">
<p>Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.
Algebra » Arithmetic with Polynomials and Rational Expressions » Use polynomial identities to solve problems
Codes: CCSS.Math.Content.HSA-APR.C.4, CCSS.Math.Content.HSA.APR.C.4, A-APR.4
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.APR.C.5">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR.C.5</h2>
</header>
<section data-field="body">
<p>(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
Algebra » Arithmetic with Polynomials and Rational Expressions » Use polynomial identities to solve problems
Codes: CCSS.Math.Content.HSA-APR.C.5, CCSS.Math.Content.HSA.APR.C.5, A-APR.5
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.APR.D.6">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR.D.6</h2>
</header>
<section data-field="body">
<p>Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Algebra » Arithmetic with Polynomials and Rational Expressions » Rewrite rational expressions
Codes: CCSS.Math.Content.HSA-APR.D.6, CCSS.Math.Content.HSA.APR.D.6, A-APR.6
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.APR.D.7">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR.D.7</h2>
</header>
<section data-field="body">
<p>(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Algebra » Arithmetic with Polynomials and Rational Expressions » Rewrite rational expressions
Codes: CCSS.Math.Content.HSA-APR.D.7, CCSS.Math.Content.HSA.APR.D.7, A-APR.7
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.APR">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.APR</h2>
</header>
<section data-field="body">
<p>Algebra » Arithmetic with Polynomials and Rational Expressions
Other codes: CCSS.Math.Content.HSA-APR, CCSS.Math.Content.HSA.APR, A-APR
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.CED.A.1">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.CED.A.1</h2>
</header>
<section data-field="body">
<p>Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Algebra » Creating Equations » Create equations that describe numbers or relationships
Big Ideas Algebra 1 Chapters: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 6.5, 9.3, 9.4, 9.5, 10.3
Codes: CCSS.Math.Content.HSA-CED.A.1, CCSS.Math.Content.HSA.CED.A.1, A-CED.1
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.CED.A.2">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.CED.A.2</h2>
</header>
<section data-field="body">
<p>Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Algebra » Creating Equations » Create equations that describe numbers or relationships
Big Ideas Algebra 1 Chapters: 3.2, 3.3, 3.4, 3.5, 3.7, 4.1, 4.2, 4.3, 4.7, 6.3, 6.4, 8.1, 8.2, 8.3, 8.4, 8.5, 10.1, 10.2
Codes: CCSS.Math.Content.HSA-CED.A.2, CCSS.Math.Content.HSA.CED.A.2, A-CED.2
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.CED.A.3">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.CED.A.3</h2>
</header>
<section data-field="body">
<p>Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Algebra » Creating Equations » Create equations that describe numbers or relationships
Big Ideas Algebra 1 Chapters: 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7
Codes: CCSS.Math.Content.HSA-CED.A.3, CCSS.Math.Content.HSA.CED.A.3, A-CED.3
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.CED.A.4">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.CED.A.4</h2>
</header>
<section data-field="body">
<p>Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.
Algebra » Creating Equations » Create equations that describe numbers or relationships
Big Ideas Algebra 1 Chapters: 1.5, 9.3
Codes: CCSS.Math.Content.HSA-CED.A.4, CCSS.Math.Content.HSA.CED.A.4, A-CED.4
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.CED">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.CED</h2>
</header>
<section data-field="body">
<p>Algebra » Creating Equations
Other codes: CCSS.Math.Content.HSA-CED, CCSS.Math.Content.HSA.CED, A-CED
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.A.1">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.A.1</h2>
</header>
<section data-field="body">
<p>Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Algebra » Reasoning with Equations and Inequalities » Understand solving equations as a process of reasoning and explain the reasoning
Big Ideas Algebra 1 Chapters: 1.1, 6.5
Codes: CCSS.Math.Content.HSA-REI.A.1, CCSS.Math.Content.HSA.REI.A.1, A-REI.1
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.A.2">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.A.2</h2>
</header>
<section data-field="body">
<p>Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Algebra » Reasoning with Equations and Inequalities » Understand solving equations as a process of reasoning and explain the reasoning
Codes: CCSS.Math.Content.HSA-REI.A.2, CCSS.Math.Content.HSA.REI.A.2, A-REI.2
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.B.3">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.B.3</h2>
</header>
<section data-field="body">
<p>Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Algebra » Reasoning with Equations and Inequalities » Solve equations and inequalities in one variable
Big Ideas Algebra 1 Chapters: 1.1, 1.2, 1.3, 1.4, 2.2, 2.3, 2.4, 2.5, 2.6
Codes: CCSS.Math.Content.HSA-REI.B.3, CCSS.Math.Content.HSA.REI.B.3, A-REI.3
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.B.4">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.B.4</h2>
</header>
<section data-field="body">
<p>Solve quadratic equations in one variable.
Algebra » Reasoning with Equations and Inequalities » Solve equations and inequalities in one variable
Codes: CCSS.Math.Content.HSA-REI.B.4, CCSS.Math.Content.HSA.REI.B.4, A-REI.4
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.B.4a">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.B.4a</h2>
</header>
<section data-field="body">
<p>Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
Algebra » Reasoning with Equations and Inequalities » Solve equations and inequalities in one variable
Big Ideas Algebra 1 Chapters: 9.4, 9.5
Codes: CCSS.Math.Content.HSA-REI.B.4a, CCSS.Math.Content.HSA.REI.B.4a, A-REI.4a
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.B.4b">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.B.4b</h2>
</header>
<section data-field="body">
<p>Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Algebra » Reasoning with Equations and Inequalities » Solve equations and inequalities in one variable
Big Ideas Algebra 1 Chapters: 7.4, 9.3, 9.4, 9.5
Codes: CCSS.Math.Content.HSA-REI.B.4b, CCSS.Math.Content.HSA.REI.B.4b, A-REI.4b
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.C.5">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.C.5</h2>
</header>
<section data-field="body">
<p>Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Algebra » Reasoning with Equations and Inequalities » Solve systems of equations
Big Ideas Algebra 1 Chapters: 5.3
Codes: CCSS.Math.Content.HSA-REI.C.5, CCSS.Math.Content.HSA.REI.C.5, A-REI.5
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.C.6">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.C.6</h2>
</header>
<section data-field="body">
<p>Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Algebra » Reasoning with Equations and Inequalities » Solve systems of equations
Big Ideas Algebra 1 Chapters: 5.1, 5.2, 5.3, 5.4
Codes: CCSS.Math.Content.HSA-REI.C.6, CCSS.Math.Content.HSA.REI.C.6, A-REI.6
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.C.7">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.C.7</h2>
</header>
<section data-field="body">
<p>Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x^2 + y^2 = 3.
Algebra » Reasoning with Equations and Inequalities » Solve systems of equations
Big Ideas Algebra 1 Chapters: 9.6
Codes: CCSS.Math.Content.HSA-REI.C.7, CCSS.Math.Content.HSA.REI.C.7, A-REI.7
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.C.8">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.C.8</h2>
</header>
<section data-field="body">
<p>(+) Represent a system of linear equations as a single matrix equation in a vector variable.
Algebra » Reasoning with Equations and Inequalities » Solve systems of equations
Codes: CCSS.Math.Content.HSA-REI.C.8, CCSS.Math.Content.HSA.REI.C.8, A-REI.8
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.C.9">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.C.9</h2>
</header>
<section data-field="body">
<p>(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
Algebra » Reasoning with Equations and Inequalities » Solve systems of equations
Codes: CCSS.Math.Content.HSA-REI.C.9, CCSS.Math.Content.HSA.REI.C.9, A-REI.9
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.D.10">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.D.10</h2>
</header>
<section data-field="body">
<p>Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Algebra » Reasoning with Equations and Inequalities » Represent and solve equations and inequalities graphically
Big Ideas Algebra 1 Chapters: 3.2, 3.7, 4.7
Codes: CCSS.Math.Content.HSA-REI.D.10, CCSS.Math.Content.HSA.REI.D.10, A-REI.10
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.D.11">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.D.11</h2>
</header>
<section data-field="body">
<p>Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Algebra » Reasoning with Equations and Inequalities » Represent and solve equations and inequalities graphically
Big Ideas Algebra 1 Chapters: 5.5, 6.5, 9.2, 9.6
Codes: CCSS.Math.Content.HSA-REI.D.11, CCSS.Math.Content.HSA.REI.D.11, A-REI.11
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI.D.12">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI.D.12</h2>
</header>
<section data-field="body">
<p>Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Algebra » Reasoning with Equations and Inequalities » Represent and solve equations and inequalities graphically
Big Ideas Algebra 1 Chapters: 5.6, 5.7
Codes: CCSS.Math.Content.HSA-REI.D.12, CCSS.Math.Content.HSA.REI.D.12, A-REI.12
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.REI">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.REI</h2>
</header>
<section data-field="body">
<p>Algebra » Reasoning with Equations and Inequalities
Other codes: CCSS.Math.Content.HSA-REI, CCSS.Math.Content.HSA.REI, A-REI
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.A.1">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.A.1</h2>
</header>
<section data-field="body">
<p>Interpret expressions that represent a quantity in terms of its context.
Algebra » Seeing Structure in Expressions » Interpret the structure of expressions
Codes: CCSS.Math.Content.HSA-SSE.A.1, CCSS.Math.Content.HSA.SSE.A.1, A-SSE.1
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.A.1a">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.A.1a</h2>
</header>
<section data-field="body">
<p>Interpret parts of an expression, such as terms, factors, and coefficients.
Algebra » Seeing Structure in Expressions » Interpret the structure of expressions
Codes: CCSS.Math.Content.HSA-SSE.A.1a, CCSS.Math.Content.HSA.SSE.A.1a, A-SSE.1a
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.A.1b">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.A.1b</h2>
</header>
<section data-field="body">
<p>Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.
Algebra » Seeing Structure in Expressions » Interpret the structure of expressions
Codes: CCSS.Math.Content.HSA-SSE.A.1b, CCSS.Math.Content.HSA.SSE.A.1b, A-SSE.1b
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.A.2">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.A.2</h2>
</header>
<section data-field="body">
<p>Use the structure of an expression to identify ways to rewrite it. For example, see x^4 - y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 - y^2)(x^2 + y^2).
Algebra » Seeing Structure in Expressions » Interpret the structure of expressions
Big Ideas Algebra 1 Chapters: 7.5, 7.6, 7.7, 7.8
Codes: CCSS.Math.Content.HSA-SSE.A.2, CCSS.Math.Content.HSA.SSE.A.2, A-SSE.2
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.B.3">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.B.3</h2>
</header>
<section data-field="body">
<p>Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Algebra » Seeing Structure in Expressions » Write expressions in equivalent forms to solve problems
Codes: CCSS.Math.Content.HSA-SSE.B.3, CCSS.Math.Content.HSA.SSE.B.3, A-SSE.3
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.B.3a">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.B.3a</h2>
</header>
<section data-field="body">
<p>Factor a quadratic expression to reveal the zeros of the function it defines.
Algebra » Seeing Structure in Expressions » Write expressions in equivalent forms to solve problems
Big Ideas Algebra 1 Chapters: 7.5, 7.6, 7.7, 7.8, 8.5
Codes: CCSS.Math.Content.HSA-SSE.B.3a, CCSS.Math.Content.HSA.SSE.B.3a, A-SSE.3a
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.B.3b">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.B.3b</h2>
</header>
<section data-field="body">
<p>Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Algebra » Seeing Structure in Expressions » Write expressions in equivalent forms to solve problems
Big Ideas Algebra 1 Chapters: 9.4
Codes: CCSS.Math.Content.HSA-SSE.B.3b, CCSS.Math.Content.HSA.SSE.B.3b, A-SSE.3b
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.B.3c">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.B.3c</h2>
</header>
<section data-field="body">
<p>Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈ 1.01212^t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Algebra » Seeing Structure in Expressions » Write expressions in equivalent forms to solve problems
Big Ideas Algebra 1 Chapters: 6.4
Codes: CCSS.Math.Content.HSA-SSE.B.3c, CCSS.Math.Content.HSA.SSE.B.3c, A-SSE.3c
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE.B.4">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE.B.4</h2>
</header>
<section data-field="body">
<p>Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
Algebra » Seeing Structure in Expressions » Write expressions in equivalent forms to solve problems
Codes: CCSS.Math.Content.HSA-SSE.B.4, CCSS.Math.Content.HSA.SSE.B.4, A-SSE.4
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSA.SSE">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSA.SSE</h2>
</header>
<section data-field="body">
<p>Algebra » Seeing Structure in Expressions
Other codes: CCSS.Math.Content.HSA-SSE, CCSS.Math.Content.HSA.SSE, A-SSE
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.A.1">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.A.1</h2>
</header>
<section data-field="body">
<p>Write a function that describes a relationship between two quantities.
Functions » Building Functions » Build a function that models a relationship between two quantities
Codes: CCSS.Math.Content.HSF-BF.A.1, CCSS.Math.Content.HSF.BF.A.1, F-BF.1
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.A.1a">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.A.1a</h2>
</header>
<section data-field="body">
<p>Determine an explicit expression, a recursive process, or steps for calculation from a context.
Functions » Building Functions » Build a function that models a relationship between two quantities
Big Ideas Algebra 1 Chapters: 4.1, 4.2, 4.6, 6.3, 6.4, 6.7, 8.4, 8.5, 8.6
Codes: CCSS.Math.Content.HSF-BF.A.1a, CCSS.Math.Content.HSF.BF.A.1a, F-BF.1a
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.A.1b">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.A.1b</h2>
</header>
<section data-field="body">
<p>Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
Functions » Building Functions » Build a function that models a relationship between two quantities
Codes: CCSS.Math.Content.HSF-BF.A.1b, CCSS.Math.Content.HSF.BF.A.1b, F-BF.1b
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.A.1c">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.A.1c</h2>
</header>
<section data-field="body">
<p>(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Functions » Building Functions » Build a function that models a relationship between two quantities
Codes: CCSS.Math.Content.HSF-BF.A.1c, CCSS.Math.Content.HSF.BF.A.1c, F-BF.1c
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.A.2">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.A.2</h2>
</header>
<section data-field="body">
<p>Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Functions » Building Functions » Build a function that models a relationship between two quantities
Big Ideas Algebra 1 Chapters: 4.6, 6.6, 6.7
Codes: CCSS.Math.Content.HSF-BF.A.2, CCSS.Math.Content.HSF.BF.A.2, F-BF.2
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.B.3">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.B.3</h2>
</header>
<section data-field="body">
<p>Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Functions » Building Functions » Build new functions from existing functions
Big Ideas Algebra 1 Chapters: 3.6, 3.7, 6.3, 8.1, 8.2, 8.4
Codes: CCSS.Math.Content.HSF-BF.B.3, CCSS.Math.Content.HSF.BF.B.3, F-BF.3
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.B.4">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.B.4</h2>
</header>
<section data-field="body">
<p>Find inverse functions.
Functions » Building Functions » Build new functions from existing functions
Codes: CCSS.Math.Content.HSF-BF.B.4, CCSS.Math.Content.HSF.BF.B.4, F-BF.4
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.B.4a">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.B.4a</h2>
</header>
<section data-field="body">
<p>Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x^3 or f(x) = (x+1)/(x-1) for x ≠ 1.
Functions » Building Functions » Build new functions from existing functions
Big Ideas Algebra 1 Chapters: 10.4
Codes: CCSS.Math.Content.HSF-BF.B.4a, CCSS.Math.Content.HSF.BF.B.4a, F-BF.4a
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.B.4b">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.B.4b</h2>
</header>
<section data-field="body">
<p>(+) Verify by composition that one function is the inverse of another.
Functions » Building Functions » Build new functions from existing functions
Codes: CCSS.Math.Content.HSF-BF.B.4b, CCSS.Math.Content.HSF.BF.B.4b, F-BF.4b
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.B.4c">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.B.4c</h2>
</header>
<section data-field="body">
<p>(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
Functions » Building Functions » Build new functions from existing functions
Codes: CCSS.Math.Content.HSF-BF.B.4c, CCSS.Math.Content.HSF.BF.B.4c, F-BF.4c
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.B.4d">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.B.4d</h2>
</header>
<section data-field="body">
<p>(+) Produce an invertible function from a non-invertible function by restricting the domain.
Functions » Building Functions » Build new functions from existing functions
Codes: CCSS.Math.Content.HSF-BF.B.4d, CCSS.Math.Content.HSF.BF.B.4d, F-BF.4d
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF.B.5">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF.B.5</h2>
</header>
<section data-field="body">
<p>(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Functions » Building Functions » Build new functions from existing functions
Codes: CCSS.Math.Content.HSF-BF.B.5, CCSS.Math.Content.HSF.BF.B.5, F-BF.5
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.BF">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.BF</h2>
</header>
<section data-field="body">
<p>Functions » Building Functions
Other codes: CCSS.Math.Content.HSF-BF, CCSS.Math.Content.HSF.BF, F-BF
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.A.1">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.A.1</h2>
</header>
<section data-field="body">
<p>Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Functions » Interpreting Functions » Understand the concept of a function and use function notation
Big Ideas Algebra 1 Chapters: 3.1, 3.3
Codes: CCSS.Math.Content.HSF-IF.A.1, CCSS.Math.Content.HSF.IF.A.1, F-IF.1
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.A.2">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.A.2</h2>
</header>
<section data-field="body">
<p>Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Functions » Interpreting Functions » Understand the concept of a function and use function notation
Big Ideas Algebra 1 Chapters: 3.3
Codes: CCSS.Math.Content.HSF-IF.A.2, CCSS.Math.Content.HSF.IF.A.2, F-IF.2
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.A.3">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.A.3</h2>
</header>
<section data-field="body">
<p>Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
Functions » Interpreting Functions » Understand the concept of a function and use function notation
Big Ideas Algebra 1 Chapters: 4.6, 6.6, 6.7
Codes: CCSS.Math.Content.HSF-IF.A.3, CCSS.Math.Content.HSF.IF.A.3, F-IF.3
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.B.4">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.B.4</h2>
</header>
<section data-field="body">
<p>For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Functions » Interpreting Functions » Interpret functions that arise in applications in terms of the context
Big Ideas Algebra 1 Chapters: 3.5, 6.3, 8.4, 8.5, 10.1, 10.2
Codes: CCSS.Math.Content.HSF-IF.B.4, CCSS.Math.Content.HSF.IF.B.4, F-IF.4
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.B.5">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.B.5</h2>
</header>
<section data-field="body">
<p>Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Functions » Interpreting Functions » Interpret functions that arise in applications in terms of the context
Big Ideas Algebra 1 Chapters: 3.2
Codes: CCSS.Math.Content.HSF-IF.B.5, CCSS.Math.Content.HSF.IF.B.5, F-IF.5
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.B.6">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.B.6</h2>
</header>
<section data-field="body">
<p>Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Functions » Interpreting Functions » Interpret functions that arise in applications in terms of the context
Big Ideas Algebra 1 Chapters: 8.6, 10.1, 10.2
Codes: CCSS.Math.Content.HSF-IF.B.6, CCSS.Math.Content.HSF.IF.B.6, F-IF.6
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.C.7">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.C.7</h2>
</header>
<section data-field="body">
<p>Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Functions » Interpreting Functions » Analyze functions using different representations
Codes: CCSS.Math.Content.HSF-IF.C.7, CCSS.Math.Content.HSF.IF.C.7, F-IF.7
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.C.7a">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.C.7a</h2>
</header>
<section data-field="body">
<p>Graph linear and quadratic functions and show intercepts, maxima, and minima.
Functions » Interpreting Functions » Analyze functions using different representations
Big Ideas Algebra 1 Chapters: 3.2, 3.4, 3.5, 3.6, 8.1, 8.2, 8.3, 9.2
Codes: CCSS.Math.Content.HSF-IF.C.7a, CCSS.Math.Content.HSF.IF.C.7a, F-IF.7a
</p>
</section>
</article>
</li>
<li data-standard-id="CCSS.Math.Content.HSF.IF.C.7b">
<article>
<header>
<h2 data-field="name">CCSS.Math.Content.HSF.IF.C.7b</h2>
</header>
<section data-field="body">
<p>Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Functions » Interpreting Functions » Analyze functions using different representations
Big Ideas Algebra 1 Chapters: 3.7, 4.7, 10.1, 10.2
Codes: CCSS.Math.Content.HSF-IF.C.7b, CCSS.Math.Content.HSF.IF.C.7b, F-IF.7b
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<h2 data-field="name">CCSS.Math.Content.HSF.IF.C.7c</h2>
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