Repository: Hestenb62/_legacy_backup
Author: Hesten Berger
Commit Message: standards update
URL: https://github.com/Hestenb62/_legacy_backup/commit/79b01363381ece910bbfa154a43c024fd18a1eba
Code Changes:
diff --git a/assets/data/standards-ccss-math.json b/assets/data/standards-ccss-math.json
index e909b4a..f5ec7d2 100644
--- a/assets/data/standards-ccss-math.json
+++ b/assets/data/standards-ccss-math.json
@@ -331,6 +331,8 @@
"<p class=\"curr-standard-desc\"><strong>4.NF.B.3c:</strong> Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.</p>",
"<p class=\"curr-standard-desc\"><strong>4.NF.B.3d:</strong> Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.</p>",
"<p class=\"curr-standard-desc\"><strong>4.NF.B.4:</strong> Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.</p>",
+ "<p class=\"curr-standard-desc\"><strong>4.NF.B.4a:</strong> Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4).</p>",
+ "<p class=\"curr-standard-desc\"><strong>4.NF.B.4b:</strong> Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.</p>",
"<p class=\"curr-standard-desc\"><strong>4.NF.B.4c:</strong> Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.</p>",
"<p class=\"curr-standard-desc\"><strong>4.NF.C.5:</strong> Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.</p>",
"<p class=\"curr-standard-desc\"><strong>4.NF.C.6:</strong> Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.</p>",
@@ -394,8 +396,13 @@
"<p class=\"curr-standard-desc\"><strong>5.NF.B.4a:</strong> Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.</p>",
"<p class=\"curr-standard-desc\"><strong>5.NF.B.4b:</strong> Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.</p>",
"<p class=\"curr-standard-desc\"><strong>5.NF.B.5:</strong> Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.</p>",
+ "<p class=\"curr-standard-desc\"><strong>5.NF.B.5a:</strong> Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.</p>",
+ "<p class=\"curr-standard-desc\"><strong>5.NF.B.5b:</strong> Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.</p>",
"<p class=\"curr-standard-desc\"><strong>5.NF.B.6:</strong> Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.</p>",
"<p class=\"curr-standard-desc\"><strong>5.NF.B.7:</strong> Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.</p>",
+ "<p class=\"curr-standard-desc\"><strong>5.NF.B.7a:</strong> Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.</p>",
+ "<p class=\"curr-standard-desc\"><strong>5.NF.B.7b:</strong> Interpret division of a whole number by a unit fraction, and compute such quotients.</p>",
+ "<p class=\"curr-standard-desc\"><strong>5.NF.B.7c:</strong> Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.</p>",
"</div>",
"<div class=\"curr-standard-item\">",
"<h4 class=\"curr-standard-title\">Measurement and Data (5.MD)</h4>",
@@ -448,7 +455,14 @@
"<p class=\"curr-standard-desc\"><strong>6.NS.B.4:</strong> Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.</p>",
"<p class=\"curr-standard-desc\"><strong>6.NS.C.5:</strong> Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.</p>",
"<p class=\"curr-standard-desc\"><strong>6.NS.C.6:</strong> Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.NS.C.6a:</strong> Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.NS.C.6b:</strong> Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.NS.C.6c:</strong> Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.</p>",
"<p class=\"curr-standard-desc\"><strong>6.NS.C.7:</strong> Understand ordering and absolute value of rational numbers.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.NS.C.7a:</strong> Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.NS.C.7b:</strong> Write, interpret, and explain statements of order for rational numbers in real-world contexts.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.NS.C.7c:</strong> Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.NS.C.7d:</strong> Distinguish comparisons of absolute value from statements about order.</p>",
"<p class=\"curr-standard-desc\"><strong>6.NS.C.8:</strong> Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.</p>",
"</div>",
"<div class=\"curr-standard-item\">",
@@ -456,6 +470,7 @@
"<p class=\"curr-standard-desc\"><strong>6.EE.A.1:</strong> Write and evaluate numerical expressions involving whole-number exponents.</p>",
"<p class=\"curr-standard-desc\"><strong>6.EE.A.2:</strong> Write, read, and evaluate expressions in which letters stand for numbers.</p>",
"<p class=\"curr-standard-desc\"><strong>6.EE.A.2a:</strong> Write expressions that record operations with numbers and with letters standing for numbers.</p>",
+ "<p class=\"curr-standard-desc\"><strong>6.EE.A.2b:</strong> Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.</p>",
"<p class=\"curr-standard-desc\"><strong>6.EE.A.2c:</strong> Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).</p>",
"<p class=\"curr-standard-desc\"><strong>6.EE.A.3:</strong> Apply the properties of operations to generate equivalent expressions.</p>",
"<p class=\"curr-standard-desc\"><strong>6.EE.A.4:</strong> Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).</p>",
@@ -509,8 +524,14 @@
"<div class=\"curr-standard-item\">",
"<h4 class=\"curr-standard-title\">The Number System (7.NS)</h4>",
"<p class=\"curr-standard-desc\"><strong>7.NS.A.1:</strong> Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.</p>",
+ "<p class=\"curr-standard-desc\"><strong>7.NS.A.1a:</strong> Describe situations in which opposite quantities combine to make 0.</p>",
+ "<p class=\"curr-standard-desc\"><strong>7.NS.A.1b:</strong> Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.</p>",
"<p class=\"curr-standard-desc\"><strong>7.NS.A.1c:</strong> Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.</p>",
+ "<p class=\"curr-standard-desc\"><strong>7.NS.A.1d:</strong> Apply properties of operations as strategies to add and subtract rational numbers.</p>",
"<p class=\"curr-standard-desc\"><strong>7.NS.A.2:</strong> Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.</p>",
+ "<p class=\"curr-standard-desc\"><strong>7.NS.A.2a:</strong> Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.</p>",
+ "<p class=\"curr-standard-desc\"><strong>7.NS.A.2b:</strong> Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.</p>",
+ "<p class=\"curr-standard-desc\"><strong>7.NS.A.2c:</strong> Apply properties of operations as strategies to multiply and divide rational numbers.</p>",
"<p class=\"curr-standard-desc\"><strong>7.NS.A.2d:</strong> Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.</p>",
"<p class=\"curr-standard-desc\"><strong>7.NS.A.3:</strong> Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)</p>",
"</div>",
@@ -591,6 +612,9 @@
"<div class=\"curr-standard-item\">",
"<h4 class=\"curr-standard-title\">Geometry (8.G)</h4>",
"<p class=\"curr-standard-desc\"><strong>8.G.A.1:</strong> Verify experimentally the properties of rotations, reflections, and translations.</p>",
+ "<p class=\"curr-standard-desc\"><strong>8.G.A.1a:</strong> Lines are taken to lines, and line segments to line segments of the same length.</p>",
+ "<p class=\"curr-standard-desc\"><strong>8.G.A.1b:</strong> Angles are taken to angles of the same measure.</p>",
+ "<p class=\"curr-standard-desc\"><strong>8.G.A.1c:</strong> Parallel lines are taken to parallel lines.</p>",
"<p class=\"curr-standard-desc\"><strong>8.G.A.2:</strong> Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.</p>",
"<p class=\"curr-standard-desc\"><strong>8.G.A.3:</strong> Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.</p>",
"<p class=\"curr-standard-desc\"><strong>8.G.A.4:</strong> Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.</p>",
@@ -620,45 +644,63 @@
},
"9th Grade": {
"ccss": {
- "title": "9th Grade Math (CCSS)",
- "overview": "<p>High school standards specify the mathematics that all students should study in order to be college and career ready, organized by conceptual categories (Number/Quantity, Algebra, Functions, Geometry, Statistics/Probability) rather than by grade.</p>",
+ "title": "9th Grade Math (CCSS) - Algebra I Focus",
+ "overview": "<p>High school standards specify the mathematics that all students should study in order to be college and career ready. In 9th Grade (Algebra I), instructional time typically focuses on linear, quadratic, and exponential functions, modeling, and data analysis.</p>",
"standards": [
"<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Number and Quantity (HSN)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSN-RN (The Real Number System):</strong> Extend the properties of exponents to rational exponents; use properties of rational and irrational numbers.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-Q (Quantities):</strong> Reason quantitatively and use units to solve problems.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-CN (The Complex Number System):</strong> Perform arithmetic operations with complex numbers; represent complex numbers and their operations on the complex plane; use complex numbers in polynomial identities and equations.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-VM (Vector and Matrix Quantities):</strong> Represent and model with vector quantities; perform operations on vectors; perform operations on matrices and use matrices in applications.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Algebra (HSA)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSA-SSE (Seeing Structure in Expressions):</strong> Interpret the structure of expressions; write expressions in equivalent forms to solve problems.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-APR (Arithmetic with Polynomials and Rational Expressions):</strong> Perform arithmetic operations on polynomials; understand the relationship between zeros and factors of polynomials; use polynomial identities to solve problems; rewrite rational expressions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-CED (Creating Equations):</strong> Create equations that describe numbers or relationships.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-REI (Reasoning with Equations and Inequalities):</strong> Understand solving equations as a process of reasoning and explain the reasoning; solve equations and inequalities in one variable; solve systems of equations; represent and solve equations and inequalities graphically.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Functions (HSF)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSF-IF (Interpreting Functions):</strong> Understand the concept of a function and use function notation; interpret functions that arise in applications in terms of the context; analyze functions using different representations.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-BF (Building Functions):</strong> Build a function that models a relationship between two quantities; build new functions from existing functions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-LE (Linear, Quadratic, and Exponential Models):</strong> Construct and compare linear, quadratic, and exponential models and solve problems; interpret expressions for functions in terms of the situation they model.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-TF (Trigonometric Functions):</strong> Extend the domain of trigonometric functions using the unit circle; model periodic phenomena with trigonometric functions; prove and apply trigonometric identities.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Geometry (HSG)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSG-CO (Congruence):</strong> Experiment with transformations in the plane; understand congruence in terms of rigid motions; prove geometric theorems; make geometric constructions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-SRT (Similarity, Right Triangles, and Trigonometry):</strong> Understand similarity in terms of similarity transformations; prove theorems involving similarity; define trigonometric ratios and solve problems involving right triangles; apply trigonometry to general triangles.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-C (Circles):</strong> Understand and apply theorems about circles; find arc lengths and areas of sectors of circles.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-GPE (Expressing Geometric Properties with Equations):</strong> Translate between the geometric description and the equation for a conic section; use coordinates to prove simple geometric theorems algebraically.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-GMD (Geometric Measurement and Dimension):</strong> Explain volume formulas and use them to solve problems; visualize relationships between two-dimensional and three-dimensional objects.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-MG (Modeling with Geometry):</strong> Apply geometric concepts in modeling situations.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Statistics and Probability (HSS)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSS-ID (Interpreting Categorical and Quantitative Data):</strong> Summarize, represent, and interpret data on a single count or measurement variable; summarize, represent, and interpret data on two categorical and quantitative variables; interpret linear models.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSS-IC (Making Inferences and Justifying Conclusions):</strong> Understand and evaluate random processes underlying statistical experiments; make inferences and justify conclusions from sample surveys, experiments, and observational studies.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSS-CP (Conditional Probability and the Rules of Probability):</strong> Understand independence and conditional probability and use them to interpret data; use the rules of probability to compute probabilities of compound events in a uniform probability model.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSS-MD (Using Probability to Make Decisions):</strong> Calculate expected values and use them to solve problems; use probability to evaluate outcomes of decisions.</p>",
+ "<h4 class=\"curr-standard-title\">Number and Quantity</h4>",
+ "<p class=\"curr-standard-desc\"><strong>HSN-Q.A.1:</strong> Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSN-Q.A.2:</strong> Define appropriate quantities for the purpose of descriptive modeling.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSN-Q.A.3:</strong> Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.</p>",
+ "</div>",
+ "<div class=\"curr-standard-item\">",
+ "<h4 class=\"curr-standard-title\">Algebra</h4>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-SSE.A.1:</strong> Interpret expressions that represent a quantity in terms of its context.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-SSE.A.2:</strong> Use the structure of an expression to identify ways to rewrite it.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-SSE.B.3:</strong> Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-APR.A.1:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-CED.A.1:</strong> Create equations and inequalities in one variable and use them to solve problems.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-CED.A.2:</strong> Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-CED.A.3:</strong> Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-CED.A.4:</strong> Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.A.1:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.B.3:</strong> Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.B.4:</strong> Solve quadratic equations in one variable.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.C.5:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.C.6:</strong> Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.D.10:</strong> 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).</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.D.11:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSA-REI.D.12:</strong> Graph the solutions to a linear inequality in two variables as a half-plane (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.</p>",
+ "</div>",
+ "<div class=\"curr-standard-item\">",
+ "<h4 class=\"curr-standard-title\">Functions</h4>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.A.1:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.A.2:</strong> Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.A.3:</strong> Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.B.4:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.B.5:</strong> Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.B.6:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.C.7:</strong> Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.C.8:</strong> Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-IF.C.9:</strong> Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-BF.A.1:</strong> Write a function that describes a relationship between two quantities.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-BF.B.3:</strong> 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.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-LE.A.1:</strong> Distinguish between situations that can be modeled with linear functions and with exponential functions.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-LE.A.2:</strong> Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-LE.A.3:</strong> Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSF-LE.B.5:</strong> Interpret the parameters in a linear or exponential function in terms of a context.</p>",
+ "</div>",
+ "<div class=\"curr-standard-item\">",
+ "<h4 class=\"curr-standard-title\">Statistics and Probability</h4>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.A.1:</strong> Represent data with plots on the real number line (dot plots, histograms, and box plots).</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.A.2:</strong> Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.A.3:</strong> Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.A.4:</strong> Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.B.5:</strong> Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies).</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.B.6:</strong> Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.C.7:</strong> Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.C.8:</strong> Compute (using technology) and interpret the correlation coefficient of a linear fit.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSS-ID.C.9:</strong> Distinguish between correlation and causation.</p>",
"</div>"
],
"competencies": [
@@ -673,45 +715,48 @@
},
"10th Grade": {
"ccss": {
- "title": "10th Grade Math (CCSS)",
- "overview": "<p>High school standards specify the mathematics that all students should study in order to be college and career ready, organized by conceptual categories (Number/Quantity, Algebra, Functions, Geometry, Statistics/Probability) rather than by grade.</p>",
+ "title": "10th Grade Math (CCSS) - Geometry Focus",
+ "overview": "<p>High school standards specify the mathematics that all students should study in order to be college and career ready. In 10th Grade (Geometry), instructional time typically focuses on geometric properties, transformations, congruence, similarity, right triangles, and modeling with geometry.</p>",
"standards": [
"<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Number and Quantity (HSN)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSN-RN (The Real Number System):</strong> Extend the properties of exponents to rational exponents; use properties of rational and irrational numbers.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-Q (Quantities):</strong> Reason quantitatively and use units to solve problems.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-CN (The Complex Number System):</strong> Perform arithmetic operations with complex numbers; represent complex numbers and their operations on the complex plane; use complex numbers in polynomial identities and equations.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-VM (Vector and Matrix Quantities):</strong> Represent and model with vector quantities; perform operations on vectors; perform operations on matrices and use matrices in applications.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Algebra (HSA)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSA-SSE (Seeing Structure in Expressions):</strong> Interpret the structure of expressions; write expressions in equivalent forms to solve problems.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-APR (Arithmetic with Polynomials and Rational Expressions):</strong> Perform arithmetic operations on polynomials; understand the relationship between zeros and factors of polynomials; use polynomial identities to solve problems; rewrite rational expressions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-CED (Creating Equations):</strong> Create equations that describe numbers or relationships.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-REI (Reasoning with Equations and Inequalities):</strong> Understand solving equations as a process of reasoning and explain the reasoning; solve equations and inequalities in one variable; solve systems of equations; represent and solve equations and inequalities graphically.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Functions (HSF)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSF-IF (Interpreting Functions):</strong> Understand the concept of a function and use function notation; interpret functions that arise in applications in terms of the context; analyze functions using different representations.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-BF (Building Functions):</strong> Build a function that models a relationship between two quantities; build new functions from existing functions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-LE (Linear, Quadratic, and Exponential Models):</strong> Construct and compare linear, quadratic, and exponential models and solve problems; interpret expressions for functions in terms of the situation they model.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-TF (Trigonometric Functions):</strong> Extend the domain of trigonometric functions using the unit circle; model periodic phenomena with trigonometric functions; prove and apply trigonometric identities.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Geometry (HSG)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSG-CO (Congruence):</strong> Experiment with transformations in the plane; understand congruence in terms of rigid motions; prove geometric theorems; make geometric constructions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-SRT (Similarity, Right Triangles, and Trigonometry):</strong> Understand similarity in terms of similarity transformations; prove theorems involving similarity; define trigonometric ratios and solve problems involving right triangles; apply trigonometry to general triangles.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-C (Circles):</strong> Understand and apply theorems about circles; find arc lengths and areas of sectors of circles.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-GPE (Expressing Geometric Properties with Equations):</strong> Translate between the geometric description and the equation for a conic section; use coordinates to prove simple geometric theorems algebraically.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-GMD (Geometric Measurement and Dimension):</strong> Explain volume formulas and use them to solve problems; visualize relationships between two-dimensional and three-dimensional objects.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-MG (Modeling with Geometry):</strong> Apply geometric concepts in modeling situations.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Statistics and Probability (HSS)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSS-ID (Interpreting Categorical and Quantitative Data):</strong> Summarize, represent, and interpret data on a single count or measurement variable; summarize, represent, and interpret data on two categorical and quantitative variables; interpret linear models.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSS-IC (Making Inferences and Justifying Conclusions):</strong> Understand and evaluate random processes underlying statistical experiments; make inferences and justify conclusions from sample surveys, experiments, and observational studies.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSS-CP (Conditional Probability and the Rules of Probability):</strong> Understand independence and conditional probability and use them to interpret data; use the rules of probability to compute probabilities of compound events in a uniform probability model.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSS-MD (Using Probability to Make Decisions):</strong> Calculate expected values and use them to solve problems; use probability to evaluate outcomes of decisions.</p>",
+ "<h4 class=\"curr-standard-title\">Geometry</h4>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.A.1:</strong> Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.A.2:</strong> Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.A.3:</strong> Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.A.4:</strong> Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.A.5:</strong> Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.B.6:</strong> Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.B.7:</strong> Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.B.8:</strong> Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.C.9:</strong> Prove theorems about lines and angles.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.C.10:</strong> Prove theorems about triangles.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.C.11:</strong> Prove theorems about parallelograms.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.D.12:</strong> Make formal geometric constructions with a variety of tools and methods.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-CO.D.13:</strong> Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.A.1:</strong> Verify experimentally the properties of dilations given by a center and a scale factor.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.A.2:</strong> Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.A.3:</strong> Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.B.4:</strong> Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.B.5:</strong> Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.C.6:</strong> Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.C.7:</strong> Explain and use the relationship between the sine and cosine of complementary angles.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-SRT.C.8:</strong> Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-C.A.1:</strong> Prove that all circles are similar.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-C.A.2:</strong> Identify and describe relationships among inscribed angles, radii, and chords.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-C.A.3:</strong> Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-C.B.5:</strong> Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GPE.A.1:</strong> Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GPE.A.2:</strong> Derive the equation of a parabola given a focus and directrix.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GPE.B.4:</strong> Use coordinates to prove simple geometric theorems algebraically.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GPE.B.5:</strong> Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GPE.B.6:</strong> Find the point on a directed line segment between two given points that partitions the segment in a given ratio.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GPE.B.7:</strong> Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GMD.A.1:</strong> Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GMD.A.3:</strong> Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-GMD.B.4:</strong> Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-MG.A.1:</strong> Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-MG.A.2:</strong> Apply concepts of density based on area and volume in modeling situations.</p>",
+ "<p class=\"curr-standard-desc\"><strong>HSG-MG.A.3:</strong> Apply geometric methods to solve design problems.</p>",
"</div>"
],
"competencies": [
@@ -726,45 +771,53 @@
},
"11th Grade": {
"ccss": {
- "title": "11th Grade Math (CCSS)",
- "overview": "<p>High school standards specify the mathematics that all students should study in order to be college and career ready, organized by conceptual categories (Number/Quantity, Algebra, Functions, Geometry, Statistics/Probability) rather than by grade.</p>",
+ "title": "11th Grade Math (CCSS) - Algebra II / Probability Focus",
+ "overview": "<p>High school standards specify the mathematics that all students should study in order to be college and career ready. In 11th Grade (Algebra II), time typically focuses on complex numbers, rational/radical expressions, extending functions, and conditional probability.</p>",
"standards": [
"<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Number and Quantity (HSN)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSN-RN (The Real Number System):</strong> Extend the properties of exponents to rational exponents; use properties of rational and irrational numbers.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-Q (Quantities):</strong> Reason quantitatively and use units to solve problems.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-CN (The Complex Number System):</strong> Perform arithmetic operations with complex numbers; represent complex numbers and their operations on the complex plane; use complex numbers in polynomial identities and equations.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSN-VM (Vector and Matrix Quantities):</strong> Represent and model with vector quantities; perform operations on vectors; perform operations on matrices and use matrices in applications.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Algebra (HSA)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSA-SSE (Seeing Structure in Expressions):</strong> Interpret the structure of expressions; write expressions in equivalent forms to solve problems.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-APR (Arithmetic with Polynomials and Rational Expressions):</strong> Perform arithmetic operations on polynomials; understand the relationship between zeros and factors of polynomials; use polynomial identities to solve problems; rewrite rational expressions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-CED (Creating Equations):</strong> Create equations that describe numbers or relationships.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSA-REI (Reasoning with Equations and Inequalities):</strong> Understand solving equations as a process of reasoning and explain the reasoning; solve equations and inequalities in one variable; solve systems of equations; represent and solve equations and inequalities graphically.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Functions (HSF)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSF-IF (Interpreting Functions):</strong> Understand the concept of a function and use function notation; interpret functions that arise in applications in terms of the context; analyze functions using different representations.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-BF (Building Functions):</strong> Build a function that models a relationship between two quantities; build new functions from existing functions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-LE (Linear, Quadratic, and Exponential Models):</strong> Construct and compare linear, quadratic, and exponential models and solve problems; interpret expressions for functions in terms of the situation they model.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSF-TF (Trigonometric Functions):</strong> Extend the domain of trigonometric functions using the unit circle; model periodic phenomena with trigonometric functions; prove and apply trigonometric identities.</p>",
- "</div>",
- "<div class=\"curr-standard-item\">",
- "<h4 class=\"curr-standard-title\">Geometry (HSG)</h4>",
- "<p class=\"curr-standard-desc\"><strong>HSG-CO (Congruence):</strong> Experiment with transformations in the plane; understand congruence in terms of rigid motions; prove geometric theorems; make geometric constructions.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-SRT (Similarity, Right Triangles, and Trigonometry):</strong> Understand similarity in terms of similarity transformations; prove theorems involving similarity; define trigonometric ratios and solve problems involving right triangles; apply trigonometry to general triangles.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-C (Circles):</strong> Understand and apply theorems about circles; find arc lengths and areas of sectors of circles.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-GPE (Expressing Geometric Properties with Equations):</strong> Translate between the geometric description and the equation for a conic section; use coordinates to prove simple geometric theorems algebraically.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-GMD (Geometric Measurement and Dimension):</strong> Explain volume formulas and use them to solve problems; visualize relationships between two-dimensional and three-dimensional objects.</p>",
- "<p class=\"curr-standard-desc\"><strong>HSG-MG (Modeling with Geometry):</strong> Apply geometric concepts in modeling situations.</p>",