Cluster: Working with numbers 11-19 to gain foundations for place value. Standards Key ideas and Details Intervention Supports K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 +8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. A – ML – ML – Grade 1 Cluster: Extend the counting sequence. Standards Key ideas and Details Intervention Supports 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. ML – ML – Cluster: Understand place value. Standards Key ideas and Details Intervention Supports 1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). PL – A – V – ML – ML – A –
1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. V – ML – Cluster: Use place value understanding and properties of operations to add and subtract. Standards Key ideas and Details Intervention Supports 1.NBT.4 1.NBT.5 1.NBT.6 Add within 100, including adding a two-digit number and a number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. A – S – ML – ML – A – R – ML – V – A – Grade 2 Cluster: Understand place value. Standards Key ideas and Details Intervention Supports 2.NBT.1 R –
3.NBT.1 3.NBT.2 3.NBT.3 Use place value understanding to round whole numbers to the nearest 10 or 100. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. V – R – A – ML – PL – V – V – V – V – ML – R – Grade 4 Cluster: Generalize place value understanding for multi-digit whole numbers. Standards Key ideas and Details Intervention Supports 4.NBT.1 4.NBT.2 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. ML – A – A – ML – Cluster: Work with time and money. Standards Key ideas and Details Intervention Supports 2.MD.7 2.MD.8 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? ML – V – A – R – A – A – ML – Cluster: Represent and interpret data. Standards Key ideas and Details Intervention Supports 2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. ML – ML – A –
Standards Key ideas and Details Intervention Supports A.CED.1 A.CED.2 A.CED.3 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. Create equations in two or more variables to represent relationships between quantities, graph equations on a coordinate axes with labels and scales. 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. 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. R: Shows the steps for writing an equation from a word problem. ML: Shows students how to write and solve linear equations for a specific value. V: A set of videos that show how to determine constraints of equations and inequalities. V: Shows the process of solving an equation for a specific variable
A.REI.4a A.REI.4b Solve quadratic equations in one variable. a. 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. b. Solve quadratic equations by inspection (e.g., for x2 = 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. V: Shows how the quadratic formula results from completing the square. V: Song on the quadratic formula ML: Lesson on factoring. V: Multiple videos on how to solve quadratics. Standards Key ideas and Details Intervention Supports
G.SRT.3 to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Cluster: Prove theorems involving similarity. Standards Key ideas and Details Intervention Supports G.SRT.4 G.SRT.5 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. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. R/V: Discusses standard G.SRT.4 and includes a funny video for students. R: Discusses standard G.SRT.5 and includes a real life example to present to students. Cluster: Define trigonometric ratios and solve problems involving right triangles Standards Key ideas and Details Intervention Supports G.SRT.6 G.SRT.7 G.SRT.8 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. Explain and use the relationship between the sine and cosine of complementary angles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. * R: A graphic organizer on trigonometric ratios. V/R: Features several videos and examples of trigonometry. V: Provides several videos on standard G.SRT.7. A: A real world activity on trigonometry.
S.ID.6b S.ID.6c b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. (Statistics and Probability is a Modeling Conceptual Category.) Cluster: Interpret linear models Standards Key ideas and Details Intervention Supports S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (Statistics and Probability is a Modeling Conceptual Category.) A: An interactive activity that shows how bungee jumping relates to scatter plots and line of best fit. R: Discusses the meaning of a correlation coefficient.
S.ID.8 S.ID.9 Compute (using technology) and interpret the correlation coefficient of a linear fit. (Statistics and Probability is a Modeling Conceptual Category.) Distinguish between correlation and causation. (Statistics and Probability is a Modeling Conceptual Category.) R: Provides a clear explanation of causation and correlation. Domain: Making Inferences and Justifying Conclusions*(Modeling Conceptual Category) Cluster: Understand and evaluate random processes underlying statistical experiments Standards Key ideas and Details Intervention Supports S.IC.1 S.IC.2 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. *Statistics and Probability is a Modeling Conceptual Category Decide if a specified model is consistent with results from a given data-generating process, eg., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a V/R: Shows several examples on standard S.IC.1 and has a funny video. V/R: Provides several examples and videos on statistics. V: Video on collecting data.
Cluster: Use rules of probability to compute probabilities of compound events in a uniform probability model Standards Key ideas and Details Intervention Supports S.CP.6 S.CP.7 S.CP.8 (+) S.CP.9 (+) Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A and interpret the answer in terms of the model. *Statistics and Probability is a Modeling Conceptual Category. Apply the Additional Rule, P(A or B) = P(A) + P(B) – P(A and B) and interpret the answer in terms of the model. *Statistics and Probability is a Modeling Conceptual Category. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. *Statistics and Probability is a Modeling Conceptual Category. Use permutations and combinations to compute probabilities of compound events and solve problems. *Statistics and Probability is a Modeling Conceptual Category. V: Videos on conditional probability. R: Discusses standard S.CP.6 and provides examples. V: Video on the addition rule. R: Discusses standard S.CP.8 and provides examples. V: Several videos on the multiplication rule. R: Shows examples of permutations and combinations. V: Several videos and examples on permutations and combinations. Domain: Using Probability to Make Decisions Cluster: Calculate expected values and use them to solve problems Standards Key ideas and Details Intervention Supports S.MD.1 (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. ML: Lesson on expected values. R: Discusses standard S.MD.3. V: Videos on probability.
F.IF.7b F.IF.8a F.IF.8b F.IF.9 a. Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*(Modeling standard) b. Graph square root, cube root, and functions, including step functions and absolute value functions. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function: b. Use the properties of exponents to interpret expressions for exponential functions. For example: identify percent rate of change in functions such as y= (1.02)t, y=(.97)t, y=(1.01)12t, y=(1.2)t/10, and classify them as representing exponential growth or decay. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. R: Shows the steps for graphing linear equations. ML: A lesson helping students to identify parts of quadratic functions. R: Shows examples of graphing. V: Multiple videos and examples on graphing. R: Discusses the process of finding zeros. R: Provides several useful handouts for finding the zeros. V: Features several videos on graphing parabolas. ML: A complete lesson on quadratics. R: Provides a full explanation of standard F.IF.8b along with examples. V: Features several short video lessons on how to make connections between functions. Domain: Building Functions Cluster: Build a function that models a relationship between two quantities Standards Key ideas and Details Intervention Supports
Kentucky Core Academic Progression of Standards and Related Intervention Supports MATHEMATICS- Algebra 2 R-Resources S- Strategy A- Activities V- Video ML- Model Lesson PL- Professional Learning QC: Quality Core Standards Algebra 2 Unit 1 Domain: The Complex Number System Cluster: Perform arithmetic operations with complex numbers Standards Key ideas and Details Intervention Supports N.CN.1 QC: C.1.a N.CN.2 QC: C.1.b Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real numbers. Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. R: Shows examples involving complex numbers. R: Provides examples of operations with complex numbers. V: Videos of operations with complex numbers. ! Cluster: Use complex numbers in polynomial identities and equations Standards Key ideas and Details Intervention Supports N.CN.7 QC: E.1.c N.CN.8 (+) Solve quadratic equations with real coefficients that have complex solutions. R: Several examples of quadratics. V: Videos on quadratics.
quadratic function and an algebraic expression for another, say which has the larger maximum. Domain: Building Functions Cluster: Build a function that models a relationship between two quantities Standards Key ideas and Details Intervention Supports F.BF.1b QC: C.1.d, E.2.a Write a function that describes a relationship between two quantities.*(Modeling standard) b. 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. ML: Students write equations based on patterns. ML: Students write equations based on patterns. V: A video showing how to write equations based on sequences. Cluster: Build new functions from existing functions Standards Key ideas and Details Intervention Supports F.BF.3 QC: E.2.b, E.3.b F.BF. 4a QC: G.2.b, H.2.b, H.2.d 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. Find the inverse functions a. 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) = 2x3 or f(x) = (x+1)/(x-1) for x ≠ 1. ML: A guided lesson on transformations. R: Explains the process of finding the inverse of a function. Domain: Linear and Exponential Models* Cluster: Construct and compare linear, quadratic, and exponential models and solve problems Standards Key ideas and Details Intervention Supports