## High School Algebra 1 – CA Common Core – Standards & Learning Objectives

### 9-12.N Number and Quantity

#### 9-12.N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Evaluate integers raised to rational exponents (Algebra 1 – V.10)

Evaluate rational exponents (Algebra 2 – M.1)

Evaluate rational exponents (Precalculus – H.4)

#### 9-12.N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Simplify radical expressions (Algebra 1 – EE.1)

Simplify radical expressions involving fractions (Algebra 1 – EE.2)

Multiply radical expressions (Algebra 1 – EE.3)

Simplify radical expressions using the distributive property (Algebra 1 – EE.5)

Simplify radical expressions: mixed review (Algebra 1 – EE.7)

Simplify radical expressions (Geometry – A.4)

Roots of integers (Algebra 2 – L.1)

Roots of rational numbers (Algebra 2 – L.2)

Nth roots (Algebra 2 – L.4)

Simplify radical expressions with variables I (Algebra 2 – L.5)

Simplify radical expressions with variables II (Algebra 2 – L.6)

Multiply radical expressions (Algebra 2 – L.7)

Divide radical expressions (Algebra 2 – L.8)

Simplify radical expressions using the distributive property (Algebra 2 – L.10)

Simplify radical expressions using conjugates (Algebra 2 – L.11)

Multiplication with rational exponents (Algebra 2 – M.2)

Division with rational exponents (Algebra 2 – M.3)

Power rule (Algebra 2 – M.4)

Simplify expressions involving rational exponents I (Algebra 2 – M.5)

Simplify expressions involving rational exponents II (Algebra 2 – M.6)

Operations with rational exponents (Precalculus – H.5)

Nth roots (Precalculus – H.6)

Simplify radical expressions with variables (Precalculus – H.7)

Simplify expressions involving rational exponents (Precalculus – H.8)

#### 9-12.N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Classify rational and irrational numbers (Precalculus – Q.1)

Sort rational and irrational numbers (Precalculus – Q.2)

Properties of operations on rational and irrational numbers (Precalculus – Q.3)

#### 9-12.N-Q.1 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.

Scale drawings and scale factors (Algebra 1 – C.7)

Convert rates and measurements: customary units (Algebra 1 – E.1)

Convert rates and measurements: metric units (Algebra 1 – E.2)

Unit prices with unit conversions (Algebra 1 – E.3)

Scale maps and drawings (Geometry – A.2)

Convert rates and measurements: customary units (Geometry – W.1)

Convert rates and measurements: metric units (Geometry – W.2)

Convert square and cubic units of length (Geometry – W.3)

#### 9-12.N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.

Interpret bar graphs, line graphs, and histograms (Algebra 1 – N.1)

Create bar graphs, line graphs, and histograms (Algebra 1 – N.2)

Interpret stem-and-leaf plots (Algebra 1 – N.4)

Interpret box-and-whisker plots (Algebra 1 – N.5)

Interpret a scatter plot (Algebra 1 – N.6)

Scatter plots: line of best fit (Algebra 1 – N.7)

#### 9-12.N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Precision (Algebra 1 – E.4)

Greatest possible error (Algebra 1 – E.5)

Precision (Geometry – W.4)

Greatest possible error (Geometry – W.5)

Minimum and maximum area and volume (Geometry – W.6)

Percent error (Geometry – W.7)

Percent error: area and volume (Geometry – W.8)

### 9-12.A. Algebra

#### 9-12.A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

Polynomial vocabulary (Algebra 1 – Z.1)

Polynomial vocabulary (Algebra 2 – K.1)

#### 9-12.A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

Factor using a quadratic pattern (Algebra 2 – I.4)

Factor using a quadratic pattern (Precalculus – D.14)

#### 9-12.A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

Simplify variable expressions using properties (Algebra 1 – H.3)

Simplify variable expressions involving like terms and the distributive property (Algebra 1 – I.2)

Simplify expressions involving exponents (Algebra 1 – V.8)

Powers of monomials (Algebra 1 – Y.5)

Factor out a monomial (Algebra 1 – AA.2)

Simplify variable expressions using properties (Algebra 2 – A.3)

Pascal’s triangle and the Binomial Theorem (Algebra 2 – K.17)

Binomial Theorem I (Algebra 2 – K.18)

Binomial Theorem II (Algebra 2 – K.19)

Simplify radical expressions with variables I (Algebra 2 – L.5)

Simplify radical expressions with variables II (Algebra 2 – L.6)

Simplify radical expressions using conjugates (Algebra 2 – L.11)

Simplify expressions involving rational exponents I (Algebra 2 – M.5)

Simplify expressions involving rational exponents II (Algebra 2 – M.6)

Simplify rational expressions (Algebra 2 – N.4)

Pascal’s triangle and the Binomial Theorem (Precalculus – D.17)

Binomial Theorem I (Precalculus – D.18)

Binomial Theorem II (Precalculus – D.19)

Simplify radical expressions with variables (Precalculus – H.7)

Simplify expressions involving rational exponents (Precalculus – H.8)

#### 9-12.A-SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

Factor quadratics: special cases (Algebra 1 – AA.5)

Solve a quadratic equation by factoring (Algebra 1 – BB.6)

Factor quadratics (Algebra 2 – I.2)

Solve a quadratic equation by factoring (Algebra 2 – J.8)

Solve a quadratic equation by factoring (Precalculus – C.6)

#### 9-12.A-SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Complete the square (Algebra 1 – BB.7)

Complete the square (Algebra 2 – J.9)

Convert equations of parabolas from general to vertex form (Algebra 2 – T.7)

Find properties of a parabola from equations in general form (Algebra 2 – T.8)

#### 9-12.A-SSE.3.c Use the properties of exponents to transform expressions for exponential functions.

Negative exponents (Algebra 1 – V.3)

Multiplication with exponents (Algebra 1 – V.4)

Division with exponents (Algebra 1 – V.5)

Multiplication and division with exponents (Algebra 1 – V.6)

Power rule (Algebra 1 – V.7)

Simplify expressions involving exponents (Algebra 1 – V.8)

Evaluate an exponential function (Algebra 1 – X.1)

Match exponential functions and graphs (Algebra 1 – X.2)

Properties of exponents (Geometry – A.3)

Evaluate rational exponents (Algebra 2 – M.1)

Multiplication with rational exponents (Algebra 2 – M.2)

Division with rational exponents (Algebra 2 – M.3)

Power rule (Algebra 2 – M.4)

Simplify expressions involving rational exponents I (Algebra 2 – M.5)

Simplify expressions involving rational exponents II (Algebra 2 – M.6)

Evaluate exponential functions (Algebra 2 – S.2)

Match exponential functions and graphs (Algebra 2 – S.3)

Solve exponential equations using factoring (Algebra 2 – S.4)

Solve exponential equations using factoring (Precalculus – F.9)

#### 9-12.A-APR.1 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.

Model polynomials with algebra tiles (Algebra 1 – Z.2)

Add and subtract polynomials using algebra tiles (Algebra 1 – Z.3)

Add and subtract polynomials (Algebra 1 – Z.4)

Add polynomials to find perimeter (Algebra 1 – Z.5)

Multiply a polynomial by a monomial (Algebra 1 – Z.6)

Multiply two polynomials using algebra tiles (Algebra 1 – Z.7)

Multiply two binomials (Algebra 1 – Z.8)

Multiply two binomials: special cases (Algebra 1 – Z.9)

Multiply polynomials (Algebra 1 – Z.10)

Add and subtract polynomials (Algebra 2 – K.2)

Multiply polynomials (Algebra 2 – K.3)

#### 9-12.A-CED.1 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

Write variable equations (Algebra 1 – I.4)

Model and solve equations using algebra tiles (Algebra 1 – J.1)

Write and solve equations that represent diagrams (Algebra 1 – J.2)

Solve linear equations: word problems (Algebra 1 – J.8)

Write inequalities from graphs (Algebra 1 – K.2)

Write compound inequalities from graphs (Algebra 1 – K.13)

Weighted averages: word problems (Algebra 1 – O.5)

Write variable expressions and equations (Geometry – A.5)

Solve linear equations (Geometry – A.6)

Solve linear inequalities (Geometry – A.7)

Solve linear equations (Algebra 2 – B.1)

Solve linear equations: word problems (Algebra 2 – B.2)

Write inequalities from graphs (Algebra 2 – C.3)

Solve linear inequalities (Algebra 2 – C.5)

Solve equations with sums and differences of cubes (Precalculus – D.13)

Solve equations using a quadratic pattern (Precalculus – D.15)

#### 9-12.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Graph a function (Algebra 1 – Q.9)

Write a function rule: word problems (Algebra 1 – Q.10)

Write a rule for a function table (Algebra 1 – Q.12)

Write direct variation equations (Algebra 1 – R.4)

Write inverse variation equations (Algebra 1 – R.7)

Write and solve inverse variation equations (Algebra 1 – R.8)

Find a missing coordinate using slope (Algebra 1 – S.4)

Slope-intercept form: graph an equation (Algebra 1 – S.6)

Slope-intercept form: write an equation from a graph (Algebra 1 – S.7)

Slope-intercept form: write an equation (Algebra 1 – S.8)

Linear function word problems (Algebra 1 – S.10)

Write equations in standard form (Algebra 1 – S.11)

Standard form: graph an equation (Algebra 1 – S.13)

Point-slope form: graph an equation (Algebra 1 – S.16)

Point-slope form: write an equation (Algebra 1 – S.18)

Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)

Graph an absolute value function (Algebra 1 – DD.3)

Graph a linear equation (Geometry – E.3)

Equations of lines (Geometry – E.4)

Graph a linear inequality in the coordinate plane (Algebra 2 – C.2)

Graph a quadratic function (Algebra 2 – J.4)

Write and solve direct variation equations (Algebra 2 – Q.1)

Write and solve inverse variation equations (Algebra 2 – Q.2)

Write joint and combined variation equations I (Algebra 2 – Q.4)

Write joint and combined variation equations II (Algebra 2 – Q.6)

Solve variation equations (Algebra 2 – Q.7)

Graph parabolas (Algebra 2 – T.9)

Graph circles (Algebra 2 – U.7)

Graph sine functions (Algebra 2 – Z.4)

Graph cosine functions (Algebra 2 – Z.8)

Graph sine and cosine functions (Algebra 2 – Z.9)

Graph a quadratic function (Precalculus – C.3)

Graph sine functions (Precalculus – N.4)

Graph cosine functions (Precalculus – N.8)

Graph sine and cosine functions (Precalculus – N.9)

Graph parabolas (Precalculus – P.3)

Graph circles (Precalculus – P.6)

#### 9-12.A-CED.3 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.

Solve a system of equations by graphing: word problems (Algebra 1 – U.3)

Solve a system of equations using substitution: word problems (Algebra 1 – U.9)

Solve a system of equations using elimination: word problems (Algebra 1 – U.11)

Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)

Solve a system of equations using any method: word problems (Algebra 1 – U.15)

Solve systems of linear equations (Geometry – A.8)

Solve a system of equations by graphing: word problems (Algebra 2 – E.3)

Solve a system of equations using substitution: word problems (Algebra 2 – E.7)

Solve a system of equations using elimination: word problems (Algebra 2 – E.9)

Solve a system of equations using any method: word problems (Algebra 2 – E.11)

Solve systems of linear inequalities by graphing (Algebra 2 – F.2)

Solve systems of linear and absolute value inequalities by graphing (Algebra 2 – F.3)

Find the vertices of a solution set (Algebra 2 – F.4)

Linear programming (Algebra 2 – F.5)

Solve a system of equations by graphing (Precalculus – I.1)

Solve a system of equations by graphing: word problems (Precalculus – I.2)

Solve a system of equations using substitution (Precalculus – I.4)

Solve a system of equations using substitution: word problems (Precalculus – I.5)

Solve a system of equations using elimination (Precalculus – I.6)

Solve a system of equations using elimination: word problems (Precalculus – I.7)

Solve systems of linear inequalities by graphing (Precalculus – J.1)

Solve systems of linear and absolute value inequalities by graphing (Precalculus – J.2)

Find the vertices of a solution set (Precalculus – J.3)

Linear programming (Precalculus – J.4)

#### 9-12.A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Rate of travel: word problems (Algebra 1 – O.4)

Solve multi-variable equations (Algebra 2 – B.5)

#### 9-12.A-REI.1 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.

Properties of equality (Algebra 1 – H.4)

Weighted averages: word problems (Algebra 1 – O.5)

#### 9-12.A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Model and solve equations using algebra tiles (Algebra 1 – J.1)

Write and solve equations that represent diagrams (Algebra 1 – J.2)

Solve one-step linear equations (Algebra 1 – J.3)

Solve two-step linear equations (Algebra 1 – J.4)

Solve advanced linear equations (Algebra 1 – J.5)

Solve equations with variables on both sides (Algebra 1 – J.6)

Identities and equations with no solutions (Algebra 1 – J.7)

Solve linear equations: word problems (Algebra 1 – J.8)

Solve linear equations: mixed review (Algebra 1 – J.9)

Identify solutions to inequalities (Algebra 1 – K.3)

Solve one-step linear inequalities: addition and subtraction (Algebra 1 – K.4)

Solve one-step linear inequalities: multiplication and division (Algebra 1 – K.5)

Solve one-step linear inequalities (Algebra 1 – K.6)

Graph solutions to one-step linear inequalities (Algebra 1 – K.7)

Solve two-step linear inequalities (Algebra 1 – K.8)

Graph solutions to two-step linear inequalities (Algebra 1 – K.9)

Solve advanced linear inequalities (Algebra 1 – K.10)

Graph solutions to advanced linear inequalities (Algebra 1 – K.11)

Graph compound inequalities (Algebra 1 – K.12)

Write compound inequalities from graphs (Algebra 1 – K.13)

Solve compound inequalities (Algebra 1 – K.14)

Graph solutions to compound inequalities (Algebra 1 – K.15)

Solve linear equations (Geometry – A.6)

Solve linear inequalities (Geometry – A.7)

Solve linear equations (Algebra 2 – B.1)

Solve linear equations: word problems (Algebra 2 – B.2)

Solve linear inequalities (Algebra 2 – C.5)

Graph solutions to linear inequalities (Algebra 2 – C.6)

#### 9-12.A-REI.3.1 Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.

Solve absolute value equations (Algebra 1 – L.1)

Graph solutions to absolute value equations (Algebra 1 – L.2)

Solve absolute value inequalities (Algebra 1 – L.3)

Graph solutions to absolute value inequalities (Algebra 1 – L.4)

Solve absolute value equations (Algebra 2 – B.3)

Graph solutions to absolute value equations (Algebra 2 – B.4)

Solve absolute value inequalities (Algebra 2 – C.7)

Graph solutions to absolute value inequalities (Algebra 2 – C.8)

#### 9-12.A-REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x â€“ p)Â² = q that has the same solutions. Derive the quadratic formula from this form.

Complete the square (Algebra 1 – BB.7)

Complete the square (Algebra 2 – J.9)

#### 9-12.A-REI.4.b Solve quadratic equations by inspection (e.g., for xÂ² = 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 Â± bi for real numbers a and b.

Solve a quadratic equation using square roots (Algebra 1 – BB.4)

Solve an equation using the zero product property (Algebra 1 – BB.5)

Solve a quadratic equation by factoring (Algebra 1 – BB.6)

Complete the square (Algebra 1 – BB.7)

Solve a quadratic equation by completing the square (Algebra 1 – BB.8)

Solve a quadratic equation using the quadratic formula (Algebra 1 – BB.9)

Using the discriminant (Algebra 1 – BB.10)

Solve quadratic equations (Geometry – A.9)

Solve a quadratic equation using square roots (Algebra 2 – J.6)

Solve a quadratic equation using the zero product property (Algebra 2 – J.7)

Solve a quadratic equation by factoring (Algebra 2 – J.8)

Solve a quadratic equation using the quadratic formula (Algebra 2 – J.11)

Using the discriminant (Algebra 2 – J.12)

Solve a quadratic equation using square roots (Precalculus – C.5)

Solve a quadratic equation by factoring (Precalculus – C.6)

Solve a quadratic equation by completing the square (Precalculus – C.7)

#### 9-12.A-REI.5 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.

Solve a system of equations using elimination (Algebra 1 – U.10)

Solve a system of equations using elimination: word problems (Algebra 1 – U.11)

Solve a system of equations using augmented matrices (Algebra 1 – U.12)

Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)

Solve a system of equations using elimination (Algebra 2 – E.8)

Solve a system of equations using elimination: word problems (Algebra 2 – E.9)

Solve a system of equations using elimination (Precalculus – I.6)

Solve a system of equations using elimination: word problems (Precalculus – I.7)

#### 9-12.A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Is (x, y) a solution to the system of equations? (Algebra 1 – U.1)

Solve a system of equations by graphing (Algebra 1 – U.2)

Solve a system of equations by graphing: word problems (Algebra 1 – U.3)

Find the number of solutions to a system of equations by graphing (Algebra 1 – U.4)

Find the number of solutions to a system of equations (Algebra 1 – U.5)

Classify a system of equations by graphing (Algebra 1 – U.6)

Classify a system of equations (Algebra 1 – U.7)

Solve a system of equations using substitution (Algebra 1 – U.8)

Solve a system of equations using substitution: word problems (Algebra 1 – U.9)

Solve a system of equations using elimination (Algebra 1 – U.10)

Solve a system of equations using elimination: word problems (Algebra 1 – U.11)

Solve a system of equations using augmented matrices (Algebra 1 – U.12)

Solve a system of equations using augmented matrices: word problems (Algebra 1 – U.13)

Solve a system of equations using any method (Algebra 1 – U.14)

Solve a system of equations using any method: word problems (Algebra 1 – U.15)

Solve systems of linear equations (Geometry – A.8)

Is (x, y) a solution to the system of equations? (Algebra 2 – E.1)

Solve a system of equations by graphing (Algebra 2 – E.2)

Solve a system of equations by graphing: word problems (Algebra 2 – E.3)

Find the number of solutions to a system of equations (Algebra 2 – E.4)

Classify a system of equations (Algebra 2 – E.5)

Solve a system of equations using substitution (Algebra 2 – E.6)

Solve a system of equations using substitution: word problems (Algebra 2 – E.7)

Solve a system of equations using elimination (Algebra 2 – E.8)

Solve a system of equations using elimination: word problems (Algebra 2 – E.9)

Solve a system of equations using any method (Algebra 2 – E.10)

Solve a system of equations using any method: word problems (Algebra 2 – E.11)

Solve a system of equations by graphing (Precalculus – I.1)

Solve a system of equations by graphing: word problems (Precalculus – I.2)

Classify a system of equations (Precalculus – I.3)

Solve a system of equations using substitution (Precalculus – I.4)

Solve a system of equations using substitution: word problems (Precalculus – I.5)

Solve a system of equations using elimination (Precalculus – I.6)

Solve a system of equations using elimination: word problems (Precalculus – I.7)

#### 9-12.A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Solve a non-linear system of equations (Algebra 2 – E.15)

#### 9-12.A-REI.10 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).

Relations: convert between tables, graphs, mappings, and lists of points (Algebra 1 – Q.1)

Complete a function table (Algebra 1 – Q.6)

Graph a function (Algebra 1 – Q.9)

Find points on a function graph (Algebra 1 – Q.11)

#### 9-12.A-REI.11 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.

Solve a system of equations by graphing (Algebra 1 – U.2)

Solve a system of equations by graphing: word problems (Algebra 1 – U.3)

Find the number of solutions to a system of equations by graphing (Algebra 1 – U.4)

Solve a system of equations by graphing (Precalculus – I.1)

Solve a system of equations by graphing: word problems (Precalculus – I.2)

#### 9-12.A-REI.12 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.

Graph a linear inequality in the coordinate plane (Algebra 1 – T.3)

Graph a linear inequality in the coordinate plane (Algebra 2 – C.2)

Solve systems of linear inequalities by graphing (Algebra 2 – F.2)

Solve systems of linear inequalities by graphing (Precalculus – J.1)

### 9-12.F Functions

#### 9-12.F-IF.1 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).

Domain and range of relations (Algebra 1 – Q.2)

Identify independent and dependent variables (Algebra 1 – Q.3)

Identify functions (Algebra 1 – Q.4)

Identify functions: vertical line test (Algebra 1 – Q.5)

Domain and range of absolute value functions (Algebra 1 – DD.2)

Domain and range of radical functions (Algebra 1 – FF.2)

Domain and range (Algebra 2 – D.1)

Identify functions (Algebra 2 – D.2)

Domain and range (Precalculus – A.1)

Identify functions (Precalculus – A.2)

Domain and range of exponential and logarithmic functions (Precalculus – F.1)

Domain and range of radical functions (Precalculus – G.1)

#### 9-12.F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Complete a function table (Algebra 1 – Q.6)

Evaluate function rules I (Algebra 1 – Q.7)

Evaluate function rules II (Algebra 1 – Q.8)

Evaluate an exponential function (Algebra 1 – X.1)

Complete a function table: quadratic functions (Algebra 1 – BB.2)

Complete a function table: absolute value functions (Algebra 1 – DD.1)

Evaluate a radical function (Algebra 1 – FF.1)

Evaluate functions (Algebra 2 – D.3)

Evaluate logarithms (Algebra 2 – R.4)

Evaluate natural logarithms (Algebra 2 – R.5)

Evaluate logarithms: mixed review (Algebra 2 – R.12)

Evaluate exponential functions (Algebra 2 – S.2)

Evaluate functions (Precalculus – A.5)

#### 9-12.F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Identify arithmetic and geometric sequences (Algebra 1 – P.1)

Arithmetic sequences (Algebra 1 – P.2)

Geometric sequences (Algebra 1 – P.3)

Evaluate variable expressions for number sequences (Algebra 1 – P.4)

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Number sequences: mixed review (Algebra 1 – P.7)

Classify formulas and sequences (Algebra 2 – BB.1)

Find terms of an arithmetic sequence (Algebra 2 – BB.2)

Find terms of a geometric sequence (Algebra 2 – BB.3)

Find terms of a recursive sequence (Algebra 2 – BB.4)

Evaluate formulas for sequences (Algebra 2 – BB.5)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Write a formula for a recursive sequence (Algebra 2 – BB.8)

Sequences: mixed review (Algebra 2 – BB.9)

Find terms of a sequence (Precalculus – W.1)

Find terms of a recursive sequence (Precalculus – W.2)

Identify a sequence as explicit or recursive (Precalculus – W.3)

Find a recursive formula (Precalculus – W.4)

#### 9-12.F-IF.4 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.

Identify proportional relationships (Algebra 1 – R.1)

Find the constant of variation (Algebra 1 – R.2)

Graph a proportional relationship (Algebra 1 – R.3)

Identify direct variation and inverse variation (Algebra 1 – R.6)

Slope-intercept form: find the slope and y-intercept (Algebra 1 – S.5)

Standard form: find x- and y-intercepts (Algebra 1 – S.12)

Slopes of parallel and perpendicular lines (Algebra 1 – S.19)

Characteristics of quadratic functions (Algebra 1 – BB.1)

Identify linear, quadratic, and exponential functions from graphs (Algebra 1 – CC.1)

Identify linear, quadratic, and exponential functions from tables (Algebra 1 – CC.2)

Graph an absolute value function (Algebra 1 – DD.3)

Rational functions: asymptotes and excluded values (Algebra 1 – GG.1)

Slopes of lines (Geometry – E.2)

Characteristics of quadratic functions (Algebra 2 – J.1)

Graph a quadratic function (Algebra 2 – J.4)

Match quadratic functions and graphs (Algebra 2 – J.5)

Match polynomials and graphs (Algebra 2 – K.14)

Rational functions: asymptotes and excluded values (Algebra 2 – N.1)

Classify variation (Algebra 2 – Q.3)

Find the constant of variation (Algebra 2 – Q.5)

Match exponential functions and graphs (Algebra 2 – S.3)

Linear functions (Precalculus – A.3)

Characteristics of quadratic functions (Precalculus – C.1)

Find the maximum or minimum value of a quadratic function (Precalculus – C.2)

Match quadratic functions and graphs (Precalculus – C.4)

Match polynomials and graphs (Precalculus – D.11)

Rational functions: asymptotes and excluded values (Precalculus – E.1)

#### 9-12.F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Domain and range of absolute value functions (Algebra 1 – DD.2)

Domain and range of radical functions (Algebra 1 – FF.2)

Domain and range (Algebra 2 – D.1)

Domain and range of radical functions (Algebra 2 – L.12)

Domain and range of exponential and logarithmic functions (Algebra 2 – S.1)

Domain and range (Precalculus – A.1)

Domain and range of exponential and logarithmic functions (Precalculus – F.1)

Domain and range of radical functions (Precalculus – G.1)

#### 9-12.F-IF.6 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.

Find the constant of variation (Algebra 1 – R.2)

Find the slope of a graph (Algebra 1 – S.2)

Find the slope from two points (Algebra 1 – S.3)

Slope-intercept form: find the slope and y-intercept (Algebra 1 – S.5)

Find the slope of a linear function (Algebra 2 – D.4)

Linear functions (Precalculus – A.3)

#### 9-12.F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

Slope-intercept form: graph an equation (Algebra 1 – S.6)

Standard form: graph an equation (Algebra 1 – S.13)

Point-slope form: graph an equation (Algebra 1 – S.16)

Characteristics of quadratic functions (Algebra 1 – BB.1)

Graph a linear equation (Geometry – E.3)

Graph a linear function (Algebra 2 – D.5)

Graph a quadratic function (Algebra 2 – J.4)

Match quadratic functions and graphs (Algebra 2 – J.5)

Characteristics of quadratic functions (Precalculus – C.1)

Find the maximum or minimum value of a quadratic function (Precalculus – C.2)

Graph a quadratic function (Precalculus – C.3)

Match quadratic functions and graphs (Precalculus – C.4)

#### 9-12.F-IF.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Graph an absolute value function (Algebra 1 – DD.3)

#### 9-12.F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Match exponential functions and graphs (Algebra 1 – X.2)

Find properties of sine functions (Algebra 2 – Z.1)

Graph sine functions (Algebra 2 – Z.4)

Find properties of cosine functions (Algebra 2 – Z.5)

Graph cosine functions (Algebra 2 – Z.8)

Graph sine and cosine functions (Algebra 2 – Z.9)

Find properties of sine functions (Precalculus – N.1)

Graph sine functions (Precalculus – N.4)

Find properties of cosine functions (Precalculus – N.5)

Graph cosine functions (Precalculus – N.8)

Graph sine and cosine functions (Precalculus – N.9)

#### 9-12.F-IF.8.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.

Characteristics of quadratic functions (Algebra 1 – BB.1)

Solve a quadratic equation by factoring (Algebra 1 – BB.6)

Complete the square (Algebra 1 – BB.7)

Solve a quadratic equation by completing the square (Algebra 1 – BB.8)

Characteristics of quadratic functions (Algebra 2 – J.1)

Solve a quadratic equation by factoring (Algebra 2 – J.8)

Complete the square (Algebra 2 – J.9)

Convert equations of parabolas from general to vertex form (Algebra 2 – T.7)

Find properties of a parabola from equations in general form (Algebra 2 – T.8)

Characteristics of quadratic functions (Precalculus – C.1)

Find the maximum or minimum value of a quadratic function (Precalculus – C.2)

Solve a quadratic equation by factoring (Precalculus – C.6)

Solve a quadratic equation by completing the square (Precalculus – C.7)

#### 9-12.F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions.

Match exponential functions and graphs (Algebra 1 – X.2)

Match exponential functions and graphs (Algebra 2 – S.3)

#### 9-12.F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Match quadratic functions and graphs (Algebra 2 – J.5)

Match polynomials and graphs (Algebra 2 – K.14)

Match quadratic functions and graphs (Precalculus – C.4)

Match polynomials and graphs (Precalculus – D.11)

#### 9-12.F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Write inverse variation equations (Algebra 1 – R.7)

Write and solve inverse variation equations (Algebra 1 – R.8)

Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Write a formula for a recursive sequence (Algebra 2 – BB.8)

Find a recursive formula (Precalculus – W.4)

#### 9-12.F-BF.1.b Combine standard function types using arithmetic operations.

Add and subtract functions (Algebra 2 – O.1)

Multiply functions (Algebra 2 – O.2)

Divide functions (Algebra 2 – O.3)

Add, subtract, multiply, and divide functions (Precalculus – A.6)

#### 9-12.F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Write a formula for a recursive sequence (Algebra 2 – BB.8)

Find a recursive formula (Precalculus – W.4)

Find recursive and explicit formulas (Precalculus – W.5)

Convert a recursive formula to an explicit formula (Precalculus – W.6)

Convert an explicit formula to a recursive formula (Precalculus – W.7)

Convert between explicit and recursive formulas (Precalculus – W.8)

#### 9-12.F-BF.3 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.

Transformations of quadratic functions (Algebra 1 – BB.3)

Transformations of absolute value functions (Algebra 1 – DD.4)

Translations of functions (Algebra 2 – P.1)

Reflections of functions (Algebra 2 – P.2)

Dilations of functions (Algebra 2 – P.3)

Transformations of functions (Algebra 2 – P.4)

Function transformation rules (Algebra 2 – P.5)

Describe function transformations (Algebra 2 – P.6)

Translations of functions (Precalculus – B.1)

Reflections of functions (Precalculus – B.2)

Dilations of functions (Precalculus – B.3)

Transformations of functions (Precalculus – B.4)

Function transformation rules (Precalculus – B.5)

Describe function transformations (Precalculus – B.6)

#### 9-12.F-BF.4.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.

Find inverse functions and relations (Algebra 2 – O.9)

Solve exponential equations using common logarithms (Algebra 2 – S.5)

Solve exponential equations using natural logarithms (Algebra 2 – S.6)

Solve logarithmic equations I (Algebra 2 – S.7)

Solve logarithmic equations II (Algebra 2 – S.8)

Solve logarithmic equations with one logarithm (Precalculus – F.11)

#### 9-12.F-LE.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Describe linear and exponential growth and decay (Algebra 1 – CC.6)

Identify linear and exponential functions (Algebra 2 – S.9)

Describe linear and exponential growth and decay (Algebra 2 – S.11)

Identify linear and exponential functions (Precalculus – F.13)

Describe linear and exponential growth and decay (Precalculus – F.15)

#### 9-12.F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Solve linear equations: word problems (Algebra 1 – J.8)

Linear functions over unit intervals (Algebra 1 – CC.4)

Solve linear equations: word problems (Algebra 2 – B.2)

Linear functions over unit intervals (Algebra 2 – D.7)

Linear functions over unit intervals (Precalculus – A.4)

#### 9-12.F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Exponential growth and decay: word problems (Algebra 1 – X.3)

Identify linear, quadratic, and exponential functions from graphs (Algebra 1 – CC.1)

Identify linear, quadratic, and exponential functions from tables (Algebra 1 – CC.2)

Exponential functions over unit intervals (Algebra 1 – CC.5)

Exponential functions over unit intervals (Algebra 2 – S.10)

Exponential growth and decay: word problems (Algebra 2 – S.12)

Exponential functions over unit intervals (Precalculus – F.14)

Exponential growth and decay: word problems (Precalculus – F.16)

#### 9-12.F-LE.2 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).

Write variable expressions for arithmetic sequences (Algebra 1 – P.5)

Write variable expressions for geometric sequences (Algebra 1 – P.6)

Write a rule for a function table (Algebra 1 – Q.12)

Slope-intercept form: write an equation (Algebra 1 – S.8)

Point-slope form: write an equation from a graph (Algebra 1 – S.17)

Point-slope form: write an equation (Algebra 1 – S.18)

Match exponential functions and graphs (Algebra 1 – X.2)

Write linear, quadratic, and exponential functions (Algebra 1 – CC.3)

Equations of lines (Geometry – E.4)

Equations of parallel and perpendicular lines (Geometry – E.6)

Write the equation of a linear function (Algebra 2 – D.6)

Write a formula for an arithmetic sequence (Algebra 2 – BB.6)

Write a formula for a geometric sequence (Algebra 2 – BB.7)

Linear functions (Precalculus – A.3)

#### 9-12.F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Solve linear equations: word problems (Algebra 1 – J.8)

Exponential growth and decay: word problems (Algebra 1 – X.3)

Solve linear equations: word problems (Algebra 2 – B.2)

Exponential growth and decay: word problems (Algebra 2 – S.12)

Compound interest: word problems (Algebra 2 – S.13)

Continuously compounded interest: word problems (Algebra 2 – S.14)

Exponential growth and decay: word problems (Precalculus – F.16)

Compound interest: word problems (Precalculus – F.17)

### 9-12.S Statistics and Probability

#### 9-12.S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

Create bar graphs, line graphs, and histograms (Algebra 1 – N.2)

#### 9-12.S-ID.2 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.

Mean, median, mode, and range (Algebra 1 – KK.1)

Quartiles (Algebra 1 – KK.2)

Mean absolute deviation (Algebra 1 – KK.7)

Variance and standard deviation (Algebra 1 – KK.8)

Variance and standard deviation (Algebra 2 – DD.2)

Variance and standard deviation (Precalculus – Z.2)

#### 9-12.S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Interpret box-and-whisker plots (Algebra 1 – N.5)

Identify an outlier (Algebra 1 – KK.3)

Identify an outlier and describe the effect of removing it (Algebra 1 – KK.4)

Identify an outlier (Algebra 2 – DD.3)

Identify an outlier and describe the effect of removing it (Algebra 2 – DD.4)

Identify an outlier (Precalculus – Z.3)

Identify an outlier and describe the effect of removing it (Precalculus – Z.4)

#### 9-12.S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Outliers in scatter plots (Algebra 1 – KK.5)

Outliers in scatter plots (Algebra 2 – DD.5)

Outliers in scatter plots (Precalculus – Z.5)

#### 9-12.S-ID.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Find the equation of a regression line (Precalculus – Z.8)

Interpret regression lines (Precalculus – Z.9)

Analyze a regression line of a data set (Precalculus – Z.10)

Analyze a regression line using statistics of a data set (Precalculus – Z.11)

#### 9-12.S-ID.6.b Informally assess the fit of a function by plotting and analyzing residuals.

Interpret a scatter plot (Algebra 1 – N.6)

#### 9-12.S-ID.6.c Fit a linear function for a scatter plot that suggests a linear association.

Scatter plots: line of best fit (Algebra 1 – N.7)

Find the equation of a regression line (Precalculus – Z.8)

#### 9-12.S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Interpret regression lines (Precalculus – Z.9)

Analyze a regression line using statistics of a data set (Precalculus – Z.11)

#### 9-12.S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

Match correlation coefficients to scatter plots (Precalculus – Z.6)

Calculate correlation coefficients (Precalculus – Z.7)

## Pre-K – CA Common Core – Standards & Learning Objectives

### PK.NO Number Sense

#### PK.1.1 Recite numbers in order to twenty with increasing accuracy.

Count dots (up to 20) (Pre-K – E.1)

Count shapes (up to 20) (Pre-K – E.2)

Count objects (up to 20) (Pre-K – E.3)

#### PK.1.2 Recognize and know the name of some written numerals.

Represent numbers (up to 10) (Pre-K – D.7)

Represent numbers (up to 20) (Pre-K – E.6)

#### PK.1.3 Identify, without counting, the number of objects in a collection of up to four objects (i.e., subitize).

Count dots (up to 3) (Pre-K – B.1)

Count shapes (up to 3) (Pre-K – B.2)

Count objects (up to 3) (Pre-K – B.3)

Represent numbers (up to 3) (Pre-K – B.7)

Count dots (up to 5) (Pre-K – C.1)

Count shapes (up to 5) (Pre-K – C.2)

Count objects (up to 5) (Pre-K – C.3)

Represent numbers (up to 5) (Pre-K – C.7)

#### PK.1.4 Count up to ten objects, using one-to-one correspondence (one object for each number word) with increasing accuracy.

Count dots (up to 10) (Pre-K – D.1)

Count shapes (up to 10) (Pre-K – D.2)

Count objects (up to 10) (Pre-K – D.3)

#### PK.1.5 Understand, when counting, that the number name of the last object counted represents the total number of objects in the group (i.e., cardinality).

Represent numbers (up to 10) (Pre-K – D.7)

Represent numbers (up to 20) (Pre-K – E.6)

#### PK.2.1 Compare, by counting or matching, two groups of up to five objects and communicate, “more,” “same as,” or “fewer” (or “less”).

More (Pre-K – F.2)

Compare in a chart (fewer or more) (Pre-K – F.4)

Compare in a mixed group (Pre-K – F.5)

#### PK.2.2 Understand that adding one or taking away one changes the number in a small group of objects by exactly one.

Count up and down – with pictures (Kindergarten – C.10)

#### PK.2.3 Understand that putting two groups of objects together will make a bigger group and that a group of objects can be taken apart into smaller groups.

Addition with pictures – sums up to 5 (Kindergarten – I.1)

#### PK.2.4 Solve simple addition and subtraction problems with a small number of objects (sums up to 10), usually by counting.

Addition with pictures – sums up to 10 (Kindergarten – I.6)

Subtract with pictures – numbers up to 10 (Kindergarten – J.5)

### PK.AF Algebra and Functions (Classification and Patterning)

#### PK.1.1 Sort and classify objects by one or more attributes, into two or more groups, with increasing accuracy (e.g., may sort first by one attribute and then by another attribute).

Same (Pre-K – H.1)

Different (Pre-K – H.2)

Same and different (Pre-K – H.3)

Classify by color (Pre-K – H.4)

#### PK.2.1 Recognize and duplicate simple repeating patterns.

Similar patterns (Kindergarten – H.1)

Complete missing parts of patterns (Kindergarten – H.2)

#### PK.2.2 Begin to extend and create simple repeating patterns.

Similar patterns (Kindergarten – H.1)

Complete missing parts of patterns (Kindergarten – H.2)

### PK.MEA Measurement

#### PK.1.1 Compare two objects by length, weight, or capacity directly (e.g., putting objects side by side) or indirectly (e.g., using a third object).

Long and short (Pre-K – I.1)

Tall and short (Pre-K – I.2)

Light and heavy (Pre-K – I.3)

Holds more or less (Pre-K – I.4)

Compare height, weight, and capacity (Pre-K – I.5)

Wide and narrow (Pre-K – I.6)

#### PK.1.2 Order four or more objects by size.

Long and short (Pre-K – I.1)

Tall and short (Pre-K – I.2)

Light and heavy (Pre-K – I.3)

Holds more or less (Pre-K – I.4)

Compare height, weight, and capacity (Pre-K – I.5)

Wide and narrow (Pre-K – I.6)

### PK.G Geometry

#### PK.1.1 Identify, describe, and construct a variety of different shapes, including variations of a circle, triangle, rectangle, square, and other shapes.

Identify circles, squares, and triangles (Pre-K – A.1)

Identify squares and rectangles (Pre-K – A.2)

Identify cubes and pyramids (Pre-K – A.3)

#### PK.2.1 Identify positions of objects and people in space, including in/on/ under, up/down, inside/outside, beside/between, and in front/behind.

Inside and outside (Pre-K – G.1)

Above and below (Pre-K – G.2)

Left and right (Pre-K – G.3)

Left, middle, and right (Pre-K – G.4)

Top and bottom (Pre-K – G.5)

### PK.MR Mathematical Reasoning

#### PK.1.1 Identify and apply a variety of mathematical strategies to solve problems in their environment.

Compare in a mixed group (Pre-K – F.5)

Same and different (Pre-K – H.3)

## Kindergarten – CA Common Core – Standards & Learning Objectives

### K.K.CC Counting and Cardinality

#### K.K.CC.1 Count to 100 by ones and by tens.

Count to 3 (Kindergarten – A.1)

Count using stickers – up to 3 (Kindergarten – A.2)

Count to 5 (Kindergarten – B.1)

Count using stickers – up to 5 (Kindergarten – B.2)

Count to 10 (Kindergarten – C.1)

Count using stickers – up to 10 (Kindergarten – C.4)

Count to 20 (Kindergarten – D.1)

Show numbers on ten frames – up to 20 (Kindergarten – D.4)

Count tens and ones – up to 20 (Kindergarten – D.16)

Count to 30 (Kindergarten – E.1)

Count to 100 (Kindergarten – E.2)

Counting on the hundred chart (Kindergarten – E.3)

Count groups of ten (Kindergarten – E.4)

Skip-count by tens (Kindergarten – F.4)

#### K.K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Count up – up to 5 (Kindergarten – B.6)

Count up – with pictures (Kindergarten – C.8)

Count up – with numbers (Kindergarten – C.9)

Count forward – up to 10 (Kindergarten – C.16)

Count up – up to 20 (Kindergarten – D.6)

Count forward – up to 20 (Kindergarten – D.11)

#### K.K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Count dots – 0 to 10 (Kindergarten – C.2)

Count dots – 0 to 20 (Kindergarten – D.2)

#### K.K.CC.4.a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

Count to 3 (Kindergarten – A.1)

Count to 5 (Kindergarten – B.1)

Count to 10 (Kindergarten – C.1)

Names of numbers – up to 10 (Kindergarten – C.18)

Count to 20 (Kindergarten – D.1)

Show numbers on ten frames – up to 20 (Kindergarten – D.4)

Names of numbers – up to 20 (Kindergarten – D.13)

#### K.K.CC.4.b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

Count to 3 (Kindergarten – A.1)

Count to 5 (Kindergarten – B.1)

Count to 10 (Kindergarten – C.1)

Count to 20 (Kindergarten – D.1)

#### K.K.CC.4.c Understand that each successive number name refers to a quantity that is one larger.

Count up – up to 5 (Kindergarten – B.6)

Count up and down – with pictures (Kindergarten – C.10)

#### K.K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

Count to 3 (Kindergarten – A.1)

Count on ten frames – up to 3 (Kindergarten – A.3)

Show numbers on ten frames – up to 3 (Kindergarten – A.4)

Represent numbers – up to 3 (Kindergarten – A.5)

Count to 5 (Kindergarten – B.1)

Count on ten frames – up to 5 (Kindergarten – B.3)

Show numbers on ten frames – up to 5 (Kindergarten – B.4)

Represent numbers – up to 5 (Kindergarten – B.5)

Count to 10 (Kindergarten – C.1)

Count blocks – up to 10 (Kindergarten – C.3)

Count on ten frames – up to 10 (Kindergarten – C.5)

Show numbers on ten frames – up to 10 (Kindergarten – C.6)

Represent numbers – up to 10 (Kindergarten – C.7)

Count to 20 (Kindergarten – D.1)

Count on ten frames – up to 20 (Kindergarten – D.3)

Show numbers on ten frames – up to 20 (Kindergarten – D.4)

Represent numbers – up to 20 (Kindergarten – D.5)

Count blocks – up to 20 (Kindergarten – D.15)

#### K.K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

Are there enough? (Kindergarten – G.1)

Fewer and more – compare by matching (Kindergarten – G.2)

Fewer and more – with charts (Kindergarten – G.3)

Fewer and more – mixed (Kindergarten – G.4)

Fewer, more, and same (Kindergarten – G.5)

#### K.K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.

Compare two numbers – up to 10 (Kindergarten – G.6)

### K.K.OA Operations and Algebraic Thinking

#### K.K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Addition with pictures – sums up to 5 (Kindergarten – I.1)

Add two numbers – sums up to 5 (Kindergarten – I.2)

Addition sentences – sums up to 5 (Kindergarten – I.3)

Addition with pictures – sums up to 10 (Kindergarten – I.6)

Add two numbers – sums up to 10 (Kindergarten – I.7)

Addition sentences – sums up to 10 (Kindergarten – I.8)

Subtract with pictures – numbers up to 5 (Kindergarten – J.1)

Subtraction – numbers up to 5 (Kindergarten – J.2)

Subtraction sentences – numbers up to 5 (Kindergarten – J.3)

Subtract with pictures – numbers up to 10 (Kindergarten – J.5)

Subtraction – numbers up to 9 (Kindergarten – J.6)

Subtraction sentences – numbers up to 10 (Kindergarten – J.7)

#### K.K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Addition with pictures – sums up to 5 (Kindergarten – I.1)

Addition word problems – sums up to 5 (Kindergarten – I.5)

Addition with pictures – sums up to 10 (Kindergarten – I.6)

Addition word problems – sums up to 10 (Kindergarten – I.10)

Subtract with pictures – numbers up to 5 (Kindergarten – J.1)

Subtraction sentences – numbers up to 5 (Kindergarten – J.3)

Subtraction word problems – numbers up to 5 (Kindergarten – J.4)

Subtract with pictures – numbers up to 10 (Kindergarten – J.5)

Subtraction sentences – numbers up to 10 (Kindergarten – J.7)

Subtraction word problems – numbers up to 9 (Kindergarten – J.8)

#### K.K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Addition sentences – sums up to 5 (Kindergarten – I.3)

Ways to make a number – sums up to 5 (Kindergarten – I.4)

Addition sentences – sums up to 10 (Kindergarten – I.8)

Ways to make a number – sums up to 10 (Kindergarten – I.9)

#### K.K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Count to fill a ten frame (Kindergarten – C.12)

Addition sentences – sums equal to 10 (Kindergarten – I.11)

#### K.K.OA.5 Fluently add and subtract within 5.

Addition with pictures – sums up to 5 (Kindergarten – I.1)

Add two numbers – sums up to 5 (Kindergarten – I.2)

Addition sentences – sums up to 5 (Kindergarten – I.3)

Subtract with pictures – numbers up to 5 (Kindergarten – J.1)

Subtraction – numbers up to 5 (Kindergarten – J.2)

Subtraction sentences – numbers up to 5 (Kindergarten – J.3)

### K.K.NBT Number and Operations in Base Ten

#### K.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.

Count tens and ones – up to 20 (Kindergarten – D.16)

Write tens and ones – up to 20 (Kindergarten – D.17)

### K.K.MD Measurement and Data

#### K.K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

Long and short (Kindergarten – Q.1)

Tall and short (Kindergarten – Q.2)

Light and heavy (Kindergarten – Q.3)

Holds more or less (Kindergarten – Q.4)

Compare size, weight, and capacity (Kindergarten – Q.5)

#### K.K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/”less of” the attribute, and describe the difference.

Long and short (Kindergarten – Q.1)

Tall and short (Kindergarten – Q.2)

Light and heavy (Kindergarten – Q.3)

Holds more or less (Kindergarten – Q.4)

Compare size, weight, and capacity (Kindergarten – Q.5)

#### K.K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Fewer and more – with charts (Kindergarten – G.3)

Fewer and more – mixed (Kindergarten – G.4)

Same (Kindergarten – N.1)

Different (Kindergarten – N.2)

Same and different (Kindergarten – N.3)

Classify by color (Kindergarten – N.4)

Classify and sort by color (Kindergarten – N.5)

Classify and sort by shape (Kindergarten – N.6)

Classify and sort (Kindergarten – N.7)

Sort shapes into a Venn diagram (Kindergarten – N.8)

Count shapes in a Venn diagram (Kindergarten – N.9)

Put numbers up to 10 in order (Kindergarten – N.10)

Put numbers up to 30 in order (Kindergarten – N.11)

Making graphs (Kindergarten – O.1)

Interpreting graphs (Kindergarten – O.2)

### K.K.G Geometry

#### K.K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Inside and outside (Kindergarten – K.1)

Above and below (Kindergarten – K.2)

Above and below – find solid figures (Kindergarten – K.3)

Left, middle, and right (Kindergarten – K.4)

Top, middle, and bottom (Kindergarten – K.5)

Location in a grid (Kindergarten – K.6)

Geometry of everyday objects I (Kindergarten – S.8)

Geometry of everyday objects II (Kindergarten – S.9)

#### K.K.G.2 Correctly name shapes regardless of their orientations or overall size.

Count shapes in a Venn diagram (Kindergarten – N.9)

Identify shapes I (Kindergarten – S.1)

Identify shapes II (Kindergarten – S.2)

Identify solid figures (Kindergarten – S.4)

#### K.K.G.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

Relate planar and solid figures (Kindergarten – S.5)

#### K.K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g., having sides of equal length).

Identify shapes I (Kindergarten – S.1)

Identify shapes II (Kindergarten – S.2)

Same shape (Kindergarten – S.3)

Identify solid figures (Kindergarten – S.4)

Relate planar and solid figures (Kindergarten – S.5)

Count sides and corners (Kindergarten – S.6)

Compare sides and corners (Kindergarten – S.7)

Symmetry I (Kindergarten – S.10)

Symmetry II (Kindergarten – S.11)

## Grade 2 – CA Common Core – Standards & Learning Objectives

### 2.2.OA Operations and Algebraic Thinking

#### 2.2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Comparing numbers up to 100 (Second grade – B.1)

Review – writing addition sentences – sums to 10 (Second grade – E.3)

Write addition sentences to describe pictures – sums to 20 (Second grade – E.6)

Add four or more one-digit numbers: word problems (Second grade – E.20)

Review – writing subtraction sentences – up to 10 (Second grade – F.3)

Subtraction with pictures (Second grade – F.5)

Write subtraction sentences to describe pictures – up to 18 (Second grade – F.6)

Subtraction word problems – up to 18 (Second grade – F.9)

Complete the subtraction sentence – up to 18 (Second grade – F.10)

Write the subtraction sentence – up to 18 (Second grade – F.11)

Balance subtraction equations – up to 18 (Second grade – F.12)

Subtraction equations: true or false? (Second grade – F.13)

Addition word problems – up to two digits (Second grade – G.9)

Complete the addition sentence – up to two digits (Second grade – G.10)

Write the addition sentence – up to two digits (Second grade – G.11)

Balance addition equations – up to two digits (Second grade – G.12)

Add three numbers up to two digits each: word problems (Second grade – G.14)

Add four or more numbers up to two digits each: word problems (Second grade – G.16)

Write subtraction sentences to describe pictures – up to two digits (Second grade – H.6)

Subtraction word problems – up to two digits (Second grade – H.9)

Complete the subtraction sentence – up to two digits (Second grade – H.10)

Write the subtraction sentence – up to two digits (Second grade – H.11)

Balance subtraction equations – up to two digits (Second grade – H.12)

Addition and subtraction word problems – up to 20 (Second grade – L.3)

Addition and subtraction – balance equations – up to 20 (Second grade – L.4)

Addition and subtraction equations up to 20: true or false? (Second grade – L.5)

Input/output tables – write the rule – up to 20 (Second grade – L.6)

Addition and subtraction word problems – up to 100 (Second grade – L.9)

Input/output tables – write the rule – up to 100 (Second grade – L.11)

Customary units of length: word problems (Second grade – S.4)

Metric units of length: word problems (Second grade – S.10)

#### 2.2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Review – add one-digit numbers – sums to 10 (Second grade – E.1)

Review – ways to make a number – sums to 10 (Second grade – E.2)

Review – subtract one-digit numbers – up to 10 (Second grade – F.1)

Review – ways to subtract – up to 10 (Second grade – F.2)

Subtract a one-digit number from a two-digit number up to 18 (Second grade – F.4)

Subtraction input/output tables – up to 18 (Second grade – F.7)

Subtract zero/all (Second grade – F.8)

Balance subtraction equations – up to 18 (Second grade – F.12)

Addition and subtraction – ways to make a number – up to 20 (Second grade – L.2)

Addition and subtraction – balance equations – up to 20 (Second grade – L.4)

#### 2.2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

Even and odd: counting objects (Second grade – A.6)

Even or odd I (Second grade – A.7)

Even or odd II (Second grade – A.8)

Even and odd numbers on number lines (Second grade – A.9)

#### 2.2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Identify repeated addition in arrays: sums to 10 (Second grade – E.21)

Write addition sentences for arrays: sums to 10 (Second grade – E.22)

Identify repeated addition in arrays: sums to 25 (Second grade – E.23)

Write addition sentences for arrays: sums to 25 (Second grade – E.24)

Write multiplication sentences for equal groups (Second grade – W.3)

### 2.2.NBT Number and Operations in Base Ten

#### 2.2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

Place value models – tens and ones (Second grade – M.1)

Place value models – up to hundreds (Second grade – M.2)

Place value – tens and ones (Second grade – M.4)

Convert to/from a number – tens and ones (Second grade – M.9)

Identify a digit up to the hundreds place (Second grade – M.15)

#### 2.2.NBT.1.a 100 can be thought of as a bundle of ten tens – called a “hundred.”

Hundreds chart (Second grade – A.5)

Convert between place values – up to thousands (Second grade – M.12)

#### 2.2.NBT.1.b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Place value – up to hundreds (Second grade – M.5)

Convert to/from a number – up to hundreds (Second grade – M.10)

#### 2.2.NBT.2 Count within 1000; skip-count by 2s, 5s, 10s, and 100s.

Skip-counting sequences (Second grade – A.2)

Counting patterns – up to 100 (Second grade – A.3)

Counting patterns – up to 1,000 (Second grade – A.14)

#### 2.2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Writing numbers up to 100 in words (Second grade – C.3)

Writing numbers up to 1,000 in words (Second grade – C.4)

Convert from expanded form – up to hundreds (Second grade – M.13)

#### 2.2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Comparing numbers up to 1,000 (Second grade – B.2)

Put numbers up to 100 in order (Second grade – B.3)

Put numbers up to 1,000 in order (Second grade – B.4)

Greatest and least – word problems – up to 100 (Second grade – B.5)

Greatest and least – word problems – up to 1,000 (Second grade – B.6)

#### 2.2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Add a two-digit and a one-digit number – without regrouping (Second grade – G.2)

Add a two-digit and a one-digit number – with regrouping (Second grade – G.3)

Addition input/output tables – up to two digits (Second grade – G.7)

Balance addition equations – up to two digits (Second grade – G.12)

Subtract a one-digit number from a two-digit number – without regrouping (Second grade – H.2)

Subtract a one-digit number from a two-digit number – with regrouping (Second grade – H.3)

Subtract two two-digit numbers – without regrouping (Second grade – H.4)

Subtract two two-digit numbers – with regrouping (Second grade – H.5)

Subtraction input/output tables – up to two digits (Second grade – H.7)

Ways to make a number using subtraction (Second grade – H.8)

Balance subtraction equations – up to two digits (Second grade – H.12)

Addition and subtraction – ways to make a number – up to 100 (Second grade – L.8)

Addition and subtraction – balance equations – up to 100 (Second grade – L.10)

Which sign (+ or -) makes the number sentence true? (Second grade – L.12)

#### 2.2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

Add three numbers up to two digits each (Second grade – G.13)

Add four or more numbers up to two digits each (Second grade – G.15)

#### 2.2.NBT.7 Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Addition input/output tables – up to three digits (Second grade – I.3)

Addition word problems – up to three digits (Second grade – I.4)

Complete the addition sentence – up to three digits (Second grade – I.5)

Write the addition sentence – up to three digits (Second grade – I.6)

Balance addition equations – up to three digits (Second grade – I.7)

Subtract three-digit numbers (Second grade – J.2)

Subtraction input/output tables – up to three digits (Second grade – J.3)

Subtraction word problems – up to three digits (Second grade – J.4)

Complete the subtraction sentence – up to three digits (Second grade – J.5)

Write the subtraction sentence – up to three digits (Second grade – J.6)

Balance subtraction equations – up to three digits (Second grade – J.7)

Regrouping tens and ones I (Second grade – M.7)

Regrouping tens and ones II (Second grade – M.8)

#### 2.2.NBT.7.1 Use estimation strategies to make reasonable estimates in problem solving.

Estimate sums (Second grade – N.5)

#### 2.2.NBT.8 Mentally add 10 or 100 to a given number 100â€“900, and mentally subtract 10 or 100 from a given number 100â€“900.

Subtract multiples of 10 (Second grade – H.1)

Subtract multiples of 100 (Second grade – J.1)

#### 2.2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

Related subtraction facts (Second grade – K.2)

Fact families (Second grade – K.3)

### 2.2.MD Measurement and Data

#### 2.2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measure using an inch ruler (Second grade – S.2)

Measure using a centimeter ruler (Second grade – S.8)

Choose the appropriate measuring tool (Second grade – S.15)

#### 2.2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

Which customary unit of length is appropriate? (Second grade – S.3)

Which metric unit of length is appropriate? (Second grade – S.9)

#### 2.2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

Which customary unit of length is appropriate? (Second grade – S.3)

Which metric unit of length is appropriate? (Second grade – S.9)

#### 2.2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Customary units of length: word problems (Second grade – S.4)

Metric units of length: word problems (Second grade – S.10)

#### 2.2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Customary units of length: word problems (Second grade – S.4)

Metric units of length: word problems (Second grade – S.10)

#### 2.2.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.

Number lines – up to 100 (Second grade – A.4)

#### 2.2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year).

Match analog clocks and times (Second grade – Q.1)

Match analog and digital clocks (Second grade – Q.3)

A.M. and P.M. (Second grade – Q.7)

Compare clocks (Second grade – Q.8)

Time patterns (Second grade – Q.11)

#### 2.2.MD.8 Solve word problems involving combinations of dollar bills, quarters, dimes, nickels, and pennies, using \$ and Â¢ symbols appropriately.

Names and values of common coins (Second grade – P.1)

Names and values of all coins (Second grade – P.2)

Count money – up to \$1 (Second grade – P.4)

Count money – up to \$5 (Second grade – P.5)

Equivalent amounts of money – up to \$1 (Second grade – P.6)

Equivalent coins I (Second grade – P.7)

Equivalent coins II (Second grade – P.8)

Add and subtract money – up to \$1 (Second grade – P.13)

Add and subtract money – up to \$1: word problems (Second grade – P.14)

Which picture shows more – up to \$5 (Second grade – P.15)

Least number of coins (Second grade – P.16)

Purchases – do you have enough money – up to \$1 (Second grade – P.17)

Purchases – do you have enough money – up to \$5 (Second grade – P.18)

How much more to make a dollar? (Second grade – P.19)

Making change (Second grade – P.20)

#### 2.2.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.

Interpret line plots (Second grade – R.6)

Create line plots (Second grade – R.7)

#### 2.2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Interpret bar graphs (Second grade – R.3)

Which bar graph is correct? (Second grade – R.4)

Create bar graphs (Second grade – R.5)

Interpret pictographs (Second grade – R.8)

Create pictographs (Second grade – R.9)

### 2.2.G Geometry

#### 2.2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Sort shapes into a Venn diagram (Second grade – R.12)

Count shapes in a Venn diagram (Second grade – R.13)

Identify 2-dimensional shapes (Second grade – T.1)

Identify 3-dimensional shapes (Second grade – T.2)

Identify 2-dimensional and 3-dimensional shapes (Second grade – T.3)

Count sides and angles (Second grade – T.4)

Count edges, vertices, and faces (Second grade – T.5)

Compare sides and angles (Second grade – T.6)

Compare edges, vertices, and faces (Second grade – T.7)

#### 2.2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Equal parts (Second grade – U.1)

Halves, thirds, and fourths (Second grade – U.2)

Identify the fraction (Second grade – U.3)

Fraction models equivalent to whole numbers (Second grade – U.10)

## Grade 4 – CA Common Core – Standards & Learning Objectives

### 4.4.OA Operations and Algebraic Thinking

#### 4.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 Ã— 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiplication facts up to 12: find the missing factor (Fourth grade – D.2)

Properties of multiplication (Fourth grade – D.9)

#### 4.4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Estimate products: word problems (Fourth grade – D.14)

Multiply a 2-digit number by a 2-digit number: word problems (Fourth grade – D.19)

Multiply a 2-digit number by a larger number: word problems (Fourth grade – D.23)

Multiply numbers ending in zeroes: word problems (Fourth grade – D.25)

Division facts to 12: word problems (Fourth grade – E.2)

Divide larger numbers by 1-digit numbers: word problems (Fourth grade – E.9)

Divide numbers ending in zeroes by multi-digit numbers: word problems (Fourth grade – E.19)

Divide by 2-digit numbers: word problems (Fourth grade – E.22)

Divide larger numbers by 2-digit numbers: word problems (Fourth grade – E.24)

Estimate sums, differences, products, and quotients: word problems (Fourth grade – F.3)

Price lists with multiplication (Fourth grade – M.8)

Compare customary units by multiplying (Fourth grade – N.14)

Convert between metric and customary units (Fourth grade – N.17)

#### 4.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Divide larger numbers by 1-digit numbers: interpret remainders (Fourth grade – E.11)

Estimate sums, differences, products, and quotients: word problems (Fourth grade – F.3)

Multi-step word problems (Fourth grade – F.4)

Word problems with extra or missing information (Fourth grade – F.5)

Solve word problems using guess-and-check (Fourth grade – F.6)

Choose numbers with a particular sum, difference, product, or quotient (Fourth grade – F.7)

Write variable expressions: word problems (Fourth grade – G.2)

Write variable equations to represent word problems (Fourth grade – G.5)

Find two numbers based on sum and difference (Fourth grade – K.1)

Find two numbers based on sum, difference, product, and quotient (Fourth grade – K.2)

#### 4.4.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Prime and composite numbers (Fourth grade – A.5)

Choose the multiples of a given number up to 12 (Fourth grade – D.3)

Identify factors (Fourth grade – D.4)

Choose numbers with a particular product (Fourth grade – D.20)

Divisibility rules (Fourth grade – E.15)

Divisibility rules: word problems (Fourth grade – E.16)

#### 4.4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Multiplication input/output tables (Fourth grade – D.29)

Input/output tables with addition, subtraction, multiplication, and division (Fourth grade – H.1)

Complete a table for a two-variable relationship (Fourth grade – H.2)

Geometric growth patterns (Fourth grade – L.1)

Increasing growth patterns (Fourth grade – L.2)

Numeric patterns: word problems (Fourth grade – L.3)

Mixed patterns review (Fourth grade – L.5)

Time patterns (Fourth grade – O.9)

### 4.4.NBT Number and Operations in Base Ten

#### 4.4.NBT.1 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.

Place values (Fourth grade – A.1)

Convert between place values (Fourth grade – A.2)

#### 4.4.NBT.2 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.

Place values (Fourth grade – A.1)

Word names for numbers (Fourth grade – A.3)

Compare numbers up to one billion (Fourth grade – A.9)

Inequalities with multiplication (Fourth grade – D.28)

Inequalities with division (Fourth grade – E.25)

#### 4.4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

Estimate sums (Fourth grade – B.8)

Estimate sums: word problems (Fourth grade – B.9)

Estimate differences (Fourth grade – C.6)

Estimate differences: word problems (Fourth grade – C.7)

Estimate products – multiply by 1-digit numbers (Fourth grade – D.12)

Estimate products – multiply by larger numbers (Fourth grade – D.13)

Divide by 1-digit numbers: estimate quotients (Fourth grade – E.14)

Estimate quotients (Fourth grade – E.26)

#### 4.4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Add 3 or more numbers up to millions (Fourth grade – B.5)

Choose numbers with a particular sum (Fourth grade – B.7)

Subtract numbers up to millions (Fourth grade – C.1)

Subtract numbers up to millions: word problems (Fourth grade – C.2)

Subtraction: fill in the missing digits (Fourth grade – C.3)

Choose numbers with a particular difference (Fourth grade – C.5)

#### 4.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Multiply 1-digit numbers by 2-digit numbers (Fourth grade – D.5)

Multiply 1-digit numbers by 3-digit or 4-digit numbers (Fourth grade – D.6)

Multiplication patterns over increasing place values (Fourth grade – D.8)

Properties of multiplication (Fourth grade – D.9)

Distributive property: find the missing factor (Fourth grade – D.10)

Multiply using the distributive property (Fourth grade – D.11)

Multiply a 2-digit number by a 2-digit number: complete the missing steps (Fourth grade – D.17)

Multiply a 2-digit number by a 2-digit number (Fourth grade – D.18)

Multiply numbers ending in zeroes (Fourth grade – D.24)

#### 4.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Properties of division (Fourth grade – E.3)

Divide 2-digit numbers by 1-digit numbers (Fourth grade – E.4)

Divide 2-digit numbers by 1-digit numbers: word problems (Fourth grade – E.5)

Divide 2-digit numbers by 1-digit numbers: complete the table (Fourth grade – E.6)

Divide larger numbers by 1-digit numbers (Fourth grade – E.8)

Divide larger numbers by 1-digit numbers: complete the table (Fourth grade – E.10)

Divide numbers ending in zeroes by 1-digit numbers (Fourth grade – E.13)

### 4.4.NF Number and Operations-Fractions

#### 4.4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n Ã— a)/(n Ã— b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Equivalent fractions (Fourth grade – Q.6)

Patterns of equivalent fractions (Fourth grade – Q.8)

Reduce fractions to lowest terms (Fourth grade – Q.9)

#### 4.4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Benchmark fractions (Fourth grade – Q.10)

Compare fractions using benchmarks (Fourth grade – Q.11)

Compare fractions using models (Fourth grade – Q.15)

Compare fractions (Fourth grade – Q.16)

Order fractions (Fourth grade – Q.20)

Compare sums and differences of fractions (Fourth grade – S.16)

#### 4.4.NF.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Add fractions with like denominators using number lines (Fourth grade – R.4)

Subtract fractions with like denominators using number lines (Fourth grade – R.5)

Add and subtract fractions with like denominators using number lines (Fourth grade – R.6)

Compare sums and differences of fractions with like denominators (Fourth grade – R.8)

Add 3 or more fractions with like denominators (Fourth grade – R.11)

Compare sums of unit fractions (Fourth grade – S.8)

Compare differences of unit fractions (Fourth grade – S.9)

Compare sums and differences of unit fractions (Fourth grade – S.10)

#### 4.4.NF.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

Decompose fractions into unit fractions (Fourth grade – R.1)

Decompose fractions (Fourth grade – R.2)

Decompose fractions multiple ways (Fourth grade – R.3)

Add 3 or more fractions with like denominators (Fourth grade – R.11)

#### 4.4.NF.3.c 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.

Add and subtract mixed numbers with like denominators (Fourth grade – R.12)

#### 4.4.NF.3.d 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.

Add and subtract fractions with like denominators: word problems (Fourth grade – R.9)

Add and subtract fractions with like denominators in recipes (Fourth grade – R.10)

#### 4.4.NF.4.a Understand a fraction a/b as a multiple of 1/b.

Multiply unit fractions by whole numbers using number lines (Fourth grade – T.1)

Multiply unit fractions by whole numbers using models (Fourth grade – T.2)

Multiples of fractions (Fourth grade – T.3)

Multiply unit fractions and whole numbers: sorting (Fourth grade – T.4)

Multiply unit fractions by whole numbers (Fourth grade – T.5)

#### 4.4.NF.4.b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Multiples of fractions (Fourth grade – T.3)

Multiply fractions by whole numbers using number lines (Fourth grade – T.7)

Multiply fractions by whole numbers using models (Fourth grade – T.8)

Multiply fractions and whole numbers: sorting (Fourth grade – T.9)

Multiply fractions by whole numbers (Fourth grade – T.10)

#### 4.4.NF.4.c 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.

Multiply unit fractions by whole numbers: word problems (Fourth grade – T.6)

Multiply fractions by whole numbers: word problems (Fourth grade – T.12)

Multiply fractions and mixed numbers by whole numbers in recipes (Fourth grade – T.13)

#### 4.4.NF.5 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.

Fractions with denominators of 10, 100, and 1000 (Fourth grade – Q.7)

Add up to 4 fractions with denominators of 10 and 100 (Fourth grade – S.5)

Add and subtract fractions with denominators of 10, 100, and 1000 (Fourth grade – S.6)

#### 4.4.NF.6 Use decimal notation for fractions with denominators 10 or 100.

Model decimals and fractions (Fourth grade – U.2)

Graph decimals on number lines (Fourth grade – U.6)

Graph fractions as decimals on number lines (Fourth grade – U.8)

Convert fractions and mixed numbers to decimals (Fourth grade – U.9)

Convert decimals to fractions and mixed numbers (Fourth grade – U.10)

Convert decimals between standard and expanded form using fractions (Fourth grade – U.11)

#### 4.4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model.

Compare money amounts (Fourth grade – M.2)

Compare decimals on number lines (Fourth grade – U.13)

Compare decimal numbers (Fourth grade – U.14)

Put decimal numbers in order I (Fourth grade – U.15)

Put decimal numbers in order II (Fourth grade – U.16)

Compare decimals and fractions on number lines (Fourth grade – U.17)

### 4.4.MD Measurement and Data

#### 4.4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

Which customary unit is appropriate? (Fourth grade – N.2)

Compare and convert customary units of length (Fourth grade – N.3)

Compare and convert customary units of weight (Fourth grade – N.4)

Compare and convert customary units of volume (Fourth grade – N.5)

Compare and convert customary units (Fourth grade – N.6)

Conversion tables – customary units (Fourth grade – N.7)

Which metric unit is appropriate? (Fourth grade – N.8)

Compare and convert metric units of length (Fourth grade – N.9)

Compare and convert metric units of weight (Fourth grade – N.10)

Compare and convert metric units of volume (Fourth grade – N.11)

Compare and convert metric units (Fourth grade – N.12)

Conversion tables – metric units (Fourth grade – N.13)

Convert mixed customary units (Fourth grade – N.15)

Convert time units (Fourth grade – O.1)

Fractions of time units (Fourth grade – O.3)

#### 4.4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Making change (Fourth grade – M.6)

Price lists with multiplication (Fourth grade – M.8)

Unit prices (Fourth grade – M.9)

Elapsed time (Fourth grade – O.5)

Elapsed time: word problems (Fourth grade – O.6)

Find start and end times: multi-step word problems (Fourth grade – O.7)

Add and subtract fractions with unlike denominators in recipes (Fourth grade – S.17)

Solve decimal problems using diagrams (Fourth grade – V.10)

#### 4.4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Area of squares and rectangles (Fourth grade – P.21)

Compare area and perimeter of two figures (Fourth grade – P.24)

Relationship between area and perimeter (Fourth grade – P.25)

Use area and perimeter to determine cost (Fourth grade – P.27)

#### 4.4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Interpret line plots (Fourth grade – J.6)

Create line plots (Fourth grade – J.7)

Create and interpret line plots with fractions (Fourth grade – J.8)

#### 4.4.MD.5.a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

Angles of 90, 180, 270, and 360 degrees (Fourth grade – P.14)

#### 4.4.MD.5.b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Angles of 90, 180, 270, and 360 degrees (Fourth grade – P.14)

Estimate angle measurements (Fourth grade – P.16)

#### 4.4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Measure angles with a protractor (Fourth grade – P.15)

Estimate angle measurements (Fourth grade – P.16)

### 4.4.G Geometry

#### 4.4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Acute, right, obtuse, and straight angles (Fourth grade – P.13)

Lines, line segments, and rays (Fourth grade – P.30)

Parallel, perpendicular, intersecting (Fourth grade – P.31)

#### 4.4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)

Identify 2-dimensional and 3-dimensional shapes (Fourth grade – P.1)

Classify triangles (Fourth grade – P.4)

Which 2-dimensional shape is being described? (Fourth grade – P.6)