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

9-12.N Number and Quantity

9-12.N-RN The Real Number System

9-12. Extend the properties of exponents to rational exponents.

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)

Add and subtract radical expressions (Algebra 1 – EE.4)

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)

Add and subtract radical expressions (Algebra 2 – L.9)

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. Use properties of rational and irrational numbers.

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 Quantities

 

9-12. Reason quantitatively and use units to solve problems.

 

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 Seeing Structure in Expressions

9-12. Interpret the structure of expressions

9-12.A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

 

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. Write expressions in equivalent forms to solve problems

 

9-12.A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

 

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

Factor quadratics with leading coefficient 1 (Algebra 1 – AA.3)

Factor quadratics with other leading coefficients (Algebra 1 – AA.4)

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 Arithmetic with Polynomials and Rational Expressions

 

9-12. Perform arithmetic operations on polynomials

 

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 Creating Equations

 

9-12. Create equations that describe numbers or relationships

 

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 Reasoning with Equations and Inequalities

 

9-12. Understand solving equations as a process of reasoning and explain the reasoning

 

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. Solve equations and inequalities in one variable

 

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 Solve quadratic equations in one variable.

 

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 – p)² = 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 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.

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)

Solve a quadratic equation using the quadratic formula (Precalculus – C.8)

 

9-12. Solve systems of equations

 

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. Represent and solve equations and inequalities graphically

 

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 Interpreting Functions

 

9-12. Understand the concept of a function and use function notation

 

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. Interpret functions that arise in applications in terms of the context

 

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. Analyze functions using different representations

 

9-12.F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

 

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 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

 

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 Building Functions

 

9-12. Build a function that models a relationship between two quantities

 

9-12.F-BF.1 Write a function that describes a relationship between two quantities.

 

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. Build new functions from existing functions

 

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 Find inverse functions.

 

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 Linear, Quadratic, and Exponential Models

 

9-12. Construct and compare linear, quadratic, and exponential models and solve problems

 

9-12.F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

 

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.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

 

9-12. Interpret expressions for functions in terms of the situation they model

 

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.F-LE.6 Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity.

9-12.S Statistics and Probability

 

9-12.S-ID Interpreting Categorical and Quantitative Data

 

9-12. Summarize, represent, and interpret data on a single count or measurement variable

 

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. Summarize, represent, and interpret data on two categorical and quantitative variables

 

9-12.S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

 

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. Interpret linear models

 

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)

 

9-12.S-ID.9 Distinguish between correlation and causation.

Kindergarten – CA Common Core – Standards & Learning Objectives

K.K.CC Counting and Cardinality

 

K. Know number names and the count sequence.

 

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. Count to tell the number of objects.

 

K.K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.

 

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. Compare numbers.

 

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. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

 

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. Work with numbers 11–19 to gain foundations for place value.

 

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. Describe and compare measurable attributes.

 

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. Classify objects and count the number of objects in each category.

 

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. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

 

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. Analyze, compare, create, and compose shapes.

 

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)

 

K.K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

 

K.K.G.6 Compose simple shapes to form larger shapes.

Grade 1 – CA Common Care – Standards & Learning Objectives

1.1.OA Operations and Algebraic Thinking

 

1 Represent and solve problems involving addition and subtraction.

 

1.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Addition with pictures – sums to 10 (First grade – B.1)

Addition sentences – sums to 10 (First grade – B.2)

Addition word problems – sums to 10 (First grade – B.4)

Word problems – write the addition sentence (First grade – B.5)

Addition word problems – sums to 18 (First grade – B.15)

Complete the addition sentence (First grade – B.16)

Subtraction with pictures – numbers up to 10 (First grade – D.1)

Subtraction sentences – numbers up to 10 (First grade – D.2)

Subtraction word problems – one-digit numbers (First grade – D.4)

Word problems – write the subtraction sentence (First grade – D.5)

Subtraction word problems – numbers up to 18 (First grade – D.14)

Complete the subtraction sentence (First grade – D.15)

Addition and subtraction word problems (First grade – F.6)

Comparison word problems (First grade – G.4)

Customary units of length: word problems (First grade – N.6)

Metric units of length: word problems (First grade – N.10)

 

1.1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Adding three numbers (First grade – B.17)

Word problems – adding three numbers (First grade – B.18)

 

1 Understand and apply properties of operations and the relationship between addition and subtraction.

 

1.1.OA.3 Apply properties of operations as strategies to add and subtract.

Adding three numbers (First grade – B.17)

Word problems – adding three numbers (First grade – B.18)

Related addition facts (First grade – B.19)

Related subtraction facts (First grade – D.16)

Fact families (First grade – F.3)

 

1.1.OA.4 Understand subtraction as an unknown-addend problem.

Complete the addition sentence (First grade – B.16)

Fact families (First grade – F.3)

 

1 Add and subtract within 20.

 

1.1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Counting forward and backward (First grade – A.11)

Skip-counting patterns – with tables (First grade – A.19)

Sequences – count up and down by 1, 2, 3, 5, and 10 (First grade – A.20)

Addition sentences to 10 using number lines (First grade – B.3)

Subtraction sentences within 10 using number lines (First grade – D.3)

 

1.1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Ways to make a number using addition (First grade – B.6)

Ways to make a number – addition sentences (First grade – B.7)

Adding zero (First grade – B.8)

Adding doubles (First grade – B.10)

Addition facts – sums to 10 (First grade – B.12)

Addition sentences to 18 using number lines (First grade – B.13)

Addition facts – sums to 18 (First grade – B.14)

Add using doubles plus 1 (First grade – B.20)

Add using doubles minus 1 (First grade – B.21)

Addition facts – sums to 20 (First grade – B.22)

Adding 0 (First grade – C.1)

Adding 1 (First grade – C.2)

Adding 2 (First grade – C.3)

Adding 3 (First grade – C.4)

Adding 4 (First grade – C.5)

Adding 5 (First grade – C.6)

Adding 6 (First grade – C.7)

Adding 7 (First grade – C.8)

Adding 8 (First grade – C.9)

Adding 9 (First grade – C.10)

Ways to make a number using subtraction (First grade – D.6)

Ways to make a number – subtraction sentences (First grade – D.7)

Ways to subtract from a number – subtraction sentences (First grade – D.8)

Subtracting zero and all (First grade – D.9)

Subtracting doubles (First grade – D.10)

Subtraction facts – numbers up to 10 (First grade – D.11)

Subtraction sentences within 18 using number lines (First grade – D.12)

Subtraction facts – numbers up to 18 (First grade – D.13)

Subtract one-digit numbers from two-digit numbers (First grade – D.20)

Subtracting 0 (First grade – E.1)

Subtracting 1 (First grade – E.2)

Subtracting 2 (First grade – E.3)

Subtracting 3 (First grade – E.4)

Subtracting 4 (First grade – E.5)

Subtracting 5 (First grade – E.6)

Subtracting 6 (First grade – E.7)

Subtracting 7 (First grade – E.8)

Subtracting 8 (First grade – E.9)

Subtracting 9 (First grade – E.10)

Addition and subtraction – ways to make a number (First grade – F.1)

Addition and subtraction facts – numbers up to 10 (First grade – F.4)

Addition and subtraction facts – numbers up to 18 (First grade – F.5)

 

1 Work with addition and subtraction equations.

 

1.1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

Addition sentences: true or false? (First grade – B.23)

Subtraction sentences: true or false? (First grade – D.17)

Which sign makes the number sentence true? (First grade – F.2)

Addition and subtraction sentences: true or false? (First grade – F.7)

 

1.1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

Complete the addition sentence (First grade – B.16)

Complete the subtraction sentence (First grade – D.15)

1.1.NBT Number and Operations in Base Ten

 

1 Extend the counting sequence.

 

1.1.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.

Counting review – 0 to 10 (First grade – A.1)

Counting review – up to 20 (First grade – A.3)

Counting – up to 30 (First grade – A.5)

Counting – up to 100 (First grade – A.6)

Counting on the hundred chart (First grade – A.13)

Writing numbers in words (First grade – A.22)

 

1 Understand place value.

 

1.1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

 

1.1.NBT.2.a 10 can be thought of as a bundle of ten ones – called a “ten.”

Counting tens and ones – up to 20 (First grade – A.4)

Counting tens and ones – up to 99 (First grade – A.8)

Hundred chart (First grade – A.14)

Convert between tens and ones (First grade – I.4)

 

1.1.NBT.2.b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

Counting review – up to 20 (First grade – A.3)

Counting tens and ones – up to 20 (First grade – A.4)

Place value models up to 20 (First grade – I.1)

Write numbers as tens and ones up to 20 (First grade – I.2)

 

1.1.NBT.2.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).

Counting by tens – up to 100 (First grade – A.7)

 

1.1.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 <.

Comparing numbers up to 100 (First grade – G.3)

Put numbers in order (First grade – R.3)

 

1 Use place value understanding and properties of operations to add and subtract.

 

1.1.NBT.4 Add within 100, including adding a two-digit number and a one-digit 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 two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Add tens I (First grade – B.24)

Add tens II (First grade – B.25)

Add a one-digit number to a two-digit number – without regrouping (First grade – B.26)

Regrouping tens and ones I (First grade – B.27)

Regrouping tens and ones II (First grade – B.28)

Add a one-digit number to a two-digit number – with regrouping (First grade – B.29)

Add and subtract tens (First grade – F.9)

 

1.1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Ten more or less (First grade – F.8)

 

1.1.NBT.6 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.

Subtract tens I (First grade – D.18)

Add and subtract tens (First grade – F.9)

1.1.MD Measurement and Data

 

1 Measure lengths indirectly and by iterating length units.

 

1.1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Compare objects: length and height (First grade – N.2)

Customary units of length: word problems (First grade – N.6)

Metric units of length: word problems (First grade – N.10)

 

1.1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

Measure using objects (First grade – N.3)

 

1 Tell and write time.

 

1.1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.

Match analog clocks and times (First grade – S.1)

Match digital clocks and times (First grade – S.2)

Match analog and digital clocks (First grade – S.3)

Read clocks and write times (First grade – S.4)

Compare clocks (First grade – S.7)

Choose the appropriate time units (First grade – S.9)

 

1 Represent and interpret data.

 

1.1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Comparing – review (First grade – G.1)

Record data with tally charts, picture graphs, tables (First grade – M.1)

Interpret data in tally charts, picture graphs, tables (First grade – M.2)

Interpret bar graphs (First grade – M.3)

Which bar graph is correct? (First grade – M.4)

Sort shapes into a Venn diagram (First grade – R.1)

Count shapes in a Venn diagram (First grade – R.2)

1.1.G Geometry

 

1 Reason with shapes and their attributes.

 

1.1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

Identify 2-dimensional shapes (First grade – K.1)

Count sides and vertices (First grade – K.6)

Count edges, vertices, and faces (First grade – K.7)

Compare sides and vertices (First grade – K.8)

Compare edges, vertices, and faces (First grade – K.9)

Open and closed shapes (First grade – K.10)

Same shape (First grade – K.13)

 

1.1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

 

1.1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Halves, thirds, and fourths (First grade – J.1)

Equal parts (First grade – J.2)

Simple fractions: what fraction does the shape show? (First grade – J.3)

Simple fractions: which shape matches the fraction? (First grade – J.4)

Compare fractions (First grade – J.7)

Fraction models equivalent to whole numbers (First grade – J.8)

Grade 2 – CA Common Core – Standards & Learning Objectives

2.2.OA Operations and Algebraic Thinking

 

2 Represent and solve problems involving addition and subtraction.

 

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)

Addition with pictures – sums to 20 (Second grade – E.5)

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

Addition word problems – one digit (Second grade – E.12)

Complete the addition sentence – one digit (Second grade – E.13)

Write the addition sentence – one digit (Second grade – E.14)

Balance addition equations – one digit (Second grade – E.15)

Addition equations: true or false? (Second grade – E.16)

Add three one-digit numbers (Second grade – E.17)

Add three one-digit numbers: word problems (Second grade – E.18)

Add four or more one-digit numbers (Second grade – E.19)

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)

Write addition sentences to describe pictures (Second grade – G.6)

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)

Write addition and subtraction sentences (Second grade – L.13)

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

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

 

2 Add and subtract within 20.

 

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)

Add one-digit numbers (Second grade – E.4)

Addition input/output tables – sums to 20 (Second grade – E.7)

Add zero (Second grade – E.8)

Balance addition equations – one digit (Second grade – E.15)

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)

Add and subtract numbers up to 20 (Second grade – L.1)

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 Work with equal groups of objects to gain foundations for multiplication.

 

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)

Add doubles using models (Second grade – E.9)

Add doubles (Second grade – E.10)

Add doubles – complete the sentence (Second grade – E.11)

 

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 Understand place value.

 

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 (Second grade – A.1)

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 Use place value understanding and properties of operations to add and subtract.

 

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)

Add two two-digit numbers – without regrouping (Second grade – G.4)

Add two two-digit numbers – with regrouping (Second grade – G.5)

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

Ways to make a number using addition (Second grade – G.8)

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)

Add and subtract numbers up to 100 (Second grade – L.7)

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 with three-digit numbers (Second grade – I.2)

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 100–900, and mentally subtract 10 or 100 from a given number 100–900.

Add multiples of 10 (Second grade – G.1)

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

Add multiples of 100 (Second grade – I.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 addition facts (Second grade – K.1)

Related subtraction facts (Second grade – K.2)

Fact families (Second grade – K.3)

Solve inequalities using addition and subtraction shortcuts (Second grade – K.5)

2.2.MD Measurement and Data

 

2 Measure and estimate lengths in standard units.

 

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 Relate addition and subtraction to length.

 

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 Work with time and money.

 

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)

Read clocks and write times (Second grade – Q.5)

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 ¢ 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 Represent and interpret data.

 

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 Reason with shapes and their attributes.

 

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.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Area (Second grade – T.13)

 

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 3 – CA Common Core – Standards & Learning Objectives

3.3.OA Operations and Algebraic Thinking

3.3.NBT Number and Operations in Base Ten

3.3.NF Number and Operations-Fractions

3.3.MD Measurement and Data

3.3.G Geometry

Grade 4 – CA Common Core – Standards & Learning Objectives

4.4.OA Operations and Algebraic Thinking

 

4 Use the four operations with whole numbers to solve problems.

 

4.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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)

Addition, subtraction, multiplication, and division word problems (Fourth grade – F.2)

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.

Rounding (Fourth grade – A.6)

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 Gain familiarity with factors and multiples.

 

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 Generate and analyze patterns.

 

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)

Patterns involving addition and multiplication (Fourth grade – L.4)

Mixed patterns review (Fourth grade – L.5)

Time patterns (Fourth grade – O.9)

4.4.NBT Number and Operations in Base Ten

 

4 Generalize place value understanding for multi-digit whole numbers.

 

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)

Addition patterns over increasing place values (Fourth grade – B.6)

Inequalities with multiplication (Fourth grade – D.28)

Inequalities with division (Fourth grade – E.25)

Inequalities involving addition, subtraction, multiplication, and division (Fourth grade – F.10)

 

4.4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

Rounding (Fourth grade – A.6)

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 Use place value understanding and properties of operations to perform multi-digit arithmetic.

 

4.4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Add numbers up to millions (Fourth grade – B.1)

Add numbers up to millions: word problems (Fourth grade – B.2)

Addition: fill in the missing digits (Fourth grade – B.3)

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 Extend understanding of fraction equivalence and ordering.

 

4.4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

 

4.4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

 

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)

Add and subtract fractions with like denominators (Fourth grade – R.7)

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 and subtract fractions with like denominators (Fourth grade – R.7)

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 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

 

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 Understand decimal notation for fractions, and compare decimal fractions.

 

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 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

 

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 addition and subtraction (Fourth grade – M.7)

Price lists with multiplication (Fourth grade – M.8)

Unit prices (Fourth grade – M.9)

Add and subtract mixed customary units (Fourth grade – N.16)

Add and subtract mixed time units (Fourth grade – O.2)

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.

Perimeter (Fourth grade – P.19)

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 Represent and interpret data.

 

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 Geometric measurement: understand concepts of angle and measure angles.

 

4.4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

 

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)

Adjacent angles (Fourth grade – P.17)

 

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.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Adjacent angles (Fourth grade – P.17)

4.4.G Geometry

 

4 Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

 

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)

Classify quadrilaterals (Fourth grade – P.8)

 

4.4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Lines of symmetry (Fourth grade – P.29)

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