High School Mathematics - Essential Elements

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Note: The Iowa Core Essential Elements are intended only for students with significant cognitive disabilities and who participate in alternate assessments.

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Number and Quantity

The Real Number System (EE.N-RN)

Extend the properties of exponents to rational exponents. (EE.N-RN.A)

  1. Determine the value of a quantity that is squared or cubed. (EE.N-RN.A.1)
  2. Not applicable. (EE.N-RN.A.2)

Use properties of rational and irrational numbers. (EE.N-RN.B)

  1. Not applicable. (EE.N-RN.B.3)

Quantities★ (EE.N-Q)

Reason quantitatively and use units to solve problems. (EE.N-Q.A)

  1. Express quantities to the appropriate precision of measurement. (EE.N-Q.A.1)
  2. Express quantities to the appropriate precision of measurement. (EE.N-Q.A.2)
  3. Express quantities to the appropriate precision of measurement. (EE.N-Q.A.3)

(IA) Understand and apply the mathematics of voting.

IA.3. Not applicable.

(IA) Understand and apply some basic mathematics of information processing and the Internet.

IA.4. Not applicable.
IA.5. Not applicable.
IA.6. Not applicable.

The Complex Number System (EE.N-CN)

Perform arithmetic operations with complex numbers. (EE.N-CN.A)

  1. Not applicable. (EE.N-CN.A.1)
  2. (EE.N-CN.A.2)
    1. Use the commutative, associative, and distributive properties to add, subtract, and multiply whole numbers. (EE.N-CN.A.2.a)
    2. Solve real-world problems involving addition and subtraction of decimals, using models when needed. (EE.N-CN.A.2.b)
    3. Solve real-world problems involving multiplication of decimals and whole numbers, using models when needed. (EE.N-CN.A.2.c)
  3. Not applicable. (EE.N-CN.A.3)

Represent complex numbers and their operations on the complex plane. (EE.N-CN.B)

  1. Not applicable. (EE.N-CN.B.4)
  2. Not applicable. (EE.N-CN.B.5)
  3. Not applicable. (EE.N-CN.B.6)

Use complex numbers in polynomial identities and equations. (EE.N-CN.C)

  1. Not applicable. (EE.N-CN.C.7)
  2. Not applicable. (EE.N-CN.C.8)
  3. Not applicable. (EE.N-CN.C.9)

Vector and Matrix Quantities (EE.N-VM)

Represent and model with vector quantities. (EE.N-VM.A)

  1. Not applicable. (EE.N-VM.A.1)
  2. Not applicable. (EE.N-VM.A.2)
  3. Not applicable. (EE.N-VM.A.3)

Perform operations on vectors. (EE.N-VM.B)

  1. Not applicable. (EE.N-VM.B.4)
  2. Not applicable. (EE.N-VM.B.5)

Perform operations on matrices and use matrices in applications. (EE.N-VM.C)

  1. Not applicable. (EE.N-VM.C.6)
  2. Not applicable. (EE.N-VM.C.7)
  3. Not applicable. (EE.N-VM.C.8)
  4. Not applicable. (EE.N-VM.C.9)
  5. Not applicable. (EE.N-VM.C.10)
  6. Not applicable. (EE.N-VM.C.11)
  7. Not applicable. (EE.N-VM.C.12)
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Algebra

Seeing Structure in Expressions (EE.A-SSE)

Interpret the structure of expressions (EE.A-SSE.A)

  1. Identify an algebraic expression involving one arithmetic operation to represent a real-world problem. (EE.A-SSE.A.1)
  2. Not applicable. (EE.A-SSE.A.2)

Write expressions in equivalent forms to solve problems (EE.A-SSE.B)

  1. Solve simple algebraic equations with one variable using multiplication and division. (EE.A-SSE.B.3)
  2. Determine the successive term in a geometric sequence given the common ratio. (EE.A-SSE.B.4)

Arithmetic with Polynomials and Rational Expressions (EE.A-APR)

Perform arithmetic operations on polynomials (EE.A-APR.A)

  1. Not applicable. (EE.A-APR.A.1)

Understand the relationship between zeros and factors of polynomials (EE.A-APR.B)

  1. Not applicable. (EE.A-APR.B.2)
  2. Not applicable. (EE.A-APR.B.3)

Use polynomial identities to solve problems (EE.A-APR.C)

  1. Not applicable. (EE.A-APR.C.4)
  2. Not applicable. (EE.A-APR.C.5)

Rewrite rational expressions (EE.A-APR.D)

  1. Not applicable. (EE.A-APR.D.6)
  2. Not applicable. (EE.A-APR.D.7)

Creating Equations★ (EE.A-CED)

Create equations that describe numbers or relationships (EE.A-CED.A)

  1. Create an equation involving one operation with one variable, and use it to solve a real-world problem. (EE.A-CED.A.1)
  2. Solve one-step inequalities. (EE.A-CED.A.2)
  3. Solve one-step inequalities. (EE.A-CED.A.3)
  4. Solve one-step inequalities. (EE.A-CED.A.4)

Reasoning with Equations and Inequalities (EE.A-REI)

Understand solving equations as a process of reasoning and explain the reasoning (EE.A-REI.A)

  1. Not applicable. (EE.A-REI.A.1)
  2. Not applicable. See EE.A-CED.1. (EE.A-REI.A.2)

Solve equations and inequalities in one variable (EE.A-REI.B)

  1. Not applicable. See EE.A-CED.1. (EE.A-REI.B.3)
  2. Not applicable. (EE.A-REI.B.4)

Solve systems of equations (EE.A-REI.C)

  1. Not applicable. (EE.A-REI.C.5)
  2. Not applicable. See EE.A-REI.10-12. (EE.A-REI.C.6)
  3. Not applicable. See EE.A-REI.10-12. (EE.A-REI.C.7)
  4. Not applicable. (EE.A-REI.C.8)
  5. Not applicable. (EE.A-REI.C.9)

Represent and solve equations and inequalities graphically (EE.A-REI.D)

  1. Interpret the meaning of a point on the graph of a line. For example, on a graph of pizza purchases, trace the graph to a point and tell the number of pizzas purchased and the total cost of the pizzas. (EE.A-REI.D.10)
  2. Interpret the meaning of a point on the graph of a line. For example, on a graph of pizza purchases, trace the graph to a point and tell the number of pizzas purchased and the total cost of the pizzas. (EE.A-REI.D.11)
  3. Interpret the meaning of a point on the graph of a line. For example, on a graph of pizza purchases, trace the graph to a point and tell the number of pizzas purchased and the total cost of the pizzas. (EE.A-REI.D.12)
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Functions

Interpreting Functions (EE.F-IF)

Understand the concept of a function and use function notation (EE.F-IF.A)

Supporting Information for Target P [m]: HSS.ID.A

  1. Use the concept of function to solve problems. (EE.F-IF.A.1)
  2. Use the concept of function to solve problems. (EE.F-IF.A.2)
  3. Use the concept of function to solve problems. (EE.F-IF.A.3)

Interpret functions that arise in applications in terms of the context (EE.F-IF.B)

Supporting Information for Target L [m]: HSF.IF.B

  1. Construct graphs that represent linear functions with different rates of change and interpret which is faster/slower, higher/lower, etc. (EE.F-IF.B.4)
  2. Construct graphs that represent linear functions with different rates of change and interpret which is faster/slower, higher/lower, etc. (EE.F-IF.B.5)
  3. Construct graphs that represent linear functions with different rates of change and interpret which is faster/slower, higher/lower, etc. (EE.F-IF.B.6)

Analyze functions using different representations (EE.F-IF.C)

Supporting Information for Target M [m]: HSF.IF.C

  1. Not applicable. See EE.F-IF.1-3. (EE.F-IF.C.7)
  2. Not applicable. (EE.F-IF.C.8)
  3. Not applicable. (EE.F-IF.C.9)

Building Functions (EE.F-BF)

Build a function that models a relationship between two quantities (EE.F-FB.A)

Supporting Information for Target N [m]: HSF.BF.A

  1. Select the appropriate graphical representation (first quadrant) given a situation involving constant rate of change. (EE.F-FB.A.1)
    1. Select the appropriate graphical representation (first quadrant) given a situation involving constant rate of change. (EE.F-FB.A.1.a)
    2. Select the appropriate graphical representation (first quadrant) given a situation involving constant rate of change. (EE.F-FB.A.1.b)
    3. Not applicable. (EE.F-FB.A.1)
  2. Determine an arithmetic sequence with whole numbers when provided a recursive rule. (EE.F-FB.A.2)

Build new functions from existing functions (EE.F-FB.B)

  1. Not applicable. (EE.F-FB.B.3)
  2. Not applicable. (EE.F-FB.B.4)
  3. Not applicable. (EE.F-FB.B.5)

Linear, Quadratic, and Exponential Models★ (EE.F-LE)

Construct and compare linear, quadratic, and exponential models and solve problems (EE.F-LE.A)

  1. Model a simple linear function such as y = mx to show that these functions increase by equal amounts over equal intervals. (EE.F-LE.A.1)
  2. Model a simple linear function such as y = mx to show that these functions increase by equal amounts over equal intervals. (EE.F-LE.A.2)
  3. Model a simple linear function such as y = mx to show that these functions increase by equal amounts over equal intervals. (EE.F-LE.A.3)
  4. Not applicable. (EE.F-LE.A.4)

Interpret expressions for functions in terms of the situation they model (EE.F-LE.B)

  1. Not applicable. See EE.F-IF.1-3. (EE.F-LE.B.5)

Trigonometric Functions (EE.F-TF)

Extend the domain of trigonometric functions using the unit circle (EE.F-TF.A)

  1. Not applicable. (EE.F-TF.A.1)
  2. Not applicable. (EE.F-TF.A.2)
  3. Not applicable. (EE.F-TF.A.3)
  4. Not applicable. (EE.F-TF.A.4)

Model periodic phenomena with trigonometric functions (EE.F-TF.B)

  1. Not applicable. (EE.F-TF.B.5)
  2. Not applicable. (EE.F-TF.B.6)
  3. Not applicable. (EE.F-TF.B.7)

Prove and apply trigonometric identities (EE.F-TF.C)

  1. Not applicable. (EE.F-TF.C.8)
  2. Not applicable. (EE.F-TF.C.9)
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Geometry

Congruence (EE.G-CO)

Experiment with transformations in the plane (EE.G-CO.A)

  1. Know the attributes of perpendicular lines, parallel lines, and line segments; angles; and circles. (EE.G-CO.A.1)
  2. Not applicable. (EE.G-CO.A.2)
  3. Not applicable. (EE.G-CO.A.3)
  4. Given a geometric figure and a rotation, reflection, or translation of that figure, identify the components of the two figures that are congruent. (EE.G-CO.A.4)
  5. Given a geometric figure and a rotation, reflection, or translation of that figure, identify the components of the two figures that are congruent. (EE.G-CO.A.5)

Understand congruence in terms of rigid motions (EE.G-CO.B)

  1. Identify corresponding congruent and similar parts of shapes. (EE.G-CO.B.6)
  2. Identify corresponding congruent and similar parts of shapes. (EE.G-CO.B.7)
  3. Identify corresponding congruent and similar parts of shapes. (EE.G-CO.B.8)

Prove geometric theorems (EE.G-CO.C)

  1. Not applicable. (EE.G-CO.C.9)
  2. Not applicable. (EE.G-CO.C.10)
  3. Not applicable. (EE.G-CO.C.11)

Make geometric constructions (EE.G-CO.D)

  1. Not applicable. (EE.G-CO.D.12)
  2. Not applicable. (EE.G-CO.D.13)

Similarity, Right Triangles, and Trigonometry (EE.G-SRT)

Understand similarity in terms of similarity transformations (EE.G-SRT.A)

  1. Not applicable. See EE.G-CO.6-8. (EE.G-SRT.A.1)
  2. Not applicable. See EE.G-CO.6-8. (EE.G-SRT.A.2)
  3. Not applicable. See EE.G-CO.6-8. (EE.G-SRT.A.3)

Prove theorems involving similarity (EE.G-SRT.B)

  1. Not applicable. (EE.G-SRT.B.4)
  2. Not applicable. See EE.G-CO.6-8. (EE.G-SRT.B.5)

Define trigonometric ratios and solve problems involving right triangles (EE.G-SRT.C)

  1. Not applicable. (EE.G-SRT.C.6)
  2. Not applicable. (EE.G-SRT.C.7)
  3. Not applicable. (EE.G-SRT.C.8)

Apply trigonometry to general triangles (EE.G-SRT.D)

  1. Not applicable. (EE.G-SRT.D.9)
  2. Not applicable. (EE.G-SRT.D.10)
  3. Not applicable. (EE.G-SRT.D.11)

Circles (EE.G-C)

Understand and apply theorems about circles (EE.G-C.A)

  1. Not applicable. (EE.G-C.A.1)
  2. Not applicable. (EE.G-C.A.2)
  3. Not applicable. (EE.G-C.A.3)
  4. Not applicable. (EE.G-C.A.4)

Find arc lengths and areas of sectors of circles (EE.G-C.B)

  1. Not applicable. (EE.G-C.B.5)

Expressing Geometric Properties with Equations (EE.G-GPE)

Translate between the geometric description and the equation for a conic section (EE.G-GPE.A)

  1. Not applicable. (EE.G-GPE.A.1)
  2. Not applicable. (EE.G-GPE.A.2)
  3. Not applicable. (EE.G-GPE.A.3)

Use coordinates to prove simple geometric theorems algebraically (EE.G-GPE.B)

  1. Not applicable. (EE.G-GPE.B.4)
  2. Not applicable. See EE.G.CO.1. (EE.G-GPE.B.5)
  3. Not applicable. See EE.G.CO.1. (EE.G-GPE.B.6)
  4. Find perimeters and areas of squares and rectangles to solve real-world problems. (EE.G-GPE.B.7)

Geometric Measurement and Dimension (EE.G-GMD)

Explain volume formulas and use them to solve problems (EE.G-GMD.A)

  1. Make a prediction about the volume of a container, the area of a figure, and the perimeter of a figure, and then test the prediction using formulas or models. (EE.G-GMD.A.1)
  2. Not applicable. (EE.G-GMD.A.2)
  3. Not applicable. See EE.8.G.9 and EE.G-GPE.7. (EE.G-GMD.A.3)

Visualize relationships between two-dimensional and three-dimensional objects (EE.G-GMD.B)

  1. Identify the shapes of two- dimensional cross-sections of three- dimensional objects. (EE.G-GMD.B.4) (DOK 1,2)

Modeling with Geometry (EE.G-MG)

Apply geometric concepts in modeling situations (EE.G-MG.A)

  1. Use properties of geometric shapes to describe real-life objects. (EE.G-MG.A.1)
  2. Use properties of geometric shapes to describe real-life objects. (EE.G-MG.A.2)
  3. Use properties of geometric shapes to describe real-life objects. (EE.G-MG.A.3)

(IA) Use diagrams consisting of vertices and edges (vertex-edge graphs) to model and solve problems related to networks.

IA.8. Not applicable.
IA.9. Not applicable.
IA.10. Not applicable.

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Statistics and Probability

Interpreting Categorical and Quantitative Data (EE.S-ID)

Summarize, represent, and interpret data on a single count or measurement variable (EE.S-ID.A)

  1. Given data, construct a simple graph (line, pie, bar, or picture) or table, and interpret the data. (EE.S-ID.A.1)
  2. Given data, construct a simple graph (line, pie, bar, or picture) or table, and interpret the data. (EE.S-ID.A.2)
  3. Interpret general trends on a graph or chart. (EE.S-ID.A.3)
  4. EE.S-ID.4. Calculate the mean of a given data set (limit the number of data points to fewer than five). (EE.S-ID.A.4)

Summarize, represent, and interpret data on two categorical and quantitative variables (EE.S-ID.B)

  1. Not applicable. See EE.F-IF.1 and EE.A-REI.6-7. (EE.S-ID.B.5)
  2. Not applicable. (EE.S-ID.B.6)

Interpret linear models (EE.S-ID.C)

  1. Not applicable. See EE.F-IF.4-6. (EE.S-ID.C.7)
  2. Not applicable. (EE.S-ID.C.8)
  3. Not applicable. (EE.S-ID.C.9)

Making Inferences and Justifying Conclusions (EE.S-IC)

Understand and evaluate random processes underlying statistical experiments (EE.S-IC.A)

  1. Determine the likelihood of an event occurring when the outcomes are equally likely to occur. (EE.S-IC.A.1)
  2. Determine the likelihood of an event occurring when the outcomes are equally likely to occur. (EE.S-IC.A.2)

Make inferences and justify conclusions from sample surveys, experiments, and observational studies (EE.S-IC.B)

  1. Not applicable. See EE.S-ID.1–2. (EE.S-IC.B.3)
  2. Not applicable. See EE.S-ID.1–2. (EE.S-IC.B.4)
  3. Not applicable. See EE.S-ID.1–2. (EE.S-IC.B.5)
  4. Not applicable. See EE.S-ID.1–2. (EE.S-IC.B.6)

Conditional Probability and the Rules of Probability (EE.S-CP)

Understand independence and conditional probability and use them to interpret data (EE.S-CP.A)

  1. Identify when events are independent or dependent. (EE.S-CP.A.1)
  2. Identify when events are independent or dependent. (EE.S-CP.A.2)
  3. Identify when events are independent or dependent. (EE.S-CP.A.3)
  4. Identify when events are independent or dependent. (EE.S-CP.A.4)
  5. Identify when events are independent or dependent. (EE.S-CP.A.5)

Use the rules of probability to compute probabilities of compound events in a uniform probability model (EE.S-CP.B)

  1. Not applicable. See EE.S-IC.1-2. (EE.S-CP.B.6)
  2. Not applicable. See EE.S-IC.1-2. (EE.S-CP.B.7)
  3. Not applicable. (EE.S-CP.B.8)
  4. Not applicable. (EE.S-CP.B.9)

Using Probability to Make Decisions (EE.S-MD)

Calculate expected values and use them to solve problems (EE.S-MD.A)
  1. Not applicable. (EE.S-MD.A.1)
  2. Not applicable. (EE.S-MD.A.2)
  3. Not applicable. (EE.S-MD.A.3)
  4. Not applicable. (EE.S-MD.A.4)

Use probability to evaluate outcomes of decisions (EE.S-MD.B)

  1. Not applicable. (EE.S-MD.B.5)
  2. Not applicable. (EE.S-MD.B.6)
  3. Not applicable. (EE.S-MD.B.7)
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