Math - Secondary Math II

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Math 1I
Review Activities and Games

These resources are intended for review and practice after initial instruction of the standards.

 

Strand: MATHEMATICAL PRACTICES (MP)
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Strand: NUMBER AND QUANTITY - The Real Number System (N.RN)
Extend the properties of exponents to rational exponents (Standards N.RN.1–2)
Use properties of rational and irrational numbers (Standard N.RN. 3).
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Strand: NUMBER AND QUANTITY - The Complex Number System (N.CN)
Perform arithmetic operations with complex numbers (Standards N.CN.1–2).
Use complex numbers in polynomial identities and equations (Standards N.CN.7–9).
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Strand: ALGEBRA - Seeing Structure in Expression (A.SSE)
Interpret the structure of expressions (Standards A.SSE.1–2)
Write expressions in equivalent forms to solve problems, balancing conceptual understanding and procedural fluency in work with equivalent expressions (Standard A.SSE.3).
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Strand: ALGEBRA - Arithmetic With Polynomials and Rational Expressions (A.APR)
Perform arithmetic operations on polynomials. Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x (Standard A.APR.1).
  • Adding and Subtracting Polynomials
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Adding and Subtracting Polynomials video
    This video introduces and explains the topic.
  • IXL Game: Polynomials: Multiply polynomials
    This game in the algebra domain will help students understand how multiply polynomials. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • Multiplying Polynomials
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Multiplying Polynomials video
    This video introduces and explains the concept.
  • Special Products of Polynomials
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Special Products of Polynomials video
    This video introduces and explains the concept.
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Strand: ALGEBRA - Creating Equations (A.CED)
Create equations that describe numbers or relationships. Extend work on linear and exponential equations to quadratic equations (Standards A.CED.1–2, 4).
  • Applications of Quadratic Functions
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Applications of Quadratic Functions video
    This video introduces and explains the topic.
  • Equations of Circles 1
    This lesson unit is intended to help educators assess how well students are able to use the Pythagorean theorem to derive the equation of a circle, as well as translate between the geometric features of circles and their equations.
  • Graphing Quadratic Functions
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Inscribing and Circumscribing Right Triangles
    This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems.
  • Non-linear Functions video
    This video introduces non-linear functions.
  • Polynomials
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Solving Quadratic Equations Using the Quadratic Formula video
    This video introduces and explains the topic.
  • Sorting Equations of Circles 2
    This lesson unit is intended to help educators assess how well students are able to translate between the equations of circles and their geometric features, and sketch a circle from its equation.
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Strand: ALGEBRA - Reasoning With Equations and Inequalities (A.REI)
Solve equations and inequalities in one variable (Standard A.REI.4)
Solve systems of equations. Extend the work of systems to include solving systems consisting of one linear and one nonlinear equation (Standard A.REI.7).
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Strand: FUNCTIONS - Interpret Functions (F.IF)
Interpret quadratic functions that arise in applications in terms of a context (Standards F.IF.4–6).
Analyze functions using different representations (Standards F.IF.7–9).
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Strand: FUNCTIONS - Building Functions (F.BF)
Build a function that models a relationship between two quantities (Standard F.BF.1).
  • Applications of Quadratic Functions
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Applications of Quadratic Functions video
    This video introduces and explains the topic.
  • Generalizing Patterns: Table Tiles
    This lesson unit is intended to help educators assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops.
  • Medical Testing
    This lesson unit is intended to help educators assess how well students are able to make sense of a real life situation and decide what math to apply to the problem, understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model, and represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams.
  • Polynomials
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Representing Trigonometric Functions - Ferris Wheel
    This lesson unit is intended to help educators assess how well students are able to model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions, and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.
Build new functions from existing functions (Standard F.BF.3).
  • Generalizing Patterns: Table Tiles
    This lesson unit is intended to help educators assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops.
  • Medical Testing
    This lesson unit is intended to help educators assess how well students are able to make sense of a real life situation and decide what math to apply to the problem, understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model, and represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams.
  • Representing Trigonometric Functions - Ferris Wheel
    This lesson unit is intended to help educators assess how well students are able to model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions, and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.
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Strand: FUNCTIONS - Linear, Quadratic, and Exponential Models (F.LE)
Construct and compare linear, quadratic, and exponential models and solve problems (Standard F.LE.3).
  • Modeling: Having Kittens
    This lesson unit is intended to help you assess how well students are able to interpret a situation and represent the constraints and variables mathematically, select appropriate mathematical methods to use, make sensible estimates and assumptions and investigate an exponentially increasing sequence.
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Strand: FUNCTIONS - Trigonometric Functions (F.TF)
Prove and apply trigonometric identities. Limit θ to angles between 0 and 90 degrees. Connect with the Pythagorean Theorem and the distance formula (Standard F.TF.8).
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Strand: GEOMETRY - Congruence (G.CO)
Prove geometric theorems. Encourage multiple ways of writing proofs, such as narrative paragraphs, flow diagrams, two-column format, and diagrams without words. Focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning (Standards G.CO.9–11).
  • Angles
    Students are introduced to all kinds of angles in this lesson plan, including acute, obtuse, right, vertical, adjacent, and corresponding among others.
  • Evaluating Statements About Length and Area
    This lesson unit is intended to help educators assess how well students can understand the concepts of length and area, use the concept of area in proving why two areas are or are not equal, and construct their own examples and counterexamples to help justify or refute conjectures.
  • Proofs of the Pythagorean Theorem
    This lesson unit is intended to help educators assess how well students are able to produce and evaluate geometrical proofs.
  • Solving Geometry Problems: Floodlights
    This lesson unit is intended to help educators assess how well students are able to identify and use geometrical knowledge to solve a problem.
  • Student Task: Circles in Triangles
    In this task, the students have to find the radius of circles inscribed in various sizes of right triangle.
  • Student Task: Floor Pattern
    In this task, students will investigate the geometrical properties of a pattern of floor tiles
  • Tessellations: Geometry and Symmetry
    Students can explore polygons, symmetry, and the geometric properties of tessellations in this lesson.
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Strand: GEOMETRY - Similarity, Right Triangles, and Trigonometry (G.SRT)
Understand similarity in terms of similarity transformations (Standards G.SRT.1–3).
  • Evaluating Conditions for Congruency
    This lesson unit is intended to help educators assess how well students are able to work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles. They will also identify and understand the significance of a counter-example, and prove and evaluate proofs in a geometric context.
  • IXL Game: Geometry: Similar Figures
    This game will reinforce geometry dealing with similar figures by looking at side lengths and angle measures. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • Introduction to Fractals: Infinity, Self-Similarity and Recursion
    This lesson is designed to help students understand aspects of fractals, specifically self-similarity and recursion.
  • Squaring the Triangle
    Students can manipulate the sides of a triangle in this applet in order to better understand the Pythagorean Theorem.
Prove theorems involving similarity (Standards G.SRT.4–5)
  • Evaluating Conditions for Congruency
    This lesson unit is intended to help educators assess how well students are able to work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles. They will also identify and understand the significance of a counter-example, and prove and evaluate proofs in a geometric context.
  • Proofs of the Pythagorean Theorem
    This lesson unit is intended to help educators assess how well students are able to produce and evaluate geometrical proofs.
  • Solving Geometry Problems: Floodlights
    This lesson unit is intended to help educators assess how well students are able to identify and use geometrical knowledge to solve a problem.
  • Squaring the Triangle
    Students can manipulate the sides of a triangle in this applet in order to better understand the Pythagorean Theorem.
  • Tessellations: Geometry and Symmetry
    Students can explore polygons, symmetry, and the geometric properties of tessellations in this lesson.
Define trigonometric ratios and solve problems involving right triangles (Standards G.SRT.6–8).
  • Access Ramp - Student Task
    This task has students design an access ramp, which complies with the Americans with Disabilities Act (ADA) requirements and include pricing based on local costs.
  • Applications of the Pythagorean Theorem
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Applications of the Pythagorean Theorem video
    This video introduces and explains the topic.
  • Applying Radical Equations
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Applying Radical Equations video
    This video introduces and explains the topic.
  • Calculating Volumes of Compound Objects
    This lesson unit is intended to help educators assess how well students solve problems involving measurement.
  • Evaluating Conditions for Congruency
    This lesson unit is intended to help educators assess how well students are able to work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles. They will also identify and understand the significance of a counter-example, and prove and evaluate proofs in a geometric context.
  • Inscribing and Circumscribing Right Triangles
    This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems.
  • Pythagorean Explorer
    This applet challenges the student to find the length of the third side of a triangle when given the two sides and the right angle.
  • Solving Problems with Circles and Triangles
    This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems
  • Squaring the Triangle
    Students can manipulate the sides of a triangle in this applet in order to better understand the Pythagorean Theorem.
  • Student Task: Hopewell Geometry
    The Hopewell people were Native Americans whose culture flourished in the central Ohio Valley about 2000 years ago. They constructed earthworks using right triangles. In this task, the student will look at some of the geometrical properties of a Hopewell earthwork.
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Strand: GEOMETRY - Circles (G.C)
Understand and apply theorems about circles (Standard G.C.1–4).
  • Inscribing and Circumscribing Right Triangles
    This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems.
  • Student Task: Circles in Triangles
    In this task, the students have to find the radius of circles inscribed in various sizes of right triangle.
  • Student Task: Temple Geometry
    During the Edo period (1603-1867) of Japanese history, geometrical puzzles were hung in the holy temples as offerings to the gods and as challenges to worshippers. Here is one such problem for students to investigate.
Find arc lengths and areas of sectors of circles. Use this as a basis for introducing the radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course (Standard G.C.5).
  • Inscribing and Circumscribing Right Triangles
    This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems.
  • Student Task: Circles in Triangles
    In this task, the students have to find the radius of circles inscribed in various sizes of right triangle.
  • Student Task: Temple Geometry
    During the Edo period (1603-1867) of Japanese history, geometrical puzzles were hung in the holy temples as offerings to the gods and as challenges to worshippers. Here is one such problem for students to investigate.
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Strand: GEOMETRY - Expressing Geometric Properties With Equations (G.GPE)
Translate between the geometric description and the equation for a conic section (Standard G.GPE.1).
Use coordinates to prove simple geometric theorems algebraically. Include simple proofs involving circles (Standard G.GPE.4).
  • Finding Equations of Parallel and Perpendicular Lines
    This lesson unit is intended to help educators assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines.
  • Sorting Equations of Circles 2
    This lesson unit is intended to help educators assess how well students are able to translate between the equations of circles and their geometric features, and sketch a circle from its equation.
Use coordinates to prove simple geometric theorems algebraically (Standard G.GPE.6).
  • Student Task: Square
    In this task, students are given four points on a graph, and must prove that they are the corners of a square.
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Strand: GEOMETRY - Geometric Measurement and Dimension (G.GMD)
Explain volume formulas and use them to solve problems (Standards G.GMD.1, 3).
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Strand: STATISTICS - Interpreting Categorical and Quantitative Data (S.ID)
Summarize, represent, and interpret data on two categorical or quantitative variables (Standard S.ID.5).
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Strand: STATISTICS - Conditional Probability and the Rules of Probability (S.CP)
Understand independence and conditional probability and use them to interpret data (Standards S.CP.1, 4–5).
  • A Better Fire!!
    A simulation of a forest fire and how it spreads helps students learn about probability in this lesson.
  • Conditional Probability and Probability of Simultaneous Events
    This lesson plan is designed to help students understand and use the formula for probability of simultaneous independent events.
  • Crazy Choices Game
    Students will understand probability by playing various games of chance in this lesson's applet.
  • Ideas that Lead to Probability
    This lesson is designed so that students will understand the concept of probability by working with random number generators.
  • Marbles
    This activity helps the student understand randomness and probability by pulling marbles out of a bag.
  • Medical Testing
    This lesson unit is intended to help educators assess how well students are able to make sense of a real life situation and decide what math to apply to the problem, understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model, and represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams.
  • Modeling Conditional Probabilities 1: Lucky Dip
    This lesson unit is intended to help educators assess how well students are able to understand conditional probability and represent events as a subset of a sample space using tables and tree diagrams.
  • Racing Game with Two Dice
    By using the applet embedded in this lesson plan, students can simulate a race and learn about probability.
Use the rules of probability to compute probabilities of compound events in a uniform probability model (Standard S.CP.6).
  • Medical Testing
    This lesson unit is intended to help educators assess how well students are able to make sense of a real life situation and decide what math to apply to the problem, understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model, and represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams.
  • Modeling Conditional Probabilities 1: Lucky Dip
    This lesson unit is intended to help educators assess how well students are able to understand conditional probability and represent events as a subset of a sample space using tables and tree diagrams.
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HONORS - Strand: NUMBER AND QUANTITY - Complex Number System (N.CN)
Perform arithmetic operations with complex numbers (Standard N.CN.3).
Represent complex numbers and their operations on the complex plane (Standards N.CN.4–5).
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HONORS - Strand: ALGEBRA - Reasoning With Equations and Inequalities (A.REI)
Solve systems of equations (Standards A.REI.8–9).
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HONORS - Strand: FUNCTIONS - Interpreting Functions (F.IF)
Analyze functions using different representations (Standards F.IF.10–11).
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HONORS - Strand: GEOMETRY - Expressing Geometric Properties With Equations (G-GPE)
Translate between the geometric description and the equation for a conic section (Standards G.GPE.2–3).
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HONORS - Strand: STATISTICS AND PROBABILITY - Conditional Probability and the Rules of Probability (S.CP)
Understand independence and conditional probability and use them to interpret data (Standards S.CP.2–3).
Use the rules of probability to compute probabilities of compound events in a uniform probability model (Standards S.CP.7–8).
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