Math - Secondary Math III

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Math 3
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 Complex Number System (N.CN)
Use complex numbers in polynomial identities and equations. Build on work with quadratic equations in Secondary Mathematics II (Standards N.CN.8–9).
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Strand: ALGEBRA - Seeing Structures in Expressions (A.SSE)
Interpret the structure of expressions. Extend to polynomial and rational expressions (Standards A.SSE.1–2)
Write expressions in equivalent forms to solve problems (Standard A.SSE.4).
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Strand: ALGEBRA - Arithmetic With Polynomials and Rational Expressions (A.APR)
Perform arithmetic operations on polynomials, extending beyond the quadratic polynomials (Standard A.APR.1).
Understand the relationship between zeros and factors of polynomials (Standards A.APR.2–3)
  • Representing Polynomials
    This lesson unit is intended to help educators assess how well students are able to translate between graphs and algebraic representations of polynomials.
Use polynomial identities to solve problems (Standards A.APR.4–5)
Rewrite rational expressions (Standards A.APR.6–7).
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Strand: ALGEBRA - Creating Equations (A.CED)
Create equations that describe numbers or relationships, using all available types of functions to create such equations (Standards A.CED.1–4).
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Strand: ALGEBRA - Reasoning with Equations and Inequalities (A.REI)
Understand solving equations as a process of reasoning and explain the reasoning (Standard A.REI.2)
  • 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.
  • Applying Rational 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 Rational Equations video
    This video introduces and explains the topic.
  • GeoGebra
    GeoGebra is dynamic online geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards.
  • Solving 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.
  • Solving Radical Equations video
    This video introduces and explains the topic.
  • Solving Rational 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.
  • Solving Rational Expressions video
    This video introduces and explains the topic.
Represent and solve equations and inequalities graphically (Standard A.REI.11).
  • GeoGebra
    GeoGebra is dynamic online geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards.
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Strand: FUNCTIONS - Interpreting Functions (F.IF)
Interpret functions that arise in applications in terms of a context (Standards F.IF.4–6).
  • Polynomials video
    The video introduces and explains the topic.
  • Simplifying Rational Expressions
    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.
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. Develop models for more complex or sophisticated situations (Standards F.BF.1).
  • 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.
  • Inductive Reasoning video
    This video introduces and explains the topic.
  • Modeling: Rolling Cups
    This lesson unit is intended to help educators assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables, and develop experimental and analytical models of a physical situation.
  • Solving Rational Expressions video
    This video introduces and explains the topic.
Build new functions from existing functions (Standards F.BF.3–4).
  • Absolute Value
    This array of resources teaching absolute value includes warm-up problems, a video introducing the topic, worked examples, practice problems, and a review.
  • 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.
  • 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.
  • Applying Rational 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 Rational Equations 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.
  • 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.
  • Graphing Quadratic Functions video
    This video introduces and explains the topic.
  • Modeling: Rolling Cups
    This lesson unit is intended to help educators assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables, and develop experimental and analytical models of a physical situation.
  • Proportional 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.
  • Reading Graphs
    Through this lesson students will understand how to graph functions.
  • Solve Quadratic Expressions by Factoring video
    This video introduces and explains the concept.
  • Solving Absolute Value 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.
  • Solving Absolute Value Equations video
    This video explains how to solve absolute value expressions.
  • Solving Equations video
    Answers the questions "what are equations?" and "how do we solve them?"
  • Solving Quadratic Equations Using the Quadratic Formula video
    This video introduces and explains the topic.
  • Solving Quadratic Equations by Completing the Square
    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 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.
  • Solving Radical Equations video
    This video introduces and explains the topic.
  • Solving Rational 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.
  • Solving Rational Expressions video
    This video introduces and explains the topic.
  • Systems of Non-Linear 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.
  • Systems of Non-Linear Equations video
    This video introduces and explains the topic.
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Strand: FUNCTIONS - Linear, Quadratic, and Exponential Models (F.LE)
Construct and compare linear, quadratic, and exponential models and solve problems (Standards F.LE.3–4).
  • Applying Rational Equations video
    This video introduces and explains the topic.
  • 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.
  • Solving Rational Expressions video
    This video introduces and explains the topic.
Interpret expressions for functions in terms of the situation it models. Introduce f(x) = ex as a model for continuous growth (Standard F.LE.5).
  • 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)
Extend the domain of trigonometric functions using the unit circle (Standards F.TF.1–3).
  • 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.
Model periodic phenomena with trigonometric functions (Standards F.TF.5–7).
  • 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.
  • Tidal Waves (pdf)
    Students analyze a problem faced by the captain of a shipping vessel. Students may use a range of functions to model the situation and reflect on their usefulness. Because trigonometric functions can be useful, this task would be particularly appropriate for students who have had an introduction to graphing sine and cosine functions.
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Strand: GEOMETRY - Similarity, Right Triangles, and Trigonometry (G.SRT)
Apply trigonometry to general triangles. With respect to the general case of the Laws of Sines and Cosines, the definitions of sine and cosine must be extended to obtuse angles (Standards G.SRT.9–11).
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Strand: GEOMETRY - Geometric Measurement and Dimension (G.GMD)
Visualize relationships between two-dimensional and three-dimensional objects (Standards G.MD.4).
  • 2D Representations of 3D Objects
    This lesson unit is intended to help educators assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects.
  • Modeling: Rolling Cups
    This lesson unit is intended to help educators assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables, and develop experimental and analytical models of a physical situation.
  • Student Task: Propane Tanks
    In this task, students must work out how much you need to change the radius of a propane gas tank in order to double its capacity.
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Strand: GEOMETRY - Modeling With Geometry (G.MG)
Apply geometric concepts in modeling situations (Standards G.MG.1–3).
  • 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.
  • Fences - student task
    This task has students design a fence that meets the city ordinances and the client's specifications.
  • Framing a House - student task
    This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed.
  • Image Tool
    Students are able to explore scale by measuring angles in various images in this activity in order to better understand ratio and proportion.
  • Miniature Golf - student task
    This task requires students to redesign a miniature golf course to make it more challenging.
  • Modeling: Rolling Cups
    This lesson unit is intended to help educators assess how well students are able to choose appropriate mathematics to solve a non-routine problem, generate useful data by systematically controlling variables, and develop experimental and analytical models of a physical situation.
  • Stairway - Student Task
    This task students to design a stairway for a custom home. They will need to gather information regarding design, safety, and the utility of staircases.
  • Storage Shed - student task
    Students are going to build storage sheds as a fund raising project, but before they can start they must determine the best dimensions for the shed, make scale drawings and decide on how much to charge for each shed.
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Strand: STATISTICS - Interpreting Categorical and Quantitative Data (S.ID)
Summarize, represent, and interpret data on a single count or measurement variable. While students may have heard of the normal distribution, it is unlikely that they will have prior experience using it to make specific estimates. Build on students’ understanding of data distributions to help them see how the normal distribution uses area to make estimates of frequencies (which can be expressed as probabilities). Emphasize that only some data are well described by a normal distribution (Standard S.ID.4).
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Strand: STATISTICS - Making Inferences and Justifying Conclusions (S.IC)
Understand and evaluate random processes underlying statistical experiments (Standard S.IC.1).
  • Fire!, Probability, and Chaos
    A simulated forest fire is the starting place to help students understand probability and graphing and graph interpretation, mean, and variance.
  • Interpreting Statistics: A Case of Muddying the Waters
    This lesson unit is intended to help educators assess how well students are able to interpret data and evaluate statistical summaries and critique someone else's interpretations of data and evaluations of statistical summaries.
  • Lesson Starter: Solving Math Problems with a Team
    Students will work in teams to solve mathematical problems; they listen to the reasoning of others and offer correction with supporting arguments; they modify their own arguments when corrected; they learn from mistakes and make repeated attempts at solving problems.
  • Marbles
    This activity helps the student understand randomness and probability by pulling marbles out of a bag.
  • Probability: Playing with Fire
    This lesson is designed to help students understand possible outcomes of a probability experiment.
  • Replacement and Probability
    This lesson will help students learn the difference between sampling with and without replacement.
  • Unexpected Answers
    This lesson shows students some unexpected outcomes to probability problems and shows how fairness in games is not always as it seems.
Draw and justify conclusions from sample surveys, experiments, and observational studies. In earlier grades, students are introduced to different ways of collecting data and use graphical displays and summary statistics to make comparisons. These ideas are revisited with a focus on how the way in which data is collected determines the scope and nature of the conclusions that can be drawn from that data. The concept of statistical significance is developed informally through simulation as meaning a result that is unlikely to have occurred solely as a result of random selection in sampling or random assignment in an experiment. For S.IC.4, focus on the variability of results from experiments - that is, focus on statistics as a way of dealing with, not eliminating, inherent randomness (Standards S.IC.3-4, 6).
  • Fire!, Probability, and Chaos
    A simulated forest fire is the starting place to help students understand probability and graphing and graph interpretation, mean, and variance.
  • Interpreting Statistics: A Case of Muddying the Waters
    This lesson unit is intended to help educators assess how well students are able to interpret data and evaluate statistical summaries and critique someone else's interpretations of data and evaluations of statistical summaries.
  • Lesson Starter: Solving Math Problems with a Team
    Students will work in teams to solve mathematical problems; they listen to the reasoning of others and offer correction with supporting arguments; they modify their own arguments when corrected; they learn from mistakes and make repeated attempts at solving problems.
  • Probability: Playing with Fire
    This lesson is designed to help students understand possible outcomes of a probability experiment.
  • Replacement and Probability
    This lesson will help students learn the difference between sampling with and without replacement.
  • Unexpected Answers
    This lesson shows students some unexpected outcomes to probability problems and shows how fairness in games is not always as it seems.
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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 (Standard N.CN.4–6).
Use complex numbers in polynomial identities and equations (Standard N.CN.10).
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HONORS - Strand: FUNCTIONS - Interpreting Functions (F.IF)
Analyze functions using different representations (Standard F.IF.7, d and f).
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HONORS - Strand: FUNCTIONS - Building Functions (F.BF).
Build a function that models a relationship between two quantities (Standard F.BF.1.c).
Build new functions from existing functions (Standards F.BF.4, b,c,d–5).
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HONORS - Strand: FUNCTIONS - Trigonometric Functions (F.TF)
Extend the domain of trigonometric functions using the unit circle (Standard T.FT.4).
Model periodic phenomena with trigonometric functions (Standards T.FT.6–7).
Prove and apply trigonometric identities (Standard T.FT.9).
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HONORS - Strand: GEOMETRY - Geometric Measurement and Dimension (G.GMD)
Explain volume formulas and use them to solve problems (Standard G.GMD.2).
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HONORS - Strand: STATISTICS AND PROBABILITY - Conditional Probability and the Rules of Probability (S.CP)
Use the rules of probability to compute probabilities of compound events in a uniform probability model (Standard S.CP.9).
  • Events and Outcomes (Counting)
    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.
  • Events and Outcomes (Counting) video
    This video introduces and explains the topic.
  • IXL Game: Probability: Permutations
    This game is designed to help students use permutations and combinations to compute probabilities of compound events and solve problems. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • Racing Game with One Die
    Students can simulate a race between two cars with the roll of a die and learn about probability through this activity.
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