Math - Secondary Math I

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Math 1
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 - Quantities (N.Q)
Reason quantitatively and use units to solve problems. Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions (Standards N.Q.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.
  • 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.
  • 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: ALGEBRA - Seeing Structure in Expressions (A.SSE)
Interpret the structure of expressions (Standard A.SSE.1).
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Strand: ALGEBRA - Creating Equations (A.CED)
Create equations that describe numbers or relationships. Limit these to linear equations and inequalities, and exponential equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs (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.1)
Solve equations and inequalities in one variable (Standard A.REI.3).
Solve systems of equations. Build on student experiences graphing and solving systems of linear equations from middle school. Include cases where the two equations describe the same line - yielding infinitely many solutions - and cases where two equations describe parallel lines - yielding no solution; connect to GPE.5, which requires students to prove the slope criteria for parallel lines (Standards A.REI.5-6)
Represent and solve equations and inequalities graphically (Standards A.REI.10-12).
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Strand: FUNCTIONS - Interpreting Linear and Exponential Functions (F.IF)
Understand the concept of a linear or exponential function and use function notation. Recognize arithmetic and geometric sequences as examples of linear and exponential functions (Standards F.IF.1–3).
  • Algebra Why and When video
    This video explains why and when algebra is needed instead of arithmetic functions.
  • Derivate
    Students may use the applet in this lesson to graph a function and a tangent line and view its equation.
  • Domain and Range
    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.
  • Function Flyer
    The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
  • Inductive Patterns
    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.
  • Inductive Patterns video
    This video explains patterns and how we can use math with patterns.
  • Inductive Reasoning
    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.
  • Inductive Reasoning video
    This video introduces and explains the topic.
  • Representing Functions and Relations
    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 Functions and Relations video
    Explains how algebra can be used to describe, represent and predict relations.
  • Representing Patterns
    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 Patterns video
    This video introduces tables and graphs as representations of patterns.
  • Sequencer
    By using this applet students are able to create sequences by changing the values of starting numbers, multipliers, and add-ons.
nterpret linear or exponential functions that arise in applications in terms of a context (Standards F.IF.4–6).
  • Coordinates and the Cartesian Plane
    This lesson helps students understand functions and the domain and range of a set of data points.
  • Derivate
    Students may use the applet in this lesson to graph a function and a tangent line and view its equation.
  • Domain and Range video
    This video introduces the concepts of domain and range.
  • Function Flyer
    The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
  • Graphing Calculator
    A free online graphing calculator.
  • Graphing Quadratic Functions video
    This video introduces and explains the topic.
  • Graphing Stories
    The purpose of this task is to have students represent each indicated relationship of a given variable vs. time graphically with special attention to representing key features of increasing and decreasing intervals, maximums and minimums, intercepts, and constant and variable rates of change.
  • Graphit
    With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
  • IXL Game: Linear Functions: Standard Form
    This game will help the student understand linear functions, specifically the standard form by finding x- and y-intercepts. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • More Complicated Functions: Introduction to Linear Functions
    This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
  • Multi-Function Data Flyer
    The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
  • Polynomials video
    The video introduces and explains the topic.
  • Possible or Not
    Students can look at graphed functions from real-life examples and determine whether the graph makes sense or not in this activity.
  • 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.
  • Rate of Change and Slope
    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.
  • Rate of Change and Slope video
    This video introduces the concepts.
  • Reading Graphs
    Through this lesson students will understand how to graph functions.
  • Solving Quadratic Equations Using the Quadratic Formula video
    This video introduces and explains the topic.
Analyze linear or exponential functions using different representations (Standards F.IF.7, 9).
  • Derivate
    Students may use the applet in this lesson to graph a function and a tangent line and view its equation.
  • Function Flyer
    The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
  • Graphing Calculator
    A free online graphing calculator.
  • Graphit
    With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
  • More Complicated Functions: Introduction to Linear Functions
    This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
  • Multi-Function Data Flyer
    The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
  • 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.
  • Representing Functions and Relations
    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 Functions and Relations video
    Explains how algebra can be used to describe, represent and predict relations.
  • 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.
  • Running Time
    This task provides an application of polynomials in computing. This purpose of this task is to serve as an introduction, and motivation, for the study of end behavior of polynomials, content specifically addresses in standard F-IF.C7c.
  • Student Task: Sorting Functions
    Students are given four graphs, four equations, four tables, and four rules. Their task is to match each graph with an equation, a table and a rule.
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Strand: FUNCTIONS - Building Linear or Exponential Functions (F.BF)
Build a linear or exponential function that models a relationship between two quantities (Standards F.BF.1–2).
  • Applications of Quadratic Functions video
    This video introduces and explains the topic.
  • Function Flyer
    The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
  • Function Matching
    In this student interactive, from Illuminations, students demonstrate their understanding of function expressions by matching a function graph to a generated graph. Choose from several function types or select random and let the computer choose.
  • Graphit
    With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
  • Inductive Patterns
    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.
  • Inductive Reasoning
    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.
  • Inductive Reasoning video
    This video introduces and explains the topic.
  • Multi-Function Data Flyer
    The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
  • 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.
  • Polynomials video
    This video introduces and explains the topic.
  • Representing Patterns
    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 Patterns video
    This video introduces tables and graphs as representations of patterns.
  • Student Task: Patchwork
    Kate makes patchwork cushions using right triangles made from squares of material. In this task, students must investigate number patterns and to find a rule, or a formula, that will help Kate figure out the number of squares she needs for cushions of different sizes.
  • Student Task: Sidewalk Stones
    In this task, students will look for rules which let them work out how many blocks of different colors are needed to make different sized patterns.
  • Writing Expressions and Equations video
    How to write an equation using what we know to solve a problem we don't know.
Build new functions from existing functions (Standard F.BF.3).
  • Function Flyer
    The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
  • 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.
  • Graphit
    With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
  • Multi-Function Data Flyer
    The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
  • 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.
  • Sample Assessment Task: Quadratic transformation
    This is a two-part assessment task. Part A asks students to interpret the symbolic representation of a transformation on a function. Part B is about connecting the representations of a function. Use the navigation at the upper right of this page to access the task.
  • 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.
  • Transforming the graph of a function
    Like "Building functions: concrete case'' this task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.
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Strand: FUNCTIONS - Linear and Exponential (F.LE)
Construct and compare linear and exponential models and solve problems (Standards F.LE.1– 3).
  • Exploring Linear Functions: Representational Relationships
    This lesson plan helps students better understand linear functions by allowing them to manipulate values and get a visual representation of the result.
  • Lesson Starter: Populated Communities
    Students will use statistics and probability knowledge, as well as critical thinking skills, to solve problems.
  • 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.
  • More Complicated Functions: Introduction to Linear Functions
    This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
  • Perpendicular Lines video
    This video introduces and explains perpendicular lines.
  • Sequencer
    By using this applet students are able to create sequences by changing the values of starting numbers, multipliers, and add-ons.
Interpret expressions for functions in terms of the situation they model. (Standard F.LE.5).
  • Possible or Not
    Students can look at graphed functions from real-life examples and determine whether the graph makes sense or not in this activity.
  • 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.
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Strand: GEOMETRY - Congruence (G.CO)
Experiment with transformations in the plane. Build on student experience with rigid motions from earlier grades (Standards G.CO.1–5).
Understand congruence in terms of rigid motions. Rigid motions are at the foundation of the definition of congruence. Reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems (Standards G.CO.6–8).
Make geometric constructions (Standards G.CO.12–13).
  • 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.
  • Introduction to Constructions
    Introduction to Euclidean Construction - tools and rules.
  • Patterns in Fractals
    In this lesson students will be introduced to patterns, the terminology used in patterns, and practice finding patterns in the observable process of fractal generation.
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Strand: GEOMETRY - Expressing Geometric Properties With Equations (G.GPE)
Use coordinates to prove simple geometric theorems algebraically (Standards G.GPE.4–5, 7).
  • 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.
  • Parallel Lines
    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.
  • Parallel Lines video
    This video explains the concept.
  • Perpendicular Lines
    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.
  • Perpendicular Lines video
    This video introduces and explains perpendicular lines.
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Strand: STATISTICS AND PROBABILITY - Interpreting Categorical and Quantitative Data (S.ID)
Summarize, represent, and interpret data on a single count or measurement variable (Standards S.ID.1–3).
  • Histogram Tool
    This tool can be used to create a histogram for analyzing the distribution of a data set using data that you enter or using pre-loaded data that you select.
  • Mean and Median
    In this applet from Illuminations, students investigate the mean, median, and box-and-whisker plot for a set of data that they create. The data set may contain up to 15 integers, each with a value from 0 to 100.
  • Measuring Variability Through Tracking Wildfires
    Data about wildfires in the U.S. is the basis of this lesson. Students examine the data about active fires as well as historical data and use that data to find changes across decades. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Normal Distribution
    Students will better understand normal distribution by changing the standard deviation in the applet of this lesson plan.
  • Representing Data 1: Using Frequency Graphs
    This lesson unit is intended to help educators assess how well students are able to use frequency graphs to identify a range of measures and make sense of this data in a real-world context.
  • Representing Data 2: Using Box Plots
    This lesson unit is intended to help educators assess how well students are able to interpret data using frequency graphs and box plots.
Summarize, represent, and interpret data on two categorical and quantitative variables (Standard S.ID.6).
Interpret linear models building on students’ work with linear relationships, and introduce the correlation coefficient (Standards S.ID.7–9).
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HONORS - Strand: NUMBER AND QUANTITY: VECTOR AND MATRIX QUANTITIES (N.VM)
Represent and model with vector quantities (Standards N.VM.1–3). Perform operations on vectors (Standards N.VM.4–5)
Perform operations on matrices and use matrices in applications (Standards N.VM.6–13).
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