Teaching the Common Core Math Standards with Hands-On Activities, Grades 9-12
Published on 17. April 2015
312 pages
978-1-119-06220-2 (ISBN)
Description
Bring Common Core Math into high school with smart, engaging activities
Teaching Common Core Math Standards with Hands-On Activities, Grades 9-12 provides high school teachers with the kind of help they need to begin teaching the standards right away. This invaluable guide pairs each standard with one or more classroom-ready activities and suggestions for variations and extensions. Covering a range of abilities and learning styles, these activities bring the Common Core Math Standards to life as students gain fluency in math communication and develop the skillset they need to tackle successively more complex math courses in the coming years. Make math anxiety a thing of the past as you show your students how they use math every day of their lives, and give them the cognitive tools to approach any math problem with competence and confidence.
The Common Core Standards define the knowledge and skills students need to graduate high school fully prepared for college and careers. Meeting these standards positions American students more competitively in the global economy, and sets them on a track to achieve their dreams. This book shows you how to teach the math standards effectively, and facilitate a deeper understanding of math concepts and calculations.
* Help students apply their understanding of math concepts
* Teach essential abstract and critical thinking skills
* Demonstrate various problem-solving strategies
* Lay a foundation for success in higher mathematics
The rapid adoption of the Common Core Standards across the nation has left teachers scrambling for aligned lessons and activities. If you want to bring new ideas into the classroom today, look no further. Teaching Common Core Math Standards with Hands-On Activities is the high school math teacher's solution for smart, engaging Common Core math.
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05/2015
1st Edition
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Person
JUDITH A. MUSCHLA has over 25 years of experience as a mathematics educator in South River, New Jersey. She was a member of the New Jersey state Standards Review Panel for the Mathematics Curriculum Content Standards.
GARY ROBERT MUSCHLA is a skilled teacher of middle school math, reading, and writing. He has co-authored several math activity books with Judith Muschla, including Algebra Teacher's Activities Kit, Hands-On Math Projects with Real Life Applications, and Math Starters.
ERIN MUSCHLA-BERRY teaches mathematics at Monroe Township Middle School in Monroe, New Jersey. This is her eighth collaboration with Judith and Gary Muschla.
Content
About This Book
About the Authors
Acknowledgments
Section 1: Standards and Activities for Number and Quantity
The Real Number System
Activity: Understanding Integer and Rational Exponents
Activity: Finding the Values of Expressions
Activity: Sums and Properties of Rational and Irrational Numbers
Quantities
Activity: A Recommendation for the Boss
Activity: Defining Appropriate Quantities
Activity: Determining Levels of Accuracy in Measurement
The Complex Number System
Activity: Classifying Complex Numbers
Activity: Operations with Complex Numbers
Activity: Matching Roots
Reproducibles for Section 1: Number and Quantity
The Meaning of Rational Exponents
Equations and Their Values
Proving the Sum of Two Rational Numbers Is Rational
Proving the Sum of Rational and Irrational Numbers Is Irrational
Guidelines for Choosing a Delivery Vehicle
Defining Appropriate Quantities for Problem Solving
Graphic Organizer for Complex Numbers
Complex Number Cards--Solutions and Problems
Quadratic Equations and Their Roots
Section 2: Standards and Activities for Algebra
Seeing Structure in Expressions
Activity: Interpreting Expressions
Activity: Rewriting Expressions
Activity: Expressions and Equivalent Forms
Activity: Deriving a Formula
Arithmetic with Polynomials and Rational Expressions
Activity: Pick the Polynomial
Activity: Solving a Division Puzzle
Activity: Matching Functions, Graphs, and Zeroes of a Function
Activity: Proving the Polynomial Identity
Activity: Mistakes in Rational Expressions
Creating Equations
Activity: Creating Equations and Inequalities
Activity: Creating and Graphing Equations
Activity: Pricing T-Shirts
Activity: Rearranging Formulas and Equations
Reasoning with Equations and Inequalities
Activity: Organizing the Steps for Solving Equations
Activity: Solving Equations
Activity: What's the Solution?
Activity: Racing to Solve Quadratic Equations
Activity: Solving a System of Equations
Activity: Solving Systems in Many Ways
Activity: Solving Systems of Equations
Activity: Tracing Equations
Activity: Selecting Pairs of Equations with the Same Solutions
Activity: Identifying Solutions through Graphing
Reproducibles for Section 2: Algebra
The Expressions Game
Identifying and Rewriting Expressions
Expressions and Equivalent Forms Cards
Identifying Errors in a Derived Formula
Polynomial Cards
Polynomial Division Cards
Finding Your Match, I
Finding Your Match, II
Correcting Mistakes in Rational Expressions
Which One Does Not Belong?
Word Problems, Equations, and Graphs
T-Shirts for the Math Club
Formula and Equation Cards
Equation and Step Cards
Rational and Radical Equation Problem Cards
Equation and Inequality Cards
Quadratic Equations and Score Sheet
Steps for Solving a System of Equations
Task Cards for Solving Systems of Linear Equations
Task Cards for Equations and Solutions
Tracing Equations with Graphing Calculators
Equations and Solutions
Solving Inequalities and Systems of Inequalities by Graphing
Section 3: Standards and Activities for Functions
Interpreting Functions
Activity: Identifying Functions
Activity: Grouping Rules, Inputs, and Outputs
Activity: Figurate Numbers
Activity: Finding Similarities and Differences in Functions
Activity: Recognizing Functions
Activity: Matching Functions, Tables, and Average Rates of Change
Activity: Making a Function Booklet
Activity: Writing Functions in Equivalent Forms
Activity: Comparing Functions
Building Functions
Activity: Writing Functions
Activity: The Game of Arithmetic and Geometric Sequences
Activity: Matching Functions with Their Graphs
Activity: Finding the Inverse of a Function--Bingo
Linear, Quadratic, and Exponential Models
Activity: Modeling Linear and Exponential Functions
Activity: Constructing Linear and Exponential Functions
Activity: Analyzing Exponential and Polynomial Functions
Activity: Logarithmic and Exponential Equations
Activity: Interpreting Parameters of Functions
Trigonometric Functions
Activity: Understanding Radian Measure
Activity: Trigonometric Functions and the Unit Circle
Activity: Modeling Monthly Precipitation
Activity: Proving and Applying the Pythagorean Theorem
Reproducibles for Section 3: Functions
Function Cards
Function Sets, I
Function Sets, II
Equations, Tables, and Average Rates of Change Cards, I
Equations, Tables, and Average Rates of Change Cards, II
A Function Booklet
Comparing Function Cards, I
Comparing Function Cards, II
Arithmetic and Geometric Sequence Game Cards
Graphs and Functions
Function Bingo Board
Functions for Bingo
Tables and Rates of Change
Information Cards for Linear and Exponential Functions
Logarithmic Equation, Exponential Equation, and Solution Cards
Drawing an Angle Whose Measure Is 1 Radian
Explaining Trigonometric Functions Using the Unit Circle
Proving the Pythagorean Identity
Angles and Their Quadrants
Section 4: Standards and Activities for Geometry
Congruence
Activity: Drawing and Defining Figures
Activity: Presenting a Mini-Lesson on Transformations
Activity: Carrying a Figure onto Itself
Activity: Identifying and Defining Transformations
Activity: Drawing and Identifying Transformations
Activity: Predicting the Effects of Transformations
Activity: Identifying Congruent Triangles
Activity: Congruence and Rigid Motions
Activity: Proving Theorems about Lines and Angles
Activity: Proofs about Triangles
Activity: Proving Theorems about Parallelograms
Activity: Constructing Geometric Figures
Activity: Constructing Regular Polygons
Similarity, Right Triangles, and Trigonometry
Activity: Dilating Lines and Line Segments
Activity: Identifying Similar Triangles
Activity: Establishing the AA Criterion for Two Similar Triangles
Activity: Proving Theorems about Triangles
Activity: Reflecting on Congruence and Symmetry
Activity: Exploring the Ratios of Sides in a Right Triangle
Activity: Relating the Sine and Cosine of Complementary Angles
Activity: Problems, Questions, and Solutions
Circles
Activity: Proving All Circles Are Similar
Activity: Eliminating Figures Based on What They Are Not
Activity: Working with Inscribed and Circumscribed Circles
Activity: Critiquing Derivations
Expressing Geometric Properties with Equations
Activity: Working with Equations
Activity: Deriving the Equation of a Parabola
Activity: Proving Geometric Theorems with Coordinates
Activity: Slopes of Parallel and Perpendicular Lines
Activity: Partitioning Line Segments
Activity: Graphing and Finding Perimeters and Areas of Polygons
Geometric Measurement and Dimension
Activity: Presenting a Mini-Lesson on Formulas
Activity: Using Volume Formulas to Solve Problems
Activity: Cross-Sections and Rotations
Modeling with Geometry
Activity: Using Properties of Geometric Shapes
Activity: A Plan for Recreational Facilities
Activity: Planning to Build a Garage
Reproducibles for Section 4: Geometry
Construction Task Cards
Inscribing Regular Polygons in Circles
Exploring Dilations
Determining if Triangles Are Similar
Drawing Triangles Based on Angle Measures
Proving the Triangle Proportionality Theorem
Proving the Converse of the Triangle Proportionality Theorem
Proving the Pythagorean Theorem by Using Similar Triangles
Ratios of Sides in a Right Triangle
Problems and Solutions
Going 'Round in Circles
A Circle with Segments, Angles, and Triangles
Inscribed and Circumscribed Circles
Miguel's Derivations
Equations of a Circle
Steps for Deriving the Equation of a Parabola
Task Cards and Coordinates
Using Slopes to Write Equations
Endpoints and Ratios
Graphs, Perimeters, and Areas of Polygons
Finding Volume
Statements for the Cross-Sections and Rotations Game
Using Properties of Geometric Shapes to Find Area
Township Facts
Instructions for Drawing Figures
Transformation Tasks
Polygons
Transformations
Figures and Transformations
Figures and Images
Triangles, Sides, and Angles
Identifying Congruent Triangles
Proof Prompts
Finding the Missing Steps in Proofs about Triangles
Steps for Proving Theorems about Parallelograms
A Plot Plan
Section 5: Standards and Activities for Statistics and Probability
Interpreting Categorical and Quantitative Data
Activity: Representing Data
Activity: Comparing Two Different Data Sets
Activity: Interpreting Data Sets
Activity: Analyzing Test Scores
Activity: Making and Interpreting Two-Way Frequency Tables
Activity: Representing Data on a Scatter Plot
Activity: Identifying Slopes and Y-Intercepts
Activity: Computing and Interpreting the Correlation Coefficient
Activity: Determining Correlation and Causation
Making Inferences and Justifying Conclusions
Activity: Random Samples and Inferences
Activity: Simulations and Probability
Activity: Surveys, Experiments, and Observational Studies
Activity: Evaluating Sample Surveys and Simulations
Activity: Comparing Two Treatments
Activity: Evaluating Reports and Data
Conditional Probability and the Rules of Probability
Activity: Describing Events as Subsets
Activity: Identifying Events
Activity: Using Conditional Probability
Activity: Understanding Independence and Conditional Probability
Activity: Explaining Conditional Probability and Independence
Activity: Finding Conditional Probability
Activity: Using the Addition Rule
Reproducibles for Section 5: Statistics and Probability
Guidelines for Comparing Two Different Data Sets
Analysis Guidelines
Examples of Two-Way Frequency Tables
Survey Questions
Description, Data, Slope, and Y-Intercept Cards
Correlation and Causation Statements
Examples of Samples
Identifying Surveys, Experiments, and Observational Studies
A Sample Survey and Simulation Samples
Bean Plant Growth Chart
Beach Revenue Data
Subsets of a Sample Space
Independent and Dependent Events
Student Data on Exercising and Dieting
Considering Outcomes
Using the Addition Rule to Find Probabilities
Index
Section 1
Standards and Activities for Number and Quantity
The Real Number System
The real number system consists of rational and irrational numbers. It is sometimes referred to as the continuum of real numbers.
Rational numbers are the set of numbers that can be expressed in the form of , where a and b are integers, b ? 0. Examples include integers, finite decimals, and repeating decimals.
Irrational numbers are the set of numbers that cannot be written as terminating or repeating decimals. Examples include , p, and e.
N-RN.1
"Extend the properties of exponents to rational exponents."
- 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."
Activity: Understanding Integer and Rational Exponents
Students will complete statements that show how the meaning of rational exponents follows from extending the properties of integer exponents.
Materials
One copy of reproducible N-RN.1, "The Meaning of Rational Exponents," for each student.
Procedure
- Explain that the meaning of rational exponents follows from the properties of integer exponents. Review the properties of exponents. a and b are real numbers and m and n are integers.
- , , and .
- , , and , a ? 0.
- Explain that these properties can be extended to rational exponents as follows: , where a > 0 and m and n are integers, n > 0.
- Explain that some expressions that have rational exponents are rational numbers. Examples include , , and . Other expressions, such as and , are irrational numbers.
- Explain that the reproducible, when completed, provides an explanation of how the value of can be found using properties of exponents. Students are to complete the statements by selecting the correct expressions, which are shown at the bottom of the page. Note that the steps are sequential and each expression can be used only once.
Closure
Ask your students to summarize how they used the properties of exponents to complete the statements.
Answers
(1) (2) 2, , 16 (3) , , 8
N-RN.2
"Extend the properties of exponents to rational exponents."
- 2. "Rewrite expressions involving radicals and rational exponents using the properties of exponents."
Activity: Finding the Values of Expressions
Working individually or in pairs, students will identify the value of expressions in simplest form.
Materials
One copy of reproducible N-RN.2, "Equations and Their Values," for the class; scissors for the teacher.
Preparation
After making one copy of the reproducible, cut out each box (each containing an "I have" and "Who has?" statement) so that you have a total of 21 slips of paper. The slips are arranged in order on the reproducible, each providing a number that is the value of the expression written on the previous slip, except for the value of the last expression, which is written on the first slip. The original reproducible will serve as your answer key.
Procedure
- Mix the slips up and then distribute one slip of paper to each student or one slip to pairs of students. For a small class, you may give some students two slips. You must distribute all 21 slips.
- Explain that each slip has a number in its simplest form on the left and a term that can be simplified on the right. Start the activity by asking a student to read the term that is written on the right side of his slip. You may find it helpful to write this term on the board. All students then should check the number they have on the left side of their slip to find the value of the term. Because of the way the slips are designed, only one slip will contain a correct match. The student who has the slip with the correct answer should say, "I have . . .," and then provide the answer. If the student is correct, she then reads the term written on the right side of her slip. If she is incorrect, point out her error. Another student should then provide the correct answer, which is printed on the left side of his slip.
- Continue this procedure until the student who read the first term has a number that is equal to the value of the last term.
Closure
Ask your students for examples of other expressions that can be simplified to the same number. For example, , and it also equals . Ask why this is so.
N-RN.3
"Use properties of rational and irrational numbers."
- 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."
Activity: Sums and Properties of Rational and Irrational Numbers
This is a two-day activity. Students will work in pairs or groups of three. On the first day, students will place in sequence the steps for proving that the sum of two rational numbers is rational. On the second day, they will place in sequence the steps for proving that the sum of a rational number and an irrational number is irrational. They will also draw conclusions about the difference between two rational numbers as well as the product of a nonzero rational number and an irrational number.
Materials
Scissors; reproducibles N-RN.3, "Proving the Sum of Two Rational Numbers Is Rational," and N-RN.3, "Proving the Sum of Rational and Irrational Numbers Is Irrational," for each pair or group of students.
Procedure
Day One
- Distribute copies of reproducible N-RN.3, "Proving the Sum of Two Rational Numbers Is Rational," to each pair or group of students. Explain that the table shows how to prove that the sum of two rational numbers is rational. The table has five rows, each containing a statement and an explanation. The statements and explanations are correct, but the rows are out of order.
- Explain that students are to place the rows in the correct order. Suggest that they cut out each row, which will make it easier to arrange the rows correctly.
Closure
Discuss the proof. Ask your students what they can conclude about the difference of two rational numbers. (The difference of two rational numbers is a rational number.)
Answers
The sequence of some rows may vary; accept any sequence students can justify. One correct order of the rows follows: 2, 3, 5, 1, 4.
Procedure
Day two
- Hand out copies of reproducible N-RN.3, "Proving the Sum of Rational and Irrational Numbers Is Irrational," to each pair or group of students. Explain that the table shows how to prove that the sum of a rational number and an irrational number is irrational. This is a proof by contradiction that uses the fact that the difference of two rational numbers is rational, which was discussed during the closure on day one.
- Explain that this proof assumes that the sum of a rational number and an irrational number is rational, but a contradiction makes the assumption incorrect, leading to the conclusion that the sum of a rational number and an irrational number must be irrational.
- Explain that the table has seven rows; each row contains a statement and an explanation. The statements and explanations are correct, but the rows are out of order. Students are to place them in the proper order. Suggest that students cut out each row to make it easier to arrange the rows correctly.
Closure
Discuss the proof. Ask your students what they think is true about the product of a nonzero rational number and an irrational number based on their understanding of the sum of a rational number and an irrational number being irrational. (The product is an irrational number.)
Answers
The sequence of some rows may vary; accept any sequence students can justify. One correct order of the rows follows: 5, 3, 1, 4, 2, 7, 6.
Quantities
Quantities are numbers with units that involve measurement. Although in the lower grades students worked with units that addressed attributes such as length, width, height, and volume, in high school students work with other units of measurement that address a variety of problems in many different areas. Some examples include solving problems that involve measurement and acceleration, population density, per capita income, the miles per gallon rating of a car, or the energy consumption of household appliances.
N-Q.1
"Reason quantitatively and use units to solve problems."
- 1. "Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays."
Activity: A Recommendation for the Boss
This activity should be implemented over a few class periods. Students can also work outside of class. Working in groups of three to five, students...
