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20 Math Critical Thinking Questions to Ask in Class Tomorrow

• November 20, 2023

The level of apathy towards math is only increasing as each year passes and it’s up to us as teachers to make math class more meaningful . This list of math critical thinking questions will give you a quick starting point for getting your students to think deeper about any concept or problem. 

Since artificial intelligence has basically changed schooling as we once knew it, I’ve seen a lot of districts and teachers looking for ways to lean into AI rather than run from it.

The idea of memorizing formulas and regurgitating information for a test is becoming more obsolete. We can now teach our students how to use their resources to make educated decisions and solve more complex problems.

With that in mind, teachers have more opportunities to get their students thinking about the why rather than the how.

Table of Contents

Looking for more about critical thinking skills? Check out these blog posts:

• Why You Need to Be Teaching Writing in Math Class Today
• How to Teach Problem Solving for Mathematics
• Turn the Bloom’s Taxonomy Verbs into Engaging Math Activities

What skills do we actually want to teach our students?

As professionals, we talk a lot about transferable skills that can be valuable in multiple jobs, such as leadership, event planning, or effective communication. The same can be said for high school students. 

It’s important to think about the skills that we want them to have before they are catapulted into the adult world. 

Do you want them to be able to collaborate and communicate effectively with their peers? Maybe you would prefer that they can articulate their thoughts in a way that makes sense to someone who knows nothing about the topic.

Whatever you decide are the most essential skills your students should learn, make sure to add them into your lesson objectives.

When should I ask these math critical thinking questions?

Critical thinking doesn’t have to be complex or fill an entire lesson. There are simple ways that you can start adding these types of questions into your lessons daily!

Start small

Add specific math critical thinking questions to your warm up or exit ticket routine. This is a great way to start or end your class because your students will be able to quickly show you what they understand. 

Asking deeper questions at the beginning of your class can end up leading to really great discussions and get your students talking about math.

Add critical thinking questions to word problems

Word problems and real-life applications are the perfect place to add in critical thinking questions. Real-world applications offer a more choose-your-own-adventure style assignment where your students can expand on their thought processes. 

They also allow your students to get creative and think outside of the box. These problem-solving skills play a critical role in helping your students develop critical thinking abilities.

Keep reading for math critical thinking questions that can be applied to any subject or topic!

When you want your students to defend their answers.

• Explain the steps you took to solve this problem
• How do you know that your answer is correct?
• Draw a diagram to prove your solution.
• Is there a different way to solve this problem besides the one you used?
• How would you explain _______________ to a student in the grade below you?
• Why does this strategy work?
• Use evidence from the problem/data to defend your answer in complete sentences.

When you want your students to justify their opinions

• What do you think will happen when ______?
• Do you agree/disagree with _______?
• What are the similarities and differences between ________ and __________?
• What suggestions would you give to this student?
• What is the most efficient way to solve this problem?
• How did you decide on your first step for solving this problem?

When you want your students to think outside of the box

• How can ______________ be used in the real world?
• What might be a common error that a student could make when solving this problem?
• How is _____________ topic similar to _______________ (previous topic)?
• What examples can you think of that would not work with this problem solving method?
• What would happen if __________ changed?
• Create your own problem that would give a solution of ______________.
• What other math skills did you need to use to solve this problem?

Let’s Recap:

• Rather than running from AI, help your students use it as a tool to expand their thinking.
• Identify a few transferable skills that you want your students to learn and make a goal for how you can help them develop these skills.
• Add critical thinking questions to your daily warm ups or exit tickets.
• Ask your students to explain their thinking when solving a word problem.
• Get a free sample of my Algebra 1 critical thinking questions ↓

7 thoughts on “20 Math Critical Thinking Questions to Ask in Class Tomorrow”

I would love to see your free math writing prompts, but there is no place for me to sign up. thank you

Ahh sorry about that! I just updated the button link!

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Algebra I is a course designed to give students a firm understanding of mathematical equations that involve variables, as well as to teach them the basics of graphing and manipulating simple functions. Students typically take Algebra I around eighth or ninth grade, though some may take the class earlier or later, after they have had a course in Pre-Algebra, but before attempting such topics as Algebra II, Geometry, or more difficult math classes. By establishing solid footing in Algebra I, students can prepare themselves for success in later math and science courses, all of which assume knowledge of algebraic concepts. Whether you need  top Algebra 1 tutors in Boston ,  Algebra 1 tutors in Detroit , or  top Algebra 1 tutors in Dallas Fort Worth , working with a pro may take your studies to the next level. Typically, the first thing students learn how to do in Algebra I is solve a single-variable equation—that is, an equation in which there is only one variable, “x.” Students then learn to graph linear functions in the “y = mx + b” format; this part of the course introduces the concepts of slope, y-intercept, and x-intercept, and teaches students to graph linear equations. A major part of Algebra I is learning to convert information from equations to graphs and from graphs to equations, and understanding how to analyze equations and graphs as related concepts is a core part of the course. For instance, certain problems in Algebra I may present students with two points on a coordinate plane, then ask them to find the equation of the line that connects the two points, determining the equations of lines that are parallel and perpendicular to that line, respectively. Varsity Tutors offers resources like  free Algebra 1 Diagnostic Tests  to help with your self-paced study, or you may want to consider an  Algebra 1 tutor . Inequalities are also taught in Algebra I in the same manner as equations—that is, with an emphasis on representing them on number lines or graphing them. After learning to solve and graph simple linear functions and inequalities, students learn how to solve systems of equations or inequalities using substitution and elimination techniques. Once students have mastered linear equations, the class moves on to tackle quadratic equations, the graphs of which form parabolas. Algebra I focuses on solving quadratic functions using the quadratic formula and FOIL, as well as graphing parabolas and manipulating their appearance through changes made to the source equation. Other concepts that may be introduced at various points within Algebra I classes are statistics and probability, percent, and percent change. While not directly related to the overarching ideas of equations, functions, and graphs, these concepts may be taught in a way that mirrors the back-and-forth logic used to teach students about functions and their graphs. For instance, a focus when learning percents is how to convert a percent to a decimal and vice versa, and when expressing the probability of an event occurring, students also necessarily figure out the probability of the event not occurring. The mathematical concepts that students master in Algebra I form the core of their mathematical understanding in many later classes in math and the sciences. For this reason, it is crucial that students gain a solid understanding of algebraic concepts before proceeding to higher-level math classes. If you’d like to start learning or reviewing Algebra I material right now, you can use Varsity Tutors’ free Algebra I Practice Tests to do so. Each twelve-question Practice Test is given like a short multiple-choice quiz touching on many concepts that are taught in Algebra I classes. After completing a quiz, you not only get to see your raw score, but also how your score stacks up against others’ scores on a question-by-question basis. This can provide some solace if you miss problems that others also found extremely difficult, or some motivation if you notice that you miss questions others found to be easy. All of Varsity Tutors’ Algebra I questions also come with complete explanations, so you can learn from questions that you get wrong. In addition to the Algebra 1 Practice Tests and  Algebra 1 tutoring , you may also want to consider taking some of our  Algebra 1 Flashcards . You might also like to kick off the review process by taking a free Full-Length Algebra I Practice Test. The extended format of these practice tests can aid you in discovering your current proficiency level and test-taking pace. After you finish the test, the results page will provide you with the same informative metrics, thorough explanations, and additional review resources offered by the concept-specific Practice Tests. These online practice tests can also help you fine-tune your customized Algebra I study plan by showing you which concepts need the most attention. After you spend some time on review, you can assess your progress by returning to take another Full-Length Algebra I Practice Test. By using Varsity Tutors’ free Algebra I Practice Tests and other free Algebra I resources, you can bolster your Algebra I knowledge and master the subject’s content in no time! This will give you a great foundation for the mathematical and scientific knowledge you will gain in future courses.  

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Algebra 1 Topics and Concepts

• The Albert Team
• Last Updated On: March 1, 2022

Looking for all the topics in Algebra 1? 

Algebra 1 is a math course exploring how to use variables, numbers, and mathematical operations to solve problems.  Explore below for a list of all Algebra 1 topics, a summary of the typical Algebra 1 course, and a discussion of what makes  Algebra 1 unique.

What We Review

What topics are in Algebra 1?

The below sequence of themes, concepts, and skills covers all of the most commonly taught Algebra 1 topics. As a bonus, many of the topics include links directly to Albert’s  Algebra 1 practice problems .

• Parts of an Expression
• Combining Like Terms
• Simplify and Evaluate Expressions
• Equivalent Expressions
• Algebraic Fractions
• Complex Fractions
• Exponent Laws and Notation
• Simplify Roots
• Radical Laws and Notation
• Rational Exponents
• Rationalize Denominators
• Polynomial Operations
• Interpret Expression Structure
• Factorization Procedures
• Factor Polynomials
• Units and Quantitative Reasoning
• One-Step Equations
• Two-Step Equations
• Multi-Step Equations
• The Coordinate Plane
• Understand Slope
• Slope-Intercept Form
• Point-Slope Form
• Standard Form
• Transformations of Linear Functions
• Parallel Lines
• Perpendicular Lines
• Understand Inequalities
• One-Step Inequalities
• Two-Step Inequalities
• Multi-Step Inequalities
• Compound Inequalities
• Linear Inequalities: Solve and Graph
• Linear Inequalities: Write and Apply
• Understand Systems of Equations
• Solve Systems of Equations
• Systems of Inequalities
• Understand Functions
• Function Notation
• Interpret and Model Functions
• Operations on Functions
• Composite Functions
• Inverse Functions
• Arithmetic Sequences
• Geometric Sequences
• Mixed Sequences
• Recursive Formulas for Sequences
• Exponential Growth and Decay
• Exponential Functions
• Piecewise Functions
• Absolute Value and Step Functions
• Function Transformations
• Explore Quadratic Functions
• Factored Form
• Vertex Form
• Understand Solving Quadratics or Polynomials
• Solve Quadratics: Factoring
• Solve Quadratics: Complete the Square
• Solve Quadratics: Graphing
• Solve Quadratics: Quadratic Formula
• Irrational Numbers
• Represent Data
• One-Variable Statistics
• Standard Deviation
• Two-Way Tables
• Scatter Plots

What is Algebra 1?

Algebra 1 is a high school math course exploring how to use letters (called variables) and numbers with mathematical symbols to solve problems.

Algebra 1 typically includes evaluating expressions, writing equations, graphing functions, solving quadratics, and understanding inequalities. Algebra 1 focuses on a variety of different types of functions such as linear, quadratic, and cubic — all of which are represented in traditional “function notation” as well as graphed on the coordinate plane.

Students in Algebra 1 typically build conceptual understanding and gain procedural fluency of concepts that are required for more advanced math subjects such as Geometry and Calculus. Abstracting real-life situations into mathematical models (expressions, equations, functions) is a key part of success in Algebra 1.

What grade is Algebra 1?

Algebra 1 is typically taught late in middle school or early in high school .

In the United States, 9th grade (freshman year) seems to be the most common grade for students to take an Algebra 1 class. Some high schools also offer Algebra 1 to 10th graders.

On the other end of the spectrum, many middle schools offer students an Algebra 1 course as early as 8th grade or even 7th grade for more advanced math students.

Is Algebra 1 hard?

It’s impossible to say exactly how easy or difficult Algebra 1 for each individual student. Students who have a strong background in middle school math topics (fractions, decimals, ratios, percents, negative numbers) should find an Algebra 1 course relatively accessible.

However, for many students, Algebra 1 will be quite a difficult challenge.

In Algebra 1, there are dozens of quickly-moving topics and skills that build on each other as the curriculum progresses. Having strong arithmetic skills is an incredibly important prerequisite for gaining confidence in an Algebra 1 course. If a student starts to get slightly behind on a specific concept, it’s likely those misconceptions will build into further confusion rather quickly.

If you’re looking for student practice at a wide range of difficulty levels, consider trying Albert’s Algebra 1 practice questions.

What is the difference between Algebra 1 and 2?

As the names suggest, there are many core similarities between Algebra 1 and Algebra 2. Both courses work extensively with variables and functions as well as using mathematical operations to find unknown quantities.

Students in Algebra 1 are typically expected to gain mastery of a wide variety of techniques for solving linear and quadratic equations. Algebra 1 focuses on “doing the same thing to both sides of the equation” to solve equations. With the lens of linear and quadratic functions, Algebra 1 pushes students to find roots (solutions) leveraging multiple methods (including the quadratic formula ), graph function relationships on the coordinate plane, and convert among various forms of quadratics .

Algebra 2 is an advanced expansion of the ideas from Algebra 1. Students in Algebra 2 are introduced to a much wider range of functions including logarithms, radicals, and rational functions. Trigonometric functions often become an important new focus area during Algebra 2 as students begin exploring the unit circle. Algebra 2 typically includes solutions with real and complex numbers — including arithmetic with imaginary numbers — as well as conic sections such as hyperbolas, parabolas, and ellipses. Basic parabolas that students used to think had no solutions during Algebra 1 are actually revealed to have two “imaginary” solutions in Algebra 2.

In general, Algebra 2 includes a wider and more intricate variety of function types than those covered in Algebra 1 topics. 

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Unit 1: Algebraic thinking

Writing expressions.

• Constructing numerical expressions (Opens a modal)
• Evaluating expressions with & without parentheses (Opens a modal)
• Translating expressions with parentheses (Opens a modal)
• Evaluate expressions with parentheses Get 5 of 7 questions to level up!
• Translate expressions with parentheses Get 3 of 4 questions to level up!
• Create expressions with parentheses Get 3 of 4 questions to level up!

Number patterns

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• Interpreting relationships in ordered pairs (Opens a modal)
• Graphing sequence relationships (Opens a modal)
• Rules that relate 2 variables Get 3 of 4 questions to level up!
• Tables from rules that relate 2 variables Get 5 of 7 questions to level up!
• Graphs of rules that relate 2 variables Get 3 of 4 questions to level up!
• Relationships between 2 patterns Get 3 of 4 questions to level up!

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Understanding Algebra I

Understanding Algebra I is part of the Mathematical Reasoning series for elementary grades which is among my Top Picks. It can be used as a high school level algebra course, but it should also be excellent for junior high students who are ready to tackle algebra.

It is available in print or as an ebook. While it is not as colorful or as heavily illustrated as the books for the younger grade levels, it has more color and illustrations than most first-year algebra texts. It has 318 pages of text plus a 36-page answer key. A free solutions PDF is available from the publisher.

It seems to be a more user-friendly course than some others. Explanations are thorough, sometimes including illustrations, graphics, and charts. A few lessons in the unit on polynomials even show how tiles (or Base Ten Blocks or similar manipulatives that include squares that can represent x 2) can be used to demonstrate multiplication of binomials. Lessons are written directly to the student, so no teaching is required.

Lessons cover the same essential content as most algebra 1 courses: sets, operations, properties, evaluating expressions, solving equations, applying algebra in words problems, inequalities, polynomials, factoring, radicals, various types of functions, quadratic equations, the quadratic formula, and various ways of solving systems of equations and inequalities.

Some lessons teach calculator usage with step-by-step directions, but they point out when calculators are useful and do not force students to rely only on the calculator.

Just as in the other Mathematical Reasoning courses, there are many word problems (e.g., time/rate/distance problems, consecutive integer problems, coin problems, and percent and ratio problems) with extensive teaching on strategies to use plus plenty of practical application and critical thinking activities. Many exercises challenge students to find and explain errors in problem solving while others ask students to explain their thinking. The chapters on word problems are particularly useful for test preparation since they present the types of word problems commonly encountered on standardized tests.

While I very much like Understanding Algebra I for its style of presentation, it lacks two important features: cumulative review and tests. Chapter questions only address topics taught in each chapter. You can try to fill these gaps with free online resources. I found a few with a quick search, but there are certainly many other options. Mathopolis has free practice problems but only for selected topics while math.com has a free worksheet generator (with answer keys) that will present various types of problems that you can select. Varsity Tutors offers free online practice tests that are scored by the computer. While none of these correlates exactly with Understanding Algebra I , they (or similar sites) might provide cumulative review and tests sufficient for your purposes.

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When comparison prices appear, please keep in mind that they are subject to change. Click on links where available to verify price accuracy.

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10 Brilliant Math Brain Teasers

Tap into rigorous problem-solving and critical thinking with these playful math brain teasers for middle and high school students.  

To break the ice during the first few awkward moments of class in the new school year, high school math teacher Lorenzo Robinson uses an unusual strategy: He reads his students’ minds.

Here’s how the mystical feat unfolds: Each student picks a number between 1 and 100. Next, they use calculators to add, subtract, multiply, and divide their way through a set of predetermined numbers. At the end, everyone ends up with the same answer: 427. Robinson isn’t psychic, of course, but because the mechanics of the teaser are always the same, regardless of which initial numbers his students select, he’s able to correctly “guess” their final result—much to their amazement. 

Starting off the lesson with a math brain teaser sets a playful tone and lowers the stakes for kids, “generating a buzz around my class,” Robinson says. “It makes students feel as though this class is not going to be scary, it’s going to be interesting. ‘We’re going to be learning, but we’re also going to have some fun.’” 

Robinson thinks of math brain teasers as a variation on brain breaks —a brief respite from dense curricular material that gives kids time to pause and process. They can also provide an opportunity to build relationships and community as kids put their heads together to find solutions. Good brain teasers can be sneaky: They get kids developing problem-solving and critical thinking skills. 

Meanwhile, before introducing a new one, Robinson works through the problem himself, identifying questions that students might have along the way and making sure his class has the background knowledge to understand how the teaser works. It’s important, he says, to provide a few minutes for kids to examine and discuss the teaser. Ask them to observe, highlight, and share things that stand out. 

“The most powerful reaction is when a kid doesn’t get the correct answer,” Robinson says, and they ask to try the problem again. “They want to feel what the other kids are feeling, that educational euphoria. They want to do it again because they want to be right.” That organic intellectual curiosity is hugely helpful in high school math, Robinson says, because it can be “parlayed into the other stuff that we do.”

We combed through dozens of math brain teasers to find 10 good ones—including several of Robinson’s tried-and-true favorites.  

Number Magic: I’ll Bet Your Number is… 427

• Start by having students pick any number between 1 and 100. 
• Add 28. 
• Multiply that number by 6. 
• Subtract 3. 
• Divide that number by 3. 
• Subtract 3 more than your original number. 
• Add 8. 
• Subtract 1 less than your original number. 
• Multiply that number by 7. 

And voilà, you’ll correctly identify each student’s final result as 427. Courtesy of: Lorenzo Robinson  

Can Your Shoe Size Tell Your Age? 

• Start with your shoe size. If you are a half size—for example, size 8.5—round up to 9.
• Multiply your shoe size by 5. 
• Add 50. 
• Multiply that number by 20. 
• Subtract the year you were born—for example, 1991. Add 1 if you already had your birthday this year. 

The first digit(s) are your shoe size, and the last two digits are your age.  Courtesy of: Lorenzo Robinson.  

Cutting Across a Cross

Ask students to draw a cross on a sheet of paper. Drawing one on the board as a point of reference is helpful. Next, ask students to draw two straight lines that will segment or cut the cross into pieces. The goal is to produce the most pieces.

The solution can be found here .  Sourced from: MathisFun.com .

Number Magic: I’ll Bet Your Final Number is… 5  

• Start with a positive number. Students shouldn’t say the number out loud.
• Square that number. 
• Add 10x the original number to what you have now. 
• Add 25 to the result of the previous step. 
• Now take the square root of that number, rounding to the nearest whole number. 
• Subtract your original number.
• Before students share their final figure, reveal that you guess their collective result is 5. 

Courtesy of: Lorenzo Robinson.

Birthday Math 

Have students work in pairs and share the following instructions with their partner:

• Start with the number 7.
• Multiply that by the month of your birth. For example, if you were born in September, you’d use the number 9 to represent your birth month. 
• Subtract 1. 
• Multiply that number by 13. 
• Add the day of your birth. 
• Add 3. 
• Multiply that number by 11. 
• Subtract the month of your birth. 
• Subtract the day of your birth. 
• Divide by 10.
• Add 11 to that number. 
• Divide by 100. 

The result on the calculator screen should be their partner’s birthday.  Sourced from: Dr. Mike’s Math Games for Kids .

Coin Conundrum

Ask students to imagine that they have two coins that total 30 cents in value. Have them try to figure out what the two coins are, only providing them with a singular piece of information: One of the coins is not a nickel. The answer: A quarter and a nickel. (Only one of the coins is not a nickel.)

Sourced from: WeAreTeachers .

The Phone Number Trick  

• Ignoring your area code, type the first three digits of your phone number into a calculator.
• Multiply that number by 80. 
• Add 1. 
• Multiply that number by 250. 
• Add the last four digits of your phone number. 
• Add the last four digits of your phone number again. 
• Subtract 250. 
• Divide this number by 2. Do you recognize your phone number?

Courtesy of: Lorenzo Robinson. 

A Number Challenge

For a slightly more independent teaser, challenge students to produce a math equation that works using these four numbers—2, 3, 4, and 5—as well as a plus (+) and equal sign (=). Students can work individually, in pairs, or in small groups as they try to create a valid equation. The answer: 2 + 5 = 3 + 4.

Sourced from: WeAreTeachers .  

Math Mind Reader 

Students can work in pairs with this teaser. One person will start off by holding the calculator so their partner cannot see it; the other person can read the steps aloud to the partner with the calculator. 

• The student with the calculator starts by choosing a whole number from 1 to 20 and writing it down on a piece of paper without letting their partner see it. 
• Next, the student with the calculator enters their secret number into the calculator. 
• Multiply that number by 3. 
• Add the secret number, then subtract 5. 
• Multiply by 3, then multiply by 3 again. 
• Add the secret number, then subtract the number of their favorite month (you don’t have to know what month it is). For example, 9 represents the ninth month of the year, September. 
• Multiply by 3, then multiply by 3 again, and then again a third time. 
• Add the secret number, then subtract their favorite day of the month (again, you don’t have to know what it is on your end). 
• Ask them to show the non-calculator partner the result. At this stage, the non-calculator partner can guess the original secret number, even though what appears on the screen may be a very large number. 

If the result is negative, their secret number is 1.

If the result has only three digits, their secret number is 2.

In all other cases, ignore the last three digits, and then add 2 to get the secret number! 

Sourced from: Dr. Mike’s Math Games for Kids .

What’s Unique About This Number?

After writing the number 8,549,176,320 on the board, ask students to observe the number and tell you everything they think is unique about the number.

Answer: It is the digits 0 to 9 in alphabetical order (eight, five, four, nine, one, seven, six, three, two, zero), but it’s surprising and fun to see what students come up with. This number can also be evenly divided by the digits 1 through 9 except for the number 7, for example. 

Sourced from: MathisFun.com . 

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Understanding Algebra 1 by The Critical Thinking Co.™

Disclosure: I received this complimentary product through the Homeschool Review Crew.

Today’s review features a detailed look at the Understanding Algebra I  workbook by The Critical Thinking Co.™ . This is a one-year course for students in grades 7th, 8th, or 9th grade. This soft-cover workbook has 384-pages, is perforated for easy removal, and includes detailed explanations of algebraic concepts. Examples, practice questions, enrichment problems, chapter reviews, a glossary, an answer key, and a final exam are also included.

Understanding Algebra I  was written by Terri Husted, a member of the National Council of Teachers of Mathematics with over 30 years of experience in education. She has also authored other popular The Critical Thinking Co.™ books. Each chapter begins with a detailed description of the concept and step-by-step teaching to solve the problems. Bold fonts show vocabulary, colored graphics note important functions, and charts. These components are a nice feature, even for older students, because it helps show important things that will be on the Chapter Review or Final Exam.

Course Contents

• Set and Set Notation
• Number Lines
• Expressions
• Inequalities
• Word Problem
• Percent Problems
• Ratio Problems
• Motion Problems 
• Work Problems
• Absolute Value
• Polynomials
• Linear Functions
• Elimination
• Substitution
• Algebraic Fractions

Understanding Algebra I  by The Critical Thinking Co.™ is an extremely user-friendly workbook. The layout makes it easy to use, review concepts, find definitions, and even view solutions. As a complete curriculum, your high school child can earn math credit after completing this book. We suggest using the Chapter Reviews as tests and having the Final Exam worth more during the end of the year grade calculation. This book can also be used as a supplement to help your student through a different Algebra I course. Either way, this course provides students with a strong foundation for higher-level math success.

Want to learn how other families used this in their homes? Check out the Crew by tapping the photo below!

Visit The Critical Thinking Co.™

• The Critical Thinking Co.™
• Understanding Algebra I

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Algebra Word Problems

Foolproof problem-solving strategies, instruction & guided practice.

Grades: 7-12+

Mathematics

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These highly-effective, step-by-step books teach students general and specific strategies to attack algebra word problems. Each lesson includes plenty of practice problems and there is a clear, detailed solution for every problem. This step-by-step approach (see contents below) has helped thousands of students master algebra word problems. Book 1 Contents      •  How to Solve Algebra Word Problems          - Many Verbs Can be Replaced by “=”          - Think About What Your Equations Say          - Take the Problem Step-by-Step          - Check Your Solutions          - Think About the Nature of the Thing the Problem Talks About          - Use Your Common Sense          - If All Else Fails, Try the “Wild Guess” Method      •  Warm-Up Problems          - Ages          - Coins          - Measurements          - Numbers          - Work Rates          - Mixtures          - Interest          - Miscellaneous      •  Problems          - Ages          - Coins          - Mixtures          - Formulas          - Rectangles          - D = rt          - Percent          - Work Rates          - Miscellaneous      •  Teaching Suggestions      •  Detailed Solutions Book 2 Contents      •  Miscellaneous 1 (Equations with 2 variables)      •  Miscellaneous 2 (Equations with 3 variables)      •  Diophantine Problems      •  Fun Time      •  Detailed Solutions

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