Math Task Cards - Creating Algebraic Equations Using Only Four Numbers

Are you ready to take your math skills to the next level? Solving algebraic math puzzles can help you hone your problem-solving skills, increase your analytical and critical thinking skills and boost your confidence in tackling difficult equations. Algebraic math puzzles are a great way to learn the fundamentals of algebra, strengthen your understanding of basic operations and apply core math concepts. 

Students need plenty of different opportunities to practice math in ways that both review and extend what they have learned. Because many of my remedial math college students (I call them mathphobics) lack problem solving skills or need practice, I use math task cards for them to complete individually or in pairs as an upfront focus activity. These math task cards rely on logic, mental math, and analytical skills and provide practice in building and creating equations while using PEMDAS. The goal is to expose students to various problem-solving strategies. 

Why task cards? Because task cards can target a specific math skill or concept while allowing the students to only focus on one problem at a time. This format prevents mathphobics from feeling overwhelmed and provides them a sense of accomplishment when a task is completed. Furthermore, the students are more engaged and often acquire a more in-depth understanding of the math concept. By trying new and different strategies and modifying their process, students will be more successful with each puzzle they solve.

The math task cards my students use contain two different math puzzles. The puzzles vary in difficulty from easy to challenging. Since there are easy, medium level and challenging puzzles, differentiation is made simple by choosing the level of difficulty appropriate for each student or team.

Each math puzzle is a square divided into four parts with a circle in the middle of the square. Each math puzzle contains four numbers, one in each corner of the square, with the answer in the circle. Using the four numbers, (each number must be used once) the student is to construct an equation that equals the answer contained in the circle. Students may use all four signs of operation (addition, subtraction, multiplication, division) or just one or two. In addition, each sign of operation may be used more than once. Parenthesis may be needed to create a true equation, and the Order of Operations (PEMDAS) must be followed.

Here is an example of what I mean. 

FREE

Were you able to figure out the puzzle, using all four numbers?

These task card or math puzzles can be used…

• At math centers
• As a math problem solving activity for students who finish early
• As enrichment work
• To give students extra practice with a math concept or skill
• As individual work
• In small groups
• As partner work

A free resource containing three such task cards is available at my TPT store.

I believe that math puzzles are key to getting students interested in mathematics, developing their skills, and creating an environment that makes learning enjoyable. So, let's unlock the door to learning with math puzzles and task cards!

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By the way, I didn't want to leave you without providing you with the answer to the above puzzle.  It is...

It Depends on the Angle - How to Distinguish between Complimentary and Supplementary Angles

My Basic Algebra Concepts class always does a brief chapter on geometry...my favorite to teach! We usually spend time working on angles and their definitions. My students always have difficulty distinguishing complimentary from supplementary angles. Since most of my students are visual learners, I had to come up with something that would help them to distinguish between the two.

The definition states that complementary angles are any two angles whose sum is 90°. (The angles do not have to be next to each other to be complementary.) As seen in the diagram on the left, a 30° angle + a 60° angle = 90° so they are complementary angles. Notice that the two angles form a right angle or 1/4 of a circle.

If I write the word complementary and change the first letter "C" into the number nine and I think of the letter "O" as the number zero, I have a memory trick my mathematical brain can remember.

Supplementary Angles are two angles whose sum is 180°. Again, the two angles do not have to be together to be supplementary, just so long as the total is 180 degrees. In the illustration on your right, a 110° angle + a 70° angle = 180°; so, they are supplementary angles. Together, they form a straight angle or 1/2 of a circle.

If I write the word supplementary and alter the "S" so it looks like an 8, I can mentally imagine 180°.

Since there are so many puns for geometric terms. I have to share a bit of geometry humor. (My students endure many geometry jokes!)

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You might be interested in a variety of hands-on ideas on how to introduce angles to your students. Check out Having Fun With Angles.  It explains how to construct different kinds of angles (acute, obtuse, right, straight) using items such as coffee filters, plastic plates, and your fingers. Each item or manipulative is inexpensive, easy to make, and simple for students to use. All of the activities are hands-on and work well for kinesthetic, logical, spatial, and/or visual learners.

Does Such a Thing as a Left Angle Exist?

Geometry is probably my favorite part of math to teach because it is so visual; plus the subject lends itself to doing many hands-on activities, even with my college students.  When our unit on points, lines and angles is finished, it is time for the unit test.  Almost every year I ask the following question:  What is a left angle?   Much to my chagrin, here are some of the responses I have received over the years NONE of which are true!

1)   A left angle is the opposite of a right angle.

2)  On a clock, 3:00 o'clock is a right angle, but 9:00 o'clock is a left angle.

3)  A left angle is when the base ray is pointing left instead of right.

    4)      A left angle is 1/2 of a straight angle, like when it is cut into two pieces, only it is the part on the left, not the part on the right.

5)      A left angle is 1/4 of a circle, but just certain parts. Here is what I mean.

Now you know why math teachers, at times, want to pull their hair out!  Just to set the record straight, in case any of my students are reading this, there is no such thing as a left angle!  No matter which way the base ray is pointing, any angle that contains 90^○ is called a right angle.

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If you would like some different hands-on ways to teach angles, you might look at the resource entitled, Angles: Hands-on Activities.  This resource explains how to construct different kinds of angles (acute, obtuse, right, straight) using items such as coffee filters, plastic plates, and your fingers. Each item or manipulative is inexpensive, easy to make, and simple for students to use. All of the activities are hands-on and work well for kinesthetic, logical, spatial, and/or visual learners.

                                      

Playing Math Games with older students

I currently teach remedial math students on the college level. These are the students who fail to pass the math placement test to enroll in College Algebra - that dreaded class that everyone must pass to graduate. The math curriculum at our community college starts with Basic Math, moves to Fractions, Decimals and Percents, and then to Basic Algebra Concepts. Most of my students are intelligent and want to learn, but they are deeply afraid of math. I refer to them as mathphobics.

We all have this type of student in our classrooms, whether it is middle school, high school, or college. When working with this type of student, it is important to bear in mind how all students learn. I always refer back to the Conceptual Development Model which states that a student must first learn at the concrete stage (use manipulatives) prior to moving to the pictorial stage, and in advance of the abstract level (the book). This means that lessons must include the use of different manipulatives. I use games a great deal because it is an easy way to introduce and use manipulatives without making the student feel like “a little kid.” I can also control the level of mathematical difficulty by varying the rules; thus, customizing the game to meet the instructional objectives my students are learning. However, as with any classroom activity, teachers should monitor and assess the effectiveness of the games.

When using games, other issues to think about are:

1) Excessive competition. The game is to be enjoyable, not a “fight to the death”.

2) Mastery of the mathematical concepts necessary for successful play. Mastery should be at an above average level unless teacher assistance is readily available when needed. A game should not be played if a concept has just been introduced.

3) Difficulty of the rules. If necessary, the rules should be modified or altered in order that the students will do well.

4) Physical requirements (students with special needs). These should be taken into account so that every player has an opportunity to win.

In addition to strengthening content knowledge, math games encourage students to develop such skills as staying on task, cooperating with others, and organization. Games also allow students to review mathematical concepts without the risk of being called “stupid”. Furthermore, students benefit from observing others solve and explain math problems using different strategies.

Games can also….

1. Pique student interest and participation in math practice and review.
2. Provide immediate feedback for the teacher. (i.e. Who is still having difficulty with a concept? Who needs verbal assurance? Why is a student continually getting the wrong answer?)
3. Encourage and engage even the most reluctant student.
4. Enhance opportunities to respond correctly.
5. Reinforce or support a positive attitude or viewpoint of mathematics.
6. Let students test new problem solving strategies without the fear of failing.
7. Stimulate logical reasoning.
8. Require critical thinking skills.
9. Allow the student to use trial and error strategies.

Mathematical games give the learner numerous opportunities to reinforce current knowledge and to try out strategies or techniques without the worry of getting the “wrong” answer. Games provide students of any age with a non-threatening environment for seeing incorrect solutions, not as mistakes, but as steps towards finding the correct mathematical solution.

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One math game my students truly enjoy playing is Bug Mania.  It provides motivation for the learner to practice addition, subtraction, and multiplication using positive and negative numbers. The games are simple to individualize since not every pair of students must use the same cubes or have the same objective. Since the goal for each game is determined by the instructor, the time required to play varies. It is always one that my students are anxious to play again and again!