Looking For and Analyzing Mathematical Patterns

Mathematics is the science of patterns.  In this post, I want to target some mathematical problems in which we investigate developing patterns.

In the first example below, you will notice we begin by multiplying one by one; then 11 by 11, and so forth. Each time we multiply, the number of digits in the multiplier and the multiplicand increases. Do you see the pattern that progresses in the answer (product)? Notice how this multiplication pattern forms a triangle? Can you figure out what kind of triangle this would be if we added a "peak" or a row at the top?

Here is another interesting pattern. In this one, instead of multiplying by 1, then 11, then 111, the answer (product) looks like the multiplier in the pattern above. Do you notice anything else significant?

Yes, we are multiplying by 9 each time. Now look at the number being added, and count the number of ones you see in each answer. Surprised? Isn’t it amazing how math is ordered, methodical and precise? Maybe that is one reason I love to teach it! Encourage your students to look for and make sense of math patterns and structure in order to deepen their mathematical understanding and retain what they learn.

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!

_________________________________________________________

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