By Jeff Twiddy Rational functions are a cornerstone of precalculus, appearing in various real-life scenarios. In essence, a rational function is any function that can be written as the quotient of two polynomials. That is, if where both P(x) and Q(x) are polynomials and Q(x) ≠0, thenf(x) is a rational function. This article will not only review […]
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Continuity, End Behavior, and Limits: A Fun & Engaging Pre-Calculus Lesson
By Jeff Twiddy Pre-calculus doesn’t have to be intimidating! In this lesson, you’ll discover how continuity, end behaviors, and limits interconnect through intuitive “if this, then that” scenarios that make learning fun and interactive. Unlocking the Mystery Behind Functions Understanding the behavior of functions can be both insightful and exciting. By exploring continuity, end behavior, […]
Mastering Operations with Complex Numbers: An Easy Pre-Calculus Lesson
By Jeff Twiddy The title might sound intimidating at first—but don’t worry! Despite its name, this lesson on operations with complex numbers is designed to be one of the most accessible and confidence-boosting topics in pre-calculus. With the right approach, both you and your students will quickly see that complex numbers are less about complexity, […]
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Preparing for Standardized Math Tests
As students progress through their academic journey, they will eventually be faced with standardized tests. These tests play a crucial role in determining a student’s academic progress and potential future opportunities. One subject that is heavily emphasized in standardized tests is math. In this article, we will explore some tips and strategies for 7th-grade students […]
Building Problem-solving Skills for 7th-Grade Math
Mathematics is a subject that requires problem-solving skills to excel. In 7th grade, students begin to encounter more complex math concepts, and the ability to analyze and solve problems becomes increasingly important. Building problem-solving skills for math not only helps students to master math concepts but also prepares them for success in higher-level math courses […]
Get Outside! Measuring Side Lengths to Determine the Perimeter of Polygons
Whether inside or outside the house, we travel different distances. We commute, we travel, we drive. We go to all sorts of places through straight paths or zigzags, or around something. The simplest act we do to go somewhere is to walk. Walking is something common that almost all of us can and know how […]
Creating a Ruler with 1 Inch, ½ Inch, and ¼ Inch Intervals
A ruler is a handy measuring device for getting length measurements either in the metric system or customary system. I am pretty sure that if you ask your students the contents of their pencil case or their school kit, a ruler is a necessity together with the pens, pencils, erasers, and scissors. You’d think that […]
Placing Fractions on a Number Line using Pizza Slices
When teaching fractions, students may still be confused in understanding the size of fractions. A child may be intimidated that fractions are composed of different numbers and symbols to represent one value, when until now, numbers have been whole. But we’ve got a great way for placing fractions on a number line by using something […]
Find and Identify Angles in the Real World
How are Angles Used in the Real World? Angles are everywhere! It’s great to have an angle hunt or to search for angles in the real world because students and teachers start to see angles that they may not have noticed before. When you look for angles in objects, you can find patterns and see […]
Money as Decimals
Money is a great way to learn about decimals. Students have learned the value of coins and they have seen prices in stores and online. Money is a real world use of decimals and it’s important to show how it works with place value. After understanding place value with coins, I thought it was […]
Factors and Multiples: The Factor Factory Activity
Factors and Multiples When I taught fifth grade, my school had a meeting with incoming fourth graders and their parents. Some of the most asked questions had to do with math and multiplication facts. I remember telling them that it’s not just knowing your times tables, what’s more important is being able to recognize factors […]
Subtraction Involving Mixed Numbers
Subtraction Involving Mixed Numbers The great thing about subtracting fractions (Specifically Subtraction Involving Mixed Numbers) is that we have the opportunity to cut up the “wholes” into the number of pieces we need! Fractions can be tough because students see the numbers and don’t always think about the value of the fraction. I like to […]
Mean and Median Climate Activity
Mean and Median When I first start to teach measures of central tendency and compare mean and median, finding the median can be fun! Some students think that calculating the average and figuring out the mean is just a bit more… mean. But if we do some games and activities, my students start to find […]
Multiplying 3 and 4 digit Numbers using Area Models
Multiplying 3 and 4 digit Numbers using Area Models Multiplying multi-digit numbers using area not only helps students to visualize the products, but also helps show them how partial products work and add up. This can help students learn and understand multiplication as well as apply it to the standard algorithm for multiplication. In this […]
Composition and Decomposition of Polygons
Composition and Decomposition of Polygons Years ago, I had my bathroom redone. The man that came in to do the tiling was quiet, meticulous, patient and efficient. I live in an old house and was amazed at how he placed those tiles and got them to fit perfectly, even though the walls were not always […]
Graphing Inequalities with Cheerios
Graphing Inequalities When I start working with graphing inequalities with my students, and show the symbol <, there is almost always someone who remembers the inequality alligator who opens his mouth to gobble up the greater number. One of the hardest parts of inequalities is figuring out which way the sign faces in terms of […]
Solving Multi-Step Addition and Subtraction Word Problems
Solving Multi-Step Addition and Subtraction Word Problems Solving multi-step addition and subtraction word problems can help students see the relationship between operations, as well as practice their calculations. When I teach subtraction, I also like to show how students can use addition to check their work! Students often think that they are done when they […]
Comparing Multi-Digit Whole Numbers
Compare Multi-Digit Whole Numbers If students really understand place value, then they can get a stronger grasp on other mathematical operations! I like to start by asking students how many digits are in the universe? And most times students say infinity! Because fourth graders love the idea of infinity. But in fact, there are only […]
Equivalent Expressions Memory Cards
Equivalent Expressions 6th Grade Math I always tell my students to remember that math is a language. Sometimes writing expressions and finding equivalent expressions can be difficult for students. When they just see variable expressions on a page, it can be tough to figure out what the letters and numbers mean. But if we talk […]
Least Common Multiple and Greatest Common Factor Worksheets
Launching GCF and LCM with a Real World Context Teachers often want to know how they can teach greatest common factor and the least common multiple in a way that is more concrete or constructivist. Using Least Common Multiple and Greatest Common Factor Worksheets is fine but we can do better. They’ve been teaching factor […]
Dividing Fractions Activities
Dividing Fractions is one of the lessons that students struggle with their whole lives. I have heard the argument over and over… “Why do they need to learn to divide fractions by hand when they all have phones and calculators that will do it for them?” “When will they ever be in a position […]
Ordered Pairs on the Coordinate Plane Activity
Ordered Pairs on the Coordinate Plane I can remember learning about longitude and latitude and looking at maps long before I learned about the coordinate plane. And I know I played battleship before learning about ordered pairs in math class! Battleship is a great way to introduce the concept, but those coordinates do not have […]
Unit Rate Activity: Find the Better Deal
Cost Comparison – What’s the better deal? Unit Rate Activity: What makes a bargain? How do you know which price is a better deal? Many products, especially snack foods and cereal, are sold in different sizes. A great way to teach unit rate is by doing unit cost and price comparisons to find out which […]
Patterns and the Coordinate Plane: Ordered Pairs Initials
Patterns and the Coordinate Plane Played Out This activity (Ordered Pairs Initials) will provide students with practice in graphing ordered pairs and seeing how patterns in the ordered pairs play out on the graph. Students are usually pretty good at graphing ordered pairs. It takes a class period or two to get the X and […]
Classifying Two Dimensional Figures: Shapes in the Real World Project
Classifying Two Dimensional Figure: Shapes in the World This lesson is a chance for students to see that the world is made up of shapes. When they ask, “Why do I need to know geometry?” this is why. Our lessons in geometry and shapes often rely on 2D shapes in a textbook or drawn on […]
How to Teach Volume of a Right Rectangular Prism
Manipulatives and Volume: Volume of a Right Rectangular Prism I have noticed that students often leave out the unit label when doing word problems or measuring. For the longest time, I didn’t understand why this was the case. However, one day I had an epiphany. My students didn’t understand what the label actually meant! When […]
Teach Multiplying Fractions by a Whole Number with Hershey Chocolate Smoothies
Fractions and Feeding a Group of People Feeding a group of people can be difficult, especially when it comes to Multiplying Fractions by a Whole Number in the recipe. So often we hear kids ask, ”When am I ever going to use this?” Well, if they are ever going to follow a recipe, the answer […]
Adding and Subtracting Fractions in the Real World
Engaging Your Students with Food: Fractions in the Real World When it comes to Fractions in the Real World, one guaranteed way to get kids to participate in class is to use food. Yes, food. I believe that food is the universal means to get participation by any group of people – especially kids! No […]
Standard Algorithm for Multiplication: Math in the Natural World
Math in the Natural World: Standard Algorithm Multiplication 5th Grade The natural world is a fantastic vehicle for getting kids to think deeply about the Standard Algorithm for Multiplication. When I show a nature video at the beginning of class, I get immediate buy in because they are all fascinated, especially when it has to […]