Multiplication with Integers: a Meaning Making Approach

I previously tackled the difference between the ” – ” symbol used to represent a negative and a subtraction problem. This post gets into multliplication through the context of buying a Wendy’s frosty. One comment to preface what is presented here. Negative numbers are abstract and challenging for many students. Multiplying by negatives is even… Continue reading Multiplication with Integers: a Meaning Making Approach

Introduction to Equations – (Meaning Making)

This is a meaning making approach to introducing equations. I will walk through the parts shown in the photo in the space below this photo. (A revised edition of this handout will be used in a video on this topic.) First I explain the difference between an expression (no =) and an equation (has =).… Continue reading Introduction to Equations – (Meaning Making)

Solving 2-Step Equation Scaffolded

Solving 2-step Equations is an escalation in terms of task demand. Starting in elementary school, they are exposed to math sentences in which there is a single operation. Now they are asked to choose a number to eliminate. This post provides details about a scaffolded handout. It addresses the choice of number to eliminate and… Continue reading Solving 2-Step Equation Scaffolded

Intro to Graphing Inequalities

For years over many settings from middle school to college I have witnessed students struggle to make sense out of inequalities like x < 4. Not only is the concept of an inequality of an inequality challenging, merely reading the symbol is problematic. This post shows an concept based approach to making sense of inequalities.… Continue reading Intro to Graphing Inequalities

Algebra 1: Concepts and Skills

I had an interesting discussion through a Facebook post recently regarding concepts vs skills. I want to share some information I have gathered regarding this topic. I do so, because there were a substantial number of teachers advocating for skill based learning. I hope to initiate some meaningful discussion. Below left is a photo of… Continue reading Algebra 1: Concepts and Skills

Math is a Language

The Gutenberg printing press was revolutionary because it provided a faster way to share words. In turn, these words and how they were structured were representations of ideas used to make sense of the world around us. Math is a language with words and other symbols that also makes sense of the world around us.… Continue reading Math is a Language

Piecewise Functions – Introduction

Here are images from a handout that serves as an introduction to piecewise functions. The focus is to develop conceptual understanding of piecewise before attempting to graph independently. The work is divided into chunks to reduce the level of task demand at a given time in the process. The first section has an application and… Continue reading Piecewise Functions – Introduction

Speeding Up and Slowing Down on a Graph looking at Velocity and Acceleration

We all understand speed intuitively. Velocity and acceleration are more mathy and harder for many students to comprehend, especially on a graph. Even harder is the idea of when an object is slowing down or speeding up. In this post I attempt to unpack both. Velocity is speed with a direction. Negative in this case… Continue reading Speeding Up and Slowing Down on a Graph looking at Velocity and Acceleration

Reading Scatterplots with Ford Mustangs

One step in reading and analyzing scatterplots is simply identifying what the dots on the graph represent. Students who do not understand the meaning of the points, including the position, will struggle to interpret the graph. This post outlines a Jamboard activity to support interpretation of the points. Overview I present the scatterplot of used… Continue reading Reading Scatterplots with Ford Mustangs

Intro to Slope of a Line

Slope is one of the most important topics in algebra but perhaps one of the most challenging topics. One issue is that students often think of the formula as opposed to the idea of slope. The images shown below are for a handout that unpacks the idea or concept of slope. Handout The images show… Continue reading Intro to Slope of a Line