Operations on integers and integers in general is challenging for many students. Negative numbers are abstract. Whole numbers and fractions can be represented with images. The activity presented draws upon student prior knowledge of thumbs up and down in a vote to make negative more accessible. The following images are from a Jamboard. Here are… Continue reading Introduction to Adding Integers

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

Absolute Value is Absolutely not the Opposite

I have frequently encountered the presentation of absolute value as a positive value or opposite. This is part of the repertoire of memory devices we (certainly I have in the past) use as a short cut to learning how to do the steps for a problem. The meaning of the absolute value of a number… Continue reading Absolute Value is Absolutely not the Opposite

Trick for subtracting integers

I have algebra students, in high school and college, who struggle with evaluating expressions like 2 – 5.  This is a ubiquitous problem. I have tried several strategies and the one that is easily the most effective is shown below. When a student is stuck on 2 – 5 the following routine plays out like… Continue reading Trick for subtracting integers

Middle School Math Topics

Click on a topic to see related blog posts. Go to the Algebra page for algebraic expressions, equations, and linear functions. Integers Proportional Relationships Rates, Ratios, Proportions Fractions Equations Geometry

Example of Using Support Class to Support Current Math Content

I have posted on how to effectively provide support for current math topics. Here is an example (below) of how support can focus on both the current topic and prerequisite skills. For example, on the 22nd in this calendar the current topic is solving equations. The steps for solving will include simplifying expressions and may involve… Continue reading Example of Using Support Class to Support Current Math Content

Introduction to Absolute Value – Distance from Home

Here is a Jamboard to introduce the concept of absolute value (make a copy and you can edit – see photo at bottom of this post). Start with prior knowledge of how many houses a child is from home. Emphasize that the number of houses is positive. Change the setting from a row of houses… Continue reading Introduction to Absolute Value – Distance from Home

Learning Itself Has Changed

I teach a math methods class for special education teacher candidates at UCONN. During a lesson on an instructional strategy on making math meaningful, I experienced an epiphany of sorts. The students were partaking in a discovery lesson in which they rotated through using four different types of manipulatives (photo below, left). They would follow… Continue reading Learning Itself Has Changed

Asking for Examples of Mastery for IEP Objectives

To ensure the IEP team is on the same page as to what mastery of an objective looks like, the person writing the objective can take two steps: provide an example problem that would be used to assess mastery (and the example problem would have the same language as used in the objective) provide an… Continue reading Asking for Examples of Mastery for IEP Objectives

Introduction to Imaginary Numbers

The topic of imaginary numbers is one of the most abstract and therefore difficult math topics to teach in algebra. Here is how I introduce it to students (emphasis that this is only an introduction). I write 1, 2, 3… on the board (see photo above) and explain to the student “at some point in… Continue reading Introduction to Imaginary Numbers