Concrete-Representation-Abstract
-
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…
-
Simplifying not so Simple Equation Solving
-
Introduction to Unit Rate using Unit Cost
-
Introduction to Unit Cost (Unit Rate)
Unit rate (e.g., hamburger meat on sale for $2.39 per pound or you make $13 per hour) is an incredibly important topic in middle and high school. First, unit rates and unit costs are common in life. Second, in the Common Core State Standards math categories you can see that Ratios and Proportions (which includes…
-
Introduction to 2 Variable Inequalities
Previously, I shared how I use a Google Jamboard to introduce 1 variable linear equalities with a focus on conceptual understanding. I use the same approach for the 2 variable version (example problem below). A conceptual gap that typically arises is the students do not understand what the shading represents. This is what I am…
-
Life Skills Math – Not So Easy
As I wrote previously, shopping is dense with math tasks as are grocery stores. Here are some division situations that are sneaky challenging and require a student to know when and why to divide before even reaching for the calculator. I will use these to help illustrate the fact that life skills math is not…
-
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.…
-
Introduction to Inequalities
For students with special needs, the teacher speaking “math” to students sounds like the teacher from the Peanuts cartoons. This is apparently the case when students are learning about inequalities such as x < 4 because I have seen many high school and college students struggle with this topic. The challenge is that teachers are…
-
Using $10 and $1 Bills to Represent Regrouping in Addition or Subtraction
Money is intuitive for many students, even when the underlying math is not. For example, I often find that students who do not understand well the concept of Base 10 place value do understand $10 and $1 bills. With this in mind, I created a virtual scaffolded handout that builds on student intuitive understanding of…
-
Base Ten Using Popsicle Sticks
I use the following method as a entry point for double digit numbers. The photo below shows 2 packs of Popsicle sticks counted as 10 each, followed by single sticks counted as 1 each. The student counts on from 20, with the use of the scaffolded handout (photo at bottom). The handout focuses only on…