Number Sense


  • 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…


  • 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…


  • Math is a Language

    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.…


  • Addition: Concept and Mechanics

    The graphic organizer below is used to show the student the steps for addition. It also addresses the concept of addition (which I have addressed previously) as an act of pulling “together” two parts to form a whole. The student is prompted to move the first part (set of coins in this case) to the…


  • WAR Card Game Modified for Height Comparision

    Comparing numbers is very challenging for some students and likely speaks to a major gap in their number sense. It is also very challenging to address effectively with these students. The photo below shows an entry point into I have used with success in helping such a student. Even for these struggling students, taller and…


  • Superhero Math

    Superhero Math

    I was recruited to help a middle school student who is having a very rough time at this time in his life. It was shared with me that he likes Marvel superheroes and he is struggling with counting money and multiplication. Below are some ideas I presented for a test run and photos of the…


  • Lego Fractions

    Lego Fractions

    The photo below is courtesy of Robert Yu, Head of Lego Education China, as shared by Jonathan Rochelle, Director for Project Management at Google. The use of Legos shown here is a classic (and wicked clever) example of manipulatives. Before writing the actual fractions students can use drawings as shown below. The sequence of manipulatives,…


  • So Easy?!

    So Easy?!

    Problems like the addition problem below are often viewed by adults as straight forward. This perception can make it difficult for adults, including teachers and even special education teachers to help students who struggle with it. I find that the math teacher candidates and special education teacher candidates struggle with breaking down math topics, especially…


  • Adding ones digits in 2 digit numbers with carrying

    Adding ones digits in 2 digit numbers with carrying

    A major obstacle in math for many students with special needs is carrying in addition problems. Below is a task analysis approach. First, I target the step of identifying the ONES and TENS place in the 2 digit sum in the ONES column (below it is 12). In a scaffolded handout I create a box…


  • Place Value Representation

    Place Value Representation

    Here is an easy way to create and implement strategy to unpack place value for students (created by one of my former graduate students). I suggest using this after manipulatives and visual representations (drawing on paper) in a CRA sequence. It is hands on but it includes the symbolic representation (numbers). Hence is another step…