Modified Multiplication Table – Area Model Included

The idea is that the student will have to count squares and eventually skip count by how many rows. By doing so the student is more engaged (or less passive) in determining the product byy engaging the visual representation. I am interested in feedback and will revise if this could be useful.

Here is a link to the document.

Hack for Multiplication (and division) Facts

A common method to learn multiplication facts is through skip counting. In turn, this is a means of learning division facts (see next paragraph). The challenge for many students is they struggle to learn the skip count routines or cannot engage brute force memorization effectively (e.g., have a working memory deficit).

https://www.homeschoolcreations.net/skip-counting-charts-from-2-through-15-printable/

The challenge with multiplication by skip counting is keeping track of two sets of numbers while memorizing the order of the skip counting. That is another example of the rubbing belly and patting head phenomena in math where one extra task demand undermines the process.

A hack I use to scaffold this process to reduce the task demand during the learning process is to provide rows from a multiplication chart (below) for the facts of focus (3s and 4s in this example). The same approach can be used for division facts, e.g., in the image below right I have the student choose the row of the divisor (3) and then skip count to until reaching the dividend (12). The idea is the student has less task demands while learning the process and seeing the number pattern. This allows for more repetitions or rehearsal.

For students more severely impacted by a disability or who simply struggle with the patting head and rubbing belly of skip counting, the appropriate times table row can be provided for each problem to allow the student to circle (below). This allows for a hands on approach with even less task demand. You could also laminate the rows to make them reusable in lieu of several consumable ones requiring more paper. I like the consumable as I use that for data collection.

Addressing Multiplication as a Gap

There is a delineated sequence for teaching multiplication over the years, including repeated addition, set modeling, arrays, single digit etc (below). It exists to build conceptual understanding of the multiplication facts that are at some point memorized by many students. When I work with students who are a more than a year behind in the sequence for multiplication, I find that programming for these students to help them catch up sometimes involves shortcuts such as a reliance on rehearsal or resorting to use of the multiplication table in isolation. I am not against use of the table or narrowing the focus, but am promoting a more comprehensive approach.

Here is a sequence, on a Jamboard, I used for a recent student who was struggling for a long time with multiplication (explanation of each step shown below images). The student was interested in Minecraft so I used Minecraft items such as stone bricks and a wagon. I would spend as much time on each step, as necessary.

  • Count out the total number of stone bricks. This allows an assessment of how the student counts: by 3s or individually. If individually, I would prompt the student to count by 3s.
  • Add 3 + 3
  • Show a short video on the wagon (this adds interest and gives the students a bit of a break)
  • Present the bricks in 2 groups of 3, in context of 2 wagons with 3 bricks each.
  • Present the same problem as a multiplication problem but with the image for one of the factors in lieu of two numbers.
  • Use the multiplication table to skip count.
  • Present additional multiplication problems for independent attempts. The student completed both problems independently, without the table. For him this was a major success.

The follow up to this would be to assess his ability to do higher groups of 3s and groups of other numbers. For some students, I work on mastery of individual numbers before moving on. This builds confidence and allows for fluency in the process of skip counting out to the appropriate number. NOTE: I don’t worry about rote memorization of the facts but of fluency in the process of skip counting out the answers.

For students who are older, I sometimes recommend that the student be presented problems with visuals but then use a calculator to compute. This can develop conceptual understanding and also address the working memory and other related issues that undermine learning math facts.