Tag Archives: division

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.

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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 simply counting money or using a calculator to add up prices. There is a great deal of problem solving and thinking skills that need to be developed.

For example, if a student has $60 to spend on gifts for her 3 teachers the student needs to understand that she can spend up to $20 per teacher (before even talking about taxes).

An entry point for division can involve a dividing situation the students intuitively understand, e.g., sharing food. Start with 2 friends sharing 8 Buffalo wings evenly (below).

This can lead into the 3 teachers sharing the $60 evenly (below). In turn, this can be followed by the online shopping shown above.

This approach can be used to develop an understanding of unit cost (cited in the shopping is dense post). Start with a pack of items to allow the students to see the cost for a single item before getting into unit cost by ounces, for example.

I have had success with teaching these division related concepts using sheer repetition as much of our learning is experiential learning. Using a Google Jamboard as shown in the photos allows for the repetition.

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Basic Skills Older Students

A widespread problem at the secondary level is addressing basic skills deficiencies – gaps from elementary school. For example, I often encounter students in algebra 1 or even higher level math who cannot compute problems like 5÷2. Often the challenges arise from learned helplessness developed over time.

How do we address this in the time allotted to teach a full secondary level math course? We cannot devote class instruction time to teach division and decimals. If we simply allow calculator use we continue to reinforce the learned helplessness.

I offer a 2 part suggestion.

  1. Periodically use chunks of class time allocated for differentiation. I provide a manilla folder to each student (below left) with an individualized agenda (below right, which shows 3 s agendas with names redacted at the top). Students identified through assessment as having deficits in basic skills can be provided related instruction, as scheduled in their agenda. Other students can work on identified gaps in the current course or work on SAT problems or other enrichment type of activities.

  • Provide instruction on basic skills that is meaningful and is also provided in a timely fashion. For example, I had an algebra 2 student who had to compute 5÷2 in a problem and immediately reached for his calculator. I stopped him and presented the following on the board (below). In a 30 second conversation he quickly computed 4 ÷ 2 and then 1 ÷ 2. He appeared to understand the answer and this was largely because it was in a context he intuitively understood. This also provided him immediate feedback on how to address his deficit (likely partially a learned behavior). The initial instruction in a differentiation setting would be similar.
  • 2018-12-20 11.20.25
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    Long Division for Students who Struggle

    Long division

    Making the concept of long division accessible:

    1. Start with simpler problem
    2. Use base ten blocks (and later with drawings as seen in the photo) and have students model each step of the long division with the base ten blocks.
    3. Do this for each step.
    4. Follow with more complicated problems

    See link  to document with full explanation.

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