Category Archives: Uncategorized

Q&A Regarding Math and Online Learning

I will be fielding questions about math and online learning in real time. As a follow up, I will respond to questions through this blog post. If you did not catch the Instagram session and have questions, you can post them here through a comment. I will post replies on this post.

Below is a list of links to resources, e.g. online handouts, activities, which align with the discussion.

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Online Academic Practice – Especially for School Closures!

I recommend 3 sites for online academic practice in multiple content areas. can be purchased for an individual or a family with access to multiple content areas. You can try 10 problems for free. It allows students to work on specific skills. Math grades covered range from kindergarten to precalculus!

Here is a link to handouts to help you access Khan Academy which covers a wide range of math grade levels and other content areas, and the ACCUPLACER practice app to prepare for college placement tests.


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 counting on from 20 and shows a photo of 2 of the bundles of sticks. Similar handouts involve counting on from 10 or from 30 etc.

By engaging in the actual counting, the student learns the 10s by doing. This would be followed by counting on from each 10 without the handout.

The use of Popsicle sticks is useful for 2 reasons. First, a bundle of items like shown below is more concrete than the rods for Base 10 blocks. Second, pulling packs of sticks apart of bundling 10 sticks together is an act that is concrete for students and ties into their prior knowledge regarding the grouping of objects (e,g. pack of gum).

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Parent Presentation

Parent Presentation on Math Supports and Instruction

Making Sense of Testing

Testing (results shown on the Present Levels of Performance page shown below) is often confusing for parents, especially in regards to math. The results are often reported in broad terms, e.g. computation or IQ.

Standardized testing

Here is an analogy for the testing (in terms usefulness for determining instruction, performance and achievement). We go to the DMV and have to take an eye test. That test is used to determine if we have the physical ability to drive or what we need to ensure we have the physical ability to drive. If our vision is diminished maybe we need glasses in order to drive.


 Passing the vision test does not mean we are ready to drive. It means we have the potential to drive. In order to determine if we can actually drive we take a driver’s test.

learning to drive\

Similarly, in order to determine what we can actually do in math we need to take a math test (quiz, checkpoint or some type of curriculum based assessment).

Below is a problem aligned with the Common Core of State Standards for Math. I used it as part of a curriculum based assessment to determine the student’s current ability or present level of performance. She had all types of  standardized testing results on record but I needed to know if she could pass the actual driver’s test.

CCSS assessment



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Geometry Application

Obtuse angle on the left (see upside down “T” figure) and perpendicular lines (right angle) on the right.

how to walk on ice

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Concepts vs Skills – Need Both

In general math is taught by focusing on the steps. Conduct a Google search for solving equations and you will see the steps presented (below). You need a video to help your student understand solving and you typically get a presenter standing at the board talking through the examples. (I’ve posted on my approach to solving equations.)

When the math is taught through the skill approach the student may be able to follow the steps but often does not understand why the steps work (below). The brain wants information to be meaningful in order to process and store it effectively.

calvin hobbs toast

To help flesh this situation out consider the definitions of concept and skills (below). Concept: An idea of what something is or how it works – WHY. Skill: Ability” to execute or perform “tasks” – DOING.

definition conceptdefinition skill

Here is how the concept first approach can play out. One consultation I provided involved an intelligent 10th grader who was perpetually stuck in the basic skills cycle of math (the notion that a student can’t move on without a foundation of basic skills). He was working on worksheet after worksheet on order of operations. I explained down and monthly payments then posed a situation shown at the top of the photo below. I prompted him to figure out the answer on his own. He originally forgot to pay the down-payment but then self-corrected. Then I showed him the “mathy” way of doing the problem. This allowed him to connect the steps in solving with the steps he understood intuitively, e.g. pay the $1,000 down payment first which is why the 1000 is subtracted first. Based on my evaluation the team immediately changed the focus of this math services to support algebra as they realized he was indeed capable of doing higher level math.

solving equation with conceptual understanding first

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Submit Questions for the Daily Mailbag

If you have questions about math support, services or strategies share them using comment bar below or email me. I will answer as many questions as I can get to.

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Rate of Change in Real Life

61 cents per ounce is a rate of change. Graph the line modeled by this (y intercept is 0) and it becomes slope of the line. In referring to algebra we often hear, “when will I ever need this?” My response is “all the time!” Our job as teachers is to make this connection for students.

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