Division with Grid Paper

Division can be accomplished using a variety of strategies. One strategy most people are familiar with is the long division method, which is often referred to in mathematics education as the standard algorithm for division.

Since the standard algorithm for division is based on understanding place value and regrouping, it can be helpful to use grid paper to record each step. Writing each digit inside of a square on the grid paper can help keep you organized as you regroup and divide; especially if the process requires multiple steps.

What’s a Reasonable Answer? Before going through this process, it’s wise to use rounding and estimation to determine what a reasonable quotient (answer) will be.
Take a look at this example:

Screenshot 2018-09-21 at 12.35.25 PM

If I round 738 to 750, and round 26 to 25, I could now look at the expression this way:

Screenshot 2018-09-21 at 12.35.41 PM
After rounding the numbers, I estimate my quotient will be near 30. The great thing about using numbers like 750 and 25 is that they are compatible numbers, and may be numbers you can divide mentally!

Here’s how I would simplify the original expression using the standard algorithm on grid paper:

Screenshot 2018-09-21 at 12.36.04 PM

I stopped after dividing to three decimal places, but the quotient is a repeating decimal, which means I could keep going forever! My quotient, 28.384, is close to my estimate, and I was able to see what was happening in each step by lining up the digits on the grid paper.

I hope the grid paper will be a helpful tool as you simplify or help others with long division expressions – and remember, there are multiple strategies for simplifying an expression using division. You can also use the Calculator Soup website to check your work.

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Let’s Talk Fractions (Part 1)

Talk FractionsI recently had a conversation with a family member who was baffled when a friend wanted to know how many quarters were in a basketball game. I initially laughed with her – as many people just understand that there are 4 quarters in a basketball game, because of the emphasis we place on the word “quarters”. I almost dismissed the conversation entirely, until I realized the question may not be as silly as I initially thought. With all the misunderstandings about fractions and fractional language floating around in the world, is it really that implausible for someone to question the use of the word “quarter” in this situation? (read more)

Middle School Math Newsletter

Breaking FreeThe acronym P.E.M.D.A.S., also known as “Please Excuse My Dear Aunt Sally”, has long been a strategy for teaching the order of operations in mathematics classrooms.
Unfortunately – and incorrectly – P.E.M.D.A.S. has been used interchangeably with the phrase “order of operations”, leading to several misconceptions for students.

So, what’s the real problem with P.E.M.D.A.S.?  Read the rest of this blog and more in today’s issue of Making Connections_Issue 1_MS Mathematics.