Factors and Multiples written lesson (with practice problems embedded)

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Pat McQueen

September 25, 2020 17:35

Today we were working through the factors and multiples information page and I noticed one thing that I wanted to ask about.

I really appreciated the clarity of the organization and the way the images of the arrays was incorporated into the lesson. I also like the number of practice / check problems to help my student know if he was on the right track.

But I was quite bothered by the wording in this section,

Finding factors without pictures

The next line states, "We can find the factors for without drawing dots by thinking about numbers that will divide into evenly."

When it says divide into 16 evenly, it sounds to me like the factor is being divided.

Another example is here, "2

is a factor of

because 2 can be divided into

with no remainder."

2 doesn't get divided to fit into 16. Instead 16 is being divided into groups of 2 OR 16 is getting divided into 2 groups. Would it be better to say, 2 is a factor of 16 because 16 can be divided into equal groups of 2 or it can be divided into 2 equal groups?

I don't know if you've tried different versions and found this to be the most clear, but it definitely seemed to be unclear to me, and seemed unclear to my student.

Thanks.

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P Rossell

January 07, 2021 06:07

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Hi Pat,

My fourth grader initially had trouble understanding this, too. The word into switches the order of divisor and dividend in the number sentence while leaving them in the same order in the word sentence.

Ex:

16 divided by 2 is 8, because 16 is the number being divided (dividend) and 2 is the number by which you divide (divisor).

16 divided in 2 is 8, because 16 is the dividend and 2 is the divisor.

16 divided into 2 is .125 or 1/8, because the word into is saying that 16 is the divisor and 2 is the dividend.

2 divided into 16 is 8, because the word into is saying that 2 is the divisor and 16 is the dividend.

By saying "numbers that will divide into evenly", the problem is stating that you are looking for divisors when the dividend is 16 and there are no remainders.

16 divided evenly by a number also states that 16 is the dividend and there is no remainder.

The problem is that a factor is defined using different verbiage in different places. In all of those places, it boils down to a one idea, a factor is any number that can be multiplied by an integer to get a given number, or in another way, a factor is a number that can be divided evenly into a given number. Because kids are using different curricula and taking different standardized tests, they need to be exposed to a variety of ways of wording the same idea.

Does this make sense? I know that word choice can be tricky sometimes.

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Factors and Multiples written lesson (with practice problems embedded)

Finding factors without pictures

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