help with a math standard

[jettharp]

I am hoping this is the right place for this and I apologize if it belongs in some other forum...
I am tutoring/helping a rising to 7th grade student with a math packet assigned by her school. One of the questions is based on the following math standard:
[FONT=Arial, Helvetica, sans-serif]6.NS.4[/FONT][FONT=Arial, Helvetica, sans-serif] Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Can anyone give me an example of how this works? I have been teaching for years and have never even seen this.
Thanks for any assistance.
j[/FONT]

 

[Mrspi]

I am hoping this is the right place for this and I apologize if it belongs in some other forum...
I am tutoring/helping a rising to 7th grade student with a math packet assigned by her school. One of the questions is based on the following math standard:
6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Can anyone give me an example of how this works? I have been teaching for years and have never even seen this.
Thanks for any assistance.
j

Here's a "review" lesson on greatest common factor and least common multiple; the examples use larger numbers than the standard specifies, but if you understand the process for the larger numbers, it is easy to apply them to smaller integers. http://www.purplemath.com/modules/lcm_gcf.htm

The part of the standard which seems most likely to be confusing it this part:

Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

This "reads" in a confusing fashion, so maybe an example might help.

We want a sum of two whole numbers in the 1-100 range, with the two numbers having a common factor. I'll write a sum of two multiples of 5; those are SURE to have a common factor of 5:

15 + 40

Let's rewrite 15 and 40 so that we can SEE the common factor of 5:

5*3 + 5*8
To perform this calculation as written, we'd need to do the two multiplications first, and the addition last.

Now, as directed, let's use the distributive property, which says that
a*b + a*c
can be written as a(b + c)

5*3 + 5*8
can be written as
5(3 + 8)

Written this way, we do the addition first (because it is inside the grouping symbols) and do the multiplication last.

15 + 40 is the sum of two numbers with a common factor.

Written as 5(3 + 8), we have a multiple of a sum of two numbers (3 + 8) with NO common factor.

15 + 40 = 5*11

Here's another example:

20 + 36

The largest common factor of 20 and 36 is 4. 4*5 + 4*9 shows that common factor in both terms. Using the distributive property, we can write 4*5 + 4*9 as 4(5 + 9).

20 + 36 = 4*5 + 4*9 ......there it is, as the sum of two whole numbers with a common factor
20 + 36 = 4(5 + 9)..........there it is, as a multiple of a sum (5 + 9) of two numbers with no common factor.

I hope I've interpreted the standard (and your question) correctly. I'll happily open the floor to any of the other volunteers!

MrsPi

 

[jettharp]

Thank you so much!
j