Share your math strategy and win free manipulatives!

5th April, 2010 - Posted by Sammie Gann - 10 Comments

Values and Variables Student Record Book

The problem below is from Math Out Of The Box Lesson 11: Subtracting Fractions

Stan has a problem. Stan’s dad gave him two boards to use in building a birdhouse. One board measured 25 5/16 inches long and the other measured 18 9/16 inches long. What was the difference in the lengths of the boards?

Solve the problem by replying below and explain your strategy in writing to have the chance to win a set of manipulatives to use in your classroom.


Grady Rose

April 8th, 2010 at 3:31 pm    

I converted both lengths into fractions with common denominator and got 405/16 – 297/16 = 108/16 or 6 12/16 or 6 and 3/4.

Tashia Dorsey

April 26th, 2010 at 4:38 pm    

Have students work in pairs to check answers and compare notes and strategies.

Sammie Lotz

April 26th, 2010 at 4:49 pm    

Tashia, this is a great idea to use when teaching problem solving and getting your students ready for the end of grade tests! What grade do you teach? Tomorrow set this up as a math station in your classroom and it would be interesting to use this tool as an assessment tool to see their varying strategies. Isn’t it amazing how creative they can be when they are solving math problems? That is the joy of inquiry based math. They all arrive at the same answer but take different paths to get there.

Sue Ottesen

May 10th, 2010 at 5:59 pm    

I would change the fraction 25 5/16 to 24 21/16 and subtract 18 9/16. Answer is 6 12/16 or 6 3/4 in simplest form (lowest terms.) corrected!!!

Sammie Lotz

May 11th, 2010 at 7:35 am    

Sue, great idea! Can you explain how you changed 25 5/16 to 24 21/16 before you subtracted. That is an interesting conversion or “change”. If you write out your problem solving technique on a sheet of notebook paper please scan it and email it to me under the become a contributor tab so I can explain this to other members.

I love how easy it was for you to use the vocabulary terms “simplest form” “lowest terms”. How do you teach this in your classroom?

Sue Ottesen

May 11th, 2010 at 11:35 pm    

In order to subtract the mixed numbers, the larger number needs to have a larger numerator than the smaller number. To accomplish this, borrow a whole number from the 25 and add the equivalent to the fraction:

25 5/16 = 24 16/16 + 5/16 = 24 21/16

Now you can subtract:

24 21/16 -18 9/16= 6 12/16.

When teaching, I model working the problems for my students to get them started. As they get proficient, I let them work the problems on the board and share with the class. I might have them
work in pairs, depending on the needs of the students or let them share in small groups as a “Professor Know-It All” or “Pair-and-Share” using small dry erase boards.

I have been teaching for a very long time, and terminology has changed over the years. I find that students don’t know the names of the parts of a fraction, the term “mixed number”, or other relevant terms. They come to me wanting to use calculators for everything, but I work with them to teach basic calculation skills and terminology.

Sammie Lotz

May 12th, 2010 at 11:20 am    

Very well said Sue!!! By looking at your explanation I think that students will be able to reflect on the equivalency between 25 and 24 16/16. I always felt that working with numbers and showing them in multiple forms was hard for my students.

I would love to see you move this discussion to a technology center in your classroom for your students to discuss. It is amazing the ways that they will be able to work with numbers to come up with problem solving strategies that they baffle me. I would love talking to them also.

Again, thanks for taking the time to share your ideas with other members. There is nothing like having the opportunity to brainstorm with other teachers and students.

Where do you teach Sue? They are lucky to have you in the classroom!

Sue Ottesen

May 12th, 2010 at 11:41 am    

I teach Remedial Math and Earth Science at Butler Educational Complex in Bossier City, LA. Our program is for at-risk students, and we are moving toward using technology more and more.

Sammie Lotz

June 4th, 2010 at 8:49 am    

Amy, great idea but can you explain to me how you got such large numerators when you converted both lengths. This is a very common conversion but most students have difficulty moving from mixed numbers to finding a common denominator before subtracting.
* Can you break down your process to try to help explain this method to 5th graders? How do you teach this in your classrom?
* Also can you explain how you changed 108/16 to 6 12/16? There are tons of ways to convert improper fractions to mixed numbers. I would love to see your strategy.
* Finally, it looks like you reduced or simplified 6 12/16 to 6 3/4. How do you teach simplifying fractions to your students.

Thank you for sharing what works in your classroom Amy! I can’t wait to see your strategies so that we all can learn from what works for you!

Sammie Lotz

August 2nd, 2010 at 9:03 am    


We value your input to the I Teach Inquiry site. As our thanks to you, you have won a free math manipulative from our Math Out of the Box program.

A downloadable lesson is available at:

Photo added on August 2, 2010

Please keep me informed on ways that you use this great manipulative in your classroom instruction.

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