Guest Blog Post: Clock Fractions!

     I'm delighted to host my friend, Cynthia, from Ms. K Math! She focuses on concept-based, hands-on math lessons. She is sharing a fractions lesson with clocks. Read and enjoy!

     Oh, my gosh!! I have wanted to post about this forever, but when I taught the lesson, I didn't think to take pictures. Well, here arose the opportunity when a 5th grade teacher wanted me to do this lesson with her class.

     First it was all out WAR with the copy machine when I shrunk a larger clock face to smaller clocks to make this original. I wanted to have smaller faces so I could give them several and not waste paper. Plus I wanted to use colored paper. I shrunk the larger face to about 60% on the copier. Fifty percent was too small. I wanted the faces to be large enough for the kids to still be able to easily see the tiny marks around the sides of the clock.
I copied a class set of these on 3 different colors of paper.
     First we discussed how many minutes were included in one hour on the clock face...Sixty of course.  Then I had the kids tell me how many minutes were in half of a clock face or half an hour…too easy…30 minutes!  Each time we found a fraction on the clock face, I had students label it with the fraction and with the amount of time.
     Next, I asked them how many minutes were in a fourth of a clock face. To see what kids knew, I didn't allow them to raise their hand or blurt out. I really wanted to know what each child thought. I had them write the minutes they thought were in a fourth on the back of the clock face and then cover it with their hand--so no cheating ;). This gave me a quick assessment of the class. Before students drew lines on the clock face for fourths, we discussed where to draw these lines so there were equal pieces. Fifteen minutes are in ¼ so students drew a line from the center to the 12,3,6, and 9. Then they snip, snip, snipped on the lines to make pull apart fraction pieces.
FractionClockFourths      Now, for one that doesn't work out quite so nicely--thirds. How can you split up 60minutes into 3 even sections?Hmmm…students gave me answers ranging from 10 to 60 when they did secret answers on the back of the pink clock face. I wrote down the ranges of answers that students gave me on the board. We weeded out the wrong answers as a class by justifying why the wrong answers couldn't be right--this way the mathematical practices were involved. Several students, however, were easily able to tell me 20 minutes and reasoned that 3 sections of 20 minutes would be able to fit in the clock face. We discussed again where to cut the clock face so that the sections would be equal.
Below are all of the clock faces together….I LOVE, LOVE, LOVE colored paper.
     Then I started posing problems to the kids, so they could use their clock pieces as manipulatives.  The picture below shows what the kids had on their desk when I asked them to show me how many minutes 2/4 of an hour was--EASY 30 minutes.
     How many minutes is ¾ of an hour?  Just look at the clock pieces to see how many.  Below is a simple sheet I gave students to do as guided practice to make sure they were following along while we discussed their clock faces.
     Yes, I do quick smileys (although usually with a pen) on every single one students get right as I walk around the room. I do this for two reasons. 1. It gives students a boost if I ask them to fix something. They don't feel defeated because they got so many right and only a few were wrong. 2. This saves me time from grading papers later because I can tell which ones I have already checked.

    To make students think outside the box, I also changed the size of the whole. For example, students had to find ⅔ of 45 minutes. This tripped up most students who were used to figuring out ⅔ of 60 minutes/the whole circle. Hmmm…if I think about 45 minutes in thirds, I can use three of the fourths pieces. Now these fourths pieces turn into thirds because three of them now make the whole of 45 minutes. If two of them are chosen then that makes ⅔.

     Finally, students will tuck their fraction clock pieces away behind fraction notes in their journals for safe keeping. We taped envelopes down in journals for this. Most kids are able to do this on their own, however, some are not as self sufficient as one would hope in 5th grade.

A little more about this lesson… I gave each student a large white sheet with the three clocks (my original copy shown way above) for them to figure out other fractions of a clock such as twelfths or fifths. Students also did two word problems following the easy guided practice sheet.

I ended up just recently taking this lesson and perfecting the materials to sell. Here are the detailed lessons for sale on TPT. These include lesson plans, small printable clock faces, worksheet practice, and word problem practice.

Pat McFadyen
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  1. Wow! I love this! I never thought to actually cut the clocks into the fractions! I have drawn lines, colored sections, etc ... but cutting the clocks into halves, thirds and quarters just makes so much sense! And I love that they are color coded! Thanks for sharing!


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