{"id":6469,"date":"2017-02-18T23:47:00","date_gmt":"2017-02-18T23:47:00","guid":{"rendered":"https:\/\/theteacherstudio.com\/2017\/02\/fraction-folding-discovery-learning.html"},"modified":"2026-01-19T15:42:37","modified_gmt":"2026-01-19T15:42:37","slug":"fraction-folding-discovery-learning","status":"publish","type":"post","link":"https:\/\/theteacherstudio.com\/fraction-folding-discovery-learning\/","title":{"rendered":"Fraction Folding–discovery learning"},"content":{"rendered":"
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Today we kicked off our fraction work, and every time I start this unit I\u2019m reminded just how important it is for intermediate students. Fractions show up everywhere in our standards. The understanding students build here truly matters! I like to take the time to document the thinking, the misconceptions, and the little moments of clarity that happen along the way. Today’s focus?\u00a0 Fraction folding!<\/div>\n

 <\/p>\n

I always invite conversation around how we teach fractions because there are so many ways to help students make sense of them. As I walk through our work, I try to share photos, student examples, and the reasoning behind each step. I do this partly to keep myself honest about my choices, and partly because I love hearing what has worked well in other classrooms, too. If you have ideas or resources that have been successful for you, I\u2019m always eager to learn from them.<\/p>\n

\"\"<\/p>\n<\/div>\n

Teaching fractions throughout the year<\/h3>\n

One thing our district math team emphasized when we built our pacing was the importance of giving fractions more than a single stretch of instructional time. We built in two units. We do one one now to develop foundational understanding. Then we built in a later one that connects fractions, decimals, and the more sophisticated ideas students will need. That structure has really shaped how I approach the beginning of this work.<\/p>\n

Today I started by asking students to reflect on what they already know about fractions and to rate their overall confidence (using our 4 \u00a03 \u00a02 \u00a01 ) scale (Click here to revisit earlier blog post about this!)<\/a>\u00a0and the results were quite amazing! \u00a0In a ten minute writing time, I got to witness a number of misconceptions, poorly explained reasoning, and a bunch of “3’s” and “4’s” in confidence!<\/p>\n

Good thing I had planned on starting slowly! \u00a0Today we started our new math notebooks, and I explained to the students that we are “raising the rigor” one level more. The poor things have heard this all year!\u00a0 I told them we are going to work hard to use our new notebooks to both record our thinking, our practicing, and our new learning.<\/p>\n

I’ll blog more about this later as it unfolds! \u00a0For today, we started the section we called “Fraction Concepts” and even talked about what the word “concept” means. \u00a0Fascinating! \u00a0I told the students that our job through this unit would be to determine some things we could determine to be “true” about fractions and that we would be working our way through a number of these “truths” during the unit.<\/p>\n

Today’s fraction “truth”<\/h3>\n

Today’s “truth” involved ensuring that students understand that fractions represent equal parts of something. (I didn’t really want to use the term “whole” yet–I don’t really like to treat fractions of “objects” and “sets” differently until I have to!) I also told them that we would be spending some time creating equal parts.<\/p>\n

Then, I put the students into pairs (I love popsicle stick picking!) and gave them each 3 minutes to find a classroom object that was either a square, rectangle, or circle. The item needed to be bigger than a deck of cards and smaller than a book. \u00a0Each team was then assigned a color of paper and we got started.<\/p>\n

The Task<\/h4>\n

With your partner, trace and cut out your shape. \u00a0You will need many of these as the investigation unfolds. \u00a0Your job is to find ways to divide your shape into equal parts. . . first in two equal parts, then three, and so on.<\/strong><\/p>\n

I made sure that we had plenty of objects accessible in a variety of sizes. You could also have cardboard tracers if that is more appropriate for your learners.<\/p>\n\n\n\n\n
\"using<\/a><\/td>\n<\/tr>\n
<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

I then showed the students the following charts–each is labeled “halves”, “thirds”, “fourths”, and so on.\u00a0 I used pieces of bulletin board paper, but you could use construction paper or even just set your shapes on the floor by the headers.\u00a0 As they discovered a way to fold their shape, they were asked to put it on the correct chart.\u00a0 I was on the prowl for work that was not accurate and precise.<\/p>\n\n\n\n\n
\"fraction<\/a><\/td>\n<\/tr>\n
Voila! \u00a0Posters are taped to the ground with deliberate “aisles” so they don’t get trampled on!<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n\n\n\n\n
\"fraction<\/a><\/td>\n<\/tr>\n
Each poster is labeled with the word for the fractional part–I will use the words and different symbols interchangeably throughout the unit. \u00a0NOTE: \u00a0The chart does NOT say “1\/3” because we were not identifying 1 out of 3 parts.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/div>\n
\n

FRACTION MISCONCEPTION ALERT! <\/em>Make sure students are aware of the difference between drawing \u201cthirds\u201d and drawing 1\/3.\u00a0 Watch for this and help students see the difference.<\/em><\/p>\n<\/div>\n

Digging In<\/h3>\n

Students dug into their work and did need some frequent reminders about using straight edges, working carefully, and so on. (I know–shocking!) That being said, they were very engaged and thoughtful. \u00a0I heard some pretty nifty stuff like:<\/p>\n

<\/div>\n
“Hey–as you try to get more pieces, the pieces get smaller!”<\/div>\n
<\/div>\n
and<\/div>\n
<\/div>\n
“Man–it’s a lot harder to fold the odd numbered pieces!”<\/div>\n
<\/div>\n
and<\/div>\n
<\/div>\n
“If you fold it in half and then in half again, each half gets cut in half!”<\/div>\n
<\/div>\n\n\n\n\n
\"students<\/a><\/td>\n<\/tr>\n
Tracing…<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
\"Students<\/a><\/td>\n<\/tr>\n
Using a straightedge for precision…<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
\"Paper<\/a><\/td>\n<\/tr>\n
Circles are the toughest as this team found!<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
<\/div>\n
As the period unfolded (and it became clear that this was going to be a TWO DAY investigation!), our charts began to fill up and things moved a little faster. I was walking around and taking notes about who was struggling and about observations I wanted to share with the whole class.<\/div>\n\n\n\n\n
\"Paper<\/a><\/td>\n<\/tr>\n
The charts started to fill…first halves and thirds, then fourths and eighths…we’ll see how it “unfolds” tomorrow! \u00a0Got to love a little math humor, right?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

What’s next?<\/h3>\n
<\/div>\n
Tomorrow we will finish up our investigation and then ask ourselves if we have discovered any new “truths” to record in our notebooks.\u00a0 I am pretty confident that my students would have been able to answer correctly if given a sheet of “shaded fractions” to identify.<\/div>\n

 <\/p>\n

<\/div>\n
That being said, today’s activity showed me that many students are maybe missing some very critical understandings about equal parts and about patterns that arise when dividing shapes. \u00a0I’m pretty sure that the work we will do over the next lessons is going to be very important as we build a foundation for the more advanced skills coming soon.<\/div>\n

 <\/p>\n

<\/div>\n
\n

This is the difference between asking students to REPRESENT and MODEL fractions rather than just identifying fractions on a piece of paper.\u00a0 This activity deepens understanding, gets students noticing and talking, and helps you as the teacher to notice misconceptions and to better understand where things might be going wrong.<\/p>\n<\/div>\n

<\/div>\n
Finally, if you aren’t familiar with what your standards require, I would encourage you to dig in and follow along with us as we try to construct meaning over the next few weeks!<\/div>\n

One more thing…<\/h4>\n

The terms \u201cnumerator\u201d and \u201cdenominator\u201d did come up in our lesson today.\u00a0 I made a poster to represent this and hung it on our math board.\u00a0 You may need to introduce the terms over the next days if your students do not bring them up!<\/p>\n

UPDATE!<\/h4>\n
This blog post is now a part of my comprehensive fraction unit (18 complete lessons!) available by clicking HERE or the image below. \u00a0Literally THOUSANDS of teachers have now used it to change the way they teach fractions!<\/div>\n

 <\/p>\n

\"Fraction<\/a><\/div>\n

 <\/p>\n

This unit is also now available as a part of a huge 12 resource bundle which offers an amazing assortment of lessons and resources to help you teach fractions at a deep level.<\/div>\n

\"Bundle<\/a><\/p>\n

Finally, are you interested in getting a short series of emails and freebies about teaching fractions?\u00a0 Just CLICK HERE<\/a> to get signed up. Want to read about the misconception some students have that fractions aren’t numbers?\u00a0 Check out this blog post<\/strong> <\/a>all about it!<\/em><\/div>\n

 <\/p>\n

\n
Hey there!\u00a0 Looking for more?\u00a0<\/strong><\/em><\/div>\n
<\/div>\n
Follow me on social media and by email!<\/strong><\/em><\/div>\n
<\/div>\n

 <\/p>\n

Find me on Facebook<\/a>,\u00a0Tiktok<\/a>,\u00a0Instagram<\/a>, and\u00a0Pinterest<\/a>\u00a0and<\/div>\n
you can also\u00a0sign up for my NEWSLETTER<\/a> where I start you off with an awesome freebie! You then will get even more teaching tips, freebies, and offers delivered right to your mailbox!<\/div>\n
\"\"<\/div>\n<\/div>\n
<\/div>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Today we kicked off our fraction work, and every time I start this unit I\u2019m reminded just how important it is for intermediate students. Fractions show up everywhere in our standards. The understanding students build here truly matters! I like to take the time to document the thinking, the misconceptions, and the little moments of […]<\/p>\n","protected":false},"author":2,"featured_media":11941391,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2,343],"tags":[225,194,179,224,182],"class_list":["post-6469","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-lessons","category-fractions","tag-common-core","tag-fractions","tag-math","tag-mathematical-practice","tag-problem-solving","wpbf-post"],"acf":[],"yoast_head":"\nFraction Folding-discovery learning - The Teacher Studio<\/title>\n<meta name=\"description\" content=\"Using hands on strategies to help teach fractions is key. 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