3 Powerful Fraction Concepts Students Need To Know

     There are so many fraction concepts that elementary students need to master! They need to read, write, model, and reason about fractions. They move on to computations with like denominators, then unlike denominators, followed by multiplication and division. The goal is to be able to apply these skills in real-life situations.

Where Is The Power?

     I've started focusing on three powerful fraction concepts that students need. Students need to clearly understand each concept and be able to explain each one in words and modeling. The power comes when students can integrate the concepts, model all three, and explain the differences between all three at the same time.
Vertical Version


Finding The Power

     When we begin our fraction work, identifying a unit fraction like 1/4, or one out of four pieces, seemed to come relatively easily. We use manipulatives, colored area models, and number lines.

     Next, we look at 4/4, or four out of four pieces. That's the whole one. This was a little tougher because one is usually written as "1" and we tend to neglect pointing out that it can be 3/3, 5/5, 10/10, or any other whole fraction.

     When we're well into fraction studies, we talk about fractions greater than one whole, often called improper fractions. That's what 4/1 looks like - and is - to my students...an improper fraction. What we were forgetting to emphasize was that 4/1 is four whole, individual things: 4 pizzas, 4 books, or 4 days. We all got that 4 means four wholes. It's the format 4/1 that kicked us a little.

     My mistake was in always teaching these three concepts in isolation from each other. Students could show an understanding of each one individually, but comparing even two caused some confusion.

     One day, almost in desperation, I wrote these exact fractions on the board: 1/4,  4/4, and  4/1. I directed students to explain the differences between the three, using pictures, words, area models, or whatever worked for them.

     "Can I use a number line?", one student immediately asked. I answered, "Absolutely", and off we went.

     As I expected, modeling and explaining 1/4 was pretty easy. Most students quickly used one of the area models you see in the first column above.

     Modeling 4/4 made a few pause to think, but most moved on quickly. Yep, it's the whole thing.

     The format of the third fraction, 4/1, slowed down almost everyone. I could almost hear students thinking, "I know that's four separate things...I think..." As I peered over shoulders to see how we were doing, I got a number of those hopeful looks that ask, "Is this right?"

     When we pulled everyone back together to share, I actually saw the relief on students' faces - the same relief  I was feeling! Yes, they knew what each fraction was in isolation and could define and model them. More importantly, I was sure that they knew the differences between the less familiar fractions and how they relate to each other. Whew! What power!
The horizontal version will resonate better with some students.

Why We Should Use This Activity

     I love this no-prep activity because of its low floor and high ceiling. We can repeat it with different fractions from time to time to keep skills sharp. I especially value it because it reaches down and builds foundational math concepts that are essential to student mastery.

     Consider trying this activity with your students. Begin with unit fractions that have smaller denominators, such as 1/3, 3/3, 3/1 or perhaps the example of fourths used in the image above. If you'd like to challenge students, move away from unit fractions and see what happens!

     I'd love to know how working with these three powerful fraction concepts works in your classroom!

See other products that support fractions at Growing Grade By Grade!

We're all in this together!
Pat at Growing Grade By Grade


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Build Powerful Math Logic With A Simple Game: Zip, Zap, Zorp!

     Are you looking for a simple, but powerful, math game that builds math logic skills?  Welcome to Zip, Zap, Zorp!  It originated with the fabulous AIMS Center for Math and Science Education, part of the AIMS Education Foundation.  I recently resurrected it for my 4th grade Math Club.  It's simple, has one quick and easy prep, has a low floor and a high ceiling, and really gets students excited about math!  Most importantly, Zip, Zap, Zorp builds math logic skills.  

Here's The Prep

-You can play this game in pairs.  We played as a large group in order to teach everyone how to play at the same time.
-Begin with two-digit numbers with no repeating digits.  
-Your only prep is to make a display like this one.  Make it once, use it all year!

Poster with explanations of Zip, Zap, Zorp game clues

How To Play Zip, Zap, Zorp:

To begin, choose a secret 2-digit number. Honestly, I have to write mine down to keep track of my responses. Let's use 89 as our example here. Here's how our first round went:

Me: Guess a 2-digit number.

Andy: 45
Me: Zip. No digit is correct. (I repeated the meaning of each clue during the first round as we all learned together.)
Me: Class, let's organize our thinking and keep track of our clues. We definitely know that neither 4 nor 5 are part of my secret number because I "zipped" them.
At this point, I wrote the digits from 0-9 on the board and crossed off the 4 and 5. Some students did the same on paper.
Barbara: 60
Me: Zip. No digit is correct. We can cross off 6 and 0.
Charlie: 28
Me: Zorp. One digit is correct but is in the wrong place.
Davis: 82
Me: Zap. One digit is correct and is in the right place. We know one digit is correct, but we still don't know which one.
Ella: 81
Me: Zap. One digit is correct and in the right place. Class, did you see how Ella "tested" the digit 8? She knows both 8 and 2 might be correct. Her new number got zapped, so she knows 8 is the digit that is correct and in the right place. We can cross off 2.
Franklin: 80
Me: Zap. We still know the 8 is correct. The number is eighty-something.

Students continued to guess numbers in the 80s until they discovered 89 was my secret number.

This is one of the most engaging games we've ever played. It is designed to be played in pairs and I suggest you transition to that as soon as students feel confident with the rules.  Challenge your students by allowing 3- and 4-digit numbers and repeated digits.  I suggest that students get in the habit of writing down their secret number to keep track and to show their partner.  Schedule some time for students to share and discuss strategies that work for them. You'll be amazed at their comments!

Would you like to access some more amazing math and science ideas? Check out what they have to offer, including free samples, at The AIMS Center for Math and Science Education.

I'd love to hear how your class builds math logic skills using Zip, Zap, Zorp! 

If you'd like some more math games, head over to my Growing Grade By Grade store on TpT and check out my "Games" page. Have fun and learn math!

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8 Best Ways To Celebrate Pi Day

Pi Day is one of the most exciting days of the year! It's on March 14 to connect with the most common estimation, 3.14. Even if your grade does not include a math standard for pi, students can still have loads of fun and learning by studying pi.

I taught 5th grade for eighteen years and we studied pi for most of them.  I gathered a nice collection of content and activities that I'd like to share with you. Here are some of my favorite Pi Day activities!

1. Introduce the concept of pi with videos and books.

There are a good number of videos and books that address the concept of pi. Math Antics has a good video.  Cindy Neuschwander's Sir Cumference and The Dragon of Pi has entertained and educated children for years.  As always, preview all videos before showing them to children.

2.  Learn through music.

Singing is one of the best ways to learn any academic content. I compiled a mini songbook of pi-related songs set to familiar tunes. We always began several weeks before the big day, singing and learning. Below are a few favorites.
One of the most amazing pieces was created by musician David Macdonald. He assigned each digit of pi to a note on the piano. The resulting song is both haunting and amazing! Listen to it here

3. Celebrate Albert Einstein's birthday!

Mathematically, it's a coincidence, but...is it really? Einstein's birthday is on March 14, Pi Day! Let your Pi Day celebrations revolve around one of the great mathematicians/scientists of all time!

4. Keep it simple. 

Pi is actually a simple concept. Even third- and fourth-graders can understand the concept if you focus on pi being just an estimation. Here's how:
  1. Define circumference (the distance around and difficult to measure because of the curves) and diameter (the distance across and easy to measure because it's straight) as two measurements of a circle. 
  2. Explain that if we multiply the diameter times 3, we can get a good estimate of the circumference. Period. End of explanation. 
  3. Let students practice, practice, practice measuring the diameters of jar lids, paper circles, mixing bowls, cups, and plates. Multiply by three and they've found the circumference - some very grown-up math! 
  4. Once students have this concept firmly in place, point out that pi is an estimate and we'll never get it exactly, but we can get a little closer by changing that 3 multiplier to 3.14. It's just a little more precise.

5. Hold an optional Digits of Pi Reciting Contest.

We did this year after year and it was a real hit! My all-time winner recited over 100 digits of pi in front of his classmates and made it into the district newsletter! 

Are you interested in holding one in your classroom? Distribute this list to students for study, then use it to keep track as students recite. As a newsletter subscriber, you can download these documents from my FREE RESOURCE LIBRARY.

6. Integrate with English Language Arts.

Teach your students to write Pi Poems. They don't have to be about pi, but poems where each word has the same number of letters as the corresponding digit of pi. The first word would have three letters, the second word would have one letter, the third word four letters, and so on.

You could also write poems where each line has the same number of words as the corresponding digit of pi. The first line would have three words, the second line would have one word, the third line four words, and so on.

7. Delve into Pi Day art!

Model how to make a Pi Day necklace or bracelet. You'll need stringing beads in ten different colors. Assign each color one of the digits from 0 to 9. Students will string the beads in the order of the digits of pi. They will be beautiful!

Take this idea really large and make a paper chain following the same concept. Using ten different colors of construction paper, assign each color one of the digits from 0 to 9. The paper chain will be long and impressive. Hang it in loops down the hall.

Another activity is to design Pi Day T-shirts or buttons. Give students a T-shirt template or round paper and turn them loose! 

8. Have a Pi Day Party!

Food is a fun way to celebrate any math concept! Provide as many round items as possible, such as cupcakes, pies, and cookies. Have students measure for pi before eating. Don't forget to measure plates and cups, too!

Remember, by joining my subscribers, you can have access to my FREE Resource Library with the materials above. 

There are any number of fun, educational Pi Day activities. I'd love to hear about what YOU do! Happy Pi Day!

Let me know how YOUR Pi Day goes!

Growing Grade By Grade
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9 Easy and Engaging St. Patrick's Day Resources

It helps to be prepared for the next special event at school as we race through the year! I'll admit I've purchased, downloaded, and prepared products just a few minutes before I needed them, but it's not the best way! It's a good feeling to go into school prepared and feeling ready.
For St. Patrick's Day, consider preparing some math materials that engage students and review content. Here's a FREEBIE:

Try these helpful activities and ideas to spice up your classroom for St. Patrick's Day:
Best wishes as in the coming week.

Growing Grade By Grade
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