Fractions, Mixed Numbers, and Division Expression

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Students will be able to express division computation as a fraction or mixed number.

Big Idea

Division and Fractions represent the same work!

Language Objective and Prior Knowledge

Language Objective: Students will be able to discuss the relationship between fractions and division using academic language. Students will be able to write out fractions as division expressions, and also the reverse.

Prior Knowledge: in 4th grade students come with basic knowledge of division facts and fractions with regards to adding and subtracting. They should also be coming with some very basic ideas of equivalent fractions.

Math Blast - Lesson Activator

15 minutes

Math Blast Number of the Day 32

Math Blast is a quick, fun, fast-paced math game! It doesn't require a lot of materials - just the PowerPoint, music, white boards, and dry erase markers. I begin every day with a Number of the Day.

Math Blast is also a great place to work on Common Core skills, especially critical thinking skills, discourse and collaboration!

I usually play music while students are working (it is the "Blast" in Math Blast). They have to the end of the song to fill in their board.

In the beginning this is more time than most need, but they will use all of the time when the numbers get bigger. Math Blast is a great way to pre-teach a concept and is really good scaffolding, especially for those struggling learners. I like to add new concepts that will be learning in the near future into Math Blast. This way students are familiar with new concepts when I go to teach them. If they haven't figured out the work through Math Blast they will have at least seen the concept. 

I allow table mates to support each other, this is also a good way to support struggling learners.

The basic content my Math Blast covers is:

  • Begin with prior knowledge tasks, factoring GCF, LCM. In 5th grade this is really good to have understanding for going into fractions.
  • I always add some rounding and estimation, good tools to know and it is pre-teaching our next lesson.
  • I always like to end with a word problem to challenge and support students' skills in answering a problem with what the question is requesting them to do.


The closing piece of Math Blast is See, Think, and Wondering.

See, Think, Wondering

5 minutes

Piet Mondrian Rhythm of Black Lines 1936

I end Math Blast and lead into my lesson with a See, Think, Wondering. The art I choose always relates to the unit I am teaching.

See, Think, Wonder is a dynamic way to get your students to think deeper about a subject without them knowing that they are doing it.

The SEE part is pretty basic thinking. I see….

The THINK part is intended to get students to think about things in ways they haven't before. This is a fun way for students to make connection to the things we're learning in math. In my class, we'll be thinking about math and art.  I use art because I am passionate about art. Use examples of things that ignite your passion! This art makes me think about….

And the WONDER requires enough engagement with the topic (the art) to be able to come up with a question. This art makes me wonder if….

See, Think, Wonder is my way to getting their brains ready to think about math and I find that the transition is great. It is also a quick chance to expose my students to different types of art.

Note: I've added a See, Think, Wondering separate from the Math Blast in case you want to do it by itself. It is also attached at the end of the Math Blast PowerPoint.

Note: You don’t have to use art; I use art because I am passionate about art. Use examples of things that ignite your passion!

The Elevator Speech

10 minutes

Concept: FOOD is GREAT for talking about fractions, mainly because so many food types come in circles. Circles are a great way to represent fraction wholes. It is a good visual.

Note: See my Reflection on Models vs. Manipulatives.

Script, if needed: So, we've talked about my grandfather and his farm. Does anyone remember what my grandfather grows? (Apples)

Well, every year my mother enters her famous apple pie recipe into the State Fair cook off.

The Washington State fair is big here. Apples are big as well so that is why I use this context. Neither my grandfather or mother do any of this but students LOVE it when you include things from your personal life.

I find that students are more engaged if it seems personal and they can relate. Make sure that if you are going to embellish (never lie) that there is some truth to it. Students will know when you are making up something that is completely not true just for a lesson. My grandfather did garden and my mother makes a killer pie.

This past year she entered 3 pies. When she was there for the judging, she saw that there were 4 judges.

She realized very quickly that she would need to divide the pies up into enough equal pieces for the four judges, because the last thing you want to do is give one judge more than another because then you’ll lose the blue ribbon.

Draw three pies on a white board. Now challenge the class for ways to write the problem, 3 ÷ 4. The pies can be divided into 4 pieces each, then count out the number of pieces trying to get them to see the division problem can be written as a fraction 3/4.

Work It Out

40 minutes

Give students a couple of different problems to solve. Students compute, but also are expected to model their thinking, as in pies. Bar models work great as well!

5 pies divided for 3 judges

6 pies divided for 4 judges

8 pies divided for 5 judges

4 pies divided for 7 judges (This is the problem to be covered in the closing discussion.)

Note: I choose these fractions as they are easy to model. This will help struggling learners. To push those higher learners, use division problems that are harder to model!

The FOUR Square Poster is a great tool here to organize their thinking. I LOVE to have students hang up their posters around the room and do a gallery walk. 1/2 the class presents while the other 1/2 walks the gallery.

You can also do a version of this gallery walk where students create a poster with a problem and a hidden answers. Students walk around with post-its and put up their answers. Once every one has enough time to get up answers, the real answer is revealed, students will run around the room to check their work

Closing The Deal

10 minutes

The Closing It section of the lesson is very important. This opportunity allows you to bring the class back together and have them make the connection to the learning objective of the day. You should also make sure that you make a connection to the word of the day. This closing gives students the opportunity to make the connection to the launch and they work that they did. It is also another chance to give a quick formative assessment to check for understanding.

I direct students to talk about why it was hard to divide the pies for 7 judges.

7 is not easy to draw.  Is there a better, more efficient way, to do this work?

Quick Assessment

5 minutes

The Post-It Poster: 4 pies for 5 judges

Look-Fors: Make sure that students are modeling correctly and making the connection to the fraction. One thing you might see is four pies divided into 4 pieces.

The Quick Assessment is supposed to be quick and on the easy to medium difficulty level. You are checking to see if students understand the basic concept of the lesson. If you make the problem difficult you are adding a different level of assessment. If you are teaching a higher level class adding a difficult layer might be appropriate but please note that I do not find it necessary to add this level.