Expressing Fractions, Mixed Numbers, and Division Expression

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Students will be able to convert fractions into decimals using place value of 10ths and 100ths.

Big Idea

0.25 is the same as 25/100. And ½ is the same as 5/10 is the same as .5

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. Fractions can also be converted into a decimal using 10ths  and 100ths

Prior Knowledge: equivalent fractions, place value of tenths and hundredths, and the work that students have done in Math Blast if you have been using this program.

Math Blast - Lesson Activator

15 minutes

Math Blast Number of the Day 33

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 RYB

I end Math Blast and lead into my lesson with a See, Think, Wondering. The art is 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: Fractions are fun. But they are complex for students, and I'm always struck by how students forget over the summer regarding fractions. This lesson address specifically Common Core Standard 5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

The concept we are thinking about today is that fractions can be changed into decimals using place value of 10ths and 100ths

32/100 is the same as 0.32, and 3/10 is the same as 0.3. We began this work in the opening of the Math Blast.

I bring the students back to the opening of Math Blast where I'm establishing the practice of writing fractions every day (day 2!) by putting the daily number over 100. This leads up to writing the daily decimal (along with the daily percent).

So now, we practice a few decimals by putting any number over 100 and converting it to a decimal. 

What if it is 7 over 10?

What if it is 9 over 100?

What if it is 24 over 100?

Here is the challenge: what do we do if the denominator isn't 10 or 100?

What if it is 3/50 (= 6/100)

What is it is 15/25 ( = 60/100)

Work It Out

40 minutes

I have the students start to create their own conversions.

First, I make sure that they know what numbers we can use for denominators (5, 10, 25, 50 are the best to begin with). This is a discussion that I have before we leave the floor to go back to our desks to work. It will be helpful for students to understand that we are going to be working with equivalent fractions. If you can foster this conversation it will be very helpful in doing the work.

The goal is to have each student (or pairs for strugglers) create a list of 10 conversions. I always like for students to be able to display their work for other students to see, I also encourage students to explain their thinking. A gallery walk about 10 minutes into the work will help those who are struggling to get the concept. When students see other students' work, and ask questions, it can be very beneficial to their own learning.

Once everyone is at the same place, students work in teams to create a 5-10 question test to then swap with another team. (This means they need to write the answers to their "test" on another sheet of paper.) I love students testing other students!

Once the tests are created have teams swap papers and take the test. Once they are done, return the test to the creators to have them score them!

Note: When students design their own tests what they don't realize they are doing is proving they can do the work. It is always fun to see students that design really hard problems to solve. Students will make tests harder than any teacher would create! This is a great quick formative assessment to check for understanding.

Closing The Deal

10 minutes

Closing a lesson is very important. When I bring the class back together, the purpose is to create a personal connection to the learning objective of the day. Also, I make sure that to make a connection to the word of the day.

What did we notice? Are fractions and decimals related, if yes why are they related and how are they related?

Can we think of this as powers of 10s or 100s?

This closing gives students the opportunity to make the connection to what decimals mean and how they work, as well as the word powers through the work that they just did. It is also my chance to give a quick formative assessment to check for understanding of today's objective.

Quick Assessment

5 minutes

The Post-It Poster: convert 20/25 into a decimal

Students write their response (and their name) on a sticky note, and stick the note on the class assessment board on their way out the door.

Look-Fors: Students that write 0.20 or 0.25, not converting it to 80/100 to be 0.80 or 0.8. Students that get it to 0.8 are showing that they have a solid foundation in place value.

My Quick Assessment is intended not only to be quick but also to be at the "easy to medium difficulty" level. I are checking to see if students understand the basic concept of the lesson. If I make the problem too difficult, I am 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.