Subtracting Unlike Fractions

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Objective

Students Will Be Able To add and subtract fractions by using common denominators and equivalent fractions.

Big Idea

Recognizing that in order to add fractions we need to have the same denominator. The denominator represents the WHOLE and the numerator represents the BITS/PIECES.

Language Objective and Prior Knowledge

Language Objective: Students will talk about adding or subtracting using academic language: numerator, denominator, and equivalent. Students will be able to rewrite fractions to have common denominators.

Prior Knowledge: In 4th grade students started working on adding and subtracting fractions with like denominators. Some will have knowledge of common denominators.

Math Blast - Lesson Activator

15 minutes

Math Blast Number of the Day 31

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 No. 3

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.

It is a real fun 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 gets them thinking a little deeper. For example, "This art makes me think about….".

And the WONDER gets them really thinking deeper. For example, This art makes me wonder if…. ".

It is my way to getting students' 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 have included a separate version of See, Think, and Wondering just in case you want to do this separately. It is also included in the full version of Math Blast.

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! If you marvel at the beauty and patterns of nature, you could share leaves, ferns, shells, flowers, and so much more and marvel at the repetition of patterns found in them.

The Elevator Speech

10 minutes

Concept: Being able to subtract fractions is as easy as finding equivalent fractions. Students will work with you to make a list of equivalent fractions. 

Concept: 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.

Have students build equivalent fractions for: 

Board Examples

Don't stop with one, see how many you can make together. This is developing students' flexibility in thinking about how the same fractional amounts can be represented differently. 

Now show the relationship to these fractions to adding /subtracting fractions. I use a comparison approach called "stacking" - in this case we stack fractions.

Add ½ - ¼ and draw lines to the fractions that you created. Do more to help students see how to make the connection.

Work It Out

40 minutes

Have students make a list of 6 to 10 subtraction problems with unlike denominators.  I like to stack fractions just as we stack whole numbers for addition. It makes room to do the equivalent fraction work!

For each math problem the students create, I make sure they also solve these problems mathematically using a model. They should write the problems on one piece of paper with the answers on another piece of paper. This way once all students have 6 (I say 6 to 10 for those students who work faster. This way there isn't down time.) Students then swap their problems and 'test' each other. 

Note: Students LOVE to test each other as it puts the learning AND teaching in their hands. They are not just working to 'please the teacher' and you'll be surprised to see how hard they try to make it. Put is also supports those struggling learners as it gives them a chance to show what they know!

Note: Look for students that have the same solution, but used different methods to solve. This is a great conversation starter - is one correct and one incorrect? For example: 1/2 - 1/4 = _______

Responses could be: 2/4 - 1/4 = ______   or 4/8 - 2/8  

Either way the solution is the same. If students are following this discussion with understanding, you might want to extend the conversation to discuss if one is more efficient than the other.

Note: This is learning that takes practice! Try to as many as the student can do. Have them create problems and test each other!

I like to give students the opportunity to create their own equations. This gives them ownership and it creates some of differentiation in the complexity of the equivalent fractions being created.

Closing The Deal

10 minutes

To close we about the struggles, check in for understanding, and discuss stacking.

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 the work that they did. It is also another chance to give a quick formative assessment to check for understanding.

 

Quick Assessment

5 minutes

The Post-It Poster: 2/3 – 1/6

This 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.