Adding 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 revise 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 for the Day 34

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

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 real fun way to get your students to think deeper about a subject without them realizing that they are doing it.

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

The THINK part gets them thinking a little deeper, This art makes me think about….

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

It is my way to get 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!

The Elevator Speech

10 minutes

Concept: Being able to add fractions is as easy as remembering common factors to create equivalent fractions. Students will work you to make list of equivalent fractions.  This lesson is addressing Common Core standard 5.NF.

Start out with the Equivalent Fractions powerpoint to start discussion about equivalent fractions. Talk about whether the two fractions bars shown are equivalent or not. The second slide shows unlike fractions - they have the same number of pieces (numerator) but different denominators.

Have a discussion why these are not alike even though the number of pieces is the same. The point of this is to get students to recognize 'size' when analyzing fractions. The third slide demonstrates that just because a fraction bars are different sizes, it doesn't mean that they are not equivalent. This is explicit and comprehensive for a reason - both of these slides cover areas of common misconception.

You may have to model, practice, and practice some more to help all of your students to understand. An important element in this practice is that students be able to model their thinking. Fraction strips or bars are great fraction models for students to use. Students need to be able to add fractions with unlike denominators and they also must be able to explain why it works. Knowing that fractions can be added together once they are the 'same size' is very important to their understanding. 

Note: The most important part of the Equivalent Fractions powerpoint is that just because fraction bars are not the same size, it doesn't mean that they do not represent the same idea.

Work It Out

40 minutes

Have students (in teams) build equivalent fractions for:

½ , ¾ , 2/5 ,  2/3 , ¼  (I cut slips of colored paper and assign the fractions by color.)

Don't do just one, see how many students can make. It is important to emphasize using numbers flexibly. Students need a lot of practice in manipulating numbers to understand that there is usually more than one way to solve a problem. That means they can pick a strategy that works for them!

Next, I demonstrate adding/subtracting fractions, using the equivalent fraction models students created (I have my own set).

Add ½ + ¼ and draw lines to the fractions that you created. Do more examples to help students see how to make the connection. (This I model with large strips on the white board.)

Give students the following fraction problems to solve using fraction strips or bars, which they can draw. The use of models is a requirement for these problems. I emphasize that showing their thinking is more important (right now) than the answer.

1/3 + 5/6      2/5 + 2/10      1/2 + 3/4     4/5 - 3/10

Have students put their thinking (paper) up on the white board. Bring students back to the carpet and have different groups (pre-chosen) to explain their thinking

Give them the following fraction problems and have them model their thinking

1/3 + 5/6      2/5 + 2/10      1/2 + 3/4     4/5 - 3/10

Students put their thinking (paper) up on the white board. Next, I bring my students back to the carpet and have different groups (pre-chosen) come to the board to explain their thinking.

*Another great way to showcase work is to have students make large posters explaining the process of adding fractions including a model. Have a gallery walk where 1/2 the students stand by their work and the other 1/2 walks around to see what they are learning!

If students finish early, have them make a list of 6 – 10 addition and subtraction problems with unlike denominators.

For those advanced students: I like to stack fractions just as we stacked whole numbers for addition. It makes room to do the equivalent fraction work!  

Adding and subtracting fractions with unlike denominators is one of those things that take practice doing the work! To get students to do as many as possible, be creative and come up with fun ways they can work such as having them create problems and testing each other!  I like to give students the opportunity to create their own equations, it give ownership and it also allows a chance to differentiate! 

Make sure you are watching out for struggling learners. Having kids making their own problems and test each other will give you more time to work with those struggling kids, especially when it comes to making equivalent fractions.

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.

Talk about the struggles, check in for understanding, talk about stacking. This is a good place to bring misconceptions to class. I like to have the students lead this discussion as it allows me the opportunity to hear and listen to the students. An easy way to do this is to ask a blanket question of 'who was struggling with fractions' or 'did anyone struggle and want to share their success?' or 'can anyone give us an example of where you struggled so the class can help us work it out'

I also like to have students that were successful to share their thinking. These students I usually talk with during the work time and ask them if they are willing to share.

You can also write a new problem on the board and do a 'turn and talk' with partners (I always have students sitting with their table mates on the floor) and discuss how to solve the problems. Then I randomly call on students and ask them to explain what their partner told them, this holds students accountable for listening!

Not only is the close critical to student learning, it is also a great time to do a quick formative assessment -- checking for understanding.

Quick Assessment

5 minutes

The Post-It Poster    2/5 + 1/10, showing a model if time allows.

Look-Fors: 2/5 + 1/10 = 3/15 will be a common error. Another thing you'll notice is the math work and the model work not matching.

A correct model helps these students solve their own confusion. Students get a great deal out of the quick assessment, because it tells then whether they've come to an understanding. Of course, I also use these quick assessments to guide my lesson for the next day. It shows me which students need more support and informs the grouping. It also tells me what types of problems I need to tackle with the small groups. I also discover which students are ready for more challenging problems as well as who I can make a class expert. 

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.