James Ewing MOUNT VIEW ELEMENTARY, SEATTLE, WA
5th Grade Math : Unit #2 - Adding and Subtracting Fractions with Unlike Denominators : Lesson #7

Subtracting Mixed Numbers

Objective: Students will be able to add and subtract mixed numbers by converting into improper fractions.
Standards: 5.NF.A.1 MP1 MP2 MP4 MP6
Subject(s): Math
60 minutes
1 Language Objective and Prior Knowledge - 0 minutes

Language Objective: Students will be able to change mixed numbers into improper fractions and explain their work using academic language

Prior Knowledge: improper fractions, adding and subtracting fractions

2 Math Blast - Lesson Activator - 15 minutes

Math Blast Number of the Day 35

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.

3 See, Think, Wondering - 5 minutes

Piet Mondrian No. 111 with Red, Yellow, and Blue

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!

4 The Elevator Speech - 10 minutes

Concept: Fractions are fun but it always amazing how student 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.

Concept: Start with talking about changing mixed numbers into improper fractions. You may need to go back and talk about what an improper fraction is to begin. There is a simple algorithm to change mixed numbers into improper fractions: multiply the denominator by the whole number, and then add the numerator. This becomes the NEW numerator. Your denominator stays the same.  Example:  3 ½  becomes 2 x 3 + 1 = 7/2

BUT before you talk about the algorithm show the attached model and ask the students what fraction is represented. Do not show them the answer. Wait to see what responses you get. I hope they see 3 1/2 but you are trying to get them to see that it is also seven 1/2s or 7/2. They are going to need this skill to be able to add Mixed Numbers.

Is this the same Elevator Speech as Adding Mixed Number Lesson?
Modeling

Simply - yes!

I used this same model in the lesson Adding Mixed Numbers but I'm OK with that. It is the concept that I am trying to get across. BUT if it is bothering you, change it and create a new model.

I didn't change the model because what I would do is use this model again and then maybe challenge them with a new one and have some students come up and draw a model.

Repetition is key, so using models that they are familiar will help students solidify their understanding.

5 Work It Out - 40 minutes

Have students create a Four Square Poster as follows:

Create mixed number with a denominator of 2 and convert it into an improper number

Create mixed number with a denominator of 4 and convert it into an improper number

Write an subtraction expression using both of the mixed number you use in the two upper boxes and then solve the expression using the improper numbers you created

 

Draw a model to represent your mathematical expression

If students finish early: have them work in teams and test each other. A gallery walk about be a great idea here, giving students a chance to show off their thinking and be able to explain it to classmates.


Note: I keep the math simple on purpose. I want to make sure that students have a solid understanding of the concept. I think sometimes we try to make things too hard for students when they are trying to learn the concept (see reflection). I use the Four Square so that students can organize their thinking. if you have students pushing through to quickly give them harder problems and challenge them!

Great Learning vs. Good Learning
Advanced Students

You may have noticed that a lot of the work that I give seems to be the 'easy side.' When I assign work I think of the outcome I need to see. When we are learning a new concept (such as adding Mixed Numbers) I am looking to see if they understand the concept.

If I use a tough problem, than I am assessing something beyond the concept. If you want to challenge different groups, differentiate with several different problems that can be handed out. I really thing students learn better when they learn a concept first and then add on the level of difficulty.

I suggest you consider why you might want to differentiate, because I think it is quite important that there are times that ALL students are working on the same problem, as this gives students a feeling of equity.

Great work comes from a solid understanding. Good work is being able to do the work, perhaps without deeper meaning.

6 Closing The Deal - 10 minutes

I close with a student discussion about the similarities between Mixed Number subtraction and simple fraction subtraction. Invite students to share what they learned and the connections they can make between the different types of fraction subtraction they have learned. Support students by encouraging them to "show" (using drawings, models, etc.) their thinking. This supports the verbal explanation, because students can describe the model and how it "works" to explain their thinking.

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. 

7 Quick Assessment - 5 minutes

Post-It Poster: 3 ½ - 2 ¼ =   (Students provide the answer + model to show the thinking which informs the answer.)

Look-Fors: Students adding denominators means that students do not have a solid foundation in adding or subtracting fractions. Getting an answer without a model shows a basic/procedural understanding.

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.