Oranges,Social Studies, Sister Anne and Studying the Whole: An integrated lesson

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SWBAT explain the various parts of a division problem.

Big Idea

In this authentic lesson, students use mandarin oranges to figure out how to create equal parts of a whole, discover why fractions exist in relation to that whole and connect it all to division. The lesson is interlaced with a lesson on prejudice.

Parts to the Whole: Discovering what dividing a whole really means

15 minutes

The goal of this lesson is to help students understand that the dividend represents the "whole". It explores the idea that the "divisor" may create fractional parts to a whole or groups of the whole. It also defines the whole as a set. So, there is a lot of thinking about the role each number plays in division!  This will help students fully understand fractional parts to the whole later on when working with fractions, and division of fractions to create decimal numbers.  I am trying to create a foundational connection to fractions and decimals. Prior to Common Core, we taught all of this separately and did not make the connections. CCSS ask us in our Math Practice Standard 7 to help students look for make use of structure. They need to make these connections and see the relationships. The second goal of this lesson is to intertwine  a lesson about prejudice in honor of Martin Luther King Jr.'s birthday. It is connecting math to real life

Setting the Stage to Master the Goal:  My students were each given a mandarin orange and a Sharpie marker ( fine). I asked them to draw lines that would create equal parts to the orange. Drawing on oranges I asked that they plan out their division before they drew their lines with the marker. I was hoping for a lot of different fractional parts drawn on their respective oranges so it would be interesting. I instructed them to self question as they drew their lines:What is the whole? Are my lines creating equal size divisions?

After they drew all of their divisions, I asked them to find the group of people that drew all the same amount of lines on their oranges. Milling to find our groups. Some students were alone. Some students had up to  20 parts.

We shared how many parts to our oranges we had drawn? We discussed that the whole could be divided into as many parts as we chose as long as the unit fractions were all equal.

I asked: So who did it the right way? Who was perfect?  Whose is best? They looked shocked! I said this to set their minds up for the lesson ahead on prejudice. They all realized and their answers supported that everyone was right as long as the parts were equal.

I emphasized the point that problems can be solved in many ways and that the "Box Method" (rectangular sections area model)  that we have been learning in division supported this truth. This connects their current skills to understanding that diverse entry points and different directions to the solutions were ok in math. We talked about how it is a great thing to have many ways to solve problems.

 I continued to get them to reflect on their problem solving through questioning carefully: Why did you choose this amount to divide? Why did other people choose different divisions? I got different answers: Why did you divide it in the size you did? reveals how students thought about how they would divide their orange. It was random thinking but they tried to logically decide how to do it. I also questioned them about how they felt if they were alone?

Social Studies Connection: We talked a minute about that people in our society associate themselves with groups they feel they belong to. I talked about how we sometimes connect ourselves by religion, skin color, ethnic backgrounds and gender. We talked about the groups of people we associate ourselves with. (Organizations and groups of friends.) I explained that sometimes there can be division in people if they begin to think they are the only "right" idea or the "only" way. If they start to think that way, it sets up barriers from other people. I told them that it gets worse when people are afraid of the differences in each other. This was the segue into reading a book I had chosen. Because I had lived through the Civil Rights Era, I could easily connect the book with my life and talk from experiences.  I asked students to place their oranges on their desks and then join me in a circle listen to a story.


Sister Anne's Hands: A Social Studies Connection

10 minutes


Pre-reading: I told them I wanted to share a favorite book in honor of Dr. Martin Luther King's Birthday. I also told them that division is a multiple meaning word and that through this book, they could understand another kind of division.

Sister Anne's Hands:  Sister Anne was a very special teacher and she made math fun...she made school fun. And then, one day, the ugliness of racism comes forth that changes a student's understanding of people and gives a beautiful example of how Sister Anne responded.  This book helps students understand prejudice through this story about this very special teacher. (The math lesson about what is the whole will come together in the last section of this lesson). They loved the pictures. I made connections as I read, because I am from that generation and the story could have taken place in the community I grew up in. My student's jaws dropped just like the students in the illustration when Sister Anne read the note thrown at her head.

Post Reading: After I read the story, I had them go back to their desks and get out their writing journals. We discussed prejudice and the different types of prejudice people show. I again carefully asked questions to create connection, satisfying CCSS language standards: Prejudice: Is that a division? How does it divide us? Do you think you understand it? I asked my students to jot down ideas in their notes to prepare themselves for the discussion. I waited and gave them a little time to get out their thoughts.

As we began our discussion: I asked them to jot down anything they heard from the discussion that they could connect to the idea of division. I asked them to keep their notes and that we would be writing an analogy during our writing lesson later today. 

How is prejudice like division?

Students responded with several ideas:

"Division separates the whole" was about the most profound answer. Wow!

Wrapping up the Social Studies Lesson

15 minutes

I told my students to pick up their oranges again. I wanted them to take their marker and create some designs on the oranges without ruining the divisions that would make their orange unique.

They drew dots, lines, triangles...

When they were finished, I had them drop them into a paper bag. I asked them to join me in a circle and one by one reach in the bag of oranges and find their orange, return to their desk and then peel it. After it was peeled, I wanted them to bring it back to the bag.

After the peeled oranges were all in the bag, I asked them to join me and one by one find their unique orange.They quickly realized they couldn't do it. They all looked alike.

I asked them how their unique orange was so easy to find? How is that orange like a person?

When we peeled the skin off...the way it looked, why couldn't we find our unique orange? How is that like a person?

I asked them: What matters? Does our skin color and uniqueness make us bad? Does it make us good? What makes us the same? How does this connect to prejudice?

What is something we should always remember about people, our uniqueness and differences? They understood that underneath our skin, we are all alike. We talked about having the same organs and red blood and that we can feel the same emotions. They understood profoundly after they had tried to find their peeled orange. I told them that like Sister Anne, we were going to take our focus back to math and make the orange a model for understanding it better.

When the discussion was done, I asked them to  return to their desks, divide up the orange sections and count them. I wanted to wrap up our math.

Throwing estimation in to get them thinking again: I asked them how many sections they thought they would have. They estimated about 10.

Wrapping up the Math

10 minutes

Counting the Sections:

I asked them to count the sections in their peeled oranges. I asked if they actually had 10 sections. Several raised their hands. I asked them to group themselves up. Then I asked for different groupings and we found that the most sections were 12. The range was 8-12. I told them that I just was curious to know if all oranges were divided into the same amount of sections.

We could see by the amount of people in the groups that 10 was the most common division of the oranges.

To wrap up the math:

We discussed how dividing the 1 whole orange produced fractions of the orange. We wrapped up the discussion with understanding that wholes can be represented by any whole number. Divisions are always meaning equal parts of, and that 1 can be divided as well as a 4 digit number.

I said: Therefore, which part of the division equation is always the whole?

Students answered: The Dividend! One student said his dividend would be 10. Another said that his would be 12. I added, can you divide them by 2? And they did, producing 5 and 6 sections per group. This was review for them, but the connection was fun.

One student suggested that we put all the sections together and make one big whole orange.

I suggested we eat the orange sections instead. So we did. They said they really liked this lesson.

I did too.




More Practice in division using "Box Method": Keeping the New Skill going strong...

15 minutes

To keep the momentum going as we are just in the learning stages of box division, I assigned students their IXL F E.4 Online work for homework. This section of IXL is one digit by larger digits of division. You have to watch it because the standard specifically says to master only up to 4 digits. This section will sometimes throw out larger numbers.

I gave them time in class as I roved the classroom to help those who were still having difficulty with getting the hang of it. This clip give you a little insight as we worked on our skills. Dividing using Box

Also, as we are learning, I stress the importance of accuracy.Accuracy