The Tree of Peace: A Division Lesson

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SWBAT solve division and multiplication word problems by focusing on key information and using a mental model.

Big Idea

Division can be used to determine the approximate age of trees. Knowing the age of trees is one factor in determining their intrinsic and human value.

Teacher Background

The Eastern White Pine can be found in almost half of the United States and are called the Tree of Peace by the Haudenosaunee (Six Nations) people of what is now New York state.  (The pronunciation of Haudenosaunee can be heard on this audio clip.)

This Pinus strobus range map from Wikipedia shows some of the places where the Tree of Peace can be found.

Many people love these trees and enjoy them for shelter, shade or play.  Sometimes people who don't like to rake pine needles will cut them down, even if the tree has survived for over 100 years.

In this lesson, students will learn about how quickly these trees grow and how tall they can be.  They will compare them to some other tall coniferous trees.  They will be developing their understanding of the natural world and how they relate to it as individuals and as part of a community.  

To read the story of how the Haudenosaunee (formerly known to most people by the name the Europeans gave them - the Iroquois Nation) came to call the eastern white pine tree the Tree of Peace, the story is told on the Iroquois Museum site. 


13 minutes

At the start of this lesson I have students fill out a the Tree of Peace: Entrance/Exit Ticket ticket.  It activates prior knowledge and increases their personal connection to the task by asking them about the tallest tree nearby and that they have ever seen.  It lights the mathematical flame for the lesson by asking them to guess how much a tree grows in an average year.  (There is no such average, of course, because of the diversity of trees and habitats in the world).  Finally, by asking them to analyze their thinking around two environmental ethics questions I’m helping them engage in higher level verbal and written discourse across the disciplines.  I firmly believe that their ability to do this in a thorough manner when they are older begins with doing so now at the sentence or paragraph level.

I then show students a 2 minute video of a White Pine Being Cut Down.  The goal is not to persuade children regarding how trees should be managed.  It is intended to get them to develop their thinking by engaging with a complex, multi-faceted issue.  

Word Problems in Context Activity

45 minutes

I teach this lesson in about January, and at this point I expect my students to be able to set up a division problem using repeated addition, subtraction or decomposition strategies for determining how many in each group.  In these word problems, students are working with the multiplication/division concepts of group size unknown and number of groups unknown.

I use a range of strategies to meet the needs of my students.  Students with a strong understanding of place value and basic multiplication facts can solve these problems by looking at division as the inverse operation of multiplication.  The majority of them can work through these problems as repeated subtraction or addition.  Some students need to draw a pictorial representation w/place value cubes.   

I suggest completing most of the Tree of Peace - Word Problems together either in a guided practice or in an independent practice with feedback after every 2 problems. 

There is extra room for many of the problems so that students have the space they need to make picture or number models that best suit their individual learning style.


5 minutes

As students are asked to reflect not only the "answers" but also the "journey" (strategy), it is critical to acknowledge this effort with opportunities to share, show, and possibly revise thinking. Some possible wrap-up questions:

Explain the steps in a strategy you used today.

What was something in the activity that was - too difficult for you, confusing/unclear, you'd like to explore further?

I feel very strongly that the emphasis on this lesson should be upon students persisting at a difficult problem and building meaningful models that enable them to use a strategy they can understand.  This doesn't mean that I tell them that incorrect answers are great.  What I do focus on and praise is their efforts to explain their thinking and persevere in the face of difficulty.

Enrichment/Writing Connection:

Reread the quotes at the beginning of the math page and in 2-3 sentences, explain what you think it means, if you agree or disagree with the sentiment expressed by John Muir, and explain why you agree or disagree.

Supplemental Reading Activity

I've included reading comprehension passage with literal, inferential and open-ended questions, based on a Haudenosaunee oral tradition about how 5 different nations joined together, and the symbolism of the Eastern White Pine.