Our Garden Problem

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SWBAT explain the fractional area of a model using the real world example of a garden.

Big Idea

Using a debate format this lesson provides students the opportunity to solve a complex problem similar to sample item from the PARCC exam.


5 minutes

I show students a picture of complex fraction to review whether it show halves, fourths, both. 

Today, you will be looking at another picture and deciding what fractional part it shows.  Today, you will be looking at a flower garden and deciding if it shows more than half or less than half. 

Look at the number line (I display a blank number line on the board).  Let's mark 0 and 1. 

Where does half go? 

Let's mark some other unit fractions that are larger than half and smaller than half. Students will use the paper fraction strips they made in the lesson Debate: Does This Shape Show Fourths.  

My goal is to have them name fractions such as 1/3, 1/4, 2/3, 3/4 and possibly even some sixths and eighths. 

Once the number line on the board has fractions on both sides of half, I ask the students to write the number line in their own math journal for today.  

I use math journals throughout lessons so that students have the opportunity to record their own thinking and to link the information from the whole group instruction to their own individual experience.  Since I have a few students who struggle with physical demand of writing and receive special ed services for this, I frequently provide sentence frames or preprinted prompts, to help them focus on the math content rather than becoming overwhelmed with a long writing assignment.  As a result, I provide this sentence frame to the entire class so as not to single out the two students.  It also makes our math time more efficient, and it keeps everyone focused on the math topic and their math thinking. 

Whole Group Discussion

10 minutes

During this section of the lesson, I began by showing the students a complex shape we had worked with in the past to determine if a shape showed half. (link to lesson) 

I have the students review what they learned about this shape and share their ideas with each other and with the group.  The reason I have them partner share at this time is so that everyone gets a chance to speak and listen, and it supports all levels of learners.  If one partner does not remember or understand the complex shape, they can gain information from their partner without being put on the spot to answer a question from me.  The peer support of this part of the lesson builds their confidence to move to the next complex shape being introduced for today's lesson. 

Reviewing this complex shape is also important because the students will remember the debate format of the lesson that was used this image.

Next, I ask a few students to share what they heard from their partner or what they explained to their partner about the shape showing half.  By asking what they heard, the students are required to repeat and use their listening skills.  Also, by asking the students to give an explanation of the shape requires more than yes it is half, or no it is not half type of response.  

This discussion also provides me with the opportunity to make a formative assessment of their prior understanding, and determine if I need to provide more review of this shape, or if the students are ready to be introduced to a new image for today's lesson.  It also addresses the rigor from a prior lesson and connect it to this lesson. 

Next, I display the image for the students to see on the screen.  I explain that this picture is a garden and we they will determine how much of the garden is already planted and growing, and how much is still available to plant. I have purposely only marked the outside border of the image without dividing any part of the garden so that the students can make their own determination about the fractional size of the garden to the whole garden area. 

I ask the students to keep their thoughts to themselves, and remind them that they will be recording this in their journal/foldable CREATE FOLDABLE.  The students return to their seats and record the fraction of the garden that is planted on the number line, and they also record their explanation for that fraction.  This is a quick write, and they are asked to keep their thinking to themselves at this time. 


30 minutes

During this lesson section, the students are divided into two groups that they determine by the fraction size they recorded in their journal.  The students choose their group if they think the garden was more than half planted or less than half planted.  I quickly count for myself how many students are on each side so that I can keep track of the majority opinion of the students. This helps me to guide the debate.  Some tips for you when you do this activity (to divide the groups).

I review our classroom rules for debate.  One person speaks at a time, and I choose the person speaking.  After one side speaks, the other side gets to speak. After each round, students may choose to switch sides. Because the Common Core math practices require students to construct viable arguments and to reason abstractly and quantitatively, I choose to create debate lessons.  This also increases the rigor of the problems I am using in my class and similar to those that will be presented on the PARCC assessment.  It makes this type of problem accessible to all students without them getting stuck or just guessing for an answer.  It is showing them how to persevere and problem solve. 

After two sets of discussions, I provide the students with the image to manipulate on their own.  This image is pre-cut to save time and make sure everyone has the same resource and tool to use throughout the lesson.  Students work with a partner or on their own to determine the fractional part of the garden.  Students record again in their journal their new thinking in the next section.

Round 2 of Debate: Students return to the debate area, and choose a side based on their analysis and discussion with their partner or from their own thinking.  Again, I count to see if there has been a change. This time there is only one round of debate, and then I pose a question to the group.  What can I do to the shape to determine the fraction of how much is shown?  

If the students have already begun to manipulate and fold the shape, I will ask the students to begin writing in lines with pencils to explain the fraction.  Students return to work with their partner to the size of the garden.   They also record their thinking and what they did in their journal.  For the students needing support with recording their thinking, I have them partner with another student and create one journal at this time.  This group journal can be photocopied, or transcribed with the occupational therapist. 

Round 3 of Debate: Students return to the debate area with their shapes in hand.  I ask the minority side to go first and explain their reasoning about the fractional part.  The majority side responds about their reasoning. 

This continues and students switch sides as needed based on the evidence provided by other students.  I have the students bring their shape to the debate area at this time so that all students can manipulate the shape as needed based on the arguments of the other students.

If needed, I send the students back to work with their partners to create other lines or folds to determine the fractional part based on the reasoning that has been presented during the debate. 

Debate ends once all students have chosen a side, or we are down to the final three to four students.  I don't want these few students to feel pressured to prove themselves or be uncomfortable in their position. It may be that they need extra support from me at this point, and I can provide small group instruction at another time to help them through this problem.    

The last task for the students is to record in the last part of the journal the fractional part of the garden that is planted with an explanation and drawing.  I give the students a new copy of the garden and they can write in new lines and drawings to support their explanation. 


15 minutes

The closing of this lesson is asking the students to record on their whiteboard what was the one thing someone said or they saw to help them figure out how to find the fraction of the garden.  I use the whiteboard because then each person is accountable, and I can use it as a formative assessment.  I may prompt them to think if it was drawing the lines, folding the shape, drawing it on a whiteboard.  I have them share their whiteboard with a partner. I want them recognize and identify the key point of the lesson for themselves and share it with someone else. 

Using what they recorded on their whiteboard, I have them add this information to their journal/foldable.  This foldable will be glued into their math journal.