To begin, we will follow a two-step reading protocol.
After reading and annotating the task description, I will ask my students the questions in bold below (each is followed by teaching moves and/or possible student responses).
What information does the problem give us? How did you annotate?
I annotate my copy under the doc camera as students share. This is the first opportunity of the school year to reinforce annotation expectations. Then, I circulate quickly to give real-time feedback.
What is the question asking us to find?
"The problem is asking us to find the largest number of balloon arrangements Jasmine can make."
What information do we not know?
"We don’t know how many groups Jasmine will make and we don’t know how many of each color balloon will go into her arrangements."
Are there any words in this problem that you don’t know?
If we don’t figure out the meaning of a word, would you still be able to solve this problem?
What do you think this word means?
Allow 1-2 students to define the word, and then add to it, if necessary.
What do you think a reasonable prediction would be for the number of arrangements Jasmine can make?
Allow 1-2 students to share their prediction, and be sure they explain why they think theirs is a reasonable prediction.
What would you say if someone predicted Jasmine could make 50 arrangements?
"That prediction isn’t reasonable because Jasmine doesn’t have 50 of any of the colors of balloons. It isn't possible for her to make 50 of the same arrangements, given the balloons she has."
For this exploration, I plan to allow my students 4 minutes to work on their own, and then 8 minutes to work in partners.
As students are working on this problem, I expect them to:
As pairs are working, I circulate and engage students in conversation. I'm asking:
During this work time, I am looking for student work samples to show on the board during the presentation section. Before I teach the lesson, I also create my own samples of Student Work. This helps me to know what to look for. It also gives me a sample to display for our discussion if students get stuck.
This is the first presentation of the school year, in the very first lesson, and I anticipate students will need much guidance, practice, praise, correction, etc. I explain the importance and role of presentations – a chance to practice public speaking, a chance to share thinking, an opportunity to ask peer questions about his/her strategy, etc. I share that I will ask questions of both presenter and the rest of the class.
The mathematical work during this section of the lesson is to make a list of factors for each balloon color, and identifying the common factors, and then greatest common factor. Although we'll talk about multiple student strategies during this section, I want the class to have a clear idea that a list of factors is the one efficient strategy for finding the GCF (and one that we'll focus on in the next lesson).
I will ask for a student volunteer to be the very first presenter of the school year. Based on my observations during the lesson, I will pick a student who used a visual strategy. The student should present his/her thinking. I help them along the way by asking probing questions:
I will also suggest sentence frames that would help him/her make his/her thinking clearer. For example, rather than "I drew a picture," I help the student say "I represented the white balloons with w’s. I know that there are 24 white balloons, so I used 24 w’s and split them into groups by…". My goal is to help students be specific and detailed as they present. I'll ask the rest of the class if they also tried the presented strategy. Then, I'll ask students who used the strategy to add to what’s been presented. Finally, I ask if there are questions about the strategy.
I'll go through the same presentation process with a piece of student work that used a list of factors as a strategy. I have a copy of this strategy ready to go, in case students don't get there themselves.
To bring this lesson to closure, I plan to guide the class through a conversation reflecting back on the problem solving strategies that were presented today. The questions I plan to ask, and possible student responses, are below:
How are the strategies similar? Different?
Which is more efficient? Why?
Which strategy would be better if Jasmine also had 12 purple balloons and 40 yellow balloons? Why?
What if Jasmine had 145 red balloons and 220 purple balloons – which strategy would be better in this situation? Why?
What if the problem just said Jasmine wanted to make equal groups? Are there other numbers of groups Jasmine could make, if we removed the constraint of needing thelargest group? Talk with your partner for 3 minutes about this.
1,2, 4, and 8 are the common factors of 32, 24, and 16. Why is 8 the correct answer to the problem we were initially asked?
I wrap up the discussion naming the key points:
My students will have the opportunity to practice finding the GCF of a set of numbers in the next two lessons in this unit.