To get the students excited about this activity, I’m going to ask them about ideas or things to put in their birthday treat bag. Then I’m going to ask them how they decide what is going to go into each bag. I’m looking for students to say that they divide the items up equally in the bag or that they put one of each item in the bag. Today we are going create our own birthday bag and it’s going to look like this
The birthday bags come in blue and green
There are 4 different kinds of pencils.
There are chocolate bunnies and lollipops
There are Mickey Mouse and Pluto stickers.
If each friend gets 1 kind of pencil, either a chocolate bunny or a lollipop, and either a Mickey Mouse or Pluto sticker in a blue or green bag, how many different combinations of Birthday gift bags can we make?
The students will be working on this problem independently. First, students must understand that they are looking for total number of outcomes which is identified in the problem (SMP1) Next, they will need to come up with a plan for solving the problem. I’m looking for students to solve this in a few ways. We have been talking about tree diagrams so I would be looking for students to correctly identify the parts of the tree diagram to come up with the possible combinations (32 different combinations). Some students may just want to multiply the options together which is fine, but encourage them to prove their answer with a diagram (SMP 4). If students finish early, ask them what is the chance that one of the birthday guests will randomly get a treat in a green bag along with a Pluto sticker. If students haven’t used a diagram they will want to show the sample space is some way so they can get the answer (green bag, Pluto sticker) (1/4 or 25%) Finding the probability is also good for students that are higher functioning. To assess whether a student understood the problem, I’m going to look to see if students not only solved the problem, but also made a relevant comment about the underlying mathematics in the task. To completely understand the problem, the student may compare an arithmetic answer with an organized list or tree diagram. Students that are able to get the problem, but not make connections will show their work and have a complete answer. Students that are not understanding the problem will use little or no math reasoning . They may attempt to represent some combinations but they will be random and will not lead to a complete solution.
Once students have completed their work and supported their answer, have them do a hands up stand up pair up to find a partner to share their answer with. This will be a great opportunity for the students to see how other students persevered through this problem. Allow students time to justify their answer and provide feedback to their partner (SMP 3). If time permits, the students can do the hands up, stand up, pair up again and find another partner to work with. The more opportunities given to justify and get feedback for their answers, for some students , will enhance the learning process.
For the closure, I want students to be thinking about this problem one more time. I’m going to ask them what would happen if we added another color bag to our list? How would this change the number of outcomes? I’m looking for students to quickly multiply out their answer or add another color to their previously made lists or diagrams. I don’t want students to create a new list. If this happens, ask the student how the new information is related to what they already have? (SMP 2) Use this question for final wrap up as a whole group discussion.