Components of a Lesson Plan - Education Focused
Concept Development Model Lesson Plan
I. Mathematics
II. 7th Grade
III. Summary: This lesson will be used as an introduction and review of the concepts of probability that will be discussed in a 7th grade mathematics classroom. This lesson will give students the opportunity to build upon their prior knowledge of probability and its different concepts as a precursor to our probability unit which will be taught later.
IV. Standards addressed:
- CCSS.MATH.CONTENT.7.SP.C.5:
o Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
- CCSS.MATH.CONTENT.7.SP.C.8:
o Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
- CCSS.MATH.CONTENT.7.SP.C.8.A:
o Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
- CCSS.MATH.CONTENT.7.SP.C.8.B:
o Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.
- CCSS.MATH.CONTENT.7.SP.C.8.C:
o Design and use a simulation to generate frequencies for compound events.
V. Objectives:
1. Students will be able to list generalizations about what probability is and how it is used in real world situations based on prior knowledge and/or personal experiences.
2. Students will be able to correctly design detailed lists or diagrams demonstrating their knowledge of what the concepts of probability are.
3. Students will be able to define probability as the chance of an event occurring between 0 and 1 on a number line.
VI. Learning Context: Students will begin to work with probability following a statistics unit. We will then branch the two concepts together into a March Madness project which will include the use of both statistics and probability. They will need to use probability to determine odds of picking winners based on given events, and then statistics to determine the winner based on more numerically based information.
A. Specific Rationale: Students are starting to experience chance outcomes, i.e. weather, options for food at a restaurant, playing card games that involve probability, in their everyday lives. With this mini-unit on probability, they will be able to explore what probability is in a deeper context and can also begin to grasp how they can correctly predict outcomes based on their current knowledge of the topic.
B. General Rationale: Probability is a necessary tool for students to use and become more familiar with. It is a skill that promotes deeper thinking processes at varying degrees and fits into the 7th grade curriculum because it promotes problem solving ability and creative thinking processes.
VII. Instructional Model: I chose to use the Concept Development Model for this lesson because students already have some idea of what probability is, but I want them to continue thinking about how it works, and the variety of forms probability can take. Using the Concept Development Model will allow students to work together to create deeper conceptual bonds of what probability is by bringing prior knowledge to the foreground before building upon those topics in a large group setting.
VIII. Methodology:
A. Preparation: Read through the Common Core State Standards for Probability, as well as the chapters on Probability discussed in the textbook to build upon background knowledge.
1. Materials: Common Core State Standards, Math in Focus Textbook, Graphic Organizers (varying degrees of concept building), SmartBoard, Note cards, Different colored pens, pencils, or markers
2. Leading Questions: What do you know about probability? What have you learned? What have you experienced?
3. Plans for Grouping: Small, heterogeneous groups with varying ability levels and personality traits (introverted vs. extrovert, leader vs. follower, etc.)
4. Location: Classroom; rearrange desks into groups of 4
5. Time Required: 1 Class Period (60 minutes)
- Each step of the Concept Development Model should take around 10 minutes (50 minutes)
- 5 minute opening and closing period
o For an introduction and review
6. Instructional materials
- Note cards
- Different colored pens, pencils, markers, etc.
- Concept webs
o Varying levels of organization
- Blank paper
o To create their own concept webs/lists
B. Procedure:
1. Review last week’s lesson [5 minutes]:
a. “Last week we discussed what statistics is and how it is used. Who can remember a few things from that unit?”
i. Mean, median, mode, range, etc.
ii. Bar graphs, histograms, circle graphs, etc.
b. “Great! Today we are going to branch away from statistics but I know our next topic is something you all know quite a bit about – Probability.”
c. “What I am going to have you all do today is work in small groups (which I have listed on the board) to discuss what you think Probability is, and then work towards some conclusions about how you use probability in your daily lives.”
d. Have students move to appropriate table numbers based on the list on the SmartBoard.
2. Listing [10 minutes]
a. Pass out Folders for today’s unit
i. Manila folders labeled with each groups number; filled with the different graphic organizers, blank pieces of paper, and several note cards
b. “Today we will be going through several steps to discuss what you already know about Probability. Each of these folders has several different tools you can use today. Please do not use them in access as I only have a few extra copies for everyone. Take your time today! This lesson can be extremely helpful if you follow directions and work closely with your group!”
c. “What I want you to think about in your group first is what do you already know about Probability? Looking through your folders, pick a tool which may be helpful to you so that you all as a group can start listing ideas that relate to Probability in any way. These do not have to be in complete sentences. Feel free to use words, pictures, or numbers to help explain what you think Probability is as a group.”
d. Walk around and make sure that each group member is contributing. Try not to direct any conversation towards an end result as this part of the lesson should be steered by the students themselves. If students are stuck, feel free to help them out while keeping the focus on what they are trying to say, whether it is correct or not.
3. Grouping [5-10 minutes]:
a. Encourage students to think about how their ideas are similar.
b. “What I want you to think about next is how all these items you listed can be grouped together. Before you write anything down, take a close look at the concepts you wrote, and see how they can be arranged. Next, please utilize any tool from your folder that you think may help you appropriately group your concepts. You can have as many groups as you think you need.”
c. Monitor student and group activity throughout this section. Make sure that students are using the tools available to the best of their ability.
4. Labeling [5-10 minutes]:
a. Ask each group of students to label each group of characteristics they created.
b. “Now that you have grouped the characteristics, I want you, as a group, to see if you can come up with labels for each of the groups. Think about some of the things each group has in common and what separates them from other groups.”
c. Students should be continuing to work on one of the tools they selected to help them with this activity. Monitor student work and group activity.
5. Regrouping [10 minutes]:
a. The next step will be to challenge each group to look at their individual characteristics and their groups to see if they can come up with any more ideas and/or regroup their current ideas to different sections.
b. “Now that you have your groups labelled, take another look at your ideas and their groups to see if they can be rearranged in a different way. Could some of your ideas belong to more than one group? Could you put them in different group’s altogether? Why would you group them that way?”
c. Students may choose to use a new graphic organizer for this part of the lesson. A Venn diagram may be useful now since students can group items in two separate groups.
6. Synthesizing [10 minutes]:
a. Students will now need to write down a sentence or two that explains what probability is. They should use another tool from the folder; a note card, blank piece of paper, etc., and they should complete this individually.
b. “Now that you have worked together to group these ideas of probability, you need to use another tool from the folder to write down in 1-2 sentences what you think probability is. Once you have your idea written down, feel free to share it with you group members. If you want to, you can edit your statement to include ideas mentioned by other group members. I will ask for a few examples when everyone is done.”
7. Review [10 minutes]: Once students are finished discussing their statements with their groups, ask for individual students to volunteer to read their responses. It may be beneficial to have a discussion about the different statements the students present to clarify any misconceptions or to elaborate on any key information students present.
a. “Now that we have had a discussion on an introduction to probability, we will begin to delve a little deeper into some concepts and uses of probability. At the end of our unit, we will go through this procedure again to see how your ideas of probability have changed, or what new concepts have been added. We will start talking about the basics of probability tomorrow and then progress pretty quickly over the next week. Make sure I have collected your final statement over your idea of what probability is before you leave today!”
C. Anticipation of Difficulties: I could foresee that students may use the incorrect tools or that they would include ideas that don’t connect to probability. In either case, as 7th graders, I would push the students to discover their own misconceptions and misuses. I would not tell them the correct idea or tool to use, as this is an individual/group activity, but I would try to steer them towards the right idea. Students who need help (differentiating the lesson) can and should be provided with tools that provide more structure for them throughout this lesson.
IX. Assessment:
A. Student Assessment:
- Monitoring students during their group work
- Collecting their final statement
- Using a rubric to assess their final statement for key points and if they correctly identified the concepts
B. Lesson Assessment:
- Monitoring student and group activity
- As the unit continues, check to see if students can continue to relay back upon this lesson as a strong foundation for the unit
- High student involvement; not many questions asked
C. Rationale: I chose this method for this unit and my students because of the content that is going to be taught, the age appropriateness of the method, and the fact that this information is being built upon from previous grades. Students in the 7th grade should be able to develop ideas on their own, especially with the help of small group activities, choose and utilize the proper tools, and build connections between past concepts. Students have already been taught some aspects of probability, but using the concept development model allows students to bridge their prior knowledge to new concepts that they have yet to learn by grouping and assimilating that prior knowledge before the unit starts.
C. Rubrics or Evaluation Tool:
|Points Possible |0 |1 |2 |Points Received |
|Define Probability |No definition included |Missing important |Defined Correctly | |
| | |concepts | | |
|Concepts are listed in |Groups not defined |Not all concepts in |Concepts | |
|appropriate groups | |proper groups |appropriately grouped| |
|Proper use of tools |Did not use any tools |Used same tool; |Used multiple tools; | |
|provided |provided; |didn’t change to |used them | |
| |Used one tool |meet different needs|appropriately | |
| |inappropriately |at each level | | |
|Group Work |Did not participate; |Participated only a |Participated | |
| |relied on group to do |few times; did not |frequently; Worked | |
| |majority of the work |provide insight very|well with others | |
| | |often | | |
Different Types of Tools for Student Use:
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