Allison Klein
Educational Psychology
I analyzed a third grade lesson plan called, “Candy Multiplication” because math is one of my favorite subjects to help children with, and I would really like to work with third grade. This lesson plan was detailed and specific enough that I could easily teach it now. The main focus of this lesson plan was to introduce the idea of multiplication.
The introduction to this lesson plan is strong because it requires students to recall previous information. Students are introduced to the idea of multiplication by comparing it to repeated addition, something that has already been taught to them. This is a useful tool to use when teaching because recalling previous knowledge requires the students to remember information that was (hopefully) stored in their long term memory. Simpler math concepts such as addition seem to stick with us throughout the years. Another term that is mentioned is grouping. The idea of grouping was originally introduced when students were taught adding so this is another concept they are having to recall. One thing that I would want to do is not only mention the concepts of repeated addition and grouping, but also explain what each is and maybe give an example of each by writing them on the board. (An example of repeated addition: 2+2+2+2=8.)
The first part of the instruction is strictly a teacher modeling what he/she wants their students to do. This plan goes into great detail of each step starting with introducing an example. Showing what an example looks like is extremely beneficial because the process of elaborative rehearsal can begin. The repetition of these concepts will assist the ideas to be stored into their long term memory which will not leave their memory. This is essential for their learning because multiplication is something that they will use everyday as they grow up, whether that’s for math class or real world problems. During this, a visual is provided and will continue to be shown throughout the whole lesson. The visual can give a clear way for some students to see the problem.
The next step of the lesson plan is in sync with the next step in rehearsing the material and that is attaching meaning. When the teacher writes on the board, 4x3, they would explain what the “x” represents which attaches meaning to the problem. Students will realize that the sign for multiplication is the “x”. Now, these students will be rehearsing this every time they complete a multiplication problem, how to set it up and what the sign represents. This was done well because the teacher provides a visual and explains the symbol’s meaning and relevance.
Next step is to show them a representation of the problem. One way to do this is to draw four circles which would be one of your factors and the other factor the student is multiplying by is a three, so they would draw three dots in each circle. This is a great schema for the students to work with, in other words, a good mental representation of the behavior. They can visualize in their minds what 4x3 looks like and also draw it out. As a class, they'll count the dots together and realize there are 12 dots in all, meaning the answer is 12. Again, touching base with the vocab usage in this lesson, the teacher would explain that 12 is the product of 4x3. After solving the problem, the plan brought the student’s attention back to their previous knowledge of repeated addition and made a connection on the whiteboard by adding addition signs in between the 4 circles with 3 dots in them. Now, it showed 3+3+3+3 which they all would know is equal to 12. Readdressing that connection continues to help rehearse the different steps in their minds. The repetition will help them memorize it quicker and then next time they do a similar problem like this, they can think of that connection over and over.
Another part of the lesson plan I liked was what the teacher explains next, which is why multiplication can be easier than addition. This gives students positive encouragement in the sense that they can now look at multiplication as an easier tool, and not something that is scary and new. The plan gave a good example of 9x8 which written out addition wise is lengthy. By giving an example like this, when students use the new technique they were taught, drawing 9 circles with 8 dots in them, they can easily count the dots out rather than trying to add 8 over and over again. This whole process was the teacher modeling the new concept which is good for them to see it on the board, but the next step can be even more beneficial to them. The teacher did a good job modeling this because she gave an example and turned it into another visual. Using an example like this gave the problem purpose and reason as to why this is easier than adding eight, nine different times. It’s important to explain the importance and reason why students are doing something new because there is less of a chance that they argue why they are being taught this concept. Explaining the purpose of lesson plans can be crucial to the success of a plan for that exact reason, it’s gives students a reason to do it because it can benefit them.
In the lesson plan, the next category is known as the guided practice or the interactive modeling. Worksheets are passed out, one having circles on them already so students do not waste time drawing them and another one which is a math recording sheet. This way, the student can see it as an addition problem (what they already know), a multiplication problem (the new way) and the product all written out. They also will receive a bag of candy which will replace the dots that the teacher was using on the board. The interaction with the candy is one way to help engage the students. Providing something for the students to hold in their hands and actually work with can make them excited to complete their work and keep them interacting and participating throughout the entirety of the plan. Another great outcome of using the candy could be that some students may associate the candy to multiplication, so when they go to complete a different multiplication problem they can refer to the candy examples if they forget how to solve the problem.
Once everything is passed out, the teacher would write a problem on the board, such as 4x5 and challenge them to solve the problem, first using the multiplication diagram that was introduced today and then the repeated addition way to check and see if the answer was the same. As the teacher, he/she should guide students and encourage them to write it all out on the paper so they can see it visually. After giving numerous problems, a question can be posed to the class, such as “How are multiplication and addition related?” The whole class can be given an opportunity to contribute something to the class, whether that’s an answer to a question or sharing an answer with the class from addition or multiplication. This is modeling good student behavior because the teacher is giving everyone a chance to demonstrate this behavior and participate.
The next phase of this lesson plan is independent working time which represents scaffolding. The scaffold is the problems that they will now complete because the teacher gave them examples while she taught the concept and she is stepping back to allow them to work on their own, which will show if they understood what she taught. Even though it is independent work time, she will be there for support if needed because some may not grasp the concept as quickly as others. During this time, a few problems should be written on the board so once a child finishes the first problem, they can move on without any other students knowing. This is a great technique because other students who may be slower at solving the problem do not feel rushed. They have a chance to take their time and really think about the process. During this time, the teacher should be walking around and checking the accuracy of the student’s work. Also, the general understanding of the class as a whole can be identified and talked about when they review the material.
As a teacher in a class of 30 students, there are going to be some students who struggle with newer concepts more than others. One way to support those students could be putting them into smaller groups to work as well during the individual time or afterwards just so those students feel they have the support they need to adapt to the new concept. Some students will be ready for challenging problems shortly after the introduction and others need more of a positive encouragement to keep them engaged. A good way to adapt to that need would be allowing the whole class to eat their candies when they have completed all of their problems today. This would be a positive reinforcer, a way for them to get something desirable when their work is completed.
This is a lesson that is advantageous for this age and grade as they are in the concrete operational stage because they are thinking about different operations using concrete concepts. Since learning is a constructive process, this lesson is constructive enough that I believe it is a strong lesson that could be a good introduction to multiplication. The hands on interaction keeps students engaged throughout the entirety of the lesson and allows them to visualize the problem, rather than just looking at numbers on a paper. The other visual, the drawing of the circles, will continue to help them until they are introduced to other shortcuts and techniques to multiplying. Piaget believed in interaction with environment and the interacting with others and the interaction with the candy and diagrams shows that this is a lesson plan that reflects Piaget’s beliefs. Overall, this was a strong, purposeful third grade math lesson that I could see myself using in my future classroom because it stayed consistent with the child development and learning process. The teacher modeled what they were going to be doing, gave examples and allowed them time to work and interact with actual candies and classmates. These simple interactions can go a long way when the students are processing all of the new information they are learning.
Link to lesson plan
