In this lesson plan I will implement a mathematical concept based on the explanation of pre-algebra class. I will show students how to analyze the problem with deep analysis of solving 2 step equations and combining like terms. This lesson plan would help me visualize how to develop understanding a pre-algebra course at the high school level to enhance student learning and proficiency in the educational field. Nevertheless, the ideas to support this lesson plan would be based on this week’s reading article 5 Practices for Orchestrating Productive Mathematics Discussion.
To continue, the development of this lesson plan would orchestrated in the following sequence following the 5 Practices for Orchestrating Productive Mathematics Discussion, 1. 1. Anticipating – Likely student responses to challenging mathematical tasks
In this part of the process, I will present to students 1 or 2 problems on the whiteboard without being solved and to solve the main problem to adhere the main process of analysis. Furthermore, in this part of the learning process ideas would be shared and discussed throughout the class as we solve it together to enhance the meaning of learning.
For example; please solve these equations
5x+25=65
7k+34=24k+42
(27+3)/6=24s

For example, problem #3
(27+3)/6=24r
Simplify the sum of the numerator
27+3=30

Then, divide the result by the denominator. 

30/6=5
Finally, solve for r

5/24=(24r )/24
r=5/24
5/24 = 0.208

It is important to anticipate by searching different ways and methods to get to the answer. The other way to solve this equation is in the following sequence. Still, this problem can be solved in another way and still get the same answers for students to explore and analyze. The following format of analysis is the following;

Another method of solving problem #3
(27+3)/6=24r
Remove the divisible denominator of 6 from the left side by multiplication. This will cancel out the 6 from the left side and just operate the numerator. Then, multiply 24 ×6 =144r
(6) (27+3)/6=24r(6)
30=144r
Then, divide by 144r to simply the equation.
30/144=144r/144
30/144=R
30/144=0.208

Then following with #2. Monitoring – Students actual responses to the tasks (while students work on the tasks in pairs or small groups). In this part of the process students will engage in open discussions, be in groups of 4 or 3 to open and share ideas and feedback is opportunistic in the process of learning. They will engage in their overall answers and process of solving mathematical equations. Still, they will be analyzing through their peer classmates, and this can enhance their learning abilities not only independently but as a teamwork. Nonetheless, students will rely on daily notes, daily assignments to make meaningful context into their overall analysis and interpretation of the problem.
Moreover, continuing with #3. Selecting – Particular students to present their mathematical work during the whole-class discussion.
In this part of the learning process students will not only work in groups but work with paper and pencil, and the use of markers is possible to write down the solving step process of the equation in a series of sequence to present it in front of the class. This would help to collaborate as learning engagement and enhance their learning through a critical thinking process of analysis. For example, group 2 will show their work at the end of the class on how to solve the following equation 3x+24=42+12x. Please show work on the square construction paper following the sequence of solving until the final answer. To mention, students will be actively engaging in the process of solving a mathematical problem and most of them would help each other to provide their work as a group for participating in the class.
Furthermore, #4 sequencing – the student responses that will be displayed in a specific order.
In this learning process students will recap all previous daily notes, class discussions and participation to connect the puzzle on how to solve an equation and the understanding of combining like terms to simplify expressions. By now, students will be mor engage enough to solve the problem on their own rather than in groups. At this stage of the learning process students would be visualizing how to solve the problem much more easily, finding unique ways to solve the problem. To mention, student will visualize in advance how to process a mathematical concept of solving single and equations and 2 step equations.
Then #5. Connecting – different students’ responses and connecting the responses to key mathematical ideas. In fact, according to reading article 5 Practices for Orchestrating Productive Mathematics Discussion “Finally, the teacher helps students draw connections between their solutions and other students solutions as well as the key mathematical ideas in the lesson.” (Smith & Stein, 2018, pg. 11).

References
Smith, M. S., & Stein, M. K. (2018). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston VA, USA: The National Council of Teachers of Mathematics, Inc. https://pubs.nctm.org/view/book/9780873538015/9780873538015.xml

Daily writing prompt

What’s a moment that made you question reality?

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