Clinical Field Experience C: Math Mini-Lesson Plan: Factorization

This document presents a math mini-lesson plan designed for 8th-grade students, focusing on the factorization of algebraic equations. The plan includes a pre-assessment to gauge students' understanding of common factors and their ability to simplify equations. The lesson incorporates a teaching strategy that tailors instruction based on the pre-assessment data, emphasizing group work and differentiated instruction. The activity focuses on identifying and factoring common factors within algebraic expressions, with detailed explanations and examples. A formative assessment is included, along with reflections on the field experience, highlighting the importance of understanding divisibility tests and providing varied examples to enhance student comprehension. The lesson plan also addresses the need for further instruction on more complex expressions and variables, and the use of grouping methods to facilitate understanding. The student reflects on the challenges of creating accessible teaching methods and strategies to cater to different learning styles and abilities. References to key research on math education are also provided.

Clinical Field Experience C: Math Mini-Lesson Plan 1
Clinical Field Experience C: Math Mini-Lesson Plan
Part 1: Math Mini-Lesson Plan
Math standard: Factorization of algebraic equations
Grade level: 8
Brief description of the unit the class is currently learning: Factorization of algebraic
equations
The Common Core in Illinois
CCSS.Math.Content.8.EE.A.1
Factorization of algebraic equations involving different variables.
Know and apply the factorization of different equations and therefore form simple
equations For example, 3y+ 3x = 3(y+x). (The Common Core in Illinois, n.d.).
1-2 learning objectives:
The objective of this pre-assessment is to help the learners to understand common factors in
equations and therefore have the knowledge to factor them together. This helps to simplify
complex algebraic equations into simple and understandable equations.
Instructional strategy:
Teaching the learners according to the difficulty in the topic. Grouping will be an important
factor as part of the instructional strategy to the learners.
Description of math learning activity that is directly related to the data received from the
pre-assessment
This pre-assessment is meant for learners to ensure that they are able to understand same
factors and any factors which are common in an algebraic equation. This helps them to gain
knowledge on how to differentiate different factors and understand common factors. The main
focus on this topic is on analyzes of algebraic equations and deriving common factors in order

Clinical Field Experience C: Math Mini-Lesson Plan 2
to factor them. This assessment will be able to indicate how to factor different algebraic
equations involving different factors and formulae. The assessment is meant to ensure that the
students weak in identifying the different parameters in an equation get it in ease and factor
common factors.
Gathering student together with common weaknesses in this area will be done to ensure that
they are able to gain the required knowledge in the factorization. The factorization pre-
assessment will start with introduction of the common factors and like terms. This will help
the learners to identify different common factors in an equation. For example, in the numbers
12y and 16y, there are several common factors. The learners will learn to express these
numbers in different ways in order to identify the common factors. 12y and 16y are divisible
by 4 and therefore 4 is a common factor.
12 = 4 x 3y and
16 = 4 x 4y
If the expression required addition of 12y and 16y then
12y + 16y = (3y x 4) + (4y x 4) = 4(3y + 4y) = 4(7y) = 28y
In this case, the expression of addition can be expressed in different formats when factoring
common factors as below
12y + 16y …………………………………..(a)
= (3y x4) + 4y x4) ………………………….. (b)
= 4(3y + 4y) …………………………………. (c)
Additionally, it can be identifying that y is a common in the equation as well.
Therefore, further factorization of the algebraic equation can be done as below;
= 4y(3 + 4)………………………………………….(d)

Clinical Field Experience C: Math Mini-Lesson Plan 3
The teacher will be able to explain that the factors outside the rackets are common in both 12y
and 16y in this case. Any mathematical formation can be done on the factors within the
brackets and then the result multiplied with the common factors to get the correct answer. This
applied when the factors within the brackets are similar as well and don not have common
factors anymore (Miao & Reynolds, 2018). With such understanding, the learners will be able
to identify and factor out common factors in any equation, simplify and resolve them with
ease.
Formative assessment:
It is clear that the factorization is done well with proper explanation of common
factors. According to Common Core in Illinois, simple explanation provided means that the
learners can be able to identify common factors with ease in any equation and therefore be
able to perform the factorization of the equations. Calculators can be used to perform the
divisibility test because the divisibility test is a common element in determining common
factors of numbers.
In addition, from the explanation, it is clear that there is need for the leaners to be
taught how to perform other expressions such as the multiplications and divisions in the
factorization. The learners seem to raise more questions on how to handle other expressions
and different variables being involved in the equations. This should be a continuation of the
study to the learners to help them gain knowledge on advanced factorizations. In addition, it is
also recommended that after understanding the factorization of equations with one variables,
more variables should be added to the equations (Sammons, 2018). This will ensure that the
learners are able to acquire the relevant knowledge in this topic. More activities in this topic
are therefore necessary to ensure that the learners are able to understand the common factors

Clinical Field Experience C: Math Mini-Lesson Plan 4
and how to factor them considering the different mathematical formulations.
Part 3: Reflection
Reflecting on the experience on this field, I can state that selection of the students with
the problems of identifying common factors is important. This is because the factorization is
based on the divisibility test (Rusczyk, 2015 and Strang, 2016). The learners should therefore be
able to understand the divisibility test for the numbers in order to be able to identify common
denominators and factors in numbers involved in an equation. Most students have issues in
factorization and therefore it is important for them to understand the sequence and order to
performing the factorization.
The teaching standard is clearly indicating that divisibility test for the numbers is
important to understand factorization (Bennett, Burton, & Nelson, 2015). More interactions with
numbers and their powers is important to help to understand the factorization. In my teaching, I
need therefore to concentrate in teaching the learners on how to identify these common
denominators in the equations. To enhance the understanding of the factorization to the learners,
different examples to the students need to be provided and monitored independently (Akiyama,
& Kano, 2011). This will ensure that any difficulties in this sector for individual students is
resolved. Special attention and further analysis of the weaknesses on the students is needed to
ensure that they are able to gain the relevant knowledge on this topic.
In addition, I understand use of grouping method to teach factorization will boost easy
understanding of the concepts (Liu, & Mathematical Association of America, 2015). For
different factors, it is important to ensure that the learners are able to first ground the similar
factors even before identifying the common factors within them (Geroldinger, & Halter-Koch,

Clinical Field Experience C: Math Mini-Lesson Plan 5
2016). This method plays an important role to ensure that the learners are able to comprehend the
concepts with ease.
The main challenge which the pre-assessment has offered is the understanding on how to
come up with different and simpler ways of teaching the factorization to different learners who
have different understanding capacity. This will depend on the ease they have in understanding
the topic. The creative ways will ensure that learners can enjoy learning and participate fully in
the exercises involved. Their involvement will ensure that they can understand and gain the
relevant knowledge easily.
References

Clinical Field Experience C: Math Mini-Lesson Plan 6
Akiyama, J., & Kano, M. (2011). Factors and factorizations of graphs: Proof techniques in
factor theory. New York: Springer.
Bennett, A. B. J., Burton, L. J., & Nelson, L. T. (2015). Mathematics for Elementary Teachers:
A Conceptual Approach. NY: McGraw-Hill Higher Education.
Geroldinger, A., & Halter-Koch, F. (2016). Non-unique factorizations: Algebraic, combinatorial
and analytic theory. Boca Raton, Fla: Chapman & Hall/CRC.
Liu, A. C. F., & Mathematical Association of America,. (2015). Arithmetical wonderland.
Washington, DC : Mathematical Association of America.
Rusczyk, R. (2015). Introduction to algebra: Art of problem solving. San Diego, CA: AoPS.
Strang, G. (2016). Introduction to linear algebra. Wellesley, MA : Cambridge Press.
Sammons, L. (2018). Teaching students to communicate mathematically. Alexandria, Virginia
USA : ASCD.
Miao, Z., & Reynolds, D. (2018). The effectiveness of mathematics teaching in primary schools:
Lessons from England and China. Abingdon, Oxon ; New York, NY: Routledge.