Planning, Teaching, Reflecting Math Lessons Rationale
Context:
This artifact was created in CI 4030 under the advisement of Dr. Arthur Quickenton. This
artifact was completed in the fall semester of 2009 as a block II requirement. I completed my
internship in Mrs. Annie Croon’s fifth grade classroom at Gamewell Elementary School in
Caldwell County. This assignment required me to plan and teach three lessons to the class and
assess the students’ growth and struggles in relation to the content being taught. In addition, a
crucial part of this assignment was to reflect upon my own teaching strategies used throughout
my instruction and how it relates to students understanding of the content.
Impact:
Through this assignment I was able to develop my skill in planning, creating, and teaching a
mathematical concept to upper elementary students. The lessons I taught were concurrent with
the North Carolina pacing guide for 5th grade students in Caldwell County Schools. In planning
these lessons I developed a better understanding of the implementation process of mathematical
manipulatives and resources in my instruction in order to help meet the learning needs of
students within the class. Upon the completion of this assignment, after an in-depth reflection, I
learned a great deal about creating mathematical lessons in alignment with the NC Standard
Course of Study as well as the benefits of analyzing student learning through constant formative
assessments.
Alignment:
Standard 3: Teachers Know the Content They Teach
Standard 3.2 – Mathematics
A. Teachers align their instruction with the NC Standard Course of Study
This standard was met by closely following and studying the mathematics curriculum for fifth
graders in North Carolina.
B. Teachers know the content appropriate to their teaching specialty
I met this standard by using content knowledge (known and researched) to create these lessons.
Standard 5 – Teachers Reflect on their Practice
5a. Teachers analyze student learning
I met this standard by completing written analysis at the end of this assignment, based on the
constant formative assessments I created throughout this unit.
5b. Teachers link professional growth to their professional goals
I met this standard by using my in depth reflection of this unit to guide me in the right directions
for future professional development.
Planning, Teaching, Reflecting Math Lessons
Title: Dividing Multiples of 10 and 100 (This lesson aligns concurrently with unit being taught
and the lessons set forth by Envision Math by North Carolina)
Day: 1 of 3
Grade: 5th
Duration: 30 min.
Objective: For students to realize the relationship between multiplication and division. As
division is just a step up from multiplication. I want students to see that if you can multiply and
subtract then you will be able to divide.
Content Area: Division / Dividing Multiples of 10 and 100 / Lesson 4-1 of Envisions Math
Materials:
- White board for the teacher to demonstrate the problem.
-
Portable white boards for every student
-
Dry erase markers for every student
-
Piece of cloth or rag for students to use as an eraser.
Vocabulary:
-
Divisor: The doing the dividing
-
Dividend: The number being divided (split)
-
Quotient: The answer to the division problem
Instructional Plan:
First provide students with some background information, explain to students that that
division is just a higher form of multiplication. Remind students of their ability to use mental
math to come up with a product, once students recall that skill, inform them that they will
practically be doing the same thing with division.
(Students will be using mental math to divide
multiples of 10 and 100 by one-digit numbers.)
Second demonstrate some problems on the board for students to observe and visually
analyze. Show students that 24,000 divided by 3 (show in the form of long division) equals
8,000. Once they arrive at the answer 8,000 ask the students if they can find a quicker and/or
easier way to reach the quotient. Expected answer is that students will say “I know that three
goes into 24, 8 times and if you add the zero’s onto the 8 you get 8,000.” Students should see the
relationship between the two numbers. (Here is when you should stress the importance of
knowing all of your math facts.) Now, write another example on the board, but this time write it
horizontally. [35,000 (division symbol) 5 = _ _ ] Again, students should be able to recognize
the pattern and realize that 5 goes into 35, 7 times and if you add the zero’s onto the 7 then you
get 7,000. Explain to students that it is important to not let the zero’s get in your way. For
multiplication (and the same will work for division) my cooperating classroom teacher tells the
students to “Take the zero’s away and put them in your pocket. Then, look only at the principle
part of the problem. Now, you have an easy division problem if you know your facts. Once you
find the answer to the principle part of the problem then take your zero’s out of your pockets and
attach them back on, well you have your quotient.” This mind trick helps students to associate a
fun saying with a concept that can be difficult for some students.
Activity: (This activity will be used as an informal formative assessment.) After students have
expressed an understanding of the information being taught, pass out the white boards, dry erase
markers, and erasers to assess student learning. This activity can be done individually or in small
groups. Once the materials are passed out write the following problems on the board:
(All problems should be written horizontally so that students do not attempt to do long division,
but instead focus on using mental math. The symbol / will be used in place of the division
symbol that elementary students are familiar with.)
36 / 6 =
3,600 / 6 =
36,000 / 6 =
360,000 / 6 =
72 / 9 =
7,200 / 9 =
72,000 / 9 =
720,000 / 9 =
16 / 4 =
1,600 / 4 =
16,000 / 4 =
160,000 / 4 =
(Once students complete these problems, omit the pattern)
49 / 7 =
120,000 / 3 =
30,000 / 6 =
10 / 2 =
6,300 / 9 =
450,000 / 5 =
Summary: Discuss with the class what they learned from the lesson. Ask if they found the
problems easy or hard? Did they begin to find it easy once the pattern was identified? Make
certain that all students are able to recall their math facts.
Title: Estimating Quotients
Day: 2 of 3
Grade: 5th
Duration: 30 min.
Objective: The objection for this lesson is to have students understand the importance and
connection that math facts shares with division.
Content Area: Continuation of Unit 4 – Division. 4.2 = Estimating Quotients
Materials:
-
White board for the teacher to demonstrate the problem.
-
Portable white boards for every student
-
Dry erase markers for every student
-
Piece of cloth or rag for students to use as an eraser.
Instructional Plan:
First, explain to students that the work they will be doing today is again, another step up
from the day before, yet some elements are still the same, such as: using mental math,
identifying the principle part of the problem, and taking away and adding back the zeros to arrive
at the desired answer.
Second, explain to students that in today’s lesson, students will be rounding and then
using mental math to come up with the answer. Help students make a connection, explain the
purpose of rounding to find an estimate. Explain to students that rounding while concurrently
using mental math is beneficial when you are trying arrive at an answer in a short amount of
time, or perhaps you have the exact numbers but you want to leave a little leeway room –
imagine if you were building a dog house and you wanted to buy some extra wood incase you
messed up, you would want to leave a little room for leeway therefore you would round up.
Lastly, present the problems on the board and ask students to observe your work. Show
students’ the process and the importance of estimating to your advantage. Example: If the
problem is 4,128 divided by 8 and we know that 5 x 8 = 40 then we would round our number
from 4,128 to 4,000 and by using mental math, we can easily determine that 4,000 / 8 = 500, this
process is called finding compatible numbers. Now, pass out the portable whiteboards, dry erase
markers, and erasers to assess student learning. (Begin by having students work individually,
next collaborate the students so they are in groups of 4 with one student who is designated to
share the answer for the group.) Problems to be presented on the board are as follows:
135 / 5 =
189 / 9 =
257 / 5 =
2,143 / 7 =
364 / 6 =
6,382 / 7 =
156 / 3 =
2,457 / 8 =
Summary: Assess the areas of comprehension and/or frustration through a class discussion of
the content discussed.
Title: Estimating Quotients
Day: 3 of 3 (A continuation and reflection of day 2’s lesson)
Grade: 5th
Duration: 30 min.
Objective: The objection for this lesson is to have students understand the importance and
connection that math facts shares with division.
Content Area: Continuation of Unit 4 – Division. 4.2 = Estimating Quotients
Materials:
-
White board for the teacher to demonstrate the problem.
-
Portable white boards for every student
-
Dry erase markers for every student
-
Piece of cloth or rag for students to use as an eraser.
Instructional Plan:
In today’s lesson, students will review the information discussed in day 2’s lesson by
doing a few problems on the board as a class, directing the teacher through the work. Problems
for review: 128 / 4 = ? Anticipated answer from the class: We know that 4 is compatible with
12, therefore we can round 128 to 120 and using mental math we know that 120 / 4 = 30.
Problem 2: 5,422 / 6 = ? Anticipated answer from the class: We know that 6 is compatible with
54, therefore we can round 5,422 to 5,400 and using mental math we know that 5,400 / 6 = 900.
Once students have expressed an understanding of the review from day 2 disperse the
whiteboards, dry erase markers, and erasers to the class to assess student learning. Now, have
students get together in partners and “write/pair/share”. Students will first write their own
practical division problem using full and complete sentences. Second, students will switch
whiteboards with their partner and complete the problem. Third, each student will take turns
explaining how they arrived at the answer and both students will then determine whether the
work was completed correctly. Students will repeat this process three or four times (depending
on how long it takes students’) then each student will chose one problem to share with the class.
Summary: Students’ work will be assessed by other students though the completion of the math
problem expressed to the class. When each student presents the problem, they will read it to the
class and wait for the other students to complete the problem on their boards. The students in the
class will determine whether or not the problem presented makes since.
Works Cited:
Foresman, S. and Wesley, A. (2008). enVisions Math – North Carolina. Scott Foresman & Co.
information retrieved on November 29th, 2009.
Reflection
While reflecting upon my three lessons that I taught I was fairly pleased with the overall
outcome. The areas of the lesson(s) that went well were the use of the whiteboard. I took the
advice of my cooperating teacher to use the boards and I believe they were a big hit. Prior to
teaching my lesson I had seen students using the boards in class and it was evident that using a
tool that was out of the ordinary for students really livened up the students and subsequently they
seemed more engaged. In this particular classroom, math is always taught first thing in the
morning and I knew I would have to try my best to wake the students up. Therefore when
creating my three lessons, it was clear to me that I needed to incorporate the use of a whiteboard
to keep the students’ levels of engagement and interest up.
As far as areas of my lessons that I believe would benefit from modification would be to
change the activities from individual work to partner or small group work and make it into a
game. On the first day of teaching my lesson, I wanted to have students work individually, but I
observed that some students would doze off into space and begin to draw on their board. My
solution to this was to have students pair up and work together to come up with the correct
answer. I would write the problem on the board and then say GO! and students’ would race to
come up with the correct answer. I found that day two went better because more students
seemed to be paying attention and eager to hear the next problem, because of course, they
wanted to win.
These three lessons, along with the help from my cooperating teacher, have taught me
that making the content interesting for your students is a sure way to increase student
involvement, and if students are involved and eager to learn, their rate of retention will increase.
As far as information that I learned about the curriculum, I found that the book, in North
Carolina Envisions, is beneficial when used as a pacing guide. However, since I am in a 5th
grade classroom, I have begun to realize that these students are becoming disengaged from their
work because they are seeing the same format of worksheets every single day. It is becoming
redundant for students and consequently they are slowly loosing interest in the work. I believe
my cooperating teacher had a genius idea to get students “woken up” in the morning and become
actively engaged in their learning through the use of a whiteboard. This teaching tool is one that
I found success in when teaching my three lessons and I will be sure to use for in the future.