This document provides five lesson plans that were part of a unit on geometry that I planned and taught. There is also a reflective essay about my experience planning curriculum.

1. Standard A
Plans Curriculum and Instruction
Unit: Geometry
o What is a Polygon
o Tangrams
o Review and Formative Assessment
o Lines
o Geometry Scavenger Hunt
Reflective Essay

2. Grade 4 – Mathematics
Frameworks and Standards
This unit is built on the Massachusetts Mathematics Curriculum Frameworks for
Geometry Grades 3-4 Standards 4.G.1 – 4.G.9 (page 40) and Grades 3-4 Standards for
Measurement 4.M.1 and 4.M.4 (page 48)
Thus unit is also built on the Braintree Public Schools Grade 4 Mathematics Geometry
Module which follows the MA Frameworks
Essential Questions (Goals)
What is geometry? How can it help me solve real world math problems?
How can I describe and tell the difference between 2-D and 3-D shapes?
How can I name angles that look different and how can I use that to help me classify
triangles and quadrilaterals?
What’s the difference between parallel, intersecting and perpendicular lines?
What happens when I move shapes in different ways?
Can all shapes and figures be cut in half equally?
When do I need to find perimeter, area or volume? What do I need to know to find
those?
The geometry unit that I planned and implemented in the classroom was done over a five week
period. The following five lesson plans are a sampling of the types of lessons I taught to create a
productive, creative and cooperative learning environment to meet the standards and answer
the essential questions as focusing goals.

3. What is a Polygon?
Grade 4 Math
February 28, 2011 (Monday)
85 minutes
Massachusetts Curriculum Framework:
Mathematics – Geometry – 4.G.1 Compare and analyze attributes and other features (e.g., number of
sides, faces, corners, right angles, diagonals and symmetry) of two and three dimensional geometric
shapes
Mathematics – Geometry – 4.G.2 Describe, model, draw, compare and classify two and three
dimensional shapes, e.g. circles, polygons – especially triangles and quadrilaterals – cubes, spheres, and
pyramids
Objective:
The objective of this lesson is for students to build a foundation for understanding polygons and how
they can be classified. One goal is that students will be able to determine whether a figure is a polygon
and describe why or why not. Another goal is that students will be able to classify polygons by the
number of sides a figure has.
Expected Student Outcomes:
At the completion of this lesson, students will be able to:
Explain the difference between an open and closed figure
Define a polygon as a two-dimensional, closed figure with straight sides
Determine whether a particular figure is a polygon or not
Classify a polygon by the number of sides it has
Instructional Procedures:
I will introduce this lesson by giving each student a half sheet of paper with two rows of figures
drawn on it. One row has open figures and one row has closed figures. I will ask the students to
look at the figures and jot down in their journals what differences and similarities they see
between the figures. The students will then turn and talk about what they wrote in their
journals. I will then ask volunteers to discuss with the whole class their thoughts on the figures. I
will use their thoughts and ideas to build the definition of open and closed figures. The students
will label the figures as open or closed and keep the sheet in their journals.

4. I will then draw a circle and a square on the whiteboard. The students will draw a circle and
square in their journals and we will have a class discussion on the similarities and differences.
Through the discussion, we will arrive at the conclusion that they are both closed figures but
only one has straight sides. (I will use the student comments to guide them to reach this
conclusion, but I only want to guide, not tell.)
I will write the word polygon on the board and write the definition as a two-dimensional, closed
figure with straight sides. I will ask the students whether they think the square can be a polygon
and whether the circle can be a polygon. In their journals, I will have them label the square as a
polygon and label the circle as not a polygon.
I will draw the figure from page 436 #26 on the board. I will have the students copy the figure in
their journals and independently write whether it can be a polygon or not. We will have a whole
class discussion about it after a couple minutes of writing.
I will then list the words triangle, quadrilateral, pentagon, hexagon and octagon on the board.
The students will copy the words into their journals and try to draw what they think each figure
looks like. I will have volunteers come up to the board to draw each figure. I will correct
misunderstandings and clarify as we progress.
The students will then work independently on Reteach 19-2 and page 435 numbers 1-5.
I will assign the homework; Practice Sheet 19-2
Materials and Resources:
Each student’s math journal
Math book for each student
Copy of open and closed figure sheet for each student
Copy of 19-2 Reteach and Practice sheets for each student
Whiteboard and dry-erase markers
Assessment of Student Achievement:
This lesson includes many opportunities for informal assessment to check what students already
know and how they are progressing during the lesson. I will assess what the students already know
about open and closed figures by watching what they are writing in their journals and listening to the
turn and talk time and whole class discussion. I will check what the students already know about
classifying polygons by watching what they are drawing for each classification listed. I do not want to

5. just tell the students how many sides each figure has before I see what they already know about it. This
will allow me to focus instruction on the figures they are confused on.
During the lesson, I will check for student understanding by walking around and monitoring
whether they are editing the ideas in their journals to match what is being taught. I want the journals to
capture thinking, but I also want them to capture how their thinking should be modified. I will also check
for understanding by monitoring how individual students are performing on the Reteach sheet and book
problems. If the students can work through these problems with ease, I will know they are successful.
Students will also have the opportunity to show what they know through the homework sheet which
will also be a way for me to assess what they have understood in the lesson.
Student Evaluation:
Students will be evaluated in this lesson through formative measures. The worksheets and
journal work provide me with ample opportunities to measure understanding and see if the objectives
are being met as we go through the lesson. I will collect the journals at the end of the unit and grade
them based on a rubric. The overall journal grade will be counted in as a quiz grade for math. The in
class work and homework are not graded with a formal grade to be entered into the grade-book, but
they serve as practice for the students and a check for me to see what they are understanding and what
needs more time to be worked on.

6. Tangrams – Polygon Puzzles
Grade 4 Math
March 1, 2011 (Tuesday)
85 minutes (Morning work 8:45-9:55 Math 10:15 – 11:30)
Massachusetts Curriculum Framework:
Mathematics – Geometry – 4.G.9 Predict and validate the results of partitioning, folding, and combining
two and three dimensional shapes
Mathematics – Geometry – 4.G.7 Describe and apply techniques such as reflections (flips), rotations
(turns), and translations (slides) for determining if two shapes are congruent
Objective:
The objective of this lesson is for students to understand how polygons can be combined and moved to
form other polygons and figures. It is a scaffold to examining flips, turns and slides in more detail in a
later lesson.
Expected Student Outcomes:
At the completion of this lesson, students will be able to:
Use two tangram pieces to form one polygon
Arrange the seven tangram pieces to form one quadrilateral
Arrange the tangram pieces to form other figures (bird, lion etc. from sheet)
Instructional Procedures:
During the Morning Work time, the students will reinforce yesterday’s polygon lesson by
completing a vocabulary sheet and gluing it into their journals. The students are well
accustomed to coming into the classroom in the morning and getting right down to work.
I will begin the 10:15 – 11:30 block by reviewing the homework from yesterday and fielding any
lingering questions from yesterday’s lesson.
I will then tell the students that today we will be exploring shapes by using tangrams. I will
explain that tangrams are a kind of puzzle. On the overhead projector, I will display each of the
seven pieces of the tangram. I will ask students whether each piece is a polygon and if so how
can it be classified.

7. The students will be working in groups so I will split the class into six groups and give each group
a tangram puzzle.
I will tell the students that their first challenge is to make a quadrilateral using two triangles. The
students will work in their groups to decide how to arrange the triangles to do this. I will give the
students a minute or two to display it on their desks. I will then demonstrate the solution on the
overhead.
I will then tell the students that their next challenge is to use all seven pieces to make one
quadrilateral. I will have the students work for about fifteen to twenty minutes to solve the
puzzle (more or less time depending on their progress). It is challenging to complete, so I want
to allow for ample time. Before starting, I will ask the students why they think we are working
with the puzzles today. I will build on their responses to come to the conclusion that we are
working with the pieces to see how polygons can work together and see how turning and
flipping changes them.
As the students are working, I will circulate among the groups and check on progress and
observe strategies. I will encourage the students to keep trying and keep working because it is
challenging but can be done. I will try to avoid giving hints unless the students are making no
progress. The first group who completes the puzzle will come up to the front and display the
solution on the overhead projector for the whole class to see.
I will then give each student a copy of the solution that they can take home and cut out the
pieces to try at home. I will also give each student a copy of the tangram packet. The packet
includes figures such as animals and people that can be built with the tangrams. The students
will continue to work in their groups to arrange the pieces into the figures.
The students who finish all of the figures early will draw a picture of anything they would like
using as many polygons as they can.
I will conclude the lesson by assigning and explaining that the homework is to make a list of
polygons they find at home and classify what type of polygon it is
Materials and Resources:
Six tangram puzzles and one tangram puzzle that can be displayed on an overhead projector
Overhead projector and screen
Copy of 2-D vocabulary sheet for each student
Copy of tangram solution sheet for each student
Copy of tangram figure packet for each student
Homework sheet with chart to list polygons discovered at home

8. Assessment of Student Achievement:
This lesson includes opportunities to informally assess student achievement. I will assess what
students already know by reviewing the homework on polygons and asking the students to identify what
type of polygon each piece of the tangram puzzle is. I will also assess what they already know by asking
the students to use two triangles to form a quadrilateral. I will be able to quickly see whether the
students already know that shapes can be turned and flipped and combined. I start with this simple
challenge to get a sense of where students’ understanding is at the beginning of the lesson.
I will check for understanding during the lesson by watching the students work together to solve
the puzzle of using the seven pieces to make a quadrilateral. I will know if they are successful if I see
them turning, flipping and rotating the pieces to form different combinations and shapes. I will also
know if they are successful if they can solve the puzzle. While they are working on combining pieces to
form the figures in the packet I will also check on their progress. I will know if they are successful if they
can complete the figures with ease because making these figures is less challenging than the single
quadrilateral.
Student Evaluation:
This lesson focuses mainly on informal assessment as the students work. A more formal
evaluation of this lesson will be how well students perform on later cumulative assessments.

9. Review and Formative Assessment
Grade 4 Math
March 4, 2011 (Friday) (On Wed. 3/2/11 and Thurs. 3/3/11 3-D shapes and nets were covered)
80 minutes
Massachusetts Curriculum Framework:
Mathematics – Geometry – 4.G.1 Compare and analyze attributes and other features (e.g., number of
sides, faces, corners, right angles, diagonals and symmetry) of two and three dimensional geometric
shapes
Mathematics – Geometry – 4.G.2 Describe, model, draw, compare and classify two and three
dimensional shapes, e.g. circles, polygons – especially triangles and quadrilaterals – cubes, spheres, and
pyramids
Objective:
The objective of this lesson is to give students a fun way to review geometry concepts learned so far and
to have students take a formative assessment to check for understanding up to this point. The objective
of a formative assessment is to be able to use the results to guide instruction.
Expected Student Outcomes:
At the completion of this lesson, students will be able to:
Extend their knowledge of polygons to a real life example
Understand which ideas and concepts from the topics of polygons, two-dimensional and three-
dimensional shapes are most important to know
Demonstrate their understanding of these concepts through a formative assessment
Instructional Procedures:
During the morning work time (8:40 – 9:00) students will choose one of the polygons found for
homework on Tuesday night and draw a picture of it. They will then cut construction paper into
the shape of the polygon and glue their picture on. I will use their polygons to put up on a
bulletin board.
I will begin the math block (10:30 – 11:30) with a BINGO review. I will give each student a blank
BINGO sheet and explain that we are going to fill in the blanks with geometry words that they
think will be important to know for the assessment. I will ask volunteers to say words while I
write them on the whiteboard. Students will fill in their sheets by writing the words in whichever

10. block they choose. I will then randomly call out words as the students try to get BINGO. When a
student does get BINGO, before they can win they must tell the whole class the definition of or
explain the words that they have gotten a BINGO with. I will continue with BINGO for about
twenty to twenty five minutes.
After BINGO, the students will take the formative assessment. When they are finished, they may
read silently or finish up any other work from the week that needs to be completed.
Materials and Resources:
White drawing paper and construction paper
Blank BINGO sheet for each student
Handful of plastic BINGO markers for each student
Copy of Geometry Quiz for each student
Crayons, expo markers
Assessment of Student Achievement:
In this lesson, I will assess what students already know by reviewing with BINGO. I will be able to
tell how well they have understood what’s important from the topics by which kinds of words they give
and also by how well they can explain the words when they win BINGO. This will allow me to clear up
any confusion or misunderstandings before the students take the quiz.
Student Evaluation:
This lesson includes a formative assessment that covers polygons, two-dimensional shapes,
three-dimensional shapes and nets. The quiz includes various types of questions to test how well the
students have understood the concepts. It is important to do this assessment now before getting too far
into geometry and realizing the students are not grasping the topics. I will be able to evaluate the
quizzes and then decide if the students are ready to move on to the topic of lines or if they need more
work on these topics.

11. Name:__________________________________________________________Date:_______________
GEOMETRY QUIZ
Directions: Use the word bank below to complete numbers 1 -13.
WORD BANK
closed figure quadrilateral open figure
triangle polygon base
hexagon 2-dimensional figure pentagon
octagon vertex edge
face
1) A shape with length and width is called a ________________________________________
2) Closed 2-D shapes that have straight sides are called _______________________________
3) A face on which a figure sits is the ______________________________________________
4) Figures that do not start and end at the same point are _____________________________
5) A three sided figure is a _______________________________________________________
6) Two faces meet at the _______________________________________________________
7) An eight sided figure is a _____________________________________________________
8) The flat side of a 3-D figure is called a ___________________________________________
9) A four sided figure is a _______________________________________________________

12. 10) A six sided figure is a _______________________________________________________
11) A five sided figure is a _______________________________________________________
12) Three or more faces meet at the ______________________________________________
13) Figures that start and end at the same point are __________________________________
14) Draw any polygon and classify which kind it is
Type of polygon___________________________________________
15) Draw a figure that is NOT a polygon and write why it is not a polygon
This is not a polygon because ___________________________________________

13. Directions: Circle the best answer to each question.
16) What shape is the base of a triangular pyramid?
square circle triangle
17) How many faces does a cylinder have?
five three two
18) How many edges does a cone have?
zero three five
19) Draw the net for a square pyramid
20) Draw the net for a rectangular prism

14. Lines
Grade 4 Math
March 7, 2011 (Monday)
35 minutes 9:00 – 9:35
Massachusetts Curriculum Framework:
Mathematics – Geometry 4.G.5 Describe and draw intersecting, parallel, and perpendicular lines.
Objective:
One goal of this lesson is for students to understand the difference between a line, line segment and
ray. Another goal is for students to be able to define and identify what parallel, intersecting and
perpendicular lines are.
Expected Student Outcomes:
At the completion of this lesson, students will be able to:
Explain the difference between a line, line segment and ray and draw each appropriately
Define what parallel, intersecting and perpendicular lines are and identify them in various “real
life” applications
Instructional Procedures:
I will introduce the concept of lines by asking the students to draw a line in their math journals. I
expect that all students will draw what they consider to be a line. I will tell them that I actually
asked them to do something impossible. I will ask if anyone knows why it is impossible. I will
then explain that the geometry definition of a line is that it is infinite. I will demonstrate on the
board that to show a line going on for infinity you need two arrows at the ends. I will explain
that what they drew in their journals was actually a line segment. I will show on the board the
different way of depicting this by using points instead of arrows. I will then ask the students if
they can think of what a ray is and how they could depict that. I will have them try it in their
journals then I will demonstrate on the board.
Next, I will draw on the board a set of parallel lines, a set of intersecting lines and a set of
perpendicular lines. I will have the students copy these into their journals and then
independently jot down the similarities and differences they see between the sets of lines. After
a few minutes, I will have the students turn and talk to one another about what they jotted
down in their journals. I will then bring the class together as whole to discuss their thoughts and
ideas about the sets of lines. I will use their ideas to construct the definitions of each set. (At
this point, I will not have the students write out the definitions in their journals because on the
next day, the students will begin math with a fill in the blank sheet with definitions that they will
glue into their journals).

15. I will then hand out a map of area Braintree streets printed from Google Maps to each student. I
will pair the students up to work together on listing parallel, intersecting and perpendicular
streets. I will ask the students to find at least three sets of parallel streets, six sets of intersecting
streets and seven sets of perpendicular streets (the map includes numerous examples of each)
We will do this as a whole class activity because I will also project the Google map on the screen
using the LCD projector. After students work in partners to find some of the streets, I will have
volunteers come to the front of the room to point out the streets on the projector screen.
At this point, the thirty five minutes will be complete. The students break for gym and then
return to math. I will continue with the map activity if not yet complete and then will reinforce
the lesson with two worksheets on lines that the students will complete independently. The
students will also have a practice worksheet for homework.
Materials and Resources:
Each student’s math journal
Copy of Braintree street map for each student
Computer with access to the internet and projection set up
Copy of reinforcing worksheets and homework worksheet for each student
Pencils, expo markers and white board
Assessment of Student Achievement:
In this lesson, I will assess what students already know by following the introduction procedures.
I will be able to tell what they understand about lines by asking the questions such as whether anyone
knows why drawing a line on a paper is technically impossible. I will also be able to assess what they
already know by reviewing their journal entries as they are writing about the similarities and differences
of parallel, intersecting and perpendicular lines. Assessing what they already know will allow me to
adjust the instruction based on how strong or weak of a background they have.
As the lesson progresses, I will check for understanding by watching as they complete the map
activity. I will be able to get a sense of whether they understood the different types of lines because in
this activity they have to apply the knowledge. They will also demonstrate what they know by
completing the reinforcing worksheets that are part of the second half of math class.

16. Student Evaluation:
Because this lesson is part of a larger unit on geometry, there is no formal culminating evaluation.
However, within the lesson there is ample opportunity for measurable formative evaluation. The math
journals serve as a check in to see what students already know and how they are thinking. I will be able
to evaluate whether they already have some background on lines or whether it is something new. I will
also be able to measure their understanding by reviewing their completed map activity. I placed a
specific number on the sets of streets that I am looking for because this will serve as a benchmark to
judge whether students understand the concept and can apply it. I did not place a specific number on
the examples of lines in the classroom because I want to evaluate the differing number of examples
students find. If a student can only find a few, I will know that they did not completely understand the
concept because the classroom includes an ample amount of examples of lines. I will also be able to
measure understanding after correcting the reinforcing worksheets, homework and vocabulary fill in the
blank that will be part of another lesson. At the end of the unit, there will be a formal test that will
include questions on lines.

17. Geometry Scavenger Hunt (Unit Review)
Grade 4 Math
March 28, 2011 (Monday)
35 minutes 9:00 – 9:35
Massachusetts Curriculum Framework:
4.G.1 Compare and analyze attributes and other features of two-dimensional and three-dimensional
geometric shapes
4.G.2 Describe, model, draw, compare, and classify two and three dimensional shapes
4.G.3 Recognize similar figures
4.G.4 Identify angles as acute, right, or obtuse
4.G.5 Describe and draw intersecting, parallel, and perpendicular lines
4.G.7 Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides)
for determining if two shapes are congruent
4.G.8 Identify and describe line symmetry in two-dimensional shapes
Objective:
The goal of this lesson is for students to work together to review all topics covered in geometry to
prepare for an upcoming cumulative assessment.
Expected Student Outcomes:
At the completion of this lesson, students will be able to:
Describe and identify a broad range of geometry topics including:
o Two-dimensional polygons and other figures
o Three-dimensional figures and nets
o Similar and congruent shapes
o Lines of symmetry
o Lines and angles
o Perimeter, area, and volume
Instructional Procedures:
I will begin the lesson by explaining to the students that they will be going on a geometry
scavenger hunt. I will explain that they will be using each other to gather all of the information
they need to fill in their scavenger hunt charts. I will hold up the chart so they can see it but will
not pass it out until I have given all of the directions.

18. I will explain that their task is to fill in all of the squares on their chart by asking a different
person each question. I will say, “For example, if John was to answer Can you find an example of
a right angle in the room? He can answer only that question on your sheet. You will fill in the
answer and write John’s name down in that square.”
I will explain that if the person who they ask a question to answers it incorrectly, they are to
help the person answer it correctly.
I will tell them that as they are walking about the room asking each other the questions, they
are to keep the noise level at an appropriate level and they are not to run. I will stress that if
they cannot handle the task then they will fill in their own charts silently.
When the students complete their scavenger hunt chart, they are to return to their seats and
work on the chapter review questions in the textbook independently. I will explain this and also
write it on the whiteboard.
I will pass out the scavenger hunt charts and a clip board to each student and have them begin.
Once all students have filled in their chart, I will have a whole class discussion going over what
students found and filled in.
At this point, the thirty five minutes will be complete and the students will break for gym.
When they return, I will continue a whole class discussion on the scavenger hunt if that has not
been completed. The students will then continue working independently on the chapter review
questions and also a review packet if there is time. I will go over the review problems from the
textbook in a whole class discussion when most have completed them.
There is no homework tonight because MCAS testing will be taking place tomorrow morning
Materials and Resources:
Copy of scavenger hunt chart for each student
Clip board for each student
Math textbook and blank math paper for each student
Geometry review packet for each student

19. Assessment of Student Achievement:
This lesson is focused primarily on assessing what students understood and remember from the
geometry unit. As the students are talking to one another to fill in their charts, I will listen in and float
around the room to assess whether they are answering the questions correctly and understanding the
topics.
As the students independently work on the chapter review questions I will check in on their
progress. I will know if they are successful if they can answer the questions with ease.
Students demonstrate what they know in this lesson by questioning and providing answers to
each other to fill in their charts. They will end up with a finished product that will serve as a review sheet
to bring home. Students also demonstrate what they know by independently answering review
questions.
Student Evaluation:
This lesson leads up to a culminating assessment at the end of the week. The students have
been working hard in geometry and performing well on formative assessments. This lesson and the
culminating assessment will be a chance for the students to show what they have learned about
geometry.

20. Reflective Essay: Standard A
Planning and implementing a unit was an invaluable experience in the student teaching
practicum. It allowed me to put into action the theories I have been studying throughout the
graduate program. While I planned and taught a number of units during the practicum
experience, I choose to focus my reflection and portfolio work on geometry because math is such
an important and at times challenging topic to teach and learn. I wanted to strengthen my own
confidence in teaching math.
To plan the unit and all lessons, I consistently drew upon the Massachusetts Frameworks
in Mathematics and the Braintree Public School Standards. This was an important step because
teaching needs to be done with objectives, goals and standards at the forefront. This allowed me
to focus my lessons on specific objectives that I knew had to be met. The Braintree Schools
module was especially helpful because it acted as a roadmap guiding me to plan the sequence of
topics. However, I did learn that while it is important to follow a roadmap, it is just as important
to take some detours from that map. For example, the Braintree module suggested that area and
perimeter be covered in only two days. I was able to introduce both topics in two days, but I had
to add in three more days of work on those two topics because the students were not performing
well on formative assessments. I needed to take a detour to make sure the students had a firm
grasp on these topics before moving on.
Using formal and informal assessments throughout the unit proved very effective. Some
informal assessments took the form of the typical reinforcing worksheets and book work, but I
also added in more creative and authentic informal assessments. For example, the students used
math journals throughout the unit to record their thinking on new topics and keep track of key
vocabulary words. Using math journals is something that I will continue in my own classroom.
As the students were writing and drawing pictures in them, I was able to walk around the room
and quickly assess what they already knew and what they were grasping from particular lessons.
They were a great snapshot into student thinking. Another informal assessment I created was a
homework assignment where the students had to compile a list of polygon shapes they found at
home and in the world around them. This informal assessment allowed me to make sure students
could connect looking at polygons in a purely mathematical sense to how they are present in the
real world. I found this to be a very authentic assessment because it checked their understanding

21. of polygons. I believe understanding happens when students can make connections and apply
their knowledge. I also included both formative and summative formal assessments. The first
formative formal assessment that students took was mainly a check on key vocabulary concepts.
I created the assessment even though it was not included as a step on the Braintree module
because I wanted to ensure students had gained a strong vocabulary foundation before moving on
to more complex topics. The majority of the students performed very well so I knew I could
move on to the next topic. The summative formal assessment that I gave students was the
assessment that was included in the Braintree module, however I modified it slightly based on
what students had focused on and I eliminated some unclear questions. I was very pleased with
the results of the summative assessment. After a few rocky points in the unit, especially with
area, perimeter and volume, the students performed at a top level. The lowest grade in the class
was a B-, which is still a great grade.
An important concept that I learned from teaching the unit was how to use appropriate
resources and materials. Teaching math seems to fall on a spectrum of focusing heavily on the
use of manipulatives to using only worksheets and sets of practice problems. I tried to balance
the two theories to reach maximum student achievement. When I introduced topics I utilized
manipulatives and allowed students to explore the topic. For example, before delving full force
into triangles and quadrilaterals and reflections, rotations and translations, I planned a lesson
using the tangram puzzles for students to experiment with shapes and see the different properties
of triangles and quadrilaterals and how they can be moved and put together. When I focused
more directly on reflections, rotations and translations, the students all had shapes and graph
paper to physically move the shapes and trace the movements. Before I asked students to identify
a net of a 3-D figure just by looking at one in a book, I had the students fold nets into 3-D shapes
to really see and touch how the faces combine to form a 3-D shape. Before students knew that
volume could be found by multiplying the length, width and height of figures, they used cubes to
build figures and count the cubic units.
Planning and teaching this unit also taught me that planning must be done with different
student abilities in mind. Some students struggled with topics that others grasped immediately.
This was especially true of area and perimeter. To work with the differing abilities, I planned a
review day where Miss Chiles took a small struggling group to re-examine the topics at a basic
level and I took a small excelling group to work on a challenging brain teaser involving area and

22. perimeter. IEPs also played a role in planning the unit. For example, some students are
guaranteed individual pull out time with the math specialist. I had to be able to coordinate the
lessons based on when these students would be in and out of the room. Differing abilities is
something that became very clear to me in teaching the unit. I know that I always have to plan
based on individual needs and knowing that not all students will be at the same level at all times.
When I planned the unit, I wrote the unit goals as essential questions because that helped
me to look at the MA and Braintree standards through the eyes of the students. I wanted to make
sure I was focusing the unit in a way that would be student friendly. I believe the unit met the
goals and reached the standards because any student in the class is now able to look at that list of
essential questions and answer most of them effectively. I do wonder though how well I achieved
the goal of making the use of geometry applicable to the real world and solving mathematical
problems. At times, I know I emphasized the use of geometry in building and designing, but I if I
were to teach this unit again, I would change how much emphasis was on learning geometry in
context. I do not think enough time was spent solving word problems and seeing what geometry
can be used for. I think this was a function of just needing to get the unit done in a set amount of
time.
Planning and teaching this unit taught me a lot. It strengthened my confidence in teaching
math because I was able to see that as long as I am well prepared and flexible I can guide the
students to a place of understanding, which was proven by their great performance on the
summative assessment. I went from a state of anxiousness about implementing this unit to
excitement to keep teaching math and trying out more learning in context and authentic projects.