Spencerphotoessay

Rationale
 Math is everywhere, just look around! Did you know
most bookshelves are comprised of rectangles? I didn’t.
Did you know there is a ratio of two shutters for every
window? I didn’t. All of the pictures that I incorporated
in the “Photo Essay” are objects/places/things that I
walk by daily on Miami University’s campus. Although I
walk by them daily, I usually have my head in the clouds
or am texting on my cell phone. I never stop to observe
these structures that have a strong connection to my
education, particularly mathematics. Each of the critical
thinking questions are geared toward the standards of
either geometry or operations and algebraic thinking.
My photos and questions were created in hopes that
students would actively see how math is incorporated in
the many objects/places/things they are familiar with.

Instructions
 There are three questions. Each question is based on
the provided picture.

 Answer each question. Refer back to the picture for
help!

Question #1
1. What shape does this piece
of brick make?

2. How many sides does this
shape have? How many
corners are there?

3. Draw a shape with the same
amount of sides and corners.
It can’t look exactly like the
picture.

Question #2
1. How many parts
are there to the
whole?

2. Shade in 1/2.

3. Find something in
the classroom that
is this shape, and
divide it into the
same amount of
equal parts.

Question #3
1. What 3D shape is this?

2. How many faces does this
shape have?

3. Name something in your
house that is also this
shape.

Hint: You find a lot of this shape
in the kitchen.

Question #4
1. This is a mosaic. What is the shape of most of the tiles that were used to form the
mosaic?

2. Outline all of the triangles you can find.

3. Design your own mosaic. Use lots of color.

Question #5
1. This picture has a lot of squares and
rectangles. Highlight/count all of the
rectangles you can find and do the
same for squares.

2. What are the similarities and
differences of these two shapes?

3. Now, find doors throughout the
school. Do the shapes included in
these doors resemble the shapes
included in the doors of your school?
Name some new shapes that you
have found.

1. How many lockers away from 14 is 20?

2. Sarah’s locker number is 9. Which locker is
closer to locker 14, 9 or 20? How do you
Question #6 know?

3. Create your own addition or subtraction word
problem using at least one of the locker
numbers. Have a friend solve the problem.

Question #7
1. How many more shutters
are there than windows?

2. The other side of the
house has the same
amount of windows. How
many windows are there
all together?

3. If there was a house with
15 windows and each
window had two
shutters, how many
shutters would there be?

Question #8
1. How many rows of
windows are there? How
many columns?

2. Write a number model for
the array.

3. Create your own
rectangular array.
Remember to include a
number model.

Hint: to make a rectangular array all of the rows
must have the same amount of objects.

Question #9

1. Name everything you
can find that comes in
twos.

2. If there were three
branches with five
leaves each, would the
number of leaves be
odd or even?

3. If you had 20 owls, how many eyes would there
be? Will the number of eyes always be odd or even,
why?

Question #10
1. There are three bikes and each bike has
two tires. How many tires are there all
together?

2. How many bikes would need to be
present to have 36 tires?

3. If there are 4 bikes, 3 tricycles, and 1
unicycle how many tires are there in all?
Set up your own equation.

1. What shape is this?

2. How many angles are there?
What type of angles are
these?

3. Draw another common
shape that has the same
amount of sides and angles.

Question #12
1. Here you see two different colored
rectangles. Divide each of them into
two equal parts.

2. If the rectangles were
chocolate, would you rather have half
of the purple rectangle or half of the
yellow rectangle, why?

3. Redraw the rectangles on a sheet of
paper and estimate how many square
pattern blocks would fit in each
rectangle. Then, test your estimate.

Question #13
1. How many chairs are present?
How can you tell?

2. If there are 16 legs, how many
chairs are there?

3. Each chair has four legs. How
many legs are there total?
Solve two different ways.

Question #14
1. What 3D object is this?

2. How many faces does
this object have? What
shape are the faces?

3. If you looked at this
object from the other
side, would it have the
same number of faces?

Question #15

1. What 3D shape is this?

2. If you cut it in half, what shape do you
think the faces would be?

3. Find something in the classroom that
resembles this 3D shape.

Conclusion
This essay is just the beginning on ways to connect
mathematics to our everyday lives. It introduces the idea
that things throughout our daily lives have
properties, just as math problems do. The photo essay
also shows that the properties of these things can be
factors in an equation. I chose to have most of the
geometry questions geared towards first graders and
most of the operations and algebraic questions geared
towards the upper elementary grades. In my head, it
made sense to first know basic 2D and 3D shapes and
their properties before trying to solve math equations
asked about the different shapes. I am really happy that I
completed this photo essay. It was very beneficial. When
I have my own classroom, I will definitely relate math to
the real world.

Common Core Standard & Bloom’s Taxonomy
 Picture 1
 Standard: Reason with shapes and their attributes  1.G1 Distinguish between defining attributes (e.g. triangles are closed
and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess
defining attributes.
 Question 1: Knowledge
 Question 2: Comprehension
 Question 3: Evaluation

 Picture 2
 Standard: Reason with shapes and their attributes.
1.G3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths,
and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares.
Understand for these examples that decomposing into more equal shares creates smaller shares.

 Picture 3
 Standard: Reason with shapes and their attributes  1.G1 Distinguish between defining attributes (e.g. triangles are closed
and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess
defining attributes.

 Picture 4
 Standard: Reason with shapes and their attributes  1.G2 Compose two-dimensional shapes
(rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes
(cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape
and compose new shapes from the composite shape.
 Question 3: Synthesis

 Picture 5
 Standard: Reason with shapes and their attributes.
1.G1 Distinguish between defining attributes (e.g. triangles are closed and three-sided) versus non-defining attributes
(e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
 Question 2: Analysis

 Picture 6
 Standard: Add and subtract within 20 2.OA2 Fluently add and subtract within 20 using mental strategies. By end of
Grade 2, know from memory all sums of two one-digit numbers.

 Picture 7
 Standard:Represent and solve problems involving addition and subtraction  2.OA1 Use addition and subtraction
within 100 to solve one and two step word problems involving situations of adding to, taking from, putting
together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with
a symbol for the unknown number to represent the problem.

 Picture 8
 Standard: 2.OA4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5
rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

 Picture 9
 Standard:Work with equal groups of objects to gain foundations for multiplication 2.OA3 Determine whether a
group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by
2s; write an equation to express an even number as a sum of two equal addends.
 Question 2: Application

 Picture 10
 Standard:3.OA4 Determine the unknown whole number in a multiplication or division equation relating three whole
numbers. For example, determine the unknown number that makes the equation true in each of the equations 8
x?=48, 5 = ? 3, 6x6 =?

 Picture 11
 Standard:Reason with shapes and their attributes  2.G1 Recognize and draw shapes having specified attributes, such
as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons,
hexagons, and cubes

 Picture 12
 Standard:2.G2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of
them.oftwo one-digit numbers.

 Picture 13
 Standard:3.OA3 Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g. by using drawings and equations with a symbol for the unknown
number to represent the problem.

 Picture 14
 Standard:Reason with shapes and their attributes  2.G1 Recognize and draw shapes having specified attributes,
such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons,
hexagons, and cubes

 Picture 15
 Standard:Reason with shapes and their attributes  2.G1 Recognize and draw shapes having specified attributes,
such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons,
hexagons, and cubes

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