Shapes,
Length,
Time,
Data
Powerpoint is on our Elementary Math Resources K-1 wiki
Goals for today
Learn the progression of geometric
thinking
 Explore activities related to the Common
Core for geometry, measurement and
data
 Consider “next steps”

Sharing
Geometric Thinking
Mrs. Ellis is designing square swimming pools. Each
pool has a square center that is the area of the
water. Mrs. Ellis uses blue tiles to represent the
water. Around each pool there is a border of
white tiles. Here are pictures of the three smallest
square pools that she can design with blue tiles
for the water and white tiles for the border.
Sorting and Counting
For each square pool, sort the tiles into blue
tiles for the water and white tiles for the
border.
 Count how many tiles are in each pile.
 Are there more blue tiles than white tiles?

Pattern in the Blue Squares
Build each of the three blue squares.
How many blue tiles are in each
square?
 Build the next-biggest square that you
can make out of the blue tiles. Then
build the next. Count the squares in
each.
 What patterns do you see?
 What is a square?

Blue square 1
Blue square 2
Blue square 3
T: Why do you call it a square? What’s a square to you?
G: A block.
T: If it were longer down like this, would it still be a square?
G: No, it would turn into a rectangle.
T: So what makes it a square?
G: That it’s not as far down as a rectangle.
T: Is there anything else about the sides? How long is this side?
G: Three squares.
T: How long is this side?
G: Three squares.
T: So what is a square?
G: Can I try something? I’m putting out three to see if I can scramble them
around and make a square. [Grace is working with three unit squares and
trying to build a square. Notice that the teacher was trying to draw
Grace’s attention to the equality of the sides. But, not unexpectedly, she
became interested instead in the number 3 and its relationship to the
square.]
T: A square out of three? [Grace notices that she will need four squares to
make a square and builds it.]
T: How can you be sure it’s a square?
G: You can, because all the sides are the same length.
Found on Peace, Love and First Grade, a blog by “Laura”
Original on Ashley Hughes Teachers Pay Teachers store
Color the Shapes

Color all the
triangles green.

Color all the
rectangles red.

Color all the circles
blue.

Are there some
shapes you haven’t
colored?
Shapes by grade

K: squares, circles, triangles, rectangles, hexagons,
cubes, cones, cylinders, and spheres

1st: rectangles, squares, trapezoids, triangles, halfcircles, and quarter-circles

2nd: triangles, quadrilaterals, pentagons, hexagons,
and cubes

3rd: rhombuses

4th: parallelogram is implied by classifying figures
based on parallel lines
Shapes All Around Us
K.G.1
Describe
objects in the
environment
using names
of shapes,
and describe
the relative
positions of
these objects
using terms
such as
above, below,
beside, in
front of,
behind, and
next to.
van Hiele Levels of Geometric Thought
Level 0:Visualization
Students recognize and name figures based on the global,
visual characteristics of the shape. Students at this level
are able to make measurements and even talk about the
properties of shapes, but these properties are not
abstracted from the shape at hand. It is the appearance of
a shape that defines it for a student. A square is a square
“because it looks like a square.”
Other visual characteristics may include “pointy,” “fat,”
“sort of dented in.” Classification of shapes at this level is
based on whether they look alike or different.
≠
from Van de Walle and Lovin, 2006
van Hiele Levels of Geometric Thought
Level 1: Analysis
Students are able to consider all shapes within a class
rather than a single shape. By focusing on a class of shapes,
students are able to think about what makes a rectangle a
rectangle (four sides, opposite sides parallel, opposite sides
equal, four right angles, etc.) Irrelevant features (e.g.
orientation or size) fall into the background.
Students begin to appreciate that a collection of shapes
goes together because of its properties.
=
K.G.2 Correctly name shapes
regardless of their orientations or
overall size.
from Van de Walle and Lovin, 2006
Attributes
Give each student a sheet of shapes. Have them
brainstorm ways to describe the shapes. Record their
responses on chart paper. Guide students to look for ways
other than color and size when describing the shapes such
as by number of sides, number of corners, or no corners.
Describe this shape

Show a shape. Ask students to say something
about what the shape looks like. Write their
descriptions on the board.

If needed, guide them to be specific: How many
sides? How many corners?

Show two squares of different color. Ask, are
these both squares? Why are they squares? Can
squares come in different colors?
Attributes
1.G.1 Distinguish between defining attributes (e.g.,
triangles are closed and three-sided) versus non-defining
attributes (e.g., color, orientation, overall size); for a wide
variety of shapes; build and draw shapes to possess
defining attributes.
2.G.1 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. (Sizes are compared
directly or visually, not compared by measuring.)
Attributes
van Hiele Levels of Geometric Thought
Level 2: Informal Deduction
Students are able to develop relationships between and
among properties of shapes. They recognize sub-classes of
properties: “If all 4 angles are right angles, it is a rectangle.
Squares have 4 right angles, so squares must be
rectangles.”
from Van de Walle and Lovin, 2006
Shape sorts
1. Take
any shape. Tell one or two
things you find interesting
about the shape.
2. Choose two shapes. Find
something alike and something
different about the two shapes.
3. The group selects one shape
and places it in the center of
the workspace. Find all other
shapes that are like this shape
according to the same rule.
4. Do a second sort with the
same target shape but using a
different property.
Shape sorts
4. Groups
share their sorting
rules with the class and
show examples. Everyone
draw a new shape that will
also fit in the group
according to the same rule.
5. Do a “secret sort” by
selecting about 5 shapes that
fit a secret rule, leaving some
similar shapes in the pile.
Others find similar shapes
and try to guess the rule.
Match the Rule
Georgia Common Core first grade workbook p. 36
Attributes
In your small group, look at the pictures of the shapes on your page.
List all the attributes you can find that all the shapes share.
•
Sides
•
Corners
(Diagonals and symmetry are introduced in 4th gr.)
The rhombus has 4 sides
4 corners
opposite sides are the same length
Orientation
Draw a triangle. Does it look like one of these triangles?
Is this a triangle? How do you know?
triangle, is it still a triangle?
If we turn this
Attribute Blocks
Which One Doesn’t Belong?
The Teacher will place attribute blocks in a brown paper
bag. One student will come to the front of the room and
grab a handful of blocks from the bag. The student will
show the blocks to the class, describe the blocks and
decide which one(s) does not belong. The teacher will
want to model this prior to the students completing in
front of the class. The student will place the blocks back in
the bag and another student will repeat. Complete this
activity several times until the students have grasped the
concept of which one does not belong.
Georgia Common Core first grade workbook p. 24
Build a Shape



K.G.5 Model shapes in the
world by building shapes from
components (e.g., sticks and clay
balls) and drawing shapes.
Read The Greedy Triangle (on wiki)
Ask students if they can make shapes with their bodies
and a piece of yarn.
Use straws, pipe cleaners, or other manipulatives to
create a triangle, rectangle, square and trapezoid. Model
how you connect the straws and pipe cleaners to create
a shape (sample below). Read The Greedy Triangle again.
Have students create the shapes as you come to each
shape in the book.
Georgia Common Core first grade workbook p. 29
Build a cube
“It is often difficult for students to visualize
as it requires a coordination of both two
and three-dimensional shapes. Activities
which require students to think about,
manipulate, or transform a shape mentally
will contribute to students’ overall
visualization skills.”
Making Shapes
What can students
learn from using
Geoboards?
National Library of Virtual Manipulatives
Composing Shapes
K.G.6 Compose simple shapes to form larger shapes. For
example, “can you join these two triangles with full sides
touching to make a rectangle?”
1.G.2 Compose two-dimensional shapes (rectangles,
squares, trapezoids, triangles, half-circles, and quartercircles) 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. (Students do not need
to learn formal names such as “right rectangular prism.”)
Composing Shapes
1.G.2 Compose two-dimensional shapes or threedimensional shapes to create a composite shape, and
compose new shapes from the composite shape.
Decomposing Shapes


Display a large square to the students and ask, “What
will happen if I cut this shape straight down the middle?
What shapes will be created?”
“Why do we call these two shapes rectangles, not
squares?
Decomposing Shapes

Emphasize the lines that students cut have to be
straight horizontal, vertical, or diagonal and then
demonstrate these to the students. Example cuts
should include ones that are not just straight through
the middle; instead the teacher should snip off one
corner demonstrating a small cut. This will show
students their cuts can be of various lengths. Take turns
having one student demonstrate a cut and then other
students model the same cut.
Decomposing Shapes

Give each student a set of shapes (p. 36) Tell them to
cut out each shape and see what shapes can be made by
making one cut. Have the students glue their pieces
down puzzle style. Have each student share how they
cut one of their shapes and identify the new shapes they
made.
Georgia Common Core first grade workbook p. 33
Differentiation
Extension
Ask students, “What kind of shapes would be created by
making two cuts?” Allow students to explore with
combining three shapes to create a new shape.
Intervention
Allow students who may be having a difficult time
describing or making the shapes extra time with pattern
blocks as a model. Students could also use tangram pieces
if they are having difficulty with the cuts.
Pattern Blocks - Composing
Pattern Blocks - Composing
Illuminations at NCTM.org
National Library of Virtual Manipulatives
Math Playground
Tangrams
Fractions of a shape
Part I Gather students in a common area. Hold up one
sheet of paper. Tell students that the paper represents a
cake that four students won at the fair and then fold it
unevenly. Tear off three small pieces to give to the three
random students and then give the one big piece to a
fourth student.
Ask, “Is this fair? Why do you say that? What should I do
to make it fair?” Invite further discussion with students
about situations where they have had to share things such
as cookies, candy or toys, and listen for them to verbalize
the importance of making sure everyone gets a fair share.
Fractions of a shape
Part II Read A Fair Bear Share by Stuart J. Murphy or similar book on
fractions. After the story, remind students of the cake scenario you
discussed before reading. Ask “Is there a way to cut the cake so it will
be fair?” Allow students to share ideas.
Give each student 3 sheets of construction paper that are the same
size. Tell the students that these represent 3 whole cakes. Have them
label one of the sheets with the number one (because it represents
one whole cake). It should also be labeled “one whole.”
Next, tell the students they are going to share the second cake (piece
of construction paper) with one friend. Tell them to fold the paper in
a way that it will create two equal pieces. Keep in mind some students
may fold their paper vertically, horizontally or diagonally. Allow all
representations to be shared and discussed. Ask questions such as:
“Are these two representations of ½ the same size?” How do you
know?
Fractions of a shape
For the third sheet of construction paper, tell the students they are
going to share this cake with 3 friends and fold it in a way that creates
four equal pieces. Some students may fold it vertically (like a fan) or
vertically and horizontally (making a grid). Allow both representations
to be shared and discussed. The discussion for ¼ should be similar to
the one you had related to ½. Label each part of the third “cake” with
both the fraction ¼ and the words fourths and quarter.
Make sure to ask students “What is happening to our pieces as we
add more folds to the paper? Why is this happening? What if we
shared this cake with ten people, would we get more or less cake?
How do you know? Which is bigger ½ or ¼? (Or ask in this way,
Which is larger, one half or one quarter?) Can you prove it?”
Fraction Fill In Game
Students will work with a
partner to play Fraction Fill In
to develop proficiency with
fractions. To use spinner, put
a paperclip in the middle.
Hold it in place with the tip
of the pencil. Have the
student thump the paper
clip to spin and see where it
lands.
pp. 55-56
Fractions from Composing

What simple fractions can be made from
pattern blocks?
1.G.3 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.
Videos
Clever Car
http://www.youtube.com/watch?v=4idPhHinb_g
Classify, Sort and Graph
K.MD.3 Classify objects into given categories; count the
numbers of objects in each category and sort the
categories by count.
2 APPLES
4 ORANGES
5 BANANAS
Classify, Sort and Graph
1.MD.4 Organize, represent, and interpret data with up to
three categories; ask and answer questions about the total
number of data points, how many in each category, and
how many more or less are in one category than in
another.
2 APPLES
4 ORANGES
5 BANANAS
1.MD.3 Tell and write time in hours and half-hours using
analog and digital clocks.
This is an introduction to clocks and how we use them to
tell time. Student look at make-believe clocks that are set
to hours or half-hours and learn the pattern of 12:30, 1:00,
1:30, etc.
Measuring


Order objects by length
Measure using “same-size length units”
Goals for today
Learn the progression of geometric
thinking
 Explore activities related to the Common
Core for geometry, measurement and
data
 Consider “next steps”
