1st Grade Mathematics
Unit # 5: Composing and Partitioning Shapes/Time
Pacing: 15 days
Unit Overview1
In lessons 1-3, students identify the defining parts, or attributes, of two- and three-dimensional shapes, building on their kindergarten experiences of sorting, analyzing, comparing,
and creating various two- and three-dimensional shapes and objects (1.G.1). Using straws, students begin the exploration by creating and describing two-dimensional shapes
without naming them. This encourages students to attend to and clarify a shape’s defining attributes. Later, students name two- and three-dimensional shapes and find them in
pictures and in their environment. New shape names are added to students’ repertoire, including trapezoid, rhombus, cone, and rectangular prism. In lessons 4-6, students
combine these shapes to create a new whole: a composite shape (1.G.2). Students identify the name of the composite shape as well as the names of each shape that forms it.
Students see that another shape can be added to a composite shape so that the composite shape becomes part of an even larger whole. In lessons 7-9, students relate geometric
figures to equal parts and name the parts as halves and fourths (or quarters) (1.G.3). For example, students now see that a rectangle can be partitioned into two equal triangles
(whole to part) and that the same triangles can be recomposed to form the original rectangle (part to whole). Students see that as they create more parts, decomposing the shares
from halves to fourths, the parts get smaller. Last, in lessons 10-13, students apply their understanding of halves (1.G.3) to tell time to the hour and half hour (1.MD.3). Students
will construct simple clocks and begin to understand the hour hand, then the minute hand, then both together. Throughout each lesson, students read both digital and analog clocks
to tell time. Throughout this unit, students continue daily fluency with addition and subtraction, preparing for Module 6, in which they will be adding within 100, and assuring their
mastery of the grade level fluency goal of sums and differences within 10.
Prerequisite Skills
K.G.2 Correctly name shapes regardless of their
orientations or overall size.
K.G.3 Identify shapes as two-dimensional (lying in a
plane, “flat”) or three-dimensional (“solid”).
K.G.4 Analyze and compare two- and threedimensional shapes, in different sizes and orientations,
using informal language to describe their similarities,
differences, parts and other attributes
K.G.6 Compose simple shapes to form larger shapes.
1
EngageNY First Grade Module 5 Unit Overview
Vocabulary
Mathematical Practices
circle
edge
hexagon
square
closed
equal shares
open
three-dimensional
combine
faces
part
trapezoid
compose
fourth(s)
partition
triangle
composite shape
fourth of
quarter(s)
two-dimensional
cone
half
quarter circle
vertex
cube
half of
rectangle
vertices
cylinder
halves
rectangular prism
whole
decompose
half-circle
side
MP.1: Make sense of problems and persevere in solving
them
MP.2: Reason abstractly and quantitatively
MP.3: Construct viable arguments and critique the reasoning
of others
MP.4: Model with mathematics
MP.5: Use appropriate tools strategically
MP.6: Attend to precision
MP.7: Look for and make use of structure
MP.8: Look for and express regularity in repeated reasoning
Common Core State Standards
Additional
Standards
(10%)
Supporting
Standards
(20%)
1.G.1 Shape
Attributes
1.G.2 Compose 2D
and 3D Shapes
1.G.3 Partitioning Shapes
1.MD.3 Time
Major
Standards
(70%)
According to the PARCC Model Content Framework,
Opportunities for connections among standards include:
 Composing shapes to create a new shape (1.G.A.2) is the spatial analogue
of composing numbers to create new numbers. This is also connected to
length measurement (1.MD.A.2) since students must visualize an object to
be measured as being built up out of equal-sized units (see also 1.G.A.3).
Though assembling two congruent right triangles into a rectangle does not
use the same facts or reasoning that assembling two 5s into a 10 uses, the
idea of looking at how objects in some domain (numbers or shapes) can be
combined to make other objects in that domain and looking for new true
statements one can make about these combinations is a big idea that is
common across mathematics.
Progression of Skills
Kindergarten
1st Grade
2nd Grade
According
to
the
PARCC
Model
Content
Framework,
1.G.1 Distinguish between
K.G.4 Analyze and
Standard
should
serve
defining
attributes
(e.g.,as an opportunity for incompare twoand three- 3.NF.2
dimensional depth
shapes, focus:
in
triangles are closed and threedifferent sizes and
orientations, using
informal language to
describe their similarities,
differences, part
K.G.5 Model shapes in
the world by building
shapes from components
(e.g., sticks and clay balls)
and drawing shapes.
K.G.6 Compose simple
shapes to form larger
shapes.
N/A
 While students are dealing with the limited precision of only whole and
half-hours, they must distinguish the position of the hour hand and connect
this to geometry standard 1.G.A.3, partitioning circles into halves and
quarters.
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N/A
sided) versus non-defining
attributes; build and draw
shapes to possess defining
attributes.
1.G.2 Compose twodimensional shapes
(rectangles, squares,
trapezoids, triangles, halfcircles, 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.
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
1.MD.3 Tell and write time in
hours and half-hours using
analog and digital clocks.
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.
2.G.2 Partition a
rectangle into rows and
columns of same-size
squares and count to find
the total number of them.
2.G.3 Partition circles
and rectangles into two,
three, or four equal
shares, describe the
shares using the words
halves, thirds, half of, a
third of, etc., and
describe the whole as
two halves, three thirds,
four fourths. Recognize
that equal shares of
identical wholes need not
have the same shape.
2.MD.7 Tell and write
time from analog and
digital clocks to the
nearest five minutes,
using a.m. and p.m.
Students Will…
Big Ideas





Shapes can be defined by certain
attributes.
Equal parts make a “whole” when
put together.
Shapes can be combined to make
new shapes.
Shapes can be divided into equal
parts.
When equal parts are divided
further, the parts get smaller.
Be Able To…
Know/Understand
1.
Defining attributes are characteristics of a shape (e.g.,
number of sides, vertices, closed, angles, etc.).
2. Non-defining attributes do not identify what the shape
is called (e.g., color, orientation, size, etc.).
3. A composite shape is a figure made up of two or more
geometric shapes.
4. Shapes fit together to create a different shape.
5. The "whole" is composed of two halves, or four fourths
or four quarters.
6. Circles and rectangles can be divided into equal shares
or pieces.
7. Halves of two different wholes are not necessarily the
same size.
8. Partitioning shapes into equal parts creates a name for
the number of parts (e.g, halves have two equal parts).
9. Decomposing equal shares into more equal shares
results in smaller equal shares.
10. Halves mean two equal shares of a whole.
11. Fourths or quarters mean four equal shares of a whole.













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Distinguishing between attributes that define a shape
and attributes that do not.
Using attribute language to describe a given twodimensional
shape (e.g. number of sides, closed, vertices, etc.).
Using attribute language to describe a given threedimensional object (e.g., number of faces, vertices, edges,
etc.).
Comparing/Contrasting two- and three-dimensional
figures
using defining attributes.
Building and drawing shapes possessing defining
attributes (e.g., faces, edges, vertices, etc.)
Identifying shapes that fit within an already existing
shape (e.g. noticing that a square can be composed of two
triangles).
Creating a composite shape with two-dimensional shapes
using tools such as pattern blocks, plastic shapes,
tangrams, virtual shapes, attribute blocks, or drawings.
Creating a composite shape with three-dimensional
shapes using tools such as clay, dough, virtual shapes,
attribute blocks.
Determining if parts of a whole are equal.
Identifying fractional parts of a whole using circles and
rectangles (e.g., half of, fourth of, and quarter of ).
Showing halves and fourths of a circle and rectangle
using a
variety of tools (e.g., paper folding/cutting, virtual
shapes)
Identifying two-dimensional shapes such as rectangles,
squares, trapezoids, triangles, half-circles, and quartercircles.
Identifying three-dimensional shapes such as cubes, right
rectangular prisms, circular cones, and circular cylinders.
Unit Sequence
1
Student Friendly
Objective
SWBAT…
SWBAT classify
shapes using
defining
attributes.
2
SWBAT identify
and describe twodimensional
shapes using
defining
attributes.
3
SWBAT identify
and describe
three-dimensional
shapes using
defining attribues.
2
Key Points/
Teaching Tips2
Instructional
Resources
In Lesson 1, students use straws cut at various
lengths to create and then classify shapes. A list of
the attributes that are common to a set of shapes is
created. As students create a new shape with their
straws, they decide if it has all the listed attributes.
The names of these shapes are intentionally omitted
during this lesson to encourage students to use
precise language as they describe each shape. In this
way, students attend to, and clarify, a shape’s
defining attributes (1.G.1). For instance, rather than
describing a shape as a triangle.
In Lesson 2, students connect defining attributes to
the classification name. Along with circle, triangle,
rectangle, and hexagon, which were introduced in
kindergarten, students learn trapezoid and rhombus.
Given three shapes (triangle, rhombus,
EngageNY First Grade
circle), students will identify the number Module 5 Lesson 1
of corners and straight sides. Given two
sets of shapes, students will eliminate the
shape that does not belong (does not have
the same number of corners or straight
sides).
Given four shapes, students will identify
the number of corners and straight sides
and match it to its geometric name (e.g. a
shape with 3 corners and 3 straight sides
is a triangle).
EngageNY First Grade
Module 5 Lesson 2
My Math Chapter 9
Lessons 1-4
In Lesson 3, defining attributes of three-dimensional
shapes are explored. Along with the threedimensional shape names learned in kindergarten
(sphere, cube, and cylinder), students expand their
vocabulary to include cone and rectangular prism.
Students are presented with models of threedimensional shapes as well as real life examples to
sort and classify based on their defining attributes.
Given a picture of two real life objects,
students analyze a given statement about
their shape to determine if it is true or
false. SW write a sentence to explain
their answer.
EngageNY First Grade
Module 5 Lesson 3
EngageNY First Grade Module 5 Topics A-
4|Page
Exit Ticket
My Math Chapter 10
Lessons 1-2
4
SWBAT create
composite shapes
from 2D shapes.
5
SWBAT create a
new shape from a
composite shape.
6
SWBAT create
composite shapes
from 3D shapes.
In Lesson 4, students create composite shapes
(hexagons, rectangles, and trapezoids) from triangles,
squares, and rectangles. The students recognize that
the same composite shape (whole) can be made from
a variety of shapes (parts).
In Lesson 5, students begin by identifying the hidden
shapes within a large square as they cut the seven
tangram pieces from this special rectangle. Students
use the pieces to form new shapes from composite
shapes, including recomposing the original square.
Students explore the variety of ways they can
compose new shapes by positioning pieces alongside
composite shapes.
In Lesson 6, students extend their exploration of parts
and wholes to three-dimensional shapes. Students
create and hide composite shapes and describe the
shape to a partner using attributes and positional
words. The partner listens and attempts to create the
same composite shape. In this way, students attend
to the parts within the whole of their created shape
and continue to develop clear, precise language use.
Students will create a hexagon using
three rhombuses; SW use 1 hexagon and
3 triangles to make a large triangle. SW
trace or draw a model of their pattern
blocks.
Students will use words and/or drawings
to show how they can make a larger
shape using three smaller shapes of their
choice. SW label the shapes used in their
model.
EngageNY First Grade
Module 5 Lesson 4
My Math Chapter 9
Lesson 5
When read the following scenario, SW
recreate a composite shape using 3D
blocks: Maria’s structure has:
 1 rectangular prism with the shortest
face touching the table.
 1 cube on the right of the rectangular
prism.
 1 cylinder on top of the cube with the
circular face touching the cube.
EngageNY First Grade
Module 5 Lesson 6
My Math Chapter 10
Lesson 4
EngageNY First Grade
Module 4 Lesson 5
My Math Chapter 9
Lesson 6
Formative Assessment: North Carolina Geometry Tasks 1a, 1b, 1c, 2
7
8
SWBAT identify
parts of a whole
using 2D shapes.
SWBAT identify
equal parts.
SWBAT identify
halves and
quarters.
5|Page
In Lesson 7, students explore composite shapes that
have been made throughout the module and sort them
into two categories of shapes, those made from equal
parts and those made from non-equal parts. Students
count the number of equal parts that form one whole.
Lesson 8 introduces the terms half and quarter, or
fourths, to name two equal parts of a whole and four
equal parts of a whole, respectively. Students learn
half-circle and quarter-circle as the names of shapes,
and recognize that they are named for their size and
shape in relation to a whole circle.
Given three shapes separated into parts,
students will identify which shape is
partitioned into equal parts. SW identify
the number of equal parts within the
whole.
Given four shapes, students will color in
halves and quarters as follows:
 Color a fourth of a square.
 Color half of a rectangle.
 Color half of a square.
 Color a quarter of a circle.
EngageNY First Grade
Module 5 Lesson 7
My Math Chapter 9
Lesson 8
EngageNY First Grade
Module 5 Lesson 8
My Math Chapter 9
Lessons 9-10
9
SWBAT partition
shapes and
identify halves
and quarters.
10 SWBAT tell time
to the hour.
In Lesson 9, students explore halves and fourths more
deeply as they identify these parts within circles and
rectangles of varying size and dimension. Students
recognize that as they partition, or decompose the
whole into more equal shares, they create smaller
units.
In Lesson 10, students count and color the parts on a
partitioned circle, forming the base of a paper clock.
Relating this 12-section circle to the clock, students
learn about the hour
hand and tell time on
both analog and digital
clocks.
11
12
11
1
10
9
4
7
12 SWBAT tell time
to the hour and
half hour.
13 SWBAT tell time
to the hour and
half hour.
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6
5
EngageNY First Grade
Module 5 Lesson 9
North Carolina
Geometry Task 3a, 3b
EngageNY First Grade
Module 5 Lesson 10
1
2
3 9
8
11 SWBAT tell time
to the half hour
on both analog
and digital clocks
12
10
2
Given a circle, students will partition it
into halves and quarters in order to
analyze the following statements as true
or false:
1. One fourth of a circle is bigger than
one half of a circle.
2. Cutting the circle into quarters gives
you more pieces than cutting the circle in
half.
Given a picture of four analog clocks,
students will use the picture to write the
time to the hour shown on each clock.
3
8
4
7
6
5
In Lesson 11, students recognize the two half-circles
on the circular clock face and connect this
understanding with the half hour. Counting by fives
to 30, students see that there are two 30-minute parts
that make 1 hour, helping them connect the time
displayed on a digital clock with the time displayed
on an analog clock. Students notice that the hour
hand is halfway through, but still within the hour
section on the partitioned paper clock.
In Lesson 12, and in Lesson 13 they extend these new
skills to telling time to the hour and half-hour using a
variety of analog and digital clock faces.
Given two pictures of an analog clock
EngageNY First Grade
with the hour hand already drawn,
Module 5 Lesson 11
students will draw the minute hand to
show the following times: 9:30, 3:30.
Given a complete analog clock, SW write
the time to the half hour.
Given four analog clocks, students will
draw the hour and minute hand to show
the following times: 1:30. 10:00. 5:30.
7:30
Given three analog clocks, identify the
clock that correctly shows half past 3
o’clock. Given three analog clocks, write
the time shown (noon) and draw the
hands to show the time (4:30, 9 o’clock).
EngageNY First Grade
Module 5 Lesson 12
EngageNY First Grade
Module 5 Lesson 13
Flex Day (Instruction Based on Data)
Recommended Resources:
 EngageNY First Grade Module 5 Assessment
Summative Performance Task
“iRobot”
Appendix B
7|Page
Appendix A:
Unpacked Standards Guide
Source: Public Schools of North Carolina NCDPI Collaborative Workspace
Reason with shapes and their attributes.
Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of partwhole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different
perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for
measurement and for initial understandings of properties such as congruence and symmetry.
Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language.
The terms students should learn to use with increasing precision with this cluster are: shape, closed, open, side, attribute1, feature1, twodimensional, rectangle, square, trapezoid, triangle, half-circle, and quarter-circle, three-dimensional, cube, cone, prism, cylinder, partition,
equal shares, halves, fourths, quarters, half of, fourth of, quarter of
From previous grades: circle, rectangle, hexagon, sphere, cube, cone, cylinder
1
“Attributes” and “features” are used interchangeably to indicate any characteristic of a shape, including properties, and other defining
characteristics (e.g., straight sides) and non-defining characteristics (e.g., “right-side up”). (Progressions for the CCSSM: Geometry, CCSS Writing Team, August 2011,
page 3 footnote)
Common Core Standards
Unpacking
What do these standards mean a child will know and be able to do?
1.G.1 Distinguish between
defining attributes (e.g.,
triangles are closed and
three-sided) versus nondefining attributes (e.g.,
color, orientation, overall
size); build and draw
shapes to possess defining
attributes.
First Grade students use their beginning knowledge of defining and non-defining attributes of shapes to identify, name,
build and draw shapes (including triangles, squares, rectangles, and trapezoids). They understand that defining
attributes are always-present features that classify a particular object (e.g., number of sides, angles, etc.). They also
understand that non-defining attributes are features that may be present, but do not identify what the shape is called
(e.g., color, size, orientation, etc.).
Example:
All triangles must be closed figures and have 3 sides. These are defining attributes.
Triangles can be different colors, sizes and be turned in different directions. These are non-defining attributes.
Student
I know that this shape is a triangle because it has 3 sides.
It’s also closed, not open.
Student
I used toothpicks to build a square. I know it’s a square because it has 4 sides. And, all 4 sides are the same size.
8|Page
TEACHER NOTE: In the U.S., the term “trapezoid” may have two different meanings. Research identifies these as
inclusive and exclusive definitions. The inclusive definition states: A trapezoid is a quadrilateral with at least one pair
of parallel sides. The exclusive definition states: A trapezoid is a quadrilateral with exactly one pair of parallel
sides. With this definition, a parallelogram is not a trapezoid. North Carolina has adopted the exclusive definition.
(Progressions for the CCSSM: Geometry, The Common Core Standards Writing Team, June 2012.)
1.G.2 Compose twodimensional shapes
(rectangles, squares,
trapezoids, triangles, halfcircles, 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.1
As first graders create composite shapes, a figure made up of two or more geometric shapes, they begin to see how
shapes fit together to create different shapes. They also begin to notice shapes within an already existing shape. They
may use such tools as pattern blocks, tangrams, attribute blocks, or virtual shapes to compose different shapes.
Example: What shapes can you create with triangles?
Student A: I made
a square. I used 2
triangles.
Student B: I made
a trapezoid. I used 4
triangles.
Student C: I made
a tall skinny
rectangle. I used 6
triangles.
1
Students do not need to
learn formal names such as
“right rectangular prism.”
First graders learn to perceive a combination of shapes as a single new shape (e.g., recognizing that two isosceles
triangles can be combined to make a rhombus, and simultaneously seeing the rhombus and the two triangles). Thus,
they develop competencies that include:
 Solving shape puzzles
 Constructing designs with shapes
 Creating and maintaining a shape as a unit
As students combine shapes, they continue to develop their sophistication in describing geometric attributes and
properties and determining how shapes are alike and different, building foundations for measurement and initial
understandings of properties such as congruence and symmetry.
(Progressions for the CCSS in Mathematics: Geometry, The Common Core Standards Writing Team, June 2012)
9|Page
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.
First Graders begin to partition regions into equal shares using a context (e.g., cookies, pies, pizza). This is a
foundational building block of fractions, which will be extended in future grades. Through ample experiences with
multiple representations, students use the words, halves, fourths, and quarters, and the phrases half of, fourth of, and
quarter of to describe their thinking and solutions. Working with the “the whole”, students understand that “the whole”
is composed of two halves, or four fourths or four quarters.
Students need many experiences with different sized circles and rectangles to recognize that when they cut something
into two equal pieces, each piece will equal one half of its original whole. Children should recognize that halves of two
different wholes are not necessarily the same size. Also they should reason that decomposing equal shares into more
equal shares results in smaller equal shares.
Example: How can you and a friend share equally (partition) this piece of paper so that you both have the same
amount of paper to paint a picture?
Student 1
I would split the paper right down the middle. That
gives us 2 halves. I have half of the paper and my
friend has the other half of the paper.
Student 2
I would split it from corner to corner
(diagonally). She gets half of the paper and I get
half of the paper. See, if we cut on the line, the
parts are the same size.
Example: Let’s take a look at this pizza.
Teacher: There is pizza for dinner. What do you notice about the slices on the pizza?
Student: There are two slices on the pizza. Each slice is the same size. Those are big slices!
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Teacher: If we cut the same pizza into four slices (fourths), do you think the slices would be the same size, larger, or
smaller as the slices on this pizza?
Student: When you cut the pizza into fourths, the slices are smaller than the other pizza. More slices mean that the
slices get smaller and smaller. I want a slice from that first pizza!
1.MD.3 Tell and write time
in hours and half-hours
using analog and digital
clocks.
For young children, reading a clock can be a difficult skill to learn. In particular, they must understand the differences
between the two hands on the clock and the functions of these hands. By carefully watching and talking about a clock
with only the hour hand, First Graders notice when the hour hand is directly pointing at a number, or when it is slightly
ahead/behind a number. In addition, using language, such as “about 5 o’clock” and “a little bit past 6 o’clock”, and
“almost 8 o’clock” helps children begin to read an hour clock with some accuracy. Through rich experiences, First
Grade students read both analog (numbers and hands) and digital clocks, orally tell the time, and write the time to the
hour and half-hour.
All of these clocks indicte the hour of “two”, although they look slightly different.
This is an important idea for students as they learn to tell time.
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