KINDERGARTEN-MATH
August 2012
Counting and Cardinality
Big Ideas
Essential Questions
A. Know the number names and
the count sequence.
1. We can count to 100 in different
ways.
2. We count in order to know how
many we have.
3. Counting is a purposeful skill that
assigns a number name to an
object or set of objects.
A. Know number names and count
sequence.
1. What are different ways to count to
100?
2. Why do we count objects?
3. What does a number represent?
B. Count to tell the number of
objects.
1. Counting is a purposeful skill that
assigns a number name to an
object or set of objects.
B. Count to tell the number of
objects.
1. What does a number represent?
Skills
A. Know the number names and the count
sequence.
K.CC.1
1. Count to 25 by ones and by tens.
B. Count to tell the number of objects. (0-10 ONLY)
K.CC.4
4. Understand the relationship between numbers and
quantities; connect counting to cardinality.
4a. When counting objects, say the number names in the
standard order, pairing each object with one and only one
number name and each number name with one and only
one object.
4b. Understand that the last number name said tells the
number of objects counted. The number of objects is the
same regardless of their arrangement or the order in which
they were counted.
4c. Understand that each successive number name refers
to a quantity that is one larger.
Suggested Mathematical Practices:
#6: Attend to precision.
#7: Look for and make use of structure.
September 2012
Counting and Cardinality
Big Ideas
Essential Questions
A. Know number names and count the
sequence.
1. Counting is a purposeful skill that assigns a
number name to an object or group of objects.
A. Know number names and
count the sequence.
B. Count to tell the number of objects.
1. Counting is a purposeful skill that assigns a
number name to an object or group of objects.
C. Describe and compare measurable
attributes.
1. Objects can be described and compare to
each other using different attributes.2.
Measurement processes and attributes are
used tin everyday life to describe and quantify
the world.
1. What does a number
represent?
2. How many are there?
Skills
A. Know the number names (0-10) and the count
sequence (0-25).
K.CC.1
1. Count to 25 by ones and tens.
B. Count to tell the number of objects. (0-10 ONLY)
K.CC.4
B. Count to tell the number
4. Understand the relationship between numbers and
of objects.
quantities; connect counting cardinality.
1. How do you know how many
4a. When counting objects, say the number names in
objects are in a group?
the standard order, pairing each object with one and
only one number name and each number name with
one and only one object.
C. Describe and compare
4b. Understand that the last number name said tells
measurable attributes.
the number of objects counted. The number of objects
1. How do we compare
is the same regardless of their arrangement or the
different groups of things?
2. Why does "what" we
order in which they were counted.
measure influence "how" we
4c. Understand that each successive number name
measure?
refers to a quantity that is one larger.
C. Describe and compare measurable attributes.
K.MD.1
1. Describe measurable attributes of objects, such
as length or weight. Describe several measurable
attributes of a single object.
Suggested Mathematical Practices:
#6: Attend to precision.
#7: Look for and make use of structure.
October 2012
Counting and Cardinality; Measurement and Data
Big Ideas
Essential Questions
A. Classify objects and count A. Classify objects and
the number of objects in each count the number of
category.
objects in each category.
1. We sort by using different
1. Why does "what" we
attributes. (color, shape and
measure and sort influence
size).
"how" we measure and
sort?
B. Know number names and
the count sequence.
1. Counting forward doesn't
always have to start with number
1.
2. Counting is a purposeful skill
that assigns a number name to
an object or set of objects.
C. Count to tell the number of
objects.
1. When counting objects,
numbers increase by one.
2. Arrangement of objects does
not affect the amount or total.
3. The last number counted
represents the total.
D. Compare numbers.
1. Counting is a purposeful skill
that assigns a number name to
B. Know number names
and the count sequence.
1. What does a number
represent?
Skills
A. Classify objects and count the number of objects in
each category. K.MD.3
1. Classify objects into given categories; count the
numbers of objects in each category and sort the
categories by count.
B. Know number names (Master) and the count
sequence 0-25 (Master).
K.CC.2 ONLY 0-10
2. Count forward beginning from a given number within
the known sequence (instead of having to begin at 1.)
2. How many are there?
C. Count to tell the
number of objects.
1. What does a number
represent?
2. How many are there?
C. Count to tell the number of objects.
K.CC.4 ONLY 0-10
4. Understand the relationship between numbers and
quantities; connect counting to cardinality.
4a. When counting objects, say the number names in the
standard order, pairing each object with one and only one
number name and each number name with one and only
one object.
4b. Understand that the last number name said tells the
number of objects counted. The number of objects is the
same regardless of their arrangement or the order in
which they were counted.
4c.Understand that each successive number name refers
an object or set of objects.
D. Compare numbers.
to a quantity that is one larger.
E. Know number names and
the count sequence.
1. What does a number
represent?
1. Numbers help represent how
many objects you have.
2. How many are there?
D. Compare numbers.
K.CC.6 ONLY 0-10
6. Identify whether the number of objects in one group is
greater than, less than, or equal to the number of objects
in another group, e.g., by using matching and counting
strategies.
Suggested Mathematical Practices:
#2: Reason abstractly and quantitatively.
E. Know number names
and the count sequence.
1. What does a number
represent?
E. Know number names and the count sequence
K.CC.3 Only 0-10
3. Write numbers from 0 to 20. Represent a number of
objects with a written numeral 0-20 (with 0 representing a
count of no objects).
Suggested Mathematical Practices:
#4:Model with mathematics.
#6: Attend to precision.
#7: Look for and make use of structure.
November 2012
Counting and Cardinality, Measurement and Data
Big Ideas
A. Know number names and
count the sequence.
1. We can count by 1's and 10's.
2. We count in order so we know how
many we have.
3. Numbers show how many things
we have.
Essential Questions
A. Know number names and
count the sequence.
1. How many are there?
2. What does a number
represent?
B. Compare Numbers.
1. Numbers can be compared in
many ways having more than, less
than or equal amounts.
B. Compare Numbers.
1. What are different ways we can B. Compare Numbers
compare numbers and objects?
K.CC.7
7. Compare two numbers between 1-10 as
C. Classify objects and count written numerals. (more or less)
the number in each category.
1. How does "what" we measure
and sort influence "how" we
C. Classify objects and count the number in
measure and sort?
each category. (0-20 only)
K.MD.3
3. Classify objects into given categories; count
the numbers of objects in each category and sort
the categories by count.
Mathematical Practices:
#6: Attend to precision.
#7: Look for and make use of structure.
#2: Reason abstractly and quantitatively.
C. Classify objects and count the
number in each category.
1. We measure and sort in everyday
life to describe and quantify the
world.
Skills
A. Know number names (0-20) and count the
sequence. (0-50 only) Introduce
K.CC.2
1. Count forward beginning from a given number
within the known sequence instead of having to
begin at 1.
2. Count to 50 by ones and tens to 100.
December 2012
Counting and Cardinality; Measurement and Data
Big Ideas
A. Count and tell the number of
objects.
1. Counting is a strategy for
finding the answer to how many.
Essential Questions
A. Count and tell the number
of objects
1. How do you know how many
objects are in a group?
Skills
A. Count and tell the number of objects. (0-20)
K.CC.5
1. Count 0-20 objects.
2. Given a number, count that many objects 0-20.
3. Number Identification 0-20.
B. Compare Numbers
B. Compare Numbers
1. What are different ways that
we can compare numbers?
B. Compare Numbers
K.CC.7
1. Compare two written numbers between 0-10 as
more or less. (MASTERY)
K.CC.6
1. Comparing groups of objects 0-20 as more than,
less than, or equal to. (Introduce “equal”)
1. We can compare numbers in
different ways.
C. Classify objects and count
the number in each category
1. We sort by using different
attributes.
C.. Classify objects and
count the number in each
category.
1. What are different ways we
can sort objects?
C. Classify objects and count the number in
each category.
(0-20)
K.MD.3
1. Sort and classify objects into given categories
and count the numbers in each group.
2. Sort the categories by count.
Mathematical Practices:
#6: Attend to precision.
#2: Reason abstractly and quantitatively.
January 2013
Counting and Cardinality; Measurement and Data; Geometry
Big Ideas
A. Know number names and count
the sequence.
1. Counting is a purposeful skill that
assigns a number name to an object or
set of objects without regard to where
we begin counting.
B. Describe and compare
measurable attributes.
1. Objects can be described and
compare to each other using different
attributes.2. Measurement processes
and attributes are used tin everyday life
to describe and quantify the world.
C. Identify and Describe shapes.
1. Shapes are everywhere.
2. Positional words can be used to
describe where
objects are compared to other objects
around them.
Essential Questions Skills
A. Know number names A. Know number names and count the sequence.
and count the
K.CC.1
sequence.
1. Count to 75 by ones. (Introduction)
1. What are different
Count to 100 by tens. (MASTERY)
ways we can count to
K.CC.2
100?
0-20 ONLY
2. Count forward beginning from a given number within the
known sequence (instead of having to begin at 1).
K.CC.3
3. Write the numbers 0-20. Represent a number of objects with
a written numeral 0-20 (with 0 representing a count of no
objects).
B. Describe and
compare measurable
attributes.
1. How do we compare
different groups of things?
2. Why does "what" we
measure influence "how"
we measure?
C. Identify and describe
shapes.
1. Where can you find
shapes?
B. Describe and compare measurable attributes.
K.MD.1
1. Describe measurable attributes of objects, such as length or
weight. Describe several measurable attributes of a single
object.
K.MD.2
2. Directly compare two objects with a measurable attribute in
common to see which object has "more of/less of" and
describe the difference. For example, directly compare the
heights of two children and describe one child as taller/shorter.
C. Identify and describe shapes (squares, circles,
triangles, rectangles, and hexagons)
K.G.1
3. Geometric attributes, such as
shapes, lines, angles, figures and
planes, provide descriptive information
about an object's properties and
position in space and support
visualization and problem solving.
D. Analyze, compare, create and
compose shapes.
1. Geometric attributes, such as
shapes, lines, angles, figures and
planes, provide descriptive information
about an object's properties and
position in space and support
visualization and problem solving.
2. How do we describe
where objects are
located?
3. How does geometry
describe shapes?
1. Describe objects in the environment using names of shapes
and relative positions of these objects using terms such as
above, below, beside, in front of, behind, and next to.
K.G.2
2. Correctly name shapes regardless of their orientations or
overall size.
D. Analyze, compare,
create and compose
shapes.
1. How does geometry
better describe objects?
D. Analyze, compare, create and compose shapes.
K.G.4
4. Analyze and compare two- and three-dimensional shapes
(cubes, cones, sphere, cyclinder), in different sizes and
orientations, using informal language to describe their
similarities, differences, parts (e.g., number of sides and
vertices/“corners”) and other attributes (e.g., having sides of
equal length).
K.G.5
5. Model shapes in the world by building shapes from
components (e.g., sticks and clay balls) and drawing shapes.
K.G.6
6. Compose simple shapes to form larger shapes. For
example, “Can you join these two triangles with full sides
touching to make a rectangle
Suggested Mathematical Practices:
#7: Look for and make use of structure.
#4: Model with mathematics.
#6: Attend to precision.
#8: Look for and express regularity in repeated reasoning.
#3: Construct viable arguments and critique the reasoning of
others.
February 2013
Geometry; Measurement and Data; Numbers and Operations in Base Ten
Big Ideas
Essential Questions
A. Analyze, compare, create and
compose shapes.
1. Shapes can be described in many
ways.
A. Analyze, compare, create
and compose shapes.
1. How can we compare
different shapes?
2. Geometric attributes, such as shapes,
lines, angles, figures and planes, provide
descriptive information about an object's
properties and position in space and
support visualization and problem solving.
2. How does geometry better
describe our world?
B. Identify and describe shapes
(squares, circles, triangles, rectangles,
hexagons, cubes, cones, cylinders and
spheres.
1. Geometric attributes, such as shapes,
lines, angles, figures and planes, provide
descriptive information about an object's
properties and position in space and
support visualization and problem solving.
2. Shapes are everywhere.
3. Positional words can be used to
describe where objects are compared to
other objects around them.
B. Identify and describe
shapes (squares, circles,
triangles, rectangles,
hexagons, cubes, cones,
cylinders and spheres.
1. How can you describe
shapes?
2. Where can you find
shapes?
Skills
A. Analyze, compare, create, and compose shapes.
K.G.4
4. Analyze and compare two- and three-dimensional
shapes, in different sizes and orientations, using informal
language to describe their similarities, differences, parts
(e.g., number of sides and vertices/“corners”) and other
attributes (e.g., having sides of equal length).
K.G.5
5. Model shapes in the world by building shapes from
components (e.g., sticks and clay balls) and drawing
shapes.
B. Identify and describe shapes (squares, circles,
triangles, rectangles, hexagons, cubes, cones,
cylinders, and spheres)
K.G.1
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.
K.G.3
3 Identify shapes as two-dimensional (lying in a plane, “flat”)
or three-dimensional (“solid”).
C. Describe and compare measurable
attributes
1. Measurement processes are used in
everyday life to describe and quantify the
world.
2. Different data displays describe and
represent data in alternative ways.
D. Work with numbers 11-19 to gain
foundations for place value.
1. Understanding place value can lead to
number sense and efficient strategies for
computing with numbers.
C. Describe and compare
measurable attributes.
1. Why does "what " we
measure influence "how" we
measure?
2. Why do we display or write
data in different ways?
D. Work with numbers 1119 to gain foundations for
place value.
1. How does a digit's position
affect its value?
C. Describe and compare measurable attributes
K.MD.1
1. Describe measureable attributes of objects such as
length and weight. Describe several measureable attributes
of a single object.
D. Work with numbers 11–19 to gain foundations for
place value
K.NBT.1
1. Compose and decompose numbers from 11 to 19 into ten
ones and some further ones, e.g., by using objects or
drawings, and record each composition or decomposition by
a drawing or equation (e.g., 18 = 10 + 8); understand that
these numbers are composed of ten ones and one, two,
three, four, five, six, seven, eight, or nine ones.
Suggested Mathematical Practices:
#4: Model with mathematics.
#3: Construct viable arguments and critique the reasoning of
others.
#6: Attend to precision.
March 2013
Operations and Algebraic Thinking
Big Ideas
Essential Questions
A. Understand addition is putting
together and adding to, and
understand subtraction is taking apart
and taking from.
A. Understand addition is putting
together and adding to, and
understand subtraction is taking apart
and taking from.
1. Mathematical operations are used in
solving problems in which a new value is
produced from one or more values.
2. Algebraic thinking involves choosing,
combining and applying effective
strategies for answering quantitative
questions.
1. In what ways can operations affect
numbers?
2. How can different strategies be helpful
when solving a problem?
Skills
A. Understand addition is putting together or
adding to, and understand subtraction is
taking apart or taking from.
K.OA.1
1. Represent addition and subtraction with
objects, fingers, mental images, drawings,
sounds, acting out, verbal explanations,
expressions or equations.
Drawings need not show details, but should
show the mathematics in the problem.
K.OA.2
2. Solve addition and subtraction word
problems, and add and subtract within 10, e.g.,
by using objects or drawings to represent the
problem.
Mathematical Practices:
#4: Model with mathematics.
#5: Use appropriate tools strategically.
April 2013
Operations and Algebraic Thinking
Big Ideas
Essential Questions
A. Know number names and count
the sequence.
1. Counting is a purposeful skill that
assigns a number name to an object
or set of objects without regard to
where we begin counting
A. Know number names and
count the sequence.
1. What are different ways we can
count to 100?
B. Understand addition is putting
together or adding to, and
understand subtraction is taking
apart or taking from.
1. Mathematical operations are used in
solving problems in which a new value
is produced from one or more values.
2. Algebraic thinking involves
choosing, combining and applying
effective strategies for answering
quantitative questions.
B. Understand addition is putting
together or adding to, and
understand subtraction is taking
apart or taking from.
1. In what ways can operations
affect numbers?
2. How can different strategies be
helpful when solving a problem?
Skills
A. Know number names and count the sequence.
K.CC.1
1. Count to 100 by ones. (Introduction)
Count to 100 by tens. (MASTERY)
B. Understand addition is putting together or
adding to, and understand subtraction is taking
apart or taking from.
K.OA.3
3. Decompose numbers less than or equal to 10 into
pairs in more than one way, e.g., by using objects or
drawings, and record each decomposition by a
drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1)
K.OA.4
4. For any number from 1 to 9, find the number that
makes 10 when added to the given number, e.g., by
using objects or drawings, and record the answer with
a drawing or equation.
Mathematical Practices:
#7: Look for and make use of structure.
May 2013
Operations and Algebraic Thinking
Big Ideas
Essential Questions
A. Understand addition is
putting together or adding to,
and understand subtraction is
taking apart or taking from.
A. Understand addition is
putting together or adding to,
and understand subtraction is
taking apart or taking from.
1. Mathematical operations are
used in solving problems in
which a new value is produced
from one or more values.
2. Algebraic thinking involves
choosing, combining, and
applying effective strategies for
answering quantitative
questions.
1. What are the different ways
operations affect numbers?
B. Work with numbers 11-19
to gain foundations for place
value.
1. Understanding place value
can lead to number sense and
efficient strategies for computing
with numbers.
Skills
A. Understand addition is putting together or adding to,
and understand subtraction is taking apart or taking
from.
K.OA.5
5. Fluently add and subtract within 5
2. How can different strategies be
helpful when solving a problem?
B. Work with numbers 11-19 to
gain foundations for place
value.
1. How does a digit's position
affect its value?
B. Work with numbers 11-19 to gain foundations for place
value. (HOPKINS)
K.NBT.1
MASTERY
1. Compose and decompose numbers from 11 to 19 into ten
ones and some further ones, e.g., by using objects or
drawings, and record each composition or decomposition by a
drawing or equation (e.g., 18 = 10 + 8); understand that these
numbers are composed of ten ones and one, two, three, four,
five, six, seven, eight, or nine ones.
Suggested Mathematical Practices:
#4. Model with mathematics.
#8: Look for and express regularity in repeated reasoning.