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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
1
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Pacing: 4 weeks (plus 1 week for reteaching/enrichment)
Mathematical Practices
Mathematical Practices #1 and #3 describe a classroom environment that encourages thinking mathematically and are critical for quality teaching
and learning.
Practices in bold are to be emphasized in the unit.
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Domain and Standards Overview
Counting and Cardinality K.CC
Know number names and the count sequence.
Count to tell the number of objects.
Compare numbers.
.
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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
2
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Priority and Supporting CCSS
Explanations and Examples*
K.CC.1. Count to 100 by ones and by tens.
K.CC.1.The emphasis of this standard is on the counting sequence (rote
counting).
When counting by ones, students need to understand that the next number in the
sequence is one more. When counting by tens, the next number in the sequence
is “ten more” (or one more group of ten).
Instruction on the counting sequence should be scaffolded (e.g., 1-10, then 1-
20, etc.).
Counting should be reinforced throughout the day, not in isolation.
Examples:
Count the number of chairs of the students who are absent.
Count the number of stairs, shoes, etc.
Counting groups of ten such as “fingers in the classroom” (ten fingers
per student).
When counting orally, students should recognize the patterns that exist from 1
to 100. They should also recognize the patterns that exist when counting by 10s.
K.CC3. 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).
K.CC.3. Students should be given multiple opportunities to count objects and
recognize that a numeral represents a specific quantity. Once this is established,
students begin to read and write numerals (numerals are the symbols for the
quantities). The emphasis should first be on quantity and then connecting
quantities to the written symbols.
Continued on next page
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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
3
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Priority and Supporting CCSS
Explanations and Examples*
K.CC.3. Continued
A sample unit sequence might include:
1. Counting up to 20 objects in many settings and situations over
several weeks.
2. Beginning to recognize, identify, and read the written numerals,
and match the numerals to given sets of objects.
3. Writing the numerals to represent counted objects.
Since the teen numbers are not written as they are said, teaching the teen
numbers as one group of ten and extra ones is foundational to
understanding both the concept and the symbol that represents each teen
number. For example, when focusing on the number “14,” students
should count out fourteen objects using one-to-one correspondence and
then use those objects to make one group of ten and four extra ones.
Students should connect the representation to the symbol “14.”
K.CC.4. Understand the relationship between numbers and
quantities; connect counting to cardinality.
a. 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.
b. 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.
c. Understand that each successive number name refers
to a quantity that is one larger.
K.CC.4. This standard focuses on one-to-one correspondence and how
cardinality connects with quantity.
For example, when counting three bears, the student should use the
counting sequence, “1-2-3,” to count the bears and recognize that
“three” represents the group of bears, not just the third bear. A student
may use an interactive whiteboard to count objects, cluster the objects,
and state, “This is three”. (Cardinality tells “how many”.)
In order to understand that each successive number name refers to a quantity
that is one larger, students should have experience counting objects, placing one
more object in the group at a time.
Continued on next page
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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
4
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Priority and Supporting CCSS
Explanations and Examples*
K.CC.4. Continued
For example, using cubes, the student should count the existing group,
and then place another cube in the set. Some students may need to re-
count from one, but the goal is that they would count on from the
existing number of cubes. S/he should continue placing one more cube
at a time and identify the total number in order to see that the counting
sequence results in a quantity that is one larger each time one more cube
is placed in the group.
A student may use a clicker (electronic response system) to
communicate his/her count to the teacher.
K.CC.5. Count to answer “how many?” questions about as many
as 20 things arranged in a line, a rectangular array, or a circle, or as
many as 10 things in a scattered configuration; given a number
from 120, count out that many objects.
K.CC.5. Students should develop counting strategies to help them organize the
counting process to avoid re-counting or skipping objects.
Examples:
If items are placed in a circle, the student may mark or identify the
starting object.
If items are in a scattered configuration, the student may move the
objects into an organized pattern.
Some students may choose to use grouping strategies such as placing
objects in twos, fives, or tens (note: this is not a kindergarten
expectation).
Counting up to 20 objects should be reinforced when collecting data to
create charts and graphs.
A student may use a clicker (electronic response system) to
communicate his/her count to the teacher.
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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
5
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Priority and Supporting CCSS
Explanations and Examples*
K.CC.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.*
* Include groups with up to ten objects.
K.CC.6 Students should develop a strong sense of the relationship between
quantities and numerals before they begin comparing numbers.
Other strategies:
Matching: Students use one-to-one correspondence, repeatedly
matching one object from one set with one object from the other set to
determine which set has more objects.
Counting: Students count the objects in each set, and then identify
which set has more, less, or an equal number of objects.
Observation: Students may use observation to compare two quantities
(e.g., by looking at two sets of objects, they may be able to tell which
set has more or less without counting). This method may not always be
as reliable as counting or matching.
Observations in comparing two quantities can be accomplished through
daily routines of collecting and organizing data in displays. Students
create object graphs and pictographs using data relevant to their lives
(e.g., favorite ice cream, eye color, pets, etc.). Graphs may be
constructed by groups of students as well as by individual students.
Benchmark Numbers: This would be the appropriate time to introduce
the use of 0, 5 and 10 as benchmark numbers to help students further
develop their sense of quantity as well as their ability to compare
numbers.
o Students state whether the number of objects in a set is more,
less, or equal to a set that has 0, 5, or 10 objects.
K.CC.7. Compare two numbers between 1 and 10 presented as
written numerals.
K.CC.7. Given two numerals, students should determine which is greater or less
than the other.
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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
6
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Priority and Supporting CCSS
Explanations and Examples*
K.MD.3. Classify objects into given categories; count the numbers
of objects in each category and sort the categories by\ count. **
** Limit category counts to be less than or equal to 10.
K.MD.3. Possible objects to sort include buttons, shells, shapes, beans, etc.
After sorting and counting, it is important for students to:
explain how they sorted the objects;
label each set with a category;
answer a variety of counting questions that ask, “How many …”; and
compare sorted groups using words such as, “most”, “least”, “alike” and
“different”.
Concepts
What Students Need to Know
Skills
What Students Need To Be Able To Do
Bloom’s Taxonomy Levels
Number
Relationships (zero to 20)
Number and quantity
Counting and cardinality
Number names in standard order
Number comparisons (zero to 10)
o Greater than
o Less than
o Equal to
Written numerals zero to twenty
COUNT (objects)
SAY numbers (in order)
PAIR (each object with one number)
UNDERSTAND
(last number name tells objects counted)
(number of objects is the same
regardless of arrangement)
(number of objects is the same
regardless of order)
(each successive number refers to a
quantity that is one larger)
IDENTIFY(compare) groups of objects
WRITE (numbers zero to twenty)
REPRESENT (number of objects with written
numeral)
1
2
3
3
1
1
3
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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
7
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Essential Questions
1. Why do we count?
2. How are numerals used?
3. How can two quantities be related?
Corresponding Big Ideas
1. Counting tells how many there are in a group regardless of their arrangement. The last number said when counting tells the total number of
objects counted.
2. Numerals are the symbols we read and write to communicate quantities (numbers).
3. One quantity is either greater than, less than or equal to other.
Standardized Assessment Correlations
(State, College and Career)
Expectations for Learning (in development)
This information will be included as it is developed at the national level. CT is a governing member of the Smarter Balanced Assessment Consortium
(SBAC) and has input into the development of the assessment.
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Connecticut Curriculum Design Unit Planning Organizer
Kindergarten Mathematics
Unit 1 - Counting and Matching Numerals 0-5 with Comparing
8
Adapted from The Leadership and Learning Center “Rigorous Curriculum Design” model.
*Adapted from the Arizona Academic Content Standards.
Unit Assessments
The items developed for this section can be used during the course of instruction when deemed appropriate by the teacher.
Test Mode: Administer one on one
Teacher directions: Read bolded statement aloud to child and record results on Interview Recording sheet.
Rote Count
TASK 1
a) Teacher: Count out loud starting at 1 and count as high as you can.
Record highest number student accurately counts to.
Ex: Child counts from 1-15 accurately, then skips 16. Stop student and record last correct number stated.
b) Teacher: Count out loud by tens starting at 10 and count as high as you can.
Record highest multiple of 10 student accurately counts to.
Ex: Child counts from 10 -50 accurately, then skips 60. Stop student and record last correct number stated.
TASK 2
Preparation: Teacher shows student a group of four objects.
Teacher: How many are there?
Observe and record (
or - ).
Student correctly counts 4 objects.
Note: This item can be repeated for any quantity up to 5.
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