Download KINDERGARTEN Unit 1 Counting and Cardinality

KINDERGARTEN Unit 1 Counting and Cardinality
5 Weeks
In this unit students will:
Students will count to 100 by ones
 Students will write numbers up to 10
 Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a
set
 Students will count out a given number of objects
 Students will quickly recognize the cardinalities of small sets of objects
Unit 1 Overview Video
Vocabulary Cards
Parent Letter
Parent Guides
Prerequisite Skills Assessment
Number Talks Calendar
(all documents in the outline file)
Big Ideas/Enduring Understandings:
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Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
Count with understanding and recognize “how many” in a set of objects.
Connect number words and numerals to the quantities they represent, using various physical models and representation
Counting tells how many things are in a set.
The last number word, when counting, names the quantity in a set.
A number can be represented by a set of objects, then by a word, and finally by a numeral.
Numbers are related to each other through a variety of relationships. For example, 6 is one more than 5, and is 4 less than 10.
Essential Questions:
 How can numbers be represented?
 How do we use numbers every day?
 Why do we need to be able to count objects?
 Why is it important to know how to put things in number order?
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Content Standards
Content standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to
emphasize the natural connections that exist among mathematical topics.
Counting and Cardinality
Know number names and the count sequence.
MGSEK.CC.1 Count to 100 by ones.
MGSEK.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
MGSEK.3 Write numbers from 0 to 10. Represent a number of objects with a written numeral 0-10 (with 0 representing a count of no objects).
Count to tell the number of objects.
MGSEK. CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality 0-10.
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. (one-to-one correspondence)
b. Understand that the last number name said tells the number of objects counted (cardinality). 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.
MGSEK.CC.5 Count to answer “how many?” questions about as many as 10 things arranged in a line, a rectangular array, or a circle; given a number
from 1–10, count out that many objects.
Vertical Articulation of Counting and Cardinality
First Grade Counting and Cardinality Standard
MGSE1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a
written numeral.
Counting and Cardinality Instructional Strategies
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Trajectory
Number Sense Trajectory –Putting It All Together
Subitizing
Being able
to visually
recognize a
quantity of
5 or less.
Comparison
Being able to
compare
quantities by
identifying
which has
more and
which has less.
Counting
Rote procedure
of counting. The
meaning
attached to
counting is
developed
through one-toone
correspondence.
One-to-One
Correspondence
Students can
connect one
number with
one object and
then count
them with
understanding.
Cardinality
Tells how many things
are in a set. When
counting a set of objects,
the last word in the
counting sequence
names the quantity for
that set.
Hierarchical
Inclusion
Numbers are nested
inside of each other
and that the number
grows by one each
count. 9 is inside 10
or 10 is the same as 9
+ 1.
Number
Conservation
The number of
objects remains
the same when
they are
rearranged
spatially. 5 is 4&1
OR 3&2.
Number Relationships
Each concept builds on the previous idea and students should explore and construct concepts in such a sequence
Spatial Relationship
Patterned Set Recognition
Students can learn to
recognize sets of objects in
patterned arrangements and
tell how many without
counting.
One and Two-More or Less
Students need to understand the relationship of number as it
relates to +/- one or two. Here students should begin to see
that 5 is 1 more than 4 and that it is also 2 less than 7.
Understanding
Anchors
Students need to see
the relationship
between numbers
and how they relate
to 5s and 10s. 3 is 2
away from 5 and 7
away from 10.
Part-Part-Whole
Relationship
Students begin to
conceptualize a
number as being
made up from two
or more parts.
Have students say number words as a chant or a rote procedure plays a part in students constructing meaning for the conceptual idea of counting.
They will learn how to count before they understand cardinality, i.e. that the last count word is the amount of the set.
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Counting on or counting from a given number conflicts with the learned strategy of counting from the beginning. In order to be successful in
counting on, students must understand cardinality. Students often merge or separate two groups of objects and then re-count from the
beginning to determine the final number of objects represented. For these students, counting is still a rote skill or the benefits of counting on
have not been realized. Games that require students to add on to a previous count to reach a goal number encourage developing this
concept. Frequent and brief opportunities utilizing counting on and counting back are recommended. These concepts emerge over time and
cannot be forced.
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One of the first major concepts in a student’s mathematical development is cardinality. Cardinality, knowing that the number word said tells
the quantity you have and that the number you end on when counting represents the entire amount counted. The big idea is that number
means amount and, no matter how you arrange and rearrange the items, the amount is the same. Until this concept is developed, counting is
merely a routine procedure done when a number is needed.
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To determine if students have the cardinality rule, listen to their responses when you discuss counting tasks with them.
For example, ask, “How many are here?”. The student counts correctly and says that there are seven. Then ask, “Are there seven?”. Students may
count or hesitate if they have not developed cardinality. Students with cardinality may emphasize the last count or explain that there are seven
because they counted them. These students can now use counting to find a matching set.
Students develop the understanding of counting and cardinality from experience. Almost any activity or game that engages children in counting and
comparing quantities, such as board games, will encourage the development of cardinality.
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Like counting to 100 by either ones, writing numbers from 0 to 10 is a rote process. Initially, students mimic the actual formation of the
written numerals while also assigning it a name. Over time, children create the understanding that number symbols signify the meaning of
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counting.
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Numbers have meaning when children can see mental images of the number symbols and use those images with which to think. Practice
count words and written numerals paired with pictures, representations of objects, and objects that represent quantities within the context
of life experiences for kindergarteners. For example, dot cards, dominoes and number cubes all create different mental images for relating
quantity to number words and numerals.
One way students can learn the left to right orientation of numbers is to use a finger to write numbers in air (sky writing). Children will see
mathematics as something that is alive and that they are involved.
Students should study and write numbers 0 to 10 in this order: numbers 1 to 9, the number 0, and then numbers 10.
Counting and Cardinality Common Misconceptions
1. Some students might not see zero as a number. Ask students to write 0 and say zero to represent the number of items left when all items have
been taken away. Avoid using the word none to represent this situation.
2. Some students might think that the count word used to tag an item is permanently connected to that item. So when the item is used again for
counting and should be tagged with a different count word, the student uses the original count word. For example, a student counts four geometric
figures: triangle, square, circle and rectangle with the count words: one, two, three, and four. If these items are rearranged as rectangle, triangle,
circle and square and counted, the student says these count words: four, one, three, and two.
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Evidence of Learning
 Students will count to 100 by ones
 Students will write numbers up to 10
 Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a
set
 Students will count out a given number of objects
 Students will quickly recognize the cardinalities of small sets of objects
Assessment
Formative Assessment Lesson (FAL) Counting Dots (dots of various arrangements) MGSEK.CC.1-4 One to one correspondence, Counting Objects to
10, Numeral recognition, Understanding number relationships. Students are assessed on the standards taught so far in the unit. This allows teachers
to address any students who may need remediation or acceleration.
Adopted Resources
Adopted Online Resources
My Math:
Chapter 1: Counting numbers to 5
1.1 Count 1,2 and 3
1.2 Read, and write 1, 2, and 3
1.3 Count 4 and 5
1.4 Read and write 4 and 5
1.5 Read and write zero
My Math
http://connected.mcgrawhill.com/connected/login.do
Chapter 2 Numbers to 10
2.1 Numbers 6 and 7
2.2 Number 8
2.3 Read and write 6 and 7
2.4 Number 9
2.5 Number 10
2.6 Read and write 9 and 10
Teacher User ID: ccsde0(enumber)
Password: cobbmath1
Student User ID: ccsd(student ID)
Password: cobbmath1
Examplar
http://www.exemplarslibrary.com/
User: Cobb Email
Password: First Name
Think Math:
Chapters 1: Numbers to Ten
1.1 Number One
1.2 Number Two
1.3 Number Three
1.4 Number Four
1.5 Number Five
1.6 Working with Five
1.7 Number Six
1.8 Working with Six
1.9 Number Seven
1.10 Number Eight
1.11 Number Nine
1.12 Number Zero
1.13 Number Ten
100th Birthday Celebration
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*These lessons are not to be completed in
seven days as it is way too much material.
They are designed to help support you as
you teach your standards.
First in Math
http://www.firstinmath.com
Student User ID:
Password:
Additional Resources
National Council of Teachers of Mathematics – How Many Buttons:
http://illuminations.nctm.org/Lesson.aspx?id=286
National Council of Teachers of Mathematics – Writing Numbers to Five: http://illuminations.nctm.org/Lesson.aspx?id=1620
K-5 Math teaching Resources
Mathematics TEKS Toolkit
http://www.k-5mathteachingresources.com/3rd-grade-number-activities.html
http://www.utdanacenter.org/mathtoolkit/instruction/lessons/3_hundred.php
Estimation 180 is a website of 180 days of estimation ideas that build number sense. http://www.estimation180.com/days.html
Illustrative Mathematics provides instructional and assessment tasks, lesson plans, and other resources. https://www.illustrativemathematics.org/
http://www.gregtang.com
Suggested Manipulatives
Vocabulary
Suggested Literature
number lines
five frames
ten frames
100 chart
Dot cards (subitizing)
dice and dominos
rekenreks
objects to count (counters, snap/unifix cubes,
bears, pattern blocks, plane shapes, attri-
zero
one
two
three
four
five
six
seven
eight
One Gorilla
Ten Black Dots
Grey Rabbit’s 1,2,3
Feast for Ten
Roll Over- a Counting Song
Sitting in a Tree
Fireflies
Anno’s Counting Book
Ten Red Apples
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Five Silly Fishermen
Mouse Count
Only One
Five Little Ducks
Five Little Monkeys
Ten Flashing
Count and See
One Duck Stuck
2015-2016
linkscoins)
nine
ten
count
number
Ten Little Bears
Puppies in the Snow
Afro-Bets
Let’s Go Visiting
Rooster’s Off to See the World
George’s Store at the Shore
Five Little Monkeys Jumping on a Bed
Task Descriptions
Scaffolding Task
Constructing Task
Practice Task
Culminating Task
Formative
Assessment Lesson
(FAL)
3-Act Task
Tasks that build up to the learning task.
Constructing understanding through deep/rich contextualized problem solving tasks.
Tasks that provide students opportunities to practice skills and concepts.
Designed to require students to use several concepts learned during the unit to answer a new or unique situation. Allows
students to give evidence of their own understanding toward the mastery of the standard and requires them to extend
their chain of mathematical reasoning.
Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key
mathematical ideas and applications. These lessons enable teachers and students to monitor in more detail their progress
towards the targets of the standards.
A Three-Act Task is a whole-group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an
information and solution seeking Act Two, and a solution discussion and solution revealing Act Three. More information
along with guidelines for 3-Act Tasks may be found in the Guide to Three-Act Tasks on georgiastandards.org and the K-5
CCGPS Mathematics Wiki.
Unit 1 Counting and Cardinality Tasks
Task Name
Standards
MGSEK.CC.2-4a, b, c
Dotty
Got Dots? (0-10)
MGSEK.CC.1-4a,b,c
Kindergarten Quarter 1 Unit 1
Task Type/ Grouping Strategy
Content Addressed
Brief Description
Students use counting and sequence of
3-Act Task
Subitizing, Counting,
numbers to figure out what comes
Whole Group
Sequencing numbers
next.
Subitizing, Counting objects
Students practice counting and
Scaffolding
to 10, Sequencing
subitizing objects to 10 in a variety of
Whole/Small/Partner/Individual
Numbers,
activities.
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Numerals, Pictures,
Words (0-10)
MGSEK.CC.2, 4a,b,c
Fill in the Line (0-9)
MGSEK.CC.1-4
What in the Heck is
Rkenrek?
Fill the Chutes
Race to 20
MGSEK.CC.1-4
MGSEK.MD.3
MGSEK.CC.2, 4
MGSEK.CC.1, 2, 4
MGSEK.CC.1-4
Counting Dots
The Cardinal Cup (010)
MGSEK.CC.1, 2, 4
MGSEK.MD.3
MGSEK.CC.1,2,4
Order the Dice
MGSEK.CC.1-4b,c
More of Less
How Many are in the
Bag?
Kindergarten Quarter 1 Unit 1
MGSEK.CC.1-4
MGSEK.MD.3
Subitizing, Counting objects Students begin to make the connection
Constructing Task
to 10, Sequencing
between numeral, pictures and words
Whole/Small/Partner/Individual
Numbers, Matching
in a variety of activities.
Number Words to Numbers
Numeral recognition,
Students practice connecting numerals
Constructing Task
number word recognition,
to sets.
Whole/partner
Numeral writing
Subitizing, Modeling
Constructing Task
Students make a Rekenrek and
numbers,
understanding
Whole/partner
practice modeling numbers through
number relationships
a variety of activities.
Students practice counting and making
Practice Task
One to one
a set of objects to represent a number.
Whole/Small/Partner/Individual
correspondence
Students use one to one
Practice Task
One to one
correspondence to count their way
Partner
correspondence
around a game board.
One to one
Students that need remediation or
correspondence, counting
acceleration.
FAL
objects to 10, numeral
recognition, understanding
number relationships
One to one
Students practice counting forwards
Constructing Task
correspondence, Counting and backwards as they participate in a
Whole/Partner
objects to 10, Numeral
variety of activities.
recognition
Students practice ordering sets from
Constructing Task
Sequencing numerals,
numeral recognition
least to greatest
Partner
Numeral recognition,
Students begin to understand more
Constructing Task
understanding number
and less in a variety of activities.
Whole/Partner
relationships
Numeral recognition,
Students practice connecting sets to
Constructing Task
understanding number
numerals and words.
Small Groups/Individual
relationships
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Numeral recognition,
Sequencing numerals,
MGSEK.CC.1,2,4b,c
Practice Task
Whole/Partner
More or Less-Make a
Guess
Find the 5th Tower
Kindergarten Quarter 1 Unit 1
MGSEK.CC.1-4
MGSEK.G.1
MGSEK.MD.3
Culminating Task
Whole or Small Group
11
Students practice their understanding
of more or less to guess their partners
number on a number line.
understanding number
relationships
One to one
Students use all the concepts they
correspondence,
have learned in this unit to complete a
understanding number
task.
relationships, numeral
writing, positional words,
ordinal words
2015-2016