Introductory Lesson – Counting and Cardinality
K.CC7-Compare numbers between 1 and 10 presented as written numerals.
Lesson OverviewStudents should begin the year with many different concrete materials that they can
manipulate and count. Students need practice counting objects of one through ten and
matching the objects to the numbers that they represent by the teacher utilizing mats,
flashcards, and any other manipulatives that show the relationship between numerals and
the correct number of items.
This lesson gives students practice in matching the written numeral with the appropriate
set of objects. Students will match the cards together by working in a small group. The
first objective is for the group to be able to match them up together, but after students
become familiar with the cards (perhaps in a few days) they should be able to match them
on their own.
Materials:
 Board
 Pre-made cards with the numerals 1-10 on 10 cards and pictures of objects in the
amounts of 1 to 10 objects on 10 other cards. Each group of 4 students will need
these 20 cards per group.
Lesson Steps:
 Write the numbers 1-10 on the board along with dots, balls, or other simple
shapes that correspond to the numbers.
 Tell students that the mathematics goal/objective for today is to learn how the
numbers and the amounts 1-10 go together. They must know when they see
objects how many are there and which number matches the group of objects.
 Model reading the numbers aloud and matching them to the correct objects.
Model the counting process as you decide which number matches the objects.
Explain why you chose the objects that you chose.
 Provide groups of 4 students (preferably ability grouped with 1 high student, 2
middle students, and 1 low student) with 20 pre-made cards with 1-10 objects on
10 cards and 10 cards with the numerals 1-10.
 Have the groups work together to match the cards to the correct objects. Have
them discuss with each other or with you as you monitor groups how they know
the cards match and what they did to make sure they had them matched up the
right way. (First they should learn to match them as a group, then they can move
toward matching them up individually. Make sure after a couple of days that each
student can do this individually.)
Sample questions1. How did you know that number matches that picture?
2. Show me how you know that _ matches _ objects.
3. What could help you match these?
4. How can knowing how to count help you?
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Continue this activity each day or at centers. Students need practice with
matching objects with the numeral before they can compare two sets of objects
and numbers.
Assessment: Teacher evaluation during activity to see if all students can match
numbers with correct objects.
Additional Resources: www.softschools.com
www.apples4theteacher.org
Lesson 1-Counting and Cardinality
KCC.7 Comparing two numbers between 1 and 10 presented as written numerals
Lesson Overview: This lesson utilizes the circle map from Draw Your Thinking by
Marjann Ball and Jennifer McLeod. The circle map can be easily introduced as the
teacher models how to define a number through the mapping procedure. Circle maps
are used to define concepts. Students will move toward making their own circle maps
after the modeling and guided map-making.
Materials:
 Chart paper for making several circle maps for modeling
 Paper for students to create their own circle maps
 Draw Your Thinking as a reference
Lesson Steps:
 Introduce the lesson by explaining to the students that they will soon be learning
to compare numbers, but that first they need practice or review of what each
number represents.
 Explain that they will be thinking of different objects that a person might have 2
of or thinking of different ways to show the number 2.
 Model ways to represent the number 2 on a circle map. (Place the number in the
center small circle of a much larger outer circle.) Draw different types of objects
in different spots inside the larger circle. For example, 2 dots or 2 stars, etc. Also,
write the number in words-two. Provide many examples of 2 objects grouped or
drawn in different ways.
 Model making a circle map of another number between 1 and 10. Place the
number inside of the smaller circle. Draw or write different examples of objects
that could be found in that number.
 Make a map together as a guided activity. Allow students to come to the board
and draw the correct number of objects in the larger circle to match the number in
the middle.
 Assessment: Have students make their own circle map to represent a number from
1 to 10.
Lesson 2 – Counting and Cardinality
K.CC7-Compare numbers between 1 and 10 presented as written numerals.
Students should begin the year with many different concrete materials that they can
manipulate and count. Students need practice counting objects of one through ten and
matching the objects to the numbers that they represent by the teacher utilizing mats,
flashcards, and any other manipulatives that show the relationship between numerals and
the correct number of items.
Materials:
 Board
 pre-made cards with the numbers 1-10 and cards with objects 1-10
 pre-planned groups of students of varying abilities
Lesson Steps:
 Write the numbers 1-10 on the board along with dots, balls, or other simple
shapes that correspond to the numbers.
 Tell students that the mathematics goal/objective for today is to learn how the
numbers and the amounts 1-10 go together. They must know when they see
objects how many are there and which number matches the group of objects.
 Model reading the numbers aloud and matching them to the correct objects.
Model the counting process as you decide which number matches the objects.
Explain why you chose the objects that you chose.
 Provide groups of 4 students (preferably ability grouped with 1 high student, 2
middle students, and 1 low student) with 20 pre-made cards with 1-10 objects on
10 cards and 10 cards with the numerals 1-10.
 Have the groups work together to match the cards to the correct objects. Have
them discuss with each other or with you as you monitor groups how they know
the cards match and what they did to make sure they had them matched up the
right way. (First they should learn to match them as a group, then they can move
toward matching them up individually. Make sure after a couple of days that each
student can do this individually.)
Sample questions1.How did you know that number matches that picture?
2.Show me how you know that _ matches _ objects.
3.What could help you match these?
4.How can knowing how to count help you?
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Continue this activity each day or at centers. Students need practice with
matching objects with the numeral before they can compare two sets of objects
and numbers.
Assessment: Teacher evaluation during activity to see if all students can match
numbers with correct objects.
Lesson 3-Counting and Cardinality
KCC7-Comparing two numbers between 1 and 10 presented as written numerals.
(Prerequisite to being able to compare numbers.)
Lesson Overview: Students will be playing a game similar to musical chairs. Have the
numbers 1through 10 written out on large 81/2 by 11 cardstock. Also make index cards
with various numbers of pictures or stickers with any number 1-10 on the cards. Give
each student a card with 1 to 10 objects on it. As the music plays, the students walk
around and find the number mat that matches their number of objects. When they find it,
they stand on their number and wait for classmates to find theirs. 10 students may play at
a time as the other classmates watch. All students must find their number by the time you
stop the music. As those 10 finish, the teacher takes up the cards and passes them out to
10 new students.
Materials:
 81/2 x 11 card stock for musical mats for students to stand on/must be prepared
ahead of time.
 markers
 index cards
 stickers or pictures of 1 to 10 objects
 a CD with music for playing “Musical Math”
 CD player
 open floor space for spreading out 10 pre-made mats with numbers on them..
Lesson Steps:
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Introduce the lesson by reminding students that all kindergartners have to know
how to correctly match and compare numbers and objects.
Model matching a number with the appropriate number of objects by counting the
objects aloud and doing a “think aloud” of the process one goes through as they
match objects with numbers.
Explain to the students that they will be playing a game called “Musical Math”.
Model how to play the game for students. Have a CD ready for playing and
stopping just as in musical chairs.
Students play the game until each student has had several turns.
At the conclusion of the activity, let students tell how they found their numbers.
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Wrap up the lesson by reminding them that they must be very familiar with how
number symbols match a certain number of objects.
Assessment: Observe as students play the game. Note their certainty and the
process they go through as they decide which mat to stop on. Also, create a
worksheet that provides pictures/objects to match with numbers.
Lesson 4-Counting and Cardinality
KCC.7 -Compare two numbers between 1 and 10 presented as written numerals.
Lesson Overview- The teacher will use mapping concepts from Draw Your Thinking to
guide students to being able to compare sets of numbers and the written numerals. Many
different type of thinking maps can be used for establishing number sense in math.
Materials:
 Draw Your Thinking as a resource on mapping strategies
 Chart paper for large maps
 Drawing paper for student maps
 Markers, pencils, or crayons
Lesson Steps:
 Introduce the lesson by explaining to students that all students in kindergarten
must be able to compare two different numbers with numbers 1-10.
 Lead students in a question and answer session in order to review their number
concepts and number sense gained from this unit.
o Sample questions:
1.When you see objects, how do you know how many are there?
2.How do you remember which number to match with the objects?
3.Can anyone tell me what the number for these objects looks like?
(Show picture or drawing of objects.)
 Model making a double bubble map (see recommended resource listed above).
For example, compare 2 objects to 4 objects by putting what they have in
common in the middle bubbles and what they have different (4 having 2 more
objects) on the outside of the double bubble on the side with 4. Include pictures of
objects in your map.
 Allow students to help you create another double bubble map that compares two
other sets of numbers.
 Provide blank double bubble maps for small groups of students to draw their own
maps. Monitor groups for participation and accuracy of comparisons.
 Assessment:
Group maps or individual maps
* Other mapping strategies/ideas will also address this standard. See Draw Your
Thinking by Marjann Ball and Jennifer McLeod
Lesson 5-Counting and Cardinality
K.CC7-Compare two numbers between 1 and 10 presented as written numerals.
Lesson Overview-This lesson will take the background information from the four
previous lessons and address the standard now that pre-learning has taken place.
Materials:
 Board or chart paper
 Power point entitled “Comparing Numbers 1-10”
Lesson Steps:
 Introduce the lesson by explaining to students that they must be able to compare
numbers between 1 and 10. Tell them that in order to do that they must know how
many the numbers 1 through 10 stand for or represent. Introduce the vocabulary
“more than” and “less than.” They will need further explanation such as, “more”
means the most and “less” means not as many.
 Model with your students the comparison of two different groups of objects such
as 3 girls and 1 boy. Explain that comparing often means matching them to see
who or which one does not have a match. When one or more are left over, that
means that there are more of that one. If they know their number quantities, they
will be able to tell which is more by counting and knowing which number has a
higher value. Continue giving them a several examples of more and less than
situations with groups of objects.
 Guide them through another example that they help you solve. For example, Mrs.
Smith has 5 pens and Mrs. Hanes has 8 pens. Who has more? Demonstrate
drawing a visual to go with this on the board or on chart paper. Let the students
help you think of the two ways to solve this. (lining the objects up and matching
or counting the quantity.)
 Show your students the power point lesson entitled “Comparing Numbers 1-10.”
 Assessment:
Teacher will evaluate class participation or observation of answers to last slide.
Introductory Lesson-Operations and Algebraic Thinking
K.OA5-Fluently add (and subtract ) within 5.
Lesson Overview- This lesson will help students to practice putting groups of
manipulatives together and then counting them. For example, a group of 2 objects joined
with a group of 3 objects. Have students practice using math language along with the
activity. “2 plus/add 3 equals 5.” Spend several days practicing this language with
groups of objects within 5.
Materials:
 objects for counting
 board or chart for showing process of joining groups
 drawing paper
 Power point lesson entitled “Adding within 5”
Lesson Steps:
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Begin the lesson by explaining that all kindergarten students need to be able to
add and subtract numbers1-5. Share the importance of being able to add/subtract
in real life.
Introduce the plus sign and explain that it means putting things together or adding
them.
Model putting two groups of objects together and counting them several times.
Complete guided activity with students helping you join and count objects. Be
sure to write it in terms of objects being joined and the numbers that represent
them.
Provide small groups of students in 3’s or 4’s with 5 objects to join and count.
Allow them time to explore with manipulatives and count various groups of
objects as they join or add them together. Monitor the activity and ask questions
about how they knew how many objects they have.
After the group practice with manipulatives, have students draw a picture of
joining 2 groups of objects and have them write the numbers to match those
objects. All students may not be able to write the information, but there will be
some capable of translating this information to paper.
Assessment: Teacher observation of students joining and counting objects.
Also, written drawings of objects added or joined.
Additional Resource:
Power point lesson on “ Adding within 5.”
Lesson 2-Operations and Algebraic Thinking
K.OA5-Fluently add (and subtract) within 5.
Lesson OverviewStudents need time to explore with 10 cubes each day. (5 of one color and 5 of a different
color.) Have them make trains with different numbers of cubes on each train. Have them
count aloud how many of one color or the other that they have. This lesson is an
introduction to the use of unifix cubes as manipulatvies for teaching the
addition/subtraction of 5 objects.
Materials:
 unifix cubes that students can use to make trains of 5 cubes. (Different colors are
preferred in order for students to see one group joined to another group)
 Drawing paper
Lesson Steps:
 Introduce the lesson by explaining that all kindergarten students need to be able to
add and subtract up to 5 very well. Tell them that they will need these skills in
real life and for school. Make sure they know that practice with counting and
joining objects together will help them.
 Model joining groups of objects together and counting them.
 Provide students with their own 10 cubes as described above. Ask them to join 2
cubes of one color with 1 cube of another color. Have them count to learn that
there are 3 objects on the train now. Lead them in making trains of other
combinations and compare them. Be sure to include the following combinations:
 1 and 4, 2 and 3, 2 and 2 , 1 and 2, 1 and 3, etc. until students begin to form
mental pictures of the different combinations that can be made with numbers
under 5.
 Have students practice the language that goes with the joining of the cubes.
 Assessment: Have students draw or demonstrate the joining of cubes. Have them
tell you the number of each and the sum when the two are joined. (Continue to
leave cubes in a center and encourage the joining/separating of the cubes.)
Lesson 3-Operations and Algebraic Thinking
K.OA5-Fluently add and subtract within 5.
Lesson OverviewStudents need time to explore with 10 cubes each day. (5 of one color and 5 of a different
color.) Have them take trains with different numbers of cubes on each train apart. Have
them count aloud how many of cubes are on one train. Then have them take off 1 to 4 of
these and count to see how many are left. This lesson is an introduction to the use of
unifix cubes as manipulatvies for teaching the subtraction of 5 objects.
Materials:
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unifix cubes that students can use to make trains of 5 cubes. (Different
colors are preferred in order for students to see one group taken apart
from the other group)
Drawing paper
Lesson Steps:
 Introduce the lesson by explaining that all kindergarten students need to be able to
add and subtract up to 5 very well. Tell them that they will need these skills in
real life and for school. Make sure they know that practice with counting, joining,
and separating objects will help them learn to add and subtract fluently.
 Model separating groups of objects and counting them.
 Provide students with their own 5 cubes as described above. Ask them to take off
2 cubes of one color. Have them count to learn that there are 3 objects left on the
train now. Lead them in making and taking apart trains of other combinations and
compare them. Be sure to include the following combinations:
1 and 4, 2 and 3, 2 and 2 , 1 and 2, 1 and 3, etc. until students begin to form
mental pictures of the different combinations that can be taken from numbers 5
and under to make less.
 Have students practice the language that goes with the taking apart/subtracting of
the cubes.
 Assessment: Have students draw or demonstrate the separating of cubes. Have
them tell you the number of each and the difference when the two are taken apart.
(Continue to leave cubes in a center and encourage the joining/separating of the
cubes.)