Math Solutions Lesson from the Classroom
Using the Calendar to Develop Number Sense
Activities for Grades K–2
About the Contributor
These ideas were contributed by Math Coach Miryam Alter. Miryam has taught elementary and middle
school math for twenty-eight years. She is Chairperson of the Math Department at Manhattan Day
School in New York City. She coaches all math teachers within the school and oversees the math
curriculum for grades 1–8.
Overview
The start of a new school year is the perfect time to introduce the calendar. The calendar provides a
great source for developing number sense and fluency. The calendar affords many opportunities to
understand and experience concepts such as consecutive numbers, odd and even numbers, numbers
greater than and less than a given number, and the numbers 1–31. The activities described here address
these opportunities. The activities are also an excellent way of assessing the math fluency level of your
class and of individual students throughout the school year.
Continuing these activities at the beginning of each month will reinforce the concepts and heighten
students’ awareness of the flow of the calendar year. Rather than do all the activities in the same month,
spread them throughout the months of the year. As the months progress, revisit some of the activities
you have done and add some of the others.
The activities span the grades K–2. They are meant to be mixed and matched depending on the fluency
level of the students.
Materials
• September calendar (see the reproducible at the end of this lesson), 1 copy enlarged for classroom
use (for other months, search online for a printable calendar)
• September calendar (see the reproducible at the end of this lesson), 1 copy for each student
• A list of students with September birthdays (or whichever month you’re studying)
• Numeral cards 1–31, 1 set
• Crayons, for teacher’s use on the calendar used with the class
• Game markers (tiles, etc.), 25 per group
• Four Boxes in a Row on the Calendar cards (see the reproducible at the end of this lesson), 1 set per
group of student teams
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
Activity 1: Introducing the Calendar
1. Gather students on the floor in front of an enlarged calendar.
2. Ask students to describe some things about themselves (name, age, number of siblings, address, and
telephone number).
3. Connect students’ descriptions to the calendar; explain that just as there are several ways to describe
each person, there are also several ways to describe each day.
4. Elaborate on how we can describe a day. First, we can tell what day of the week it is (Monday, Tuesday,
etc.). We can also tell what month it is in (September, October, etc.). Finally, we can say what day of the
month it is (for example, the first of September).
5. Introduce the word date. Describe today’s date by stating the day of the week, the month, and the day
of the month. Point out the day on the calendar.
6. Explain that a specific month and day of the month may be considered a date. Say, “For example, on
this date [point to a date on the calendar], we are going to study math.”
7. Help students understand how a calendar is organized. Explore the placement of the days of the week,
Sunday through Saturday. Then discuss how each row of the calendar represents either a week or a
part of a week. Each column represents the dates of that day of the week. Ask, “What day of the week
is the first day of September 2013?” In 2013, September 1 conveniently falls on a Sunday. Consider
discussing these other key questions:
• What is the date of a Monday in September? The other days of the week?
• What day of the week is the last day of September? What is its date?
• What happens on the day after September 30?
8. Refer to your list of students with September birthdays. Mark one of the birthdays on the calendar.
Continue to ask key questions:
• On what day of the week will [student’s name]’s birthday fall?
• What is the name of the day before?
• What is the name of the day after?
• What is the number of the day before?
• What is the number of the day after?
9. Repeat step 8 with another student’s September birthday. Proceed through the birthday list as needed.
10.Now point at and count each day of the month out loud with the class.
11.Ask, “Did we skip any numbers?” Explain that the numbers on a calendar are consecutive numbers.
One number comes right after the other to describe consecutive days. Ask key questions:
• Who can point out and name three consecutive days in September?
• What are the three consecutive days after today?
• What are the three consecutive days before today?
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
12.Point out that at the end of a week (row on the calendar), the next day is the first box in the next week
(row).
13.Distribute numeral cards for 1–30 to the class. Each student should have a different number. Ask each
student to come up and point to the number on the calendar that corresponds to the number on his
or her card. This is a quick assessment of number recognition. Consider also asking, “What day of the
week is that number on?”
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
Activity 2: Exploring Odd and Even Numbers Using the Calendar
As with a number line, the calendar supports students’ understanding of even and odd numbers. Looking
at the calendar helps a student see the placement of an even number between two odd numbers and vice
versa.
1. Distribute a calendar and two different-color crayons to every student.
2. Ask students to color (using the same crayon) all the even numbers.
3. Make a list of the even numbers where everyone can see them.
4. Ask, “Can you see a pattern in these numbers? What is it?”
5. Repeat steps 1–4, having students use a different-color crayon to color all the odd numbers.
6. Distribute numeral cards 1–30 to the class. Each student should have a different number. Ask the
following questions; have each student with a corresponding card come up to the class calendar and
point out his or her answer. If possible, each student should also tell what day of the week his or her
number lands on.
• Who has an even number?
• Who has an odd number?
• Who has a number less than 10?
• Who has a number greater than 15?
• Who has a number two days before 5?
• Who has a number three days after 9?
Teaching Moment
Are your students not yet familiar with the concept of odd and even numbers? If so, consider doing this
activity first.
1. Distribute a crayon and 20 beans or tiles to each student, as well as copies of a number chart like this:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2. Ask students to count out the number of beans corresponding to the number in each box of the number
chart. Start with the box marked number 1.
3. Now ask students to make pairs out of the number of beans in each box. Are there any beans without
pairs?
4. Ask students to color the boxes that have numbers that can be made into pairs with none left over.
5. Ask, “Is there a pattern?”
6. Ask, “What about the numbers that have one left over? Is there a pattern?”
7. Explain that numbers with none left over are called even numbers. Numbers that have one left over are
called odd numbers.
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
Activity 3: Using the Calendar for Calculations
1. Before doing calendar calculations, review odd and even numbers with students. Distribute a copy of
the calendar to each student (or direct students to the class-sized calendar).
2. Direct students’ attention to the dates of the Sundays in September (for a 2013 calendar, the dates
would be 1, 8, 15, 22, and 29).
3. Ask, “What pattern do you see?” Students should be able to point out that odd numbers are followed
by even numbers (if students are still struggling with this, refer back to the previous activity).
4. Ask questions to reinforce students’ understanding,
such as these:
• Is the pattern the same for the other days of the week?
• How many days do you have to count to get from one
Sunday to another Sunday?
• What about the other days of the week?
In a Child’s Mind
Some students may be able to
conclude that the next Sunday’s date
will be seven more than the Sunday
before it. Therefore, these are the
dates of all the other Sundays in
September: 1 + 7 = 8; 8 + 7 = 15;
15 + 7 = 22; 22 + 7 = 29.
5. Once you feel students are comfortable with the organization of the
calendar, explain that they can begin using the calendar for calculations.
6. Start with this calculation: “Find two consecutive days whose sum is eleven.” Continue sharing and
working through calculations with students. Following are some other ideas:
• Find three consecutive numbers whose sum is 27.
• A diagonal is any box on the calendar together with the box down and to the right (or left). For
example, in the September calendar, 4 and 12 form a diagonal. Four and 10 also form a diagonal.
Can you find a diagonal whose sum is 12?
• If you keep doing the previous movement to form a diagonal, what are the dates of the longest
diagonal in September?
• A square on the calendar is four boxes, two on top and the two directly underneath. On the
September calendar the numbers 1, 2, 8, and 9 form a square. What is the sum of the numbers in
this square?
• Can you find a square whose sum is 28?
Increase the Challenge
To increase the challenge, consider posing the following to students:
• Find a shortcut for calculating the sum of a square without adding all the numbers in the square. (There
are several possibilities. Since each number in a box under a box is 7 more than the one on top, you can
add 14 to the sum of the two top numbers. Since both diagonals in a square have the same sum, another
possibility is to find the sum of one diagonal and double it.)
• Given the first number, can you predict what the rest of the numbers in a diagonal are? (Just keep adding
8! Note that when students get past 30, they usually don’t stop until they realize the month goes only
through 28, 29, 30, or 31.)
• Depending on the students’ fluency with addition, increase the difficulty level of finding a sum. For example:
What is the largest sum of two consecutive days? What is the largest sum of a diagonal? What is the
largest sum of any square? What about a 3 × 3 square?
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
Activity 4: Four Boxes in a Row on the Calendar
There are two variations of this game: one for students who can read and one for students who need help
reading.
Version 1 (For Students Who Can Read)
1. Group students into teams of two or three and then have teams play against each other. Give
each group of students a copy of the September calendar, a set of the Four Boxes in a Row on the
Calendar cards, and 25 game markers of different colors (one color for each team).
2. Explain that for this game, the calendar serves as the game board.
3. Explain the game rules:
a. Place the cards in a stack facedown by the game board. Determine how teams will decide who will
go first. Teams then take turns drawing cards from the stack one at a time. When a team draws a
card, it must select a box on the calendar that corresponds with the description on the card. The
team then puts one of its game markers down on that box. For example, if a team draws the card
reading, “An odd number,” the team may place one of its game markers on the box marked with
the number 5.
b. Once a team has placed its marker down, the opposing team must agree or disagree with the
placement of the marker. After placement has been “approved” the team in play keeps the card
and the next team takes a turn. The first team to place four game markers in a row (vertically,
horizontally, or diagonally) is the winner.
Note: If a team draws a card that cannot be used because all the corresponding spaces are already
taken, that team loses that turn.
Note: If you include the “Free” card, the team that draws that card may take one of the cards from any
other team and use it for that turn.
Version 2 (For Non-readers)
1. Divide the class into teams of two or three students. Give each
team a copy of the September calendar and 25 game markers.
2. Read a card from the Four Boxes in a Row on the Calendar cards
aloud to the class.
3. Each team must select a box on the calendar that corresponds
with the description on the card. The team puts a game marker
down on that box.
Technology Tip
If you have an interactive
whiteboard or overhead projector,
consider playing this game on it.
Pull up or project a September
calendar. Two or three teams can
play against each other on the
board. This time, each team may
use only the card from its turn.
4. The first team to place four game markers in a row (vertically,
horizontally, or diagonally) is the winner.
Find more classroom lessons online at mathsolutions.com.
Visit the “Educator Tools” section and click “Free Classroom Lessons.”
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
Four Boxes in a Row on the Calendar Cards
Note: The two cards with asterisks are more challenging and can be optional.
An odd number
An even number
A number that has
two digits
A number that has
one digit
A number less than 20
A number more than 15
A number that has a 2
in the ones digit
A number that has a 3 as
one of its digits
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
Four Boxes in a Row on the Calendar Cards
Note: The two cards with asterisks are more challenging and can be optional.
A number that has a 5 as
one of its digits
A number two days before
or after 11
A number in the first week
of the month
A number in the third week
of the month
The number of a day that
is a Monday
The number of a day that
is a Friday
The number above
or below 13
The number above
or below 18
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
Four Boxes in a Row on the Calendar Cards
Note: The two cards with asterisks are more challenging and can be optional.
The number above
or below 9
An even number
less than 16
An odd number
more than 19
A number two days before
or after 26
*
*
A number that is double
another number on the
calendar
A number that is half
another number on the
calendar
FREE CARD
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Using the Calendar to Develop Number Sense, Activities for Grades K–2, continued
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