Happy Birthday to You10
Students will investigate the patterns that arise in calendars by comparing the day of the week for
a particular date and use division to explain why the patterns occur. Students will then use
observed patterns to ultimately find the day of the week on which they were born.
Suggested Grade Range: 6-8
Approximate Time: 1 hour
State of California Content Standards:
California Standards Grade 6: Number Sense
2.0 Students calculate and solve problems involving addition, subtraction, multiplication,
and division.
California Standards Grade 7: Number Sense
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and
terminating decimals) and take positive rational numbers to whole-number powers.
Relevant National Standards:
Common Core State Standard: 7NS
3. Solve real-world and mathematical problems involving the four operations with
rational numbers.
Lesson Content Objectives:
 Describe the pattern that occurs in calendars for the day of the week for a particular
date.
 Use division to justify why the day of the week changes for a particular date.
 Use observed patterns to determine the day of the week for dates in the future and/or
past.
Materials Needed:
 One “America’s Birthday” activity sheet per pair of students (included)
 One “Days of Week Investigations” activity sheet per student (included)
Adapted From:
http://illuminations.nctm.org
10
An early version of this lesson was adapted and field-tested by Gina Hryze and Katiria Hernandez,
participants in the California State University, Long Beach Foundational Level Mathematics/General
Science Credential Program.
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Summary of Lesson Sequence
 Introduce the lesson by asking students whether they know their birthday–that is, the
day of the week on which they were born.
 Guide pairs of students through their investigation of the patterns that arise in
calendars for the day of the week for a particular date using the “America’s Birthday”
activity sheet (included).
 Link students’ findings to finding days of week in multiple contexts through guided
practice using the “Days of the Week Investigations” activity sheet (included).
 Check for students’ understanding by asking the provided key questions while they
are working.
 To close the lesson, students will determine the day of the week on which they were
born.
Assumed Prior Knowledge
Prior to this lesson students should know how to divide whole numbers and understand
what the remainder and the quotient of a division problem represent.
Classroom Set Up
Students will be asked to work in pairs for portions of this lesson.
Lesson Description
Introduction
Begin a class discussion by asking if any students know their birthday. Many students
will likely respond by sharing their birth date. Ask if any students know the day of the
week on which they were born. If any students do know the day on which they were
born, let them know that they will be exploring a method for finding this day.
Input and Investigation
Provide student pairs with the “America’s Birthday” activity sheet (included). Allow
students to work in pairs to find a pattern in the calendars for the 4th of July. Ask: Is
there a pattern for how the day of the week changes from one year to another? Students
should develop conclusions based on their observations. [The date moves to the next
day of the week each year, or moves forward two days in some years due to leap year
(years that have February 29th). Leap year occurs every four years.]
Call on pairs of students to share what they have concluded about the patterns they
observed. Students should notice that the date moves forward one day in most years and
moves forward two days in leap years. Ask students to try to determine why.
Ask: How many weeks are there in a year? How many weeks in a leap year? Then have
students divide the number of days in a year by the number of weeks to realize that the
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remainder after dividing is the number of days that the date will move. [365/52 = 7
remainder 1; 366/52 = 7 remainder 2]
Encourage students to relate the remainders they find to the pattern on the “America’s
Birthday” activity sheet and then determine which years were leap years.
Guided and Independent Practice
Provide each student with the “Days of Week Investigations” activity sheet. After
students attempt problem #1, have students share their responses, and then discuss this
problem as a whole class. Students should complete the rest of the activity independently.
Check for Understanding
As students are working independently, check their understanding by moving around the
room and asking the following key questions:





What pattern helps to predict the day of the week for a particular date from one year
to the next year? [Dates move forward one day every year, except in leap years when
they move forward two days.]
Why does a particular date always change from one year to the next? [The number of
weeks in a year is not a whole number.]
How do the math problems 365 ÷ 7 and 366 ÷ 7 explain the calendar pattern for the
day of the week on which a date falls from year to year? [The remainders tell how
many days the date move forward.]
What do you need to know in order to figure out what the day is for a particular date?
[You must know which day the date is for a specific year so that you can work
forward or backward.]
What is the challenge for finding the day for a particular date in the far future or
past? [Years that end in double zeroes (such as 1900, 1800, etc.) do not follow a
regular pattern for leap years.]
Closure
First, have students meet in pairs; have them share and discuss their solutions for birth
day. As a whole class, have volunteers share their conjectures for their birth day, as well
as how they arrived at their solution. Compare methods. Close with a discussion of key
questions listed above.
Suggestions for Differentiation and Extension
 Students who are struggling during the independent work may be encouraged to work
with a partner or may benefit from discussing the key questions further with a partner or
with the instructor.
 Encouraging students to find the day one of their family members was born on may
extend this activity.
 There are websites that calculate the day of the week for any particular date. Students can
check several websites to see if they all give the same results.
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Days of the Week Investigations
1. In 2009, Mother’s Day was Sunday, May 10. Using division as discussed in class, what
day of the week was June 10, 2009? __________________________
Explain how you arrived at your solution. Verify your result with the calendar at the end of
this activity.
2. I do my laundry every 20 days. Last week, laundry day fell on a Friday. On what day of the
week must I do my laundry again? ___________________ Show your work.
3. For this problem, you will find the day on which you were born (your actual birth day).
(a) What is your birth date (mm/dd/yy)? ______________________
(b) What was the matching day for your birth date in 2009? Use the provided 2009 calendar
at the end of this activity sheet. _____________________________
(c) On what day were you born? Justify your answer. ___________________________
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