Day of the Week: Using Factors and Multiples

Algebra 1 Grades High School 5:22 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to determine the day of the week for any given day number using factors, multiples, and remainders. This lesson explores the cyclical nature of the week and applies division to solve problems related to patterns.

Video Resource

Using factors and multiples to figure out days of the week | Pre-Algebra | Khan Academy

Khan Academy

Duration: 5:22
Watch on YouTube

Key Concepts

  • Factors
  • Multiples
  • Remainders
  • Division Algorithm
  • Cyclical Patterns

Learning Objectives

  • Students will be able to calculate the day of the week for a given day number using division and remainders.
  • Students will be able to explain the relationship between the remainder and the day of the week.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students if they've ever wondered how to quickly calculate what day of the week a date will be far in the future. Introduce the concept of cyclical patterns, such as the days of the week, and how mathematics can help predict these patterns. Show the Khan Academy video to introduce the problem and the method.
  • Video Explanation and Examples (15 mins)
    Play the Khan Academy video 'Using factors and multiples to figure out days of the week'. Pause at key points to explain the logic behind using division and remainders. Emphasize that the remainder after dividing by 7 corresponds to the position of the day within the week. Work through the examples provided in the video, clarifying any confusing steps.
  • Guided Practice (15 mins)
    Work through additional examples as a class, starting with smaller day numbers (e.g., Day 20, Day 50) and then progressing to larger numbers (e.g., Day 150, Day 250). Have students participate by calculating the remainders and identifying the corresponding days of the week. Encourage students to explain their reasoning.
  • Independent Practice (10 mins)
    Provide students with a set of practice problems to solve independently. These problems should include a variety of day numbers. Encourage them to check their answers with each other and discuss any discrepancies.

Interactive Exercises

  • Day of the Week Calculator
    Create a simple calculator (using a spreadsheet or online tool) where students can input a day number and the calculator outputs the corresponding day of the week. This allows students to quickly test different values and reinforce their understanding.
  • Birthday Day of the Week
    Have students determine what day of the week they were born on. This exercise is more difficult, as it requires knowledge of the specific start date of the calendar.

Discussion Questions

  • Why does dividing by 7 help us determine the day of the week?
  • How does the remainder relate to the day of the week?
  • Can you think of other cyclical patterns where this method could be applied?

Skills Developed

  • Problem-solving
  • Mathematical reasoning
  • Application of division and remainders
  • Pattern Recognition

Multiple Choice Questions

Question 1:

If Day 1 is Monday, what day of the week is Day 16?

Correct Answer: Tuesday

Question 2:

If Day 1 is Monday, what day of the week is Day 25?

Correct Answer: Thursday

Question 3:

If Day 1 is Monday, and you divide a day number by 7 and get a remainder of 3, what day of the week is it?

Correct Answer: Wednesday

Question 4:

What mathematical operation is primarily used in determining the day of the week?

Correct Answer: Division

Question 5:

The number 7 is important to this calculation because...

Correct Answer: There are 7 days in a week

Question 6:

If today is Monday, which of the following day numbers would also fall on a Monday?

Correct Answer: Day 8

Question 7:

What does the remainder represent when dividing the day number by 7?

Correct Answer: The position of the day within the week

Question 8:

If the remainder is 0 after dividing by 7, what day of the week is it (assuming Day 1 is Monday)?

Correct Answer: Sunday

Question 9:

Which of the following concepts is NOT essential to understanding this calculation?

Correct Answer: Prime Numbers

Question 10:

If today is Monday, what day of the week will be Day 30?

Correct Answer: Wednesday

Fill in the Blank Questions

Question 1:

To find the day of the week, we divide the day number by ___.

Correct Answer: 7

Question 2:

The ________ tells us the position of the day within the week.

Correct Answer: remainder

Question 3:

If Day 1 is Monday and the remainder is 1, then it is a ________.

Correct Answer: Monday

Question 4:

The days of the week follow a ________ pattern.

Correct Answer: cyclical

Question 5:

Before getting to day 25, there are three rows of ___.

Correct Answer: 7

Question 6:

If the remainder is zero after dividing a day number by 7, that means the day lands on ________.

Correct Answer: Sunday

Question 7:

The Khan Academy video teaches us to use ________ to find patterns.

Correct Answer: math

Question 8:

Day 300 divided by 7 is equal to 42 with a remainder of ____.

Correct Answer: 6

Question 9:

Division helps us determine how many full ______ of the week have passed.

Correct Answer: cycles

Question 10:

The formula that gives us the day of the week takes the form (total days)/7 = quotient + ________/7.

Correct Answer: remainder

Educational Standards

A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties. A1.F.1:Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans