Learn on PengiSaxon Math, Intermediate 3Chapter 1: Lessons 1-10, Investigation 1

Lesson 1: Months and Years, Calendars, Activity Make a Calendar

In this Grade 3 Saxon Math lesson from Chapter 1, students learn to read and use calendars by identifying the months of the year, the number of days in each month, common years versus leap years, and ordinal numbers for naming dates. Students also practice writing dates in multiple formats, such as month/day/year, and solve problems involving counting days and weeks on a calendar. The hands-on activity has students construct their own monthly calendar using rows and columns to organize days of the week.

Section 1

📘 Months and Years, Calendars

New Concept

An ordinal number names a position or an order.

What’s next

Next, you’ll apply this concept by using calendars to count days and identify dates, which are practical uses of ordering numbers.

Section 2

Example Card: Counting Days Between Dates

Let's see how careful counting is key to solving problems about time on a calendar. This first example will show you how to count days between two dates.

Example Problem

How many days are there from the 8th of the month to the 19th of the month?

Step-by-Step

  1. We need to find the number of days starting from the day after the 8th and ending on the 19th.
  2. When we count up from the 8th, we do not include the 8th in our count. We begin counting with the 9th and stop at the 19th.
  3. Let's list the days we are counting: 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
  4. By counting the numbers in our list, we find there are 11 days. A faster way is to subtract the start date from the end date: 198=1119 - 8 = 11.

Section 3

Example Card: Finding a Date Weeks Later

Using a calendar's grid makes jumping forward or backward in time surprisingly easy. The next example shows how to use the calendar structure to find a future date.

Example Problem

What date is two weeks after the 5th of the month?

Step-by-Step

  1. First, we locate the 5th on a calendar. We know that one week contains 7 days.
  2. "One week after" means moving down one row in the same column on the calendar. "Two weeks after" means moving down two rows.
  3. Alternatively, we can calculate it. Two weeks is equal to 2×7=142 \times 7 = 14 days.
  4. To find the date two weeks after the 5th, we add 14 days to 5: 5+14=195 + 14 = 19. The date is the 19th.

Section 4

Common and Leap Years

Property

A common year is 365 days long. A leap year is 366 days long. The extra day in a leap year is always added to February, giving it 29 days instead of the usual 28.

Explanation

Think of a common year as the standard, but about every four years we get a 'bonus' day! This leap day keeps our calendar aligned with Earth's orbit around the sun, so our seasons don't drift away over time. It's a cosmic correction!

Examples

The year 2023 was a common year with 365 days.
The year 2024 is a leap year with 366 days, so February had 29 days.
Use the rhyme to remember 30-day months: 'Thirty days hath September, April, June, and November.'

Section 5

Ordinal Number

Property

An ordinal number names a position or an order. When we read a date like July 4, 1776, we say, 'July fourth, seventeen seventy-six.' The word fourth is an ordinal number.

Explanation

Ordinal numbers are all about ranking and order! Instead of just counting items (one, two, three), they tell you what place something is in (first, second, third). Think of it as knowing your spot in a long line for concert tickets.

Examples

We write a date as 10/1/2025, but we read it as 'October first, twenty twenty-five.'
If you are the 7th person in line, six people are standing in front of you.
The first five ordinal numbers are: first, second, third, fourth, and fifth.

Section 6

Calendar

Property

A monthly calendar is a chart that relates the days of the month to the days of the week. It has seven columns, one for each day of the week, and five rows for the weeks.

Explanation

A calendar is your ultimate guide to the month! It organizes all the days into a neat grid so you can quickly see what day of the week your birthday is on or when a holiday is coming up. It's time, but organized visually.

Examples

To find the date one week after the 6th, look directly below the 6 on the calendar to find the 13th.
To find the date two weeks after the 10th, look two rows below the 10 on the calendar to find the 24th.
The number of days from the 4th of the month to the 12th is 124=812 - 4 = 8 days.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Lessons 1-10, Investigation 1

  1. Lesson 1Current

    Lesson 1: Months and Years, Calendars, Activity Make a Calendar

  2. Lesson 2

    Lesson 2: Counting Patterns, Activity Skip Counting

  3. Lesson 3

    Lesson 3: Reading a Clock to the Nearest Five Minutes, Activity Setting a Clock

  4. Lesson 4

    Lesson 4: Number Line, Thermometer, Activity Reading and Recording Temperature

  5. Lesson 5

    Lesson 5: Fractions of an Hour, Activity Fractions of an Hour

  6. Lesson 6

    Lesson 6: Addition

  7. Lesson 7

    Lesson 7: Subtraction

  8. Lesson 8

    Lesson 8: Addition and Subtraction Fact Families

  9. Lesson 9

    Lesson 9: Unknown Addends

  10. Lesson 10

    Lesson 10: Adding Three Numbers

  11. Lesson 11

    Lesson 11: Investigation 1 Pictographs and Bar Graphs

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Months and Years, Calendars

New Concept

An ordinal number names a position or an order.

What’s next

Next, you’ll apply this concept by using calendars to count days and identify dates, which are practical uses of ordering numbers.

Section 2

Example Card: Counting Days Between Dates

Let's see how careful counting is key to solving problems about time on a calendar. This first example will show you how to count days between two dates.

Example Problem

How many days are there from the 8th of the month to the 19th of the month?

Step-by-Step

  1. We need to find the number of days starting from the day after the 8th and ending on the 19th.
  2. When we count up from the 8th, we do not include the 8th in our count. We begin counting with the 9th and stop at the 19th.
  3. Let's list the days we are counting: 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
  4. By counting the numbers in our list, we find there are 11 days. A faster way is to subtract the start date from the end date: 198=1119 - 8 = 11.

Section 3

Example Card: Finding a Date Weeks Later

Using a calendar's grid makes jumping forward or backward in time surprisingly easy. The next example shows how to use the calendar structure to find a future date.

Example Problem

What date is two weeks after the 5th of the month?

Step-by-Step

  1. First, we locate the 5th on a calendar. We know that one week contains 7 days.
  2. "One week after" means moving down one row in the same column on the calendar. "Two weeks after" means moving down two rows.
  3. Alternatively, we can calculate it. Two weeks is equal to 2×7=142 \times 7 = 14 days.
  4. To find the date two weeks after the 5th, we add 14 days to 5: 5+14=195 + 14 = 19. The date is the 19th.

Section 4

Common and Leap Years

Property

A common year is 365 days long. A leap year is 366 days long. The extra day in a leap year is always added to February, giving it 29 days instead of the usual 28.

Explanation

Think of a common year as the standard, but about every four years we get a 'bonus' day! This leap day keeps our calendar aligned with Earth's orbit around the sun, so our seasons don't drift away over time. It's a cosmic correction!

Examples

The year 2023 was a common year with 365 days.
The year 2024 is a leap year with 366 days, so February had 29 days.
Use the rhyme to remember 30-day months: 'Thirty days hath September, April, June, and November.'

Section 5

Ordinal Number

Property

An ordinal number names a position or an order. When we read a date like July 4, 1776, we say, 'July fourth, seventeen seventy-six.' The word fourth is an ordinal number.

Explanation

Ordinal numbers are all about ranking and order! Instead of just counting items (one, two, three), they tell you what place something is in (first, second, third). Think of it as knowing your spot in a long line for concert tickets.

Examples

We write a date as 10/1/2025, but we read it as 'October first, twenty twenty-five.'
If you are the 7th person in line, six people are standing in front of you.
The first five ordinal numbers are: first, second, third, fourth, and fifth.

Section 6

Calendar

Property

A monthly calendar is a chart that relates the days of the month to the days of the week. It has seven columns, one for each day of the week, and five rows for the weeks.

Explanation

A calendar is your ultimate guide to the month! It organizes all the days into a neat grid so you can quickly see what day of the week your birthday is on or when a holiday is coming up. It's time, but organized visually.

Examples

To find the date one week after the 6th, look directly below the 6 on the calendar to find the 13th.
To find the date two weeks after the 10th, look two rows below the 10 on the calendar to find the 24th.
The number of days from the 4th of the month to the 12th is 124=812 - 4 = 8 days.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Lessons 1-10, Investigation 1

  1. Lesson 1Current

    Lesson 1: Months and Years, Calendars, Activity Make a Calendar

  2. Lesson 2

    Lesson 2: Counting Patterns, Activity Skip Counting

  3. Lesson 3

    Lesson 3: Reading a Clock to the Nearest Five Minutes, Activity Setting a Clock

  4. Lesson 4

    Lesson 4: Number Line, Thermometer, Activity Reading and Recording Temperature

  5. Lesson 5

    Lesson 5: Fractions of an Hour, Activity Fractions of an Hour

  6. Lesson 6

    Lesson 6: Addition

  7. Lesson 7

    Lesson 7: Subtraction

  8. Lesson 8

    Lesson 8: Addition and Subtraction Fact Families

  9. Lesson 9

    Lesson 9: Unknown Addends

  10. Lesson 10

    Lesson 10: Adding Three Numbers

  11. Lesson 11

    Lesson 11: Investigation 1 Pictographs and Bar Graphs