This is an activity based on the picture book *365 Penguins*

Students will be able to relate the features of the calendar to their number knowledge.

Students will be able to demonstrate how grouping is efficient way to organise their thinking and operating with larger numbers.

The parts of large sets can be understood by estimating and rounding fractions - for example the 120th day of the year is 120/365 and is *about* 1/3 of the way through a year.

calendars

Estimating Fractions of a Year

This activity is based on the picture book *365 Penguins*

Author: Jean-Luc Fromental and Joëlle Jolivet

Illustrator: Jean-Luc Fromental and Joëlle Jolivet

Publisher: Abrams (2006)

ISBN: 978-0-8109-4460-2

**Summary: **

On New Year’s Day a family receives a penguin in the mail and so unfolds the year, one penguin arriving per day. The problems and penguins pile up, as they have to come up with solutions for housing, feeding and keeping track of the ever-increasing number. The sender of the penguins is revealed on New Year’s Eve.

**Lesson Sequence:**

- Prior to reading the story assess the students understanding of the calendar year.
*How many months do we have in a year?*

What are they called?

How many days are in a whole year? Is it always the same?

Using a paged calendar, flip through the pages noting the names of the months and how the days and weeks are arranged as well as the names of the days of the week.*What is the largest number that can appear on a calendar month?*

Are all months the same?

I wonder how people decided how many days go into a month?

About how many weeks are in each month?

About how many groups of seven is that? - Share the book with your students reading through the whole story.
- Revisit the story on another day this time using a calendar frieze you have prepared (or had the students prepare). Take apart a calendar (these can be purchased from discount stores or printed off from various sites on the internet or from templates within word processing programmes) and attach the months together one after another in a long frieze. Pin this up so everyone can see how the whole year of days, weeks, and months looks as a whole. Discuss what the students observe now they are seeing the whole year at once. For some students they may never have seen the year as a whole but rather as a calendar page at a time. A calendar presented this way provides students with an image of the whole so that you can begin to engage them in conversations about the fractions of a year.
- As you read the story this time stop at various points to record how many days have passed (and therefore how many penguins are in the house) by having a student circle or cross out the days on the calendar in vivid. Discuss and record the interesting fractions as you go. For example ask:
*At the end of January they have received 31 of 365 penguins. How do we write that as a fraction? That***is about what**as an easier fraction?

When will they receive half the penguins? What day is halfway through the year? (being an odd number, students will have to decide that is half way through the 182nd day.)

There are 12 months in the year, how many months in half a year? In a quarter? In a third? When will the year be about 3/4 finished?

Describe where your birthday is as a fraction of the year- My birthday is in April, that is about 1/3 of the way through the year.

How many penguins did they have on Christmas Day? What fraction of the whole was that? - Investigate more calendar fractions by dividing the year into terms, seasons, number of lunar cycles etc. Talk about places in the world where the year is divided into halves: wet and dry seasons.
- Leave the frieze up in the class or put up a new “clean” one and track the passing of the year, number of days at school, seasons etc. supporting students to develop a visual image of the year as a whole.