fractions planner

Class/grade: 4 Age group: 8.5 to 9.5 years

School: Indus International School School code:7319

Title: Freaky fractions

Teacher(s): Archana, Grace, Lakshmi

Date: April 2009

Proposed duration: 3.5 hours per week over 4 weeks

PYP planner

1. What is our purpose?

To inquire into the following:

Tran disciplinary theme

How the world works

central idea

We use fractions to make our lives easier

Summative assessment task(s):

The children chose any one basic concept in the unit and design a lesson for that. They were each given 7-8 minutes to ‘teach’ that concept to the class. They were free to choose any re-sources available. They could also make them on their own. A project sheet was given to them and the rubric was shared. They were assessed based on their understanding of the central ides and the concepts.

The children came out with some very interesting teaching modules. Most of the children made worksheets for their peers and enjoyed assessing them. The project was shared with the children in the initial days of the unit. They hence observed the daily lessons given by the teacher. They were able to imply the lesson has to be divided into parts – tuning in, engage-ment and assessment. These guidelines made it easy for the children to plan execute their ‘lessons’ effectively.

2. What do we want to learn?

What are the key concepts (form, function, causation, change, connection, perspective, and responsibility, reflection) to be emphasized within this inquiry?

Function, change

What lines of inquiry will define the scope of the inquiry into the central idea?

Inquiry into:

The meaning of fractions Operations with fractions Application of fractions (including decimals)

What teacher questions/provocations will drive these inquiries? How best can we interpret a fraction? Where can we use fractions? Why do we need fractions? How can we ‘change’ a fraction? How are fractions and decimals connected? How can we ‘change’ decimals?

Planning the inquiry

© International Baccalaureate Organization 2007

Planning the inquiry

3. How might we know what we have learned?

This column should be used in conjunction with “How best might we learn?”

What are the possible ways of assessing students’ prior knowledge and skills? What evidence will we look for?

Pre assessment: Using Rocket writing, the children were asked to write whatever they know about fractions. Some review sheets from the previous year were solved by the children. At the beginning of every lesson, the children reflected on their learning.

What are the possible ways of assessing student learning in the context of the lines of inquiry? What evidence will we look for?

Formative assessments:

Written review on the basic elements of fractions- After the initial lessons on the basic elements of fractions and the concept of equivalent fractions, a review was given to the children.

Quiz on all the operations on fractions- Based on the concept of common denominators, a quiz was arranged by the teacher. The children were divided in groups of four (mixed) and the rules of the quiz were such that each child got a turn to answer questions.

Peer assessment- the children were divided into pairs and were asked to given problems to each other in their note books. The topic chosen was ‘addition and subtractions of unlike fractions’

The assessment cards from the fractions kits were used for multipli-cations of fractions.

Multiple choice questions on applications on fractions(decimals) were solved by the children

4. How best might we learn?

What are the learning experiences suggested by the teacher and/or students to encourage the students to engage with the inquiries and address the driving questions?

Constructing meaning of multiplication:

Children watched many videos from Digitally and the internet (visual, picture smart)) They did activities (games, puzzles, quizzes, etc.) available on the internet They listened to songs related to the topic and sang along (music smart) They understood better with the help of hands on- cubes, fractions rods, cards, decimals rods

and cards (kinesthetic) Through out the unit, a Fractions and decimal kit was used depending on the needs of the chil-

dren. This kit had fraction rods flash cards with instructions and assessments. The kids used it as tool whenever they had trouble in understanding a particular concept.

Many lessons from Digitally (resources library) were shown to the kids as a tuning in activity for many lessons.

The children also used attachable cubes to understand many concepts

Transferring meaning:

The children solved many interesting worksheets printed from the internet and other sources They used the flash cards from the fractions kit to solve fraction problems The children solved problems from their math workbooks On the math board, the children wrote their inquiries on a daily basis. They also wrote their dis-

coveries corresponding to their inquiries.

Applying meaning:

They used fractions in their daily procedures (feedback from parents and observations during break times)

They made fractions story problems on their own Some children formed questions for quizzes For assessments, refer section 7

5. What resources need to be gathered?

What people, places, audio-visual materials, related literature, music, art, computer software, etc, will be available?

Interactive white board (active studio, images), Digitally, Internet- Activities, videos, audios, articles, games, Worksheets, PowerPoint presentations, Joy of math, Note books, cubes, fractions rods and cards, decimal cards

How will the classroom environment, local environment, and/or the community be used to facilitate the inquiry?

The basic elements of the unit- the title, the theme, the central idea, inquiry points, concepts, attitudes, leaner profile and skills were put up on the math board. The children also put up their inquiry questions and discoveries on the board. Some charts, worksheets, booklets made by the children were also put up. The teaching resources that were being used were also kept in the vicinity.


Reflecting on the inquiry

6. To what extent did we achieve our purpose?

Assess the outcome of the inquiry by providing evidence of students’ understanding of the central idea. The reflections of all teachers involved in the planning and teaching of the inquiry should be included.

The intensive inquiry into the fractions unit helped the children to gain a deep understanding of the concepts of fractions. They learnt to form questions in math and find answers to the same. They realized that inquiry is not only in the Units of inquiry (UOI), but also in math. They were enthusiastic to follow these ways in other disciplines as well.

How you could improve on the assessment task(s) so that you would have a more accurate picture of each student’s understanding of the central idea.

If possible, the time given to each child (7 to 8 minutes) could be increased. Many children were eager to take lessons for an entire period, like their teacher. This could have been made possible if planned accordingly.

What was the evidence that connections were made between the central idea and the transdisciplinary theme?

The children understood that fractions were used to make the works work. They could apply the meaning of fractions in their daily lives and realize the importance of the same.

7. To what extent did we include the elements of the PYP?

What were the learning experiences that enabled students to:

Develop an understanding of the concepts identified in “What do we want to learn?”

Function: the children understood how to perform operations with fractions. They realized that there were various methods to solve fractions problems. The different processes with regards to the unit were thoroughly practiced for enduring understanding.

Change: The children were familiar with various conversions in fractions. For example: finding equivalent fractions, reducing fractions, changing denominators, etc. They understood that they could change fractions by adding, subtractions and multiplying them. Interconnecting mixed and improper fractions was also grasped by them.

Demonstrate the learning and application of particular transdisciplinary skills?

Thinking skills: Through out the unit, the children used their thinking skills to sort information, analyze and synthesis it. They also used these skills to apply their understanding to various situations.

Self-management skills: As the children had to plan a lesson for their class, they used their self-management skills to organize the lesson using resources. They also were given a time limit; hence they also planned to complete their lesson in the given period of time. As many resources were used in the unit, the children also had to record the evidence for learning in their note books.

Develop particular attributes of the learner profile and/or attitudes?

Thinker: Through this unit, the children developed as thinkers evidently. Their thoughts were more profound. Each child was given an opportunity to enhance their thinking skills by challenging them according to their level of knowledge and interest.

Knowledgeable: Through this unit, the children gained knowledge about the meaning of fractions, their types, conversions and the various operations that they could perform with fractions. The children were exited to learn about the applications of fractions- Decimals.

Curiosity: The children were curious to learn about the different ways of solving fraction problems. They enjoyed being challenged and showed readiness towards learning new concepts in the unit.

Confidence: As the children were aware that they were learning fractions in an inquiry fashion, they were confident that this understanding would stay with them forever and it would be easier for them to apply this knowledge in the higher grades. Many children for whom math was not the favorite subject, performed brilliantly in this unit.


Reflecting on the inquiry

8. What student-initiated inquiries arose from the learning?

Record a range of student-initiated inquiries and student questions and highlight any that were incorporated into the teaching and learning.

Students questions:

What are the types of fractions?

Can we interconvert them? How?

How can we add/subtract fractions if the denominators are different?

Why don’t we need common denominators while multiplying fractions?

Can we also divide fractions? How?

What does the point signify in decimals?

How can we multiply decimals?

At this point teachers should go back to box 2 “What do we want to learn?” and highlight the teacher questions/provocations that were most effective in driving the inquiries.

What student-initiated actions arose from the learning?

Record student-initiated actions taken by individuals or groups showing their ability to reflect, to choose and to act.

They used fractions in their daily lives (feedback from parents and observations)

They sometimes suggested ideas for lessons to the teacher

Their confidence in the unit showed when they planned and executed effective lessons for the summative

In the year end reflections, they spoke highly about the unit

9. Teacher notes

This was a great experience for us as it was the first time we planned a math unit using the backward model. Our excitement was contagious and it spread to the entire class.

On the whole, the children enjoyed this unit the most. It was reportedly the favorite month in terms of math for most of the children.

We could further improve the learning outcomes by increasing the time limit for the unit. We could then include many more engagements.

A foreign guest speaker who can talk about how fractions are solved in his/her country would be a good ides to support international mindedness.

We integrated fractions with English through word problems. We could have more such integration with other disciplines.


fractions planner

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