TEACHING FRACTIONS TO THE JUNIOR STUDENT
The information for this presentation was drawn largely from various reports by the Ontario Ministry of Education posted on the website http://www.eworkshop.on.ca/ . It would be presented as a PowerPoint presentation.
What’s The Big Idea?
- Major concepts that form the context for all math learning expectations
- Helps students to make connections and develop a deeper understanding
- Helps teachers to focus their professional development
The “Big Ideas” in mathematics for the junior student are the major concepts within which all of the specific learning expectations exist. Teaching within the context of the big ideas allows students to see the connections between mathematical concepts, facts, and procedures, and therefore develop a deeper understanding. With a focus on the big ideas, teachers can work on developing teaching strategies that build skills in the major math concepts, which will apply to a variety of specific expectations. This allows them to be more effective teachers.
**HAND OUT COPIES OF THE INFORMATION ON THE FOLLOWING 6 SLIDES**
In the Number Sense and Numeration strand, grades 4-6, the big ideas are:
- Quantity
- Operational Sense
- Relationships
- Representation
- Proportional Reasoning
Quantity:
The report on Number Sense and Numeration, Grades 4 to 6, by the Ontario Ministry of Education (2006), makes key points about each of the big ideas in the junior mathematics curriculum:
- “Having a sense of quantity involves understanding the “howmuchness” of whole numbers, decimal numbers, fractions, and percents.
- Experiences with numbers in meaningful contexts help to develop a sense of quantity.
- An understanding of quantity helps students estimate and reason with numbers.
- Quantity is important in understanding the effects of operations on numbers.”
Operational Sense:
- “Operational sense depends on an understanding of addition, subtraction, multiplication, and division, the properties of these operations, and the relationships among them.
- Efficiency in using the operations and in performing computations depends on an understanding of part-whole relationships.
- Students demonstrate operational sense when they can work flexibly with a variety of computational strategies, including those of their own devising.
- Solving problems and using models are key instructional components that allow students to develop conceptual and procedural understanding of the operations.”
Relationships:
- “An understanding of whole numbers and decimal numbers depends on a recognition of relationships in our base ten number system.
- Numbers can be compared and ordered by relating them to one another and to benchmark numbers.
- An understanding of the relationships among the operations of addition, subtraction, multiplication, and division helps students to develop flexible computational strategies.
- Fractions, decimal numbers, and percents are all representations of fractional relationships.”
Representation:
- “Symbols and placement are used to indicate quantity and relationships.
- Mathematical symbols and language, used in different ways, communicate mathematical ideas in various contexts and for various purposes.”
Proportional Reasoning:
- “Proportional reasoning involves recognizing multiplicative comparisons between ratios.
- Proportional relationships can be expressed using fractions, ratios, and percents.
- Students begin to develop the ability to reason proportionally through informal activities.”
(Previous key points were quoted from:
Number Sense and Numeration, Grades 4 to 6. Volume 1, The Big Ideas. Ontario Ministry of Education, 2006)
Ask teachers to discuss the following questions: Would you change anything about this list and description of the big ideas in math for the junior grades? Is there anything to add? Which big idea would you say is the most difficult for students to grasp?
Why Fractions?
Teaching fractions can help develop understanding in all of the big ideas
Quantity: A whole can be divided into parts, those parts contain different amounts of the whole and can be compared, and different numbers can represent the same parts. Understanding the concept of quantity will reduce confusion about the unfamiliar use of digits (e.g. ½ is bigger than ¼) while trying to develop the big idea of “relationships”
Operational Sense: Use of fractions in concrete examples forms the basis needed for adding and subtracting fractions later. (e.g. fractions of a pizza shared between friends adds up to a whole pizza)
Relationships: Understanding the relationship between fractions and the whole, and fractions compared to each other (Three thirds makes a whole, 1/3 is smaller than ½, even though 3 is bigger than 2)
Representation: Fractions can be represented using words, symbols, and charts or diagrams. As symbols, the meaning of the numerator and denominator are important.
Proportional Reasoning: Fractions can represent parts of a whole, and that can be related to the number of parts in more than one whole. Fractions can also represent a ratio of wholes, and ratio can be extrapolated to new amounts (e.g. price of kiwi fruits in the grocery store $0.99 for 3, how much for 9?)
General Principles for Mathematics Instruction
Students in the junior grade may be becoming discouraged and frustrated with math and develop negative attitudes towards it. Help to keep a positive attitude towards math in your class and improve student mathematical learning:
- Model enthusiasm for math personally and through classroom visuals
- Make connections with their world
- Make use of learning styles (use pictures, concrete representations, drama, art, music and drama)
- Teach at your students’ instructional level, and provide ample time
- Emphasize conceptual learning, the “Big Ideas”
- Encourage problem solving in a cooperative learning environment
- Ask questions that develop metacognition
- Be inclusive of student diversity by accommodating student needs and incorporating different genders and cultures in word problems
A Useful Resource
Includes:
- various reports on teaching math in Ontario, which include both teaching theory and practical tips for teaching and assessment
- lessons on math topics, including descriptions on how teaching theory and strategies have been implemented, and video clips of the lesson happening in a real class
- Specifically, a lesson on teaching fractions using the big ideas and the general principles for mathematics instruction. PLAY TIME! To access this lesson, under the heading “Numeracy Modules” and the heading “Grades 4 to 6″, click on “fractions”, then “open module”. Use the tabs at the top to navigate through the lesson theory, development, and implementation.
(Teachers given 15 minutes to explore the site)
Application
Ticket out the door: Answer the following questions on a piece of paper and hand in before leaving.
What is one thing that you have learned from this workshop?
Describe one change you will make to the way you currently teach math (e.g. a change in approach to planning, teaching or assessing, a new strategy you will use).
