TEACHING MATH TO JUNIOR DIVISIONBig Ideas, Fractions & eWorkshop

What are the things we should be keeping in mind when we teach math to students?(All of these things you know…we’re just refreshing memories!)

First, lets talk about the overall principles for instruction in

mathematics…..

Principles Underlying Effective Mathematics Instruction

• Positive Attitude• Active/Hands On learning for students

• Use students’ prior knowledge• Provide tasks in the Zone of Proximal

Development• Consider learning styles & special needs

• Create a culture & climate for learning• Encourage metacognition

• Focus on conceptual understanding• Focus on the Big Ideas

Today….we are going to focus a bit on the Big Ideas and Fractions!

The Big Ideas help students to see the connections between the math concepts that they are learning, building a better understanding of math in general. Understanding Big Ideas allows them to use the concepts that they learn now to make connections in the future.

Big Ideas• What are the Big Ideas we are trying to help students to

develop an understanding of?

Quantity Operational SenseRelationships

RepresentationProportional Reasoning

Big Ideas: How do fractions fit in?

Quantity• Howmuchness!• Visualizing whole

numbers as individual items or a set,

• Fractions as parts of a whole

Operation Sense• Understanding addition,

subtraction, multiplication & division and the relationships between them

• Using operations efficiently by using parts to make a whole

Big Ideas: How do fractions fit in?

Relationships• Base 10 relationships• Operation relationships• Comparing and ordering

numbers by relating them to benchmarks

• Relationship between fractionalized parts and the whole

Representation• Symbols and placement

indicate quantity & relationships

• The same number can be represented in a variety of ways

• The significance of a denominator & numerator

Big Ideas: How do fractions fit in?

Proportional Reasoning• Being able to compare objects or

sets of objects• Thinking about multiplicative

relationships

Fractions• Manipulatives and Experiential Problem Solving are Key to effective instructions in

Math

• Students need the chance to experiment with models and diagrams to solve

problems!

Some Key Experiences for StudentsUse models to see fractions as parts of a whole

Count fractional parts beyond one whole

Model the meanings of fractional symbols: proper fractions, improper fractions and mixed fractions

Relate fractions to division: dividing up a whole

Problem solve to find the whole, the part and the fraction Relate fractions to

benchmarks: 0, ½, 1

Determine equivalent fractions

Compare and order fractions

Discover the relationship between number of pieces and size of pieces

eWorkshop• Fractions is a challenging concept for our students to

learn and for us to effectively teach.• I would like to introduce you to a free, online resource that

can help us.

•http://www.eworkshop.on.ca

eWorkshop: What will you find?

• RESOURCES…RESOURCES…RESOURCES• Guides to effective instruction which explain in detail the

general principles, the Big Ideas, Key components of teaching specific subject areas.

• Modules on Literacy & Numeracy which include:• Video’s of teacher’s planning, teaching and reflecting on lessons• Lesson Plans, example problems and solutions • Printable Activity Sheets• Printable manipulatives – fraction circles, fraction strips

• Looking specifically at the Grades 4-6 module on Fractions• Printable manipulatives – fraction circles, fraction strips

THANK YOU!!!!!• Please get together in your grade

level groups or individually and look through the eWorkshop.

• Share with each other what you like, and are going to use in your classroom!

• Of course share how it went too!