Numeracy and ‘The Big Ideas’

Grades 4-6

Aimée De Abreu

Aims of the Workshop

• To review principles of mathematics instruction

• To apply the concept of ‘Big Ideas’ to the planning and instruction of Fractions.

• To explore the numeracy teaching resources available on www.eworkshop.on.ca

“Effective mathematics teaching requires understanding what students knowand need to learn and then challenging and supporting them to learn it well.”

(National Council of Teachers of Mathematics [NCTM], 2000, p. 16)

Reflection

On your T-chart, jot down some recollections of an ‘AHA’ moment in your educational experiences with mathematics:

Your AHA moment Effective Instruction of Mathematics

Leave blank.

All teaching of mathematics should:• foster positive mathematical attitudes;• focus on conceptual understanding;• involve students actively in their learning;• acknowledge and utilize students’ prior knowledge;• provide developmentally appropriate learning tasks;• respect how each student learns by considering learning

styles and other factors;• provide a culture and climate for learning;• recognize the importance of metacognition;• focus on the significant mathematical concepts (“big

ideas”).

‘Principles Underlying Effective Mathematics Instruction’ A Guide to Effective Mathematics Instruction (2006)

Reflection

Now link your AHA moment to one (or more) of the Principles Underlying Effective Mathematics Instruction.

Your AHA moment Effective Instruction of Mathematics

A Big Idea is…

A Key Mathematical Concept

The Big Ideas for Grades 4-6 are…

•Quantity

•Operational Sense

•Relationships

• Representation

•Proportional Reasoning

Why focus on The Big Ideas?

Curriculum and Instructional Planning

Connections

Assessment

Exploring the Big Ideas…

FRACTIONS

Quantity

Determining the ‘howmuchness’ of numbers

• Modeling fractions as part of a whole

• Counting fractional parts beyond one whole

Operational Sense

Understanding addition, subtraction, multiplication and using them meaningfully

to solve problems

• Relating fractions to division (e.g. “Imagine that 4 sandwiches were shared equally among 6 children. How much of a sandwich did each child eat?”)

Representation

Mathematical symbols and language as representations of amounts, operations

and concepts

• Relating fractional symbols to their meaning (including proper and improper fractions and mixed numbers)

(e.g. the quantity represented by a fraction OR by the numerator and denominator)

Proportional Reasoning

Comparison of quantities and proportions

• Establishing part-whole relationships (e.g. If this is 2/3 of the cake, what does the whole cake look like?)

• Problem-solving with fractions (e.g. If 5 girls share 2 pizzas and 7 boys share 4 pizzas,

will the girls and the boys each get the same amount?)

Relationships

“To understand mathematics is to recognize the relationships it involves, which give it both its beauty and its utility. Seeing relationships between numbers helps students make powerful connections in mathematics, allowing them to discover new mathematics in flexible,

efficient, and innovative ways.” (Guide Vol 1)

• Relationships between decimals, fractions and percentages

• Other relationships?

Features of eworkshop

• Guides to Effective Instruction• Learning Modules• Video workshops• Newsletter (this month has a fractions tip!)

• Forum, Notebook and other features if you subscribe and create a profile

Other topics and resources relate to literacy, leadership, parents, healthy schools, and more

Webhunt:

On www.eworkshop.on.ca find the following:• An interesting problem-solving activity in the

Learning Module on Fractions• A teaching video that includes a useful strategy

for exploring a Big Idea related to Fractions.• The part, most useful to you, of the Guide to

Effective Instruction related to Fractions.

“How might the use of this site improve/influence your teaching of Fractions and the Big Ideas?”

Sharing…

In groups of 4-5, discuss the guiding question:

“How might the use of this site improve/influence your teaching of

Fractions and the Big Ideas?”

References

“A Guide to Effective Instruction in Mathematics Kindergarten to Grade 6. Vol 1. Retrieved July 11, 2008 from www.eworkshop.on.ca

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.

“Number Sense and Numeration, Grades 4-6. Vol 1 The Big Ideas. Retrieved July 11, 2008 from www.eworkshop.on.ca

“Number Sense and Numeration, Grades 4-6. Vol 5 Fractions. Retrieved July 11, 2008 from www.eworkshop.on.ca