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

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 know and 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.

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

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)

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

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

A Big Idea is… A Key Mathematical Concept The Big Ideas for Grades 4-6 are… Quantity Operational Sense Relationships Representation Proportional Reasoning

A Key Mathematical Concept

Quantity

Operational Sense

Relationships

Representation

Proportional Reasoning

Why focus on The Big Ideas? Curriculum and Instructional Planning Connections Assessment

Exploring the Big Ideas… FRACTIONS

FRACTIONS

Quantity Determining the ‘howmuchness’ of numbers Modeling fractions as part of a whole Counting fractional parts beyond one whole

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?”)

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)

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?)

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?

“ 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

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?”

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?”

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

“ 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