Learning The revised curriculum supports students learning mathematics with understanding and actively building new knowledge from experience and prior knowledge.

Conceptual Understanding Conceptual understanding refers to an integrated and functional grasp of mathematics. It is more than knowing isolated facts and procedures. Eg. Multiplication the Algebraic WayMultiplication the Algebraic Way

Conceptual Understanding Conceptual understanding supports retention. When facts and procedures are learned in a connected way, they are easier to remember and use and can be reconstructed when forgotten. Hiebert and Wearne 1996; Bruner 1960, Katona 1940

Balancing Conceptual Understanding and Procedural Fluency Pitting procedural fluency against conceptual understanding creates a false dichotomy. Understanding makes learning skills easier, less susceptible to common errors and less prone to forgetting. Also, a certain level of skill is required to learn many mathematical concepts with understanding Hiebert and Carpenter 1992

Making Connections 1999 Curriculum -determine, from examination of patterns, the exponent rules for multiplying and dividing monomials and the exponent rule for the power of a power, and apply…. -determine the meaning of negative exponents and of zero as an exponent from activities involving graphing, using technology, and from activities involving patterning COURSE: GRADE 9 Applied and Academic Revision -describe the relationship between the algebraic and geometric representations of a single variable term up to degree three ( i.e., length, which is one dimensional, can be represented by x; area, which is two dimensional can be represented by x^2, and volume, which is three dimensional can be ….

1999 Curriculum Gr 9 Applied: -solve simple problems, using the formulas for the surface area of prisms and cylinders and for the volume of prisms, cylinders, cones and spheres; COURSE: GRADE 9 Applied to GRADE 10 Applied Revision Grade 10 Applied -determine, through investigation, the relationship for finding the surface area of a pyramid (e.g., use the net of a square based pyramid to determine that the surface area is the area of the square base, plus the areas of the four congruent triangles) Developmental Continuum

Continuum of Learning : Support Resource for Draft Revision Spring 2005 Number Sense and Numeration GRADE 1: read, represent, order, and compare whole numbers to 50, and investigate money amounts and fractions; GRADE 5: read, represent, order, and compare whole numbers to , decimal numbers to hundredths, proper and improper fractions, and mixed numbers; GRADE 2: read, represent, order, and compare whole numbers to 100, and represent money amounts and fractions using concrete materials GRADE 6: read, represent, order, and compare whole numbers to , decimal numbers to thousandths, proper and improper fractions, and mixed numbers GRADE 3: read, represent, order, and compare whole numbers to 1000, and demonstrate their understandings about money and fractions GRADE 7: represent, order, and compare numbers, including integers GRADE 4: read, represent, order, and compare whole numbers to , decimal numbers to tenths, and simple fractions, and expand their understandings about money GRADE 8:represent, order, and compare equivalent representations of numbers including those involving exponents

Developing Concepts Across the Grades 1997 Curriculum Proportional Reasoning Draft Revision Spring 2005 Proportional Reasoning Grade 7: No Specific ReferenceGrade 7: Number Sense and Numeration Proportional Relationships Grade 8: Under ApplicationsGrade 8: Number Sense and Numeration Proportional Relationships Grade 9 Applied: Number Sense and Algebra Solving Numerical Problems Grade 9 Applied: Number Sense and Algebra: Proportional Reasoning Grade 10 Applied: Proportional Reasoning Grade 10 Applied: Measurement and Trigonometry: Solving Problems Involving Similar Triangles

Developing Concepts - Volume Grade 4 Measure Volume Grade 5Grade 6 Grade 7 Gr 8 Gr 9 Grade 9 Grade 9 Grade 10 Academic Applied Applied Solve problems Develop formulas Solve problems Involving optimal for the volumes of involving volumes volume. Solve the pyramids, cones of prisms, pyramids max and min vol and spheres. cylinders, cones, pyramids, cones spheres, and a and spheres. combination.

Your turn to put the puzzle together Gr 7 Gr 8 Gr 9 Gr 10 Your turn to investigate expectations from grade 7, 8, 9 and 10 that build on one another.

On your tables you will find a green sheet that has an overall expectation. Determine the prerequisite expectation(s) from Grade 10 to Grade 7 and remain in the same pathway. Use the organizer and chart paper at your table. Post on the back wall when completed.