Series:

Developing Essential Understanding

2 total works

Cover of Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5
Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers' reflection.

Cover of Developing Essential Understanding of Number and Numeration in Pre-K-Grade 2
How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems.

It is organised around one big idea and supported by smaller, more specific, interconnected ideas (essential understandings). Gaining this understanding is essential because numbers and numeration are building blocks for other mathematical concepts and for thinking quantitatively about the real-world.

Essential Understanding series topics include:
  • Number and Numeration for Grades Pre-K-2
  • Addition and Subtraction for Grades Pre-K-2
  • Geometry for Grades Pre-K-2
  • Reasoning and Proof for Grades Pre-K-8
  • Multiplication and Division for Grades 3-5
  • Rational Numbers for Grades 3-5
  • Algebraic Ideas and Readiness for Grades 3-5
  • Geometric Shapes and Solids for Grades 3-5
  • Ratio, Proportion and Proportionality for Grades 6-8
  • Expressions and Equations for Grades 6-8
  • Measurement for Grades 6-8
  • Data Analysis and Statistics for Grades 6-8
  • Function for Grades 9-12
  • Geometric Relationships for Grades 9-12
  • Reasoning and Proof for Grades 9-12
  • Statistics for Grades 9-12