Focusing On The Fundamentals
What are the fundamentals of math?
Making sure that students have a strong understanding of math fundamentals is one of the best ways to prepare them for success, now and in the future. Fundamental math skills, and the concepts that underpin them, may be categorized according to the following framework:
• Working with numbers
• Recognizing and applying understanding of number properties
• Mastering math facts
• Developing mental math skills
• Developing proficiency with operations
teacher_guide_math_en.pdfFocussing on Fundamentals Teacher Guide
parent_guide_math_en.pdfFocussing on Fundamentals Parent Guide
Computational Strategies Booklet
Operational sense allows students to make sense of addition, subtraction, multiplication, and division, and to use these operations meaningfully in problem-solving situations. Students who possess a strong understanding of the operations see the relationships among them and develop flexible strategies for computing with numbers.
Please use the Computational Strategies booklet to see the many strategies that your students may be using as they move along the developmental continuum in working with numbers.
Use this link to make your own copy of the Computational Strategies booklet.
Responding to November 2019 Diagnostics
A document has been created as a response to our November 2019 Diagnostics. This document outlines number sense needs, math processes directly linked to the needs, and next steps and instructional strategies to address each need.
Number Sense Progression Videos
G Fletchy's site has a variety of resources including 3-Act Lessons as well as Progression Videos. These videos walk through the mathematical progression of student learning within a particular concept.
***NOTE: These progressions are related to the Common Core standards, not the Ontario Mathematics Curriculum.
Part Whole & Addition / Subtraction Problem Structures
Supporting Part-Whole Thinking
(Addition and Subtraction Problem Structures)
Please adapt numbers to meet the needs of your learners, while maintaining the structure of the problem.
Getting started with Part-Whole Mar2018.pdfPart Whole Pathway / Game Structure for Lessons / Games - Work of Ann Pigeon (Ministry of Education)
Addition and Subtraction Problem TypesAddition and Subtraction Problem Structures
Getting Started With Part -WholeSlideshow to Support Part Whole Lessons (Minds-On Games, Mini-Lessons and Follow-Up Problems)
Diagnostic -Addition and Subtraction SituationsPre / Post Assessment and Spreadsheet for Coding
Continuum of Numeracy Development: Addition & Subtraction
This continuum shows the development of addition and subtraction strategies. See Computation Strategies Booklet for detailed descriptions of each strategy your students may be using. Please note that students may not use all of these strategies as they move to automatic retrieval and proficiency.
Multiplication / Division Problem Structures
Multiplication and Division Problem Structures
Please adapt numbers to meet the needs of your learners, while maintaining the structure of the problem.
Games to Build Multiplication / Division FluencyMultiplication / Division Games to Support Structures and Additional Games
Multiplication and Division Problem TypesMultiplication and Division Problem Structures
Getting Started with Multiplicative Problem StructuresSlideshow to Support Problem Structures Lessons (Minds-On Games, Mini-Lessons and Follow-Up Problems)
Diagnostic-Multiplication SituationsPre/Post Assessment and Spreadsheet for Coding (Please adapt #'s to meet the needs of your learners)
Continuum of Numeracy Development: Multiplication and Division
This continuum shows the development of multiplication and division strategies. See Computation Strategies Booklet for detailed descriptions of each strategy your students may be using. Please note that students may not use all of these strategies as they move to automatic retrieval and proficiency.
Lesson Support for Teaching Operations
Includes a sequence for teaching facts and strategies, establishing foundational facts and strategies, naming and using properties, connecting computational strategies and properties, and choosing which strategy to use.
by Jo Boaler
"Mathematics facts are important but the memorization of math facts through times table repetition, practice and timed testing is unnecessary and damaging...[there are] the limitations of memorization without ‘number sense’. People with number sense are those who can use numbers flexibly. When asked to solve 7 x 8 someone with number sense may have memorized 56 but they would also be able to work out that 7 x 7 is 49 and then add 7 to make 56, or they may work out ten 7’s and subtract two 7’s (70-14). They would not have to rely on a distant memory. Math facts, themselves, are a small part of mathematics and they are best learned through the use of numbers in different ways and situations."
Whole Number: Number Sense to Operations
Supports include a literature review, developing proficiency with addition, subtraction, multiplication and division documents, examples of developing problems that involve these operations, games and learning tools.
Number Talks and Number Strings
What is a Number Talk?
A Number Talk is a short, daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply and divide.
Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day.
from Number Talks Toolkit, mathperspectives.com
Tools / Resources for Number Talks
Which One Does't Belong is a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong.
Building Number Sense, One Day at a Time.
"Each day of the school year I present my students with an estimation challenge. I love helping students improve both their number sense and problem solving skills. I'd like to share the estimation challenges with you and your students."
Questions and supports for teachers in Gr. 6-8 classrooms to establish productive math talks rountines in their classrooms.
