Representing Math Thinking Using Manipulatives

Students represent mathematical ideas and relationships and model situations using tools, pictures, diagrams, graphs, tables, numbers, words, and symbols. 

Tools, like concrete and digital manipulatives, support student learning of mathematical concepts.  Manipulatives are concrete objects that can be viewed and physically handled by students in order to represent mathematical ideas and relationships and demonstrate or model abstract concepts.

   

The use of tools and representations supports a conceptual understanding of mathematics at all grade levels.

Chosen carefully, tools and representations provide a way for students to think through problems and then communicate their thinking. Tools and representations explicitly and visually represent math ideas that are abstract. When paired with discussion, they help to demonstrate concepts and thinking.

Concrete

Pictorial

Abstract

Learn more about Tools and Representations here.

High-Impact Instructional Practices in Mathematics

While students work with concrete manipulatives, teachers find it helpful to be able to visually share the manipulative in use.  There are many virtual manipulatives available online; each having its strengths and limitations. Here are some examples that LKDSB Teachers and students regularly access.

Check them out.  Which ones work for you?

Manipulative	Division	Take Note
Mathies Learning Tools	Primary  Junior Intermediate	Introducing math concepts, Number Talks, Virtual supports Teacher Tip Sheets are excellent
Math Learning Centre Math Apps | The Math Learning Center	Primary  Junior Intermediate	Shareable links and Virtual worksheets save as pictures or copy individual links to hand in iPad: Each Manipulative is a unique app
Mathigon Polypad – Virtual Manipulatives – Mathigon	Primary  Junior Intermediate	The ‘For Teachers’ tab has some great resources: Activities and Lesson Plans
Toy Theater Virtual Manipulatives | Mathematical Modelling | Toy Theater	Primary  Junior Intermediate	Fun games to support Math concepts, Easy to use  Free
Didax https://www.didax.com/math/virtual-manipulatives.html	Primary  Junior Intermediate	Instructional Videos and activities available
Desmos Desmos	Junior Intermediate	Teachers create a free account to access activities(use a code like Kahoot). Ready-made lessons are available. Teachers can control the pace.  Real-time view of student work and easy sharing. Can anonymize names.