Part of a University of Toronto website, this page defines and describes deductive and inductive reasoning in solving mathematical problems.

The purpose of this task is to ask learners to reason about solutions without explicitly solving them to get them to understand what it means for a number to be a solution to an equation. Aligns with A-REI.A.

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree, taking into account the tree size and the density of the leaves. Aligns with...

Students are shown six equations and must identify those that have the same solution and give their reasoning, without depending on actually solving them. This task encourages students to look for structure when comparing equations and...

Biographies of Blacks in mathematics from the 1700s to the present time.

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout. Aligns with N-Q.A.3, N-Q.A.1, and N-Q.A.2.

This task examines the rigid motions which map a rectangle onto itself. The emphasis here is on careful reasoning using the definitions of reflections and rotations. Aligns with G-CO.A.3.

The purpose of this task is for students to sort the same set of objects according to different attributes and to practice counting to tell the number of objects in a set. The teacher should accept any way the child wants to sort the...

This task asks students to analyze a set of data about the height of a basketball for each time it bounces. They choose a model that reasonably fits the data and use the model to answer questions about the physical context. This second...

In this task about parking lot rates, students investigate what a function is and explain their reasoning. Aligns with F-IF.A.1.

In this task involving temperature conversions, students construct a linear function given two input-output pairs, investigate the inverse of a linear function, and reason about quantities and/or solving a linear equation. Aligns with...

This task will provide insight to teachers on students' level of understanding when reasoning about a problem. The task asks students to examine whether the sum of two numbers that are multiples of 6 produces another multiple of 6....

A discussion of Christian Huygens' contribution to wave optics, and particularly to our understanding of the reflection and refraction of light. Excellent diagrams and a geometric proof on why the law of reflection is mathematically...