Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

## Creature Caverns Teacher Guide

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Click to download this Teacher Guide for Creature Caverns, a flexible, sandbox-style game that challenges students to analyze patterns in tables and graphs. Adaptable for grades 4-7, students create a...

## Agrinautica Teacher Guide

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Click to download this Teacher Guide for Agrinautica, a flexible, sandbox-type game featuring pre-algebra skills, including mathematical expression-building and order of operations. Adaptable for stud...

## Exploring How Light Behaves at Boundaries Lesson Plan: Bending Light

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In this lesson plan, adaptable for grades 6-12, students use an interactive simulation called Bending Light to explore the bending of light between two media with different indices of refraction. Stud...

## Projectile Investigation Lesson Plan: Projectile Motion

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In this middle school lesson plan, students use an interactive simulation called Projectile Motion to design and conduct their own experiment....

## Introduction to Pendulums Lesson Plan: Pendulum Lab

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In this middle school lesson plan developed by our partner, PhET, students use an interactive simulation called Pendulum Lab to design controlled experiments to identify how variables affect the motio...

## Series and Parallel Circuits Lesson Plan: Circuit Construction Kit DC

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In this lesson plan, adaptable for grades 6-12, students use an interactive simulation called Circuit Construction Kit: DC to construct series and parallel circuits and qualitatively explore their cha...

## Computational Modeling Lesson Plan: Marvelous Models

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In this lesson plan, adaptable for grades 5-8, students play Marvelous Models, a game that challenges them to create models from scratch. Through play, students gain insight into a system through the ...

## Molecule Arrangement Lesson Plan: Crystal Cave

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In this lesson plan, adaptable for grades 5-8, students play Crystal Cave, a game that challenges them to arrange molecules of different shapes and properties into an ordered, stable configuration. Th...

## Digital Citizenship Creative Coding Lesson Plan

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Students show what they know by coding a project....

## Forming Ionic Compounds Lesson Plan: Collisions Ionic Bonding

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This lesson plan, adaptable for grades 5-8, features the game Collisions: Ionic Bonding. The game challenges students to build ionic compounds that satisfy target ratios. As they move up levels, the c...