Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

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...

Curse Reverse Teacher Guide

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Click to download this Teacher Guide for Curse Reverse, a game that builds algebraic expression and patterns skills.  Adaptable for grades 3-7, the game invites students to navigate imaginary sites, u...

Comparing Unit Rates Lesson Plan: Unit Rates

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In this middle school lesson plan students use an interactive simulation called Unit Rates to  compare prices by identifying multiplicative relationships....

Computer Coding Lesson Plan: Creative Coding

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In this lesson plan, adaptable for grades 3-12, students explore BrainPOP resources to learn about topics related to computer coding. Then they’ll show what they know about the topic by completing one...

Digital Citizenship Creative Coding Lesson Plan

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

Newscast Lesson Plan

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Students use JavaScript to create a scrolling news headline to correspond with a video....

Meme Lesson Plan

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Students embellish a video with graphics and text.  ...

Math Skills Lesson Plan: It’s All Fun and Games

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In this math skills lesson plan, which is adaptable for grades 3-12, students work collaboratively to research selected math skills. Students then create, play, and assess a math game that is designed...