Instructional Routines

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Notice/Wonder

Start problem-solving without the problem. Leave off the question, give students a math situation, graph or image and ask them: "What do you notice? What do you wonder?" 

• The 5 minute video Ever Wonder What They'd Notice by Annie Fetter is an inspiring introduction to the routine,
• Begin to Problem-Solve with I Notice, I Wonder is brief 2-page overview of the routine created by of the Math Forum. 
• What's Going On In This Graph is a collection of graphs and charts gathered by the NY Times to use with Notice/Wonder. 

Visual Patterns are a great way to utilize patterns to encourage making use of structure in problem-solving. Students make observations and build on those observations to generalizations.

Visual Patterns is a collection of hundreds of visual patterns gathered by Fawn Nguyen. There are patterns that can be used to explore linear function, quadratic functions, cubic functions, 

For some ideas about how to use visual patterns with adult students, including handouts and a lesson plan, read Developing Algebraic Reasoning Through Visual Patterns

Mathigon has a visual pattern tool that can help make students' thinking visible to classmates and teachers.  

Here are the first 3 steps of a visual pattern.

What comes next?

Estimation 180

Estimation 180 is a collection of engaging photos and short videos developed by Andrew Stadel. The visuals are used as estimation challenges (like the one to the right) that help students develop their number sense through reasoning, multiple estimation strategies, explaining their ideas, connecting to different math content, and reflecting on the process. 

To learn more about using Estimation 180 with adult education students:

• Read Number Sense: Helping Adult Students Close the Gap 
• Watch Some Numbers Walk into a Language Class: Estimation 180

Order the glasses from least to greatest

Which One Doesn't Belong?

With this instructional routine, teachers present four of something (like the 4 numbers to the right) and ask students to come up with reasons why each doesn't belong. 

The website Which One Doesn't Belong? (WODB) is a collection of Numbers, Shapes, and Graphs to explore, curated by Mary Bourassa, inspired by the book Which One Doesn't Belong by Christopher Danielson. Start there or create your own! 

What makes each of these numbers different from the other three?

Slow Reveal Graphs

Slow Reveal Graphs refers to a process for using graphs with students that promotes sense-making. You start with a graph and peel back the layers until you have a numberless graph that every student can make observations about. Then you add back the layers, step by step, encouraging students to make sense of the graph and engage with the story of the graph. 

Slow Reveal Graphs is a collection of slow reveal graph sequences organized by type of graph as well as by context. The site is curated by Jenna Laib