Instructional Routines Middle Years

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Instructional Routines

Math is everywhere! We have been using great online resources in our classrooms as routines. When students become familiar with a routine, they learn to navigate their learning because of its predictability. This predictability provides access to learning for all students. With a routine, the instructions are similar, or remain the same, and students can focus on the provocation or task – they can focus on their thinking about the math!

Instructional Routines support curricular competencies across math strands. These provocations can be used as short ‘math talks’ that follow a common discussion framework where the teacher takes on the role of facilitator and students share their reasoning and strategies with one another. Routines and provocations provide an opportunity:

to include regular practice of foundational numeracy concepts
to build a community and culture of learning
to focus on noticing and listening, and being responsive to students’ understandings and reasoning
to provide a focus on the curricular competencies

A discussion framework might look like this:

Instructional Routines Image

Collection of Resources

Website	Link	Description	Prompting Questions
Number Talk Images	http://ntimages.weebly.com/photos.html	Images, dots and number strings to use with number talks	What do you notice? What do you wonder? How many ________? How do you know? How do you see them? Can you see them another way?
Would You Rather?	http://www.wouldyourathermath.com/	Provides students with two options, both of which require basic computation, comparing value, etc.	Which would you rather: Option A or Option B? Explain your reasoning.
Splat!	http://www.stevewyborney.com/	Dot formations with part-unknown including Spats through 10 and 20, multiple splats, fraction splats and variable splats!	What do you notice about the dot pattern? How many? How do you see it? How many are covered by the Splats!? How do you know? What groups are you thinking of?
Fraction Talks	http://www.fractiontalks.com	Simple visuals to foster creative thinking around fractions	What fraction do you see? How do you see the fraction? Are there other sections that are the same size as ___? What other fractions do you notice? If the total area of the shape is ___, what is the area of the shaded section? Can you find two sections that, when combined, equal ____? How might you change the section to create exactly __?
Same or Different	https://samedifferentimages.wordpress.com/	Provocations that provide opportunity for students to learn how to talk about various features of mathematical objects such as quantity, shape, color, orientation, and arrangement.	What do you notice? What questions do you have? What is the same in each image? What is different? What other similarities or differences can you find?
Solve me Mobiles	https://solveme.edc.org/Mobiles.html	Supports algebraic reasoning in a fun and interactive format, elementary-secondary.	What do you notice about the image? What did you think about first? What do you already know? What do you need to find out?
Visual Patterns	Visual Patterns - 1-20	As students build, play, colour code and describe patterns, they build their ability to think about patterns in flexible ways. Working with visual patterns allows students to see authentic connections between concrete patterns and their symbolic representations, such as tables and graphs. Visual Patterns – Mathing Around	What do you notice? What do you wonder? What repeats? How do you see the pattern growing? What comes before/after (100th/Nth)? What affects the relationship in the pattern? How would you describe the pattern (pattern rule)? In what other ways could you record/represent the pattern? How do different representations help us understand patterns? What relationships are/could be expressed in the pattern?
Cube Conversations	Cube Conversations - Steve Wyborney's Blog: I'm on a Learning Mission.	Develops visualization and subitizing, thinking about the number of cubes that make up the structure	How many unit cubes make up this structure? How do you know? How do you see it? How else could you see the quantity? Are there even more ways to think about the structure? How might you see it if you viewed it from a different angle?
3 Act Tasks	http://blog.mrmeyer.com/category/3acts/	Math tasks that consist of three parts: Act One: a provocation, such as a picture and a question; Act Two: a video with further information; Act Three: the reveal. Students discuss their questions and reasoning with one another throughout each act.	What do you notice? What do you wonder? What question could you ask? What estimate is too low? Too high? What is the answer?
Estimation 180	Estimation 180 – Building Number Sense	Estimation and reasoning skills, justifying thinking. Teacher Resources – Estimation 180	What do you notice? Wonder? What is your estimate: how much or how many? How do you know? What was your estimation strategy? Do you want to change your estimate? Why?
Estimation Clipboard	The Estimation Clipboard - Steve Wyborney's Blog: I'm on a Learning Mission.	Develops estimation strategies by showing new information in each slide. Students practice reasoning, visualizing, and explaining their mathematical thinking in partners and with the class.	About how many? How do you know? What changed? Does this change your thinking? How many now? What strategies are you using?
Between 2 Numbers	http://www.between2numbers.com	Middle school investigations for proportionate reasoning	What do you know about each? What do you wish you knew? What number would be too high? Too low? What did you think about when estimating?
Array Chats	https://onedrive.live.com/view.aspx?resid=665A7678364788F3!150&ithint=file%2cpptx&authkey=!AL0kwFGwJ5mF0yg	Photos of arrays around the home to use for number talks	How many? How do you see it? How else could you see it? What equation would match the way that you see it? Is there another equation that would represent how you see it? How many would there be if you could see all of them?
Numberless Word Problems	https://numberlesswp.com/	Helps students to infer and to better understand the underlying structure of word problems.	What math do you see? What do you know? How does the new info change what we know about the situation? What questions could we ask about the situation?
Slow-Reveal Graphs	- Slow Reveal Graphs	Scaffolded visuals to help students make sense of data	What do you notice? Wonder? What information could this graph represent? What might the title be? What is a comparison you could make?
Graphing Stories	\| STEM	Video Provocations that students graph	What is the unit of measure? How does it change? What type of graph would represent the situation? Why? What information do you need in order to create your graph?
Math Visuals	https://mathvisuals.wordpress.com/	Helps students visualize math concepts and also shows how students can create their own visuals	What do you notice? What do you wonder? What is happening in the video? What is the math? How does the quantity or image change? How could you represent the situation symbolically?
Clothesline Math	Clothesline Math – The Master Number Sense Maker	A manipulatable number line activity where students use benchmark numbers to compare and order values and discuss their reasoning.	What benchmark is your value closest to? Why? Where will you place your number? How do you know? Do we need to adjust anything now that a new value has been added?
Menu Math	Menu Math – Beyond the Algorithm	Students create a mathematical object that satisfy a list of constraints.	Help!
Open Middle	https://www.openmiddle.com/	Using the numbers 1-9, one time only, students fill in the blanks to make the equations true.	How did you start? How did you know what to try next? What did you learn from your first attempt? How will your strategy change next time? How do you know if your equation is true?