How are you inviting your students into the learning for each activity? each lesson? each unit?
What profound ideas to consider, and that invitation is important for all learners to receive, every day.
My favorite ways to engage my mathematicians in the content play directly into the interests of the learners. Sometimes I include a really funny GIF that sparks their curiosity. Other times it’s a pop culture reference or current event that draws them in. Short video clips pique the interest of my students. Or I’ll throw out an interesting or obscure picture to consider. I might pull in some related mathematical expressions to allow students to be purposeful about making connections, while practicing mental math and building their language skills.
One classroom favorite is Which One Doesn’t Belong? In this routine, learners are shown four pictures, each with a reason for being different than the others. The images are sometimes shapes, numbers, equations, graphs, etc., but they are always relevant to the tasks and learning from the daily learning goals. This is their access point, their invitation. I’ll prompt students, “Which one doesn’t belong? Jot down some ideas, then start thinking about why the others are different, too!” After quiet think time, students share in teams, then as a whole class. I challenge students to think of as many reasons as they can! All students participate in some level of sharing. Again, all students are invited to engage and actively participate.
Number Talks are also a solid routine to get students doing mental math in class! Students can draw ideas from what they know or from previous work in the activity to evaluate each expression. The work ties into math coming up in the lesson. Allowing students to justify their thinking in this activity is crucial, and they’ll learn from any misunderstandings each time. Here is a sample of work from a task from Open Up Resources 6–8 Math Grade 7 curriculum authored by Illustrative Mathematics:
Using the Notice and Wonder instructional routine gets us picking out important information, asking unanswered questions, and making solid connections. I show my students an image, graph, table, photograph, or sometimes the task itself, and ask, “What do you notice? What do you wonder?” After quiet think time, ideas are shared and recorded for the whole class to see. The door is open to all possibilities the open-endedness of the routine brings. And the language development is incredible! Students carefully or wildly put together statements that begin with “I notice…” Then they phrase questions to extend their thinking into the unknown parts of the task, which sometimes make us ponder or smile or laugh. All ideas are valid. All thoughts are recorded. All ideas are authored by the students in the room. All students have access and are invited into the learning.
Here is one of my favorites from the Open Up Resources 6–8 Math curriculum authored by Illustrative Mathematics. It can be found as a Notice and Wonder Launch in all three (6–8) grade spans of this resource.
My Grade 7 mathematicians noticed that the pink socks were balanced and the blue were not, the socks are on hangers, and something is in the blue sock on the left! They wondered: Why are the socks on hangers? What is in the blue sock? Are the socks clean? Would they turn purple if you washed them together? We went on to discover solving equations using hanger diagrams, and the socks were a persistent reminder that equations must stay balanced. After this lesson in particular, one of my wide-eyed, curious tweens exclaimed, “This is the most sense a math lesson has made on the first day of learning something!” Mission accomplished.
There are so many resources out there to establish these routines in your classroom. One of the best places to start is with a resources from Achieve The Core, all about mathematical routines. Search the routines or check out Twitter communities, like #MTBoS or #iTeachMath, to find examples and shared ideas. These educators are generous and genuinely enjoy helping and growing the educators in their communities!
When all students have access, when students are engaged, when students are invited to the math table, they’re on their way to making sense of mathematics and finding connections to known and new ideas, while reeling peers into the conversation as well. How are you inviting your students into the learning?
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