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*By Morgan Stipe, a Middle School Maths Teacher. This is an edited version of a Blog published in www.NCTM.org. Morgan refers to format and features of Lessons in this Blog which may be accessed through www.MathsRepublic.com.au*

**How are you inviting your students into the learning within your classroom?**

That invitation is important for all learners to receive from you the Teacher, every day.

My favorite ways to engage my budding 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 also pull in some related mathematical expressions to allow students to be purposeful about making connections, while practicing mental math and building their language skills.

**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 and their invitation. I’ll prompt students by asking:

*“Which one doesn’t belong."*I ask them to 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 maths which is coming up in the lesson.

Allowing students to justify their thinking in this activity is crucial ... they’ll learn from any misunderstandings each time.

Here is a sample of work from a task from a Lesson which can be found in www.MathsRepublic.com.au:

Using the

*instructional routine gets students picking out important information, asking unanswered questions, and making solid connections.*

**Notice and Wonder**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 which 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 a Lesson.

My young mathematicians in my class 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. When all students have access, when students are engaged, when students are invited to the maths 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?**