Number Talks

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Angela Kraft, Oconomowoc, WI,

Do you have students who still struggle with memorizing multiplication facts or still use their fingers to find quick calculations? Or, have you ever had a student struggle to explain their thinking by saying, “Well, I know how I got it, but I can’t explain it.” While finger counting has its place in the math classroom, so does helping students to visualize calculations and patterns mentally. As a participant in the Teacher Redesign Corps (TRC) 3.0 I have been implementing number talks as often as possible with my 7th graders. My goals during these short sessions are to help students build mental calculation strategies and develop effective articulation of processes.

With effective communication among peers being the heart of CPM’s design, students need to be able to effectively explain their thinking to solve problems, as well as be able to listen and understand someone else’s ideas. In their book Making Number Talks Matter, Cathy Humphreys and Ruth Parker stress the importance of allowing the students to do the thinking rather than the teacher listing strategies for students to imitate. They explain in detail how to implement number talks and why they are so important. In short, number talks are quick problems that can be infused in any part of a math lesson.

A number talk can be implemented very easily and quickly. Simply post a problem you would like your students to mentally calculate. For example 18 x 5. Ask students to place a fist on their chest and raise a thumb when they have a solution. During your wait time, encourage students to try and solve the problem in more than one way. Students can indicate this by raising fingers from their fist as well. Once most students have arrived at an answer, ask a volunteer to share their solution. I find it helpful if you ask for all answers before asking students to explain their strategies. Then ask volunteers to explain their thinking on how they arrived at their answer. This can be the tricky part. As they explain, you, as the teacher record their strategy on the board being careful to not fix mistakes in the explanation or finish the strategy for the student. If a student is struggling, provide wait time to see if he/she can find the correct words to complete the explanation or ask probing question to assist the student along.

I have become such a fan of these quick number talks that I now implement them weekly, Number Talk Tuesday! My students look forward to these each week and I am amazed at how well my students have evolved at articulating their strategies. I have even begun to see this transfer to their daily teamwork where students have been much better communicators. They are also able to build number sense, recognize patterns in mathematics, and be exposed to the multitude of representations students use to mentally calculate problems. As a matter of fact, I had one class of 24 students be able to provide 12 different strategies for solving 18 x 5! Why not give one a try today!

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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.