by Jennifer Bay-Williams and Gina Kling

This ASCD Study Guide is designed to enhance your understanding and application of the information contained in *Math Fact Fluency: Sixty Plus Games and Assessment Tools to Support Learning and Retention*, an ASCD book written by Jennifer Bay-Williams and Gina Kling and published in January 2019.

You can use the study guide before or after you have read the book, or as you finish each chapter. The study questions provided are not meant to cover all aspects of the book, but, rather, to address specific ideas that might warrant further reflection, attention, or action.

Many of the questions contained in this study guide are ones you can think about on your own or in a small group, but you might consider facilitating a larger group with others who have read (or are reading) *Math Fact Fluency.*

- What was your definition of fact fluency before starting to read this book? What is your working definition of fact fluency at this point?
- The word strategy (or strategies) is used more than 60 times in this short chapter! Why are strategies important to learning math facts? How do you use reasoning strategies in your teaching and assessing of math facts? How might you use them?
- Discuss the three phases of basic fact mastery (Fundamental 2). Why is it important for students to have sufficient time in Phase 2? Why do you think so many supplemental "quick fix" programs neglect Phase 2?
- How do the flexible learning progressions (Figures 1.2 and 1.3) correspond to your current sequencing of math fact instruction? How might these progressions be used to support teaching and assessing math facts?
- Do you agree with the authors' five fundamentals of fact fluency? Which ones resonate with you the most? What questions do you have?
- What are your school's current expectations for students' fact fluency and mastery? What are you hoping to learn in this book to support your efforts to effectively teach math facts? Discuss and record your expectations and hopes. As you continue to read each chapter, revisit what you wrote and connect these expectations with the ideas in the chapter.

- Which learning activities from this chapter (storytelling, quick looks, etc.) are you currently using? Which activities were new to you? How might you integrate new activities into your math fact teaching?
- How do you, or how might you, use quick look images to support subitizing and fact fluency? How might the steps outlined on pages 15–16 inform your use of quick looks?
- To what extent do you feel your students have the opportunity to master (reach automaticity) foundational facts before they begin to learn the rest of the facts and fact strategies? If the answer is "insufficient," discuss how you might change the sequencing and timing of content in your curriculum to ensure sufficient time and space for students to master their foundational addition and subtraction facts.
- How do games support mastering foundational addition facts? Which games might you use and how will you use them (e.g., whole class, centers, send home)?

- What are the derived fact strategies for addition? How do they compare in terms of the way students think about each?
- The authors suggest that
*sequenced*quick looks with double ten frames encourage students to develop strategies while still maintaining ownership of the strategies. What is meant by "ownership" of strategies? Why might that be important? How might you integrate sequenced quick looks into your fact strategy instruction? - The authors identify potential "pitfalls" that can occur when fact strategies are introduced. Which of these pitfalls have you experienced? How might you avoid them in the future?
- Why is it important to include Using 10 as a Benchmark and not just Think Addition in teaching strategies for subtraction facts?
- What differences do you notice between the games for foundational facts and the games focused on derived fact strategies?
- Which games might you use for early experiences in practicing strategies for addition or subtraction? Which games might you use for ongoing practice once students have more facility with the strategies?
- What ideas do you have for adapting, extending, differentiating, or in other ways implementing the games in this chapter?

- The authors argue that developing a strong understanding of the meaning of multiplication as equal groups is critical for fact fluency development. What are some ways teachers can encourage students to think deeply about the meaning of multiplication as they learn their facts?
- In what ways can quick looks be used to support students' understanding of multiplication?
- The authors explain that skip counting lies within Phase 1, yet students may resort to skip counting, especially with 5s. Why is this problematic? How can we help students move away from counting to using strategies (Phase 2)?
- Multiplication facts are often introduced in order of factor size (0s, 1s, 2s, etc.). The authors suggest beginning with 2s, 10s, and 5s, then focusing on 0s and 1s. Why?
- Games are suggested for each fact set; for example, Squares Bingo for practicing multiplication squares. Which of these games can be adapted and used for other fact sets (and how would you adapt them)?
- This chapter is based on the idea that students reach automaticity with foundational facts (2s, 10s, 5s, 0s, 1s, and squares)
*before*working on other facts. In what ways is this sequence reflected in your multiplication fact sequencing? - As the authors share in the summary, the foundational facts need to be taught in a cumulative manner so that students don't forget one group once instruction has moved to another. In what ways might you use stories, quick looks, and games (in this chapter and beyond) to ensure that students continue to practice and talk about learned facts as they continue to explore more facts?

- What are the derived fact strategies for multiplication? How do they compare in terms of the way students think about each?
- In what ways are these strategies introduced in your curriculum? Which strategies might you add? What instructional techniques might you use to ensure students become adept at using these reasoning strategies?
- Figures 5.4, 5.5, and 5.6 share how students might think about derived fact strategies. What are the benefits of having students share their thinking? How might you provide regular opportunities for such talk to occur?
- The authors explain that using strategies with multiplication is more complicated (adding or subtracting
*groups*) than with addition. In what ways do visuals (e.g., quick looks with equal groups or arrays) support student reasoning? How might the visuals be connected to symbolic notation? - As the authors share, the only strategy for division is Think Multiplication. Which of the games in this chapter engage students in thinking about division (see the list of games on pp. ix–xi for reference)? How might you integrate division facts more effectively into the teaching of multiplication facts?
- Which activities and games will you use with students as they are just beginning to explore and practice a strategy? Which activities and games will you use after they have more facility with the strategies?
- Which games might you use to support practice with
*all four*operations? - Most games are easily adapted to other contexts. For example, the addition game Lucky 13 (Game 11) could become Lucky 50 and be used for multiplication facts. Which games from the previous chapters might you adapt to focus on multiplication or division?
- Beyond being able to use each strategy, students need opportunities to decide on which strategy they will want to use (and when). What might you do to provide these opportunities?

- Reflect on the tools you have used to assess math facts. Which components of fluency (flexibility, accuracy, flexibility, and appropriate strategy use) were assessed?
- The authors argue that timed tests are detrimental for a variety of reasons. What points do they make? Do you agree? Why do you think timed tests are still used?
- As an alternative to timed tests, the authors suggest using observation tools while students are engaged in games or activities. Which observation tool(s) might you use? How might you adapt them?
- What is the difference in an interview focused on strategies and an interview focused on automaticity? What purpose might each serve in supporting students' journey to mastery of their facts?
- What are the pros and cons of an observation tool (all student data recorded on one page) and a student's interview record (each student's data recorded on their own page)?
- How might the rubrics suggested help you monitor each student's progress toward mastery? How might the rubrics be useful in communicating with a principal, parent, or other school personnel?
- What aspects of fluency can be assessed through journals? What are the benefits of using journals as a way to learn and as a way to assess?
- The authors suggest a variety of ways to incorporate self-assessment. What are the benefits of self-assessment? Which ideas have you tried or might you try?
- Reflect upon the many tools suggested in this chapter to assess foundational facts. Which ones will you incorporate and how?

- The observation tools focus on fact sets as well as reasoning strategies. Why are both important? Which observation tools might you use for each purpose? How might you adapt them?
- What will you have students do so that you can observe what you intend to observe? Work with your colleagues to generate a list of facts games, journal prompts, or other activities, that are useful individual, partner, or small-group tasks for what you hope to observe.
- The authors discuss how interviews are diagnostic and therefore can help teachers determine
*why*a student is struggling to learn a strategy or a particular fact. Why might a student struggle to use a Making 10 strategy? Adding a Group strategy? - How does the data collected through interviews compare to the data gathered from written tests with respect to the four components of fluency?
- How do in-the-moment interviews compare to one-on-one? Which protocols or ideas have you used or might you use?
- Orchestrating interviews is more complicated than giving a test. What ideas do you have for managing interviews? How might you leverage support structures (parent volunteers, math specialists, substitute teachers, etc.) to make interviewing a key component to your assessment plan?
- How might you use mastery or fluency records to chart each student's learning of math facts? How might this be shared with students and their parents?
- In both Chapters 6 and 7, facts sorts (either with real bowls or a placemat with pictures of bowls) are recommended. How do facts sorts support student self-assessment? Formative assessment? How might you use this idea?
- What insights can be gained from journal writing and self-assessments when working on derived fact strategies?
- Which of the assessments described in Chapters 6 and 7 might provide valuable artifacts to share with families about their child's progress in developing an understanding of number relations, math fact strategies, or mastery of facts?

- This chapter shares a number of myths and facts that people commonly express regarding basic facts instruction and assessment. Which myths and facts have you heard at your school? Do the suggestions in the book help to address those?
- The notion of messaging is discussed in this chapter. What have been the strengths in your messaging? What are some ways you might add to or change your messaging?
- The authors argue that math (numeracy) must receive the attention literacy receives at major parent events. How might you incorporate numeracy or math facts in kindergarten orientation? Back-to-School Nights? Family Math Night?
- The authors offer the example of sending home a game in a baggie at kindergarten orientation. Reflect on the games in this book. Which game would you like to send home at your Back-to-School Night? Why that game?
- How will you ensure that parents are using positive messaging with their children?

*Math Fact Fluency: Sixty Plus Games and Assessment Tools to Support Learning and Retention* was written by Jennifer Bay-Williams and Gina Kling. This 190-page, 7-7/8" x 9-7/8" book (Stock #118014; ISBN-13: 978-1-4166-2699-2) is available from ASCD. Copyright © 2019 by ASCD. To order a copy, call ASCD at 1-800-933-2723 (in Virginia 1-703-578-9600) and press 2 for the Service Center. Or buy the book from ASCD's Online Store.

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