Mastering the Basic Math Facts: Multiplication & Division

Facilitators

Sherry Johnson & Kelsey French

Objectives

  • To learn about strategies, activities, and interventions to help move students beyond memorization of math facts to mastery.
  • To deepen our understanding and enhance our professional toolkit in meeting the needs of our students.  
  • To work as a vertically aligned professional learning community (PLC) to create a more student-centered math classroom

 

Requirements

  • We will answer  two questions and then comment on at least 2 of the posts made by members of our PLC.
  • In responding to posts, we will clearly state which aspect of our peer’s comments resonated with us and then add additional insights/examples either from the text or classroom experiences.
  • We will endeavor to post in a timely manner so we may maximize our learning time and capitalize on the expertise of members of our PLC.
  • We will earn 16 professional development credits for this book study.

Week 1

Introduction & Chapter 1

 

W1-Q1) Why is mastery of multiplication and division facts important? Are  there types of math facts practice activities that increase or decrease anxiety?

W1-Q2) What are some misconceptions that might cause early confusion for students just starting their study of multiplication? How would you address such misconceptions?

W1-Q3) What types of models might be used to help students visualize multiplication and division? Why might using a variety of models be helpful for students?

W1-Q4) What real-world experiences might make effective multiplication or division problems for students to explore?

W1-Q5) What is a quote or teaching idea that resonated with you after reading pages 1-26? Explain your thoughts? 

 

Week 2

Chapters  2, 3 & 4 (Multiplying by 2, 10, & 5) 

 

W2-Q1) What prior knowledge and skills might help students better understand multiplication of two, ten, or five as a factor?

W2-Q2) How might making connections to money concepts enhance students’ understanding of X10 facts? How might you explore these connections?

W2-Q3) What are the benefits of incorporating children’s literature into math facts lessons? How does a before, during, and after approach enhance the use of children’s literature?

W2-Q4) What type of fact card activities might be effectively used for independent practice or as part of math centers/stations? How could you differentiate such activities?

W2-Q5) What is a quote or teaching idea that resonated with you after reading pages 27-67? Explain your thoughts? 

Week 3

Chapters  5 & 6  (Multiplying by 1 and 0) 

W3-Q1) Why is it that X1 facts can be confusing to understand but easy to memorize? How will you help students to explore the rule for multiplication by one and help them to develop an understanding of why the rule is true?

W3-Q2) Why might drawing pictures to show zero facts be challenging for students? What hands-on explorations could you do in the classroom to help students understand the “zero property of multiplication” (p.80).

W3-Q3) What is the teacher’s role during math games? How might the teacher help students celebrate and track their progress towards fact mastery? 

W3-Q4) The first five sets of facts (X2, X10, X5, X1, X0) are called foundational facts. What is the significance of these facts? Why is this a good time to work on fluency with the foundation facts prior to introducing additional sets of facts? 

W3-Q5) What is a quote or teaching idea that resonated with you after reading pages 69-89? Explain your thoughts?

Mathematical Mindset Book Study

Facilitators

Michelle Bellomy (Grades: K/1), Mary Ellen Truncali ( Grades: 2&3),  Leslie Holderfield ( Grades: 4-5) & Sherry Johnson (Vertical Alignment)

General questions  (vertically aligned) will be posted about the chapters; however, each facilitator will include questions that will greatly enhance our discussion. 

     

Objectives

  • To work as a vertically aligned professional learning community (PLC) to explore the power of mindset and how it is manifested in the elementary math classroom.
  • To gain insights and strategies regarding how to help encourage a growth mindset and to create experiences that will help students to develop strong mathematical mindsets (p.9).
  • We will earn 16 professional development credits for the book study.

Requirements

  • We will read all nine chapters of the texStudents in groups
  • Our goal is to answer  two questions and then comment on at least 2 of the posts made by members of our PLC.
  • You may answer from the general questions posted, but pay attention to the questions/comments posted by your grade level cluster facilitator as well. They will help guide you to deeper reflection and examples as we go through the text.

 

 Chapter 1: The Brain and Mathematics Learning

C1Q1: What are your views regarding this statement?  “Some students are not developmentally ready for certain level mathematics” (p.8). 

C1Q2: When you are teaching math, what comments or behaviors have you noticed that indicate a student may have a growth or fixed mindset?

C1Q3: How may we help parents support the idea of growth mindset in the math classroom?

C1Q4: What are your views regarding this statement?  “Girls quickly pick up on teacher’ negative messages about math” (p.9).

 Chapter 2: The Power of Mistakes and Struggle

C2Q1: Which of the strategies for valuing mistakes resonated with you? What are some other ways to show the value of mistakes?

C2Q2: Do you recall a time when you were a student and you made a mistake, or struggled with a concept? How did your teacher react? How did it make you feel? How do you use that experience  in your classroom or life?

C2Q2: What have you done, or will do, to show parents [and/or student] that “making a mistake is a very good thing” (p. 12).

C3Q4: What are your views regarding this statement? “…if  [teachers] continue to test and grade, they should give the same grade, or higher for mistakes…” (p.17).

Chapter 3: The Creativity and Beauty in Mathematics

C3Q1: What do you find to be creative and beautiful in mathematics?

C3Q2: How is mathematics similar to and different from other subjects?

C3Q3: After reading chapter 3, how would you respond to a parent who asks, ” What is the point of my child explaining their work if they can get the answer right?” (p.28)

C3Q4: What are your views regarding this statement? “School mathematics is not real mathematics” (p.26)

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4: Creating Mathematical Mindsets: The Importance of Flexibility with Numbers

C4Q1: What ideas or quotes from chapter four resonated with you?

C4Q2: Do you have a growth or fixed mindset?  Watch one of the videos below and then share your thoughts regarding the connection between growth mindset and mathematical mindset.

Mindset Quiz: https://www.youtube.com/watch?v=pamzG81yt7g

Developing a growth mindset: https://www.youtube.com/watch?v=aNHas97iE78

C4Q3: After reading chapter 4, how would you respond to a parent who asks, ” But don’t students need a lot of math practice?” (p.42). 

C4Q4: What are your views regarding this statement? Creating a mathematical mindset goes beyond memorization of math facts, it requires “flexibility with numbers” (p. 33), “conceptual engagement” (p.37)  and opportunities to play games (p.51).

 

 

Math Mindset Book Cover

Image of Book Cover

Mastering the Basic Math Facts- Part 2

Our Math PLC

Basic Math Facts

 We will continue to work  as a vertically aligned professional learning community (PLC) to:

1.Create a more student-centered math classroom, where students  are able to select their own tools to investigate math concepts.

2. Add to our professional toolkit, strategies that we may use to differentiate instruction.

Requirements

We will answer  two questions and then comment on at least 2 of the posts made by members of our PLC.

In responding to posts, we will clearly state which aspect of our peer’s comments resonated with us and then add additional insights/examples either from the text or classroom experiences.

We will earn 16 professional development credits for the book study.

 

Week 4 – July 2-8

Chapter 3 – Zero

W4Q1: After reading chapter 3, whether you teach kindergarten or fifth grade, how would you justify the importance of zero in our number system to our students?

Chapter 4 – Adding Ten

W4Q2: Why is adding ten an important foundational skill?

W4Q3: What visual tools might help students better understand +10 facts?

W4Q4: Why are so many activities in the book focused on partner discussion? What are the benefits?

 

Week 5 – July 9 – 15

Chapters 5 & 8 – Doubles and Using Doubles

W5Q1: In what ways will visual experiences help simplify doubles facts? What tools provide effective visuals of doubles?

W5Q2: How might using the terms double and half support or confuse students?

W5Q3: How might you assess fluency for students who struggle with written Fact Checks?

W5Q4: How might you differentiate tasks for different levels of learners to help them use their doubles facts or doubles +1 or doubles +2?

 

Week 6 – July 16 – 22

Chapters 6 & 7 – Making Ten and Using Tens

W6Q1: What games and practice activities might help support automaticity of making and using ten?

W6Q2: How will students’ understanding of tens or the power of ten support them with more difficult facts/tasks?

W6Q3: What activities would be good choices for math fact centers/stations/tubs? Why?

W6Q4: What is the role of language in developing math fact strategies?

 

 

Mastering the Basic Math Facts – Addition and Subtraction

Basic Math Facts

         Objectives

  • To learn about strategies, activities, and interventions to help move students beyond memorization of math facts to mastery.
  • To deepen our own understanding and enhance our professional toolkit in meeting the needs of our students whether it is to close the achievement gap or extend their conceptual understanding.
  • To work as a vertically aligned professional learning community (PLC) to create a more student-centered math classroom where students may select their own tools to investigate math concepts.<p>

 

Requirements

  • We will answer  two questions and then comment on at least 2 of the posts made by members of our PLC.
  • In responding to posts, we will clearly state which aspect of our peer’s comments resonated with us and then add additional insights/examples either from the text or classroom experiences.
  • If there are concepts that are unclear or examples discussed that we would like additional information about, questions may asked of members of the PLC.
  • We will endeavor to post in a timely manner so we may maximize our learning time and capitalize on the expertise of members of our PLC.
  • We will earn 16 professional development credits for the book study.

Introduction & Chapter 1

Answer two of the following questions and then respond to two posts made by members of our PLC.

W1-Q1) Why is mastery of math facts important? What problems have you observed when student do not know basic math facts?

W1-Q2) What have you observed about anxiety related to memorizing math facts? Are there types of math facts practice activities that increase anxiety or decrease anxiety?

W1-Q3) How would you introduce the concept of math facts to your class and justify the need to know them?

W1-Q4) How might attention to the sequence in which facts are introduced support mastery of the facts.

W1-Q5) What real-world experiences might create an effective context for addition or subtraction problems?

 

Week 2

Chapter 2: Plus One and Plus Two

After reading pages 31-50, answer two of the following questions and then respond to two posts made by members of our PLC.

W2-Q1) Reflect on the importance of students’ understanding of the commutative property. In what ways will it support their success?

W2-Q2) Reflect on the inverse relationship between addition and subtraction. How will this early understanding support students’ success as they continue their mathematical journey?

W2-Q3) “Subtraction is a separation or comparison process” (p.33). How could we utilize the model drawings provided by our district to help students grasp this concept?

W2-Q4) After reading pages 41- 50, select an activity/game that you could adopt or adapt to help students build automaticity. Explain how you would introduce it to the class and monitor students’ progress towards mastery.

W2-Q5) What are two literature books that you could use (or have used) to help students develop an understanding of +1/+2 or -1/-2? Provide the title and summary of the text and justify why they are appropriate choices.

Week 3 

Adding Zero and Classroom Management

After reading pages 51-62, answer two of the following questions and then respond to two posts made by members of our PLC.

W3-Q1) Adding and subtracting zero is an abstract concept and might be confusing for some students. What strategies might you use to help students build their understanding of adding and subtracting zero?

W3-Q2) On page 52, there are four “big ideas” presented that will help with our exploration of adding and subtracting zero. Select one of the big ideas and suggest a hand-on or kinesthetic activity that you could use to help support that idea.

W3-Q3) On our campus we are creating student-centered math classrooms in which students are able to self-select the tools they find most useful in helping them to grasp concepts. What routines and procedures will you need to have in place to help students self-select their tools?

W3-Q4) How will you manage math games in your classroom? How will you keep track of students who are experiencing challenges?