3rd Grade
Guide to Mastering the Basic Math Facts in Multiplication and Division (O’Connell and SanGiovanni)
Unit 1
Guide for using Mastering the Basic Math Facts in Multiplication and Division: Strategies, Activities & Interventions to
Move Students Beyond Memorization (Susan O’Connnell and John SanGiovanni) as a resource.
Why is this book valuable?
“The purpose of this book is to explore ways to support all students in mastering multiplication and division facts. By
focusing on big ideas, strengthening students’ understanding of math operations, developing strategic thinking, and
providing varied and engaging practice tasks to promote fluency, our students will be better equipped to both
understand math facts and commit the facts to memory. Whether you are introducing students to basic facts, reviewing facts, or providing
remediation for struggling students, this book will provide you with insights and activities to simplify this complex, but critical, component of math
teaching.” (page 12)
Helpful Resources for Teacher Learning
Pages xiii - xiv
Forward – This provides a great justification for why this book is helpful in teaching the basic facts.
Pages 1 - 12
Introduction – This introduction is VERY helpful in explaining how the Common Core expects students to learn
these facts and how the book is sequenced to meet those needs.
It is imperative to read this section to prepare for teaching Unit 2.
Pages 13-26
Chapter 1 – Understanding Multiplication and Division
Many of the Common Core Standards are addressed in this chapter which help us understand the BIG difference
between how we learned the basic facts (“drill & kill”) to how we are expected to teach them (building on
understanding of operations, properties, patterns, and number concepts).
It is imperative to read this section to prepare for teaching Unit 2.
Pages 161 – 162
Conclusion – This provides a very nice overview/summary (depending on when you read it) of the principles
necessary for teaching the basic facts. Reading the conclusion before beginning the unit will be helpful.
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3rd Grade
Guide to Mastering the Basic Math Facts in Multiplication and Division (O’Connell and SanGiovanni)
Unit 1
Important Teacher Notes
Below is the sequence used in the book, which “focuses on the complexity of the number concepts and carefully links each new set of facts to
previously explored facts, building upon students’ prior knowledge” (page 9). Understanding the importance of the sequence of this book is
important and the sequence should be followed to allow our students the best opportunity to master fluency of these basic facts.
 Notice that multiplication and division with factors of 1 and 0 are not in Unit 2 (Multiplication and Division with Factors 2, 3, 4, 5, and 10) or
Unit 5 (Multiplication and Division by Factors of 6, 7, 8, 9. Multiples of 10 up to 90 by Single Digit Numbers). In order to maintain the
sequence of this book, it is suggested that you include 1s and 0s within Unit 2 as listed below. Facts above the bold line should be included
in Unit 2. Facts below the bold line should be included in Unit 5.
(Page 10)
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3rd Grade
Guide to Mastering the Basic Math Facts in Multiplication and Division (O’Connell and SanGiovanni)
Unit 1
Sequence for Teaching Unit 2
Multiplying by…
2
10
5
1
0
3
4
Chapter
Two
Three
Four
Five
Six
Seven
Eight
Page Numbers
27 – 41
43 – 53
55 – 67
69 – 78
79 – 89
91 – 101
103 – 113
Standards Addressed
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.0A.7
3.OA.9
Standards Addressed (in detail)
3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total
number of objects can be expressed as 5 x 7.
3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares,
or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups
can be expressed as 56 ÷ 8.
3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and
equations with a symbol for the unknown number to represent the problem.
*Each chapter may not address all parts of this standard – you may need to include additional opportunities to meet this standard within each chapter
3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes
the equation true in each of the equations 8 x ? - 48, 5 = ÷ 3, 6 x 6 = ?
3.OA.5 Apply properties of operations as strategies to multiply and divide. [Students need not use formal terms for these properties.] Examples: If 6 x 4 = 24 is known, then 4 x 6
= 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of
multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.)
3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
3.0A.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8)
or properties of operation. By the end of Grade 3, know from memory all products of two one-digit numbers.
3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4
times a number is always even and explain why 4 times a number can be decomposed into two equal addends.
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3rd Grade
Guide to Mastering the Basic Math Facts in Multiplication and Division (O’Connell and SanGiovanni)
Unit 1
Guide to Using the CD-ROM
”This CD provides you with a multitude of resources that will simplify your planning and reduce your preparation time as you explore math facts
with your students. The activities can be used as they appear or can be modified to suit your needs.”(page 173)


Features included on CD-ROM
Teaching Resources
 Fact Cards (for targeted student interventions – not a mass
o Featured Resources (shared in chapter)
practice tool)
o Additional Resources (shared in other chapters but
o Large multiplication and division fact cards – teacher
adapted for specific fact set)
use
Teaching Tools
o Small multiplication and division fact cards – student
o Generic tools for any fact set (ex: number lines,
use
multiplication charts, centimeter grids, etc.)
o Triangle fact cards – combined practice of
multiplication and division facts
 Assessment Tools
o (See assessment section below)
“The CD holds a wealth of tools and activities that are classroom-ready and aligned with today’s math standards. You can simply copy them and
begin your lesson. We recognize, however, that our students learn math facts at different rates and struggle with different sets of facts. We know
that it is unlikely that one task will provide the right practice for all of our students. A task that is easy for some is simply too difficult for many
others. Because these CD files are formatted in Microsoft Word, you are able to quickly modify the activities so they are just right for your
students.” (page 174)
Assessment of Fluency – Monitoring Progress
“Several resources are provided (on the CD-ROM) to allow you to assess students’ mastery of the facts. A Math Fact Automaticity Interview
form is included, with directions for conducting student interviews. A Classroom Observation of Automaticity recording sheet, with rubrics, for
conducting classroom observations of automaticity is also included. Three types of Fact Checks are included for each fact set: one focuses on the
targeted set of multiplication facts, one focuses on both multiplication and division within the targeted fact set, and a third provides a mixed review
with current and previously explored facts.
A Fact Check Progress Graph is also included in this section to allow students to graph their own progress. Students shade the bars to show
their number of known facts for each try. Although the graph is designed for Fact Checks with twenty-five facts, remember that it can be modified
for use with larger or smaller quantities of facts. Simply change the numbers in the left column prior to printing out the graph.” (page 174)
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3rd Grade
Guide to Mastering the Basic Math Facts in Multiplication and Division (O’Connell and SanGiovanni)
Unit 1
Assessment of Fluency – Monitoring Progress (continued)
Fact Check VS Timed Test
“Fact Checks are brief, independent fact reviews and are one tool for monitoring automaticity with math facts. The results indicate which
facts are known and unknown, and provide input into whether students are automatically recalling the fact or using other, more time-consuming
strategies to find the answers. Assessing for automaticity does mean that the time taken to complete the task is an important indicator of mastery,
but keep in mind that timed tests can have a negative effect on many students. Although automaticity is a goal, we want to refrain from
comparing one student’s time to another’s time. Rather than setting a time goal that all students’ must achieve, consider using time as a personal
motivator by providing a specific amount of time (e.g., two-and-a-half to three minutes) and challenging students to see how many facts they can
correctly answer in that amount of time, then further challenge them to “beat their own record” on the following attempt. To track their own
progress, students can record the date and the number of math facts answered correctly. These data are invaluable for student-teacher
conferences.” (page 40-41)
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