Strategies for Mastering Math Facts

Strategies for
Mastering
Math Facts
JC Sanders
Education Service Center
Region 13
[email protected]
512.919.5420
Why do you think children struggle with memorizing basic math
facts?
The Problem
They have not been taught _____________________ they can use
for learning their basic facts.
They have continued to practice math facts and take timed tests
instead of developing their _______________ ________________
of the foundations of math.
They lack ____________ ____________ and _______________
to manipulate numbers.
Goal:
Learn ways to develop basic fact fluency in students by constructing
efficient mental tools and using conceptual strategies for fact retrieval.
Define efficient drill.
Grade
1st
§111.3.
1.3
2nd
§111.4.
2.4
§111.4.
2.6
Standard
Objectives
Adopted 2012
(A) model, create, and describe contextual multiplication
situations in which equivalent sets of concrete objects are
joined; and
(B) add up to four two-digit numbers and subtract two-digit
numbers using mental strategies and algorithms based on
knowledge of place value and properties of operations;
(A) recall basic facts to add and subtract within 20 with
automaticity;
(E) explain strategies used to solve addition and subtraction
problems up to 20 using spoken words, objects, pictorial
models, and number sentences;
(D) apply basic fact strategies to add and subtract within 20,
including making 10 and decomposing a number leading to a
10;
(C) compose 10 with two or more addends with and without
concrete objects;
TEKS Connections
Number and operations. The student applies mathematical process
standards to develop and use strategies for whole number addition
and subtraction computations in order to solve problems. The
student is expected to:
Number and operations. The student applies mathematical process
standards to develop and use strategies and methods for whole
number computations in order to solve addition and subtraction
problems with efficiency and accuracy. The student is expected to:
Number and operations. The student applies mathematical process
standards to connect repeated addition and subtraction to
multiplication and division situations that involve equal groupings
and shares. The student is expected to:
Grade
3rd
§111.5.
3.4
4th
§111.6.
4.4
Standard
Objectives
Adopted 2012
(B) model, create, and describe contextual division
situations in which a set of concrete objects is separated into
equivalent sets.
TEKS Connections
Number and operations. The student applies mathematical process
standards to develop and use strategies and methods for whole
number computations in order to solve problems with efficiency
and accuracy. The student is expected to:
(A) solve with fluency one-step and two-step problems
involving addition and subtraction within 1,000 using
strategies based on place value, properties of operations,
and the relationship between addition and subtraction;
(E) represent multiplication facts by using a variety of
approaches such as repeated addition, equal-sized groups,
arrays, area models, equal jumps on a number line, and skip
counting;
Number and operations. The student applies mathematical process (F) recall facts to multiply up to 10 by 10 with automaticity
standards to develop and use strategies and methods for whole
and recall the corresponding division facts
number computations and decimal sums and differences in order to
solve problems with efficiency and accuracy. The student is
expected to:
(A) add and subtract whole numbers and decimals to the
hundredths place using the standard algorithm;
(B) determine products of a number and 10 or 100 using
properties of operations and place value understandings;
(C) represent the product of 2 two-digit numbers using
arrays, area models, or equations, including perfect squares
through 15 by 15;
Grade
5th
§111.7.
5.3
Standard
Objectives
Adopted 2012
(E) solve for products of decimals to the hundredths,
including situations involving money, using strategies based
on place-value understandings, properties of operations,
and the relationship to the multiplication of whole numbers;
(D) represent multiplication of decimals with products to
the hundredths using objects and pictorial models, including
area models;
(C) solve with proficiency for quotients of up to a four-digit
dividend by a two-digit divisor using strategies and the
standard algorithm;
(B) multiply with fluency a three-digit number by a two-digit
number using the standard algorithm;
(A) estimate to determine solutions to mathematical and
real-world problems involving addition, subtraction,
multiplication, or division;
(D) use strategies and algorithms, including the standard
algorithm, to multiply up to a four-digit number by a onedigit number and to multiply a two-digit number by a twodigit number. Strategies may include mental math, partial
products, and the commutative, associative, and distributive
properties;
TEKS Connections
Number and operations. The student applies mathematical process
standards to develop and use strategies and methods for positive
rational number computations in order to solve problems with
efficiency and accuracy. The student is expected to:
6th
Number and operations. The student applies mathematical process
§111.26. standards to represent addition, subtraction, multiplication, and
6.3
division while solving problems and justifying solutions. The student
is expected to:
(D) add, subtract, multiply, and divide integers fluently; and
(E) multiply and divide positive rational numbers fluently.
Explanation
Representation
Addition & Subtraction Math Strategies
Zero Addition
Strategy
Any fact with zero as
an addend
Zero Subtraction
Facts
Any fact with zero as
the subtrahend
Any fact with 1 as an
addend & 2 + 3, 2 +
4, 2 + 5, 2 + 6, 2 + 7,
Count-on Addition
3 + 2, 4 + 2, 5 + 2, 6 +
2, 7 + 2, 5 + 3, 6 + 3,
3 + 5, 3 + 6
Any fact with 1 or 2 as Count-back
the subtrahend
Subtraction
9 – 8, 8 – 7, 7 – 6, 6 –
Difference of 1
5, 5 – 4, 4 – 3, 3 – 2, 2
Subtraction
–1
To Drill or Not to Drill Training
Region 13
Facts
3+
4,
Doubles Plus 1
7+
Addition
9,
Explanation
Representation
Addition & Subtraction Math Strategies
Strategy
Make 10 Subtraction
1 + 9, 2 + 8, 3 + 7, 4 +
6, 5 + 5, 6 + 4, 7 + 3, * Make 10 Addition
+ 2, 9 + 1
10 – 9, 10 – 8, 10 – 7,
10 – 6, 10 – 5, 10 – 4,
10 – 3, 10 – 2, 10 – 1
3 + 2,
5, 5 +
6 + 7,
7, 8 +
Doubles Subtraction
1 + 1, 2 + 2, 3 + 3, 4 +
4, 5 + 5, 6 + 6, 7 + 7,
Doubles Addition
8 + 8, 9 + 9, 10 + 10
2 + 3,
3, 4 +
6 + 5,
8, 8 +
2 – 1, 4 – 2, 6 – 3, 8 –
4, 10 – 5, 12 – 6, 14 –
7, 16 – 8, 18 – 9, 20 –
10
1 + 2,
4, 4 +
5 + 6,
6, 7 +
9+8
To Drill or Not to Drill Training
Region 13
9 – 6, 8 – 5, 7 – 5, 6 –
4, 5 – 3, 8 – 6, 9 – 7
7 – 3, 7 – 4, 9 – 5, 9 –
4, 11 – 5, 11 – 6, 13 –
6, 13 – 7, 15 – 7, 15 –
8, 17 – 8, 17 – 9
10 Minus 1 Addition
Difference of 2 or 3
Subtraction
Doubles Plus 1
Subtraction
Explanation
Representation
Addition & Subtraction Math Strategies
Any fact with 9 as a
addend
Minus 10 Plus 1
Subtraction
Strategy
Any fact with 9 as the
subtrahend
Difference of 9
Subtraction
Facts
11 – 2, 12 – 3, 13 – 4,
14 – 5, 15 – 6, 16 – 7,
17 – 8
To Drill or Not to Drill Training
Region 13
–
–
–
–
Facts
11
12
12
14
–
–
–
–
4,
4,
7,
6,
11
12
13
14
–
–
–
–
Strategy
10 Plus More
Subtraction
Explanation
Representation
Addition & Subtraction Math Strategies
3,
5,
5,
8
4 + 7, 4 + 8, 5 +
8, 6 + 8, 7 + 4,
Make 10 Plus More
8 + 3, 8 + 4, 8 + Addition
6
8,
7,
8,
8,
3 + 8,
7, 5 +
7 + 5,
5, 8 +
11
11
12
13
To Drill or Not to Drill Training
Region 13
Multiple Representations
Draw an equal groups model for 5 ×3
Draw an array for 5 ×3
Draw an area model for 5 ×3
Draw a number line for 5 ×3
Any fact with 2 as a
factor or a divisor
Any fact with 1 as a
factor or a divisor
Any multiplication
fact with zero as a
factor
10’s Facts
2’s Facts
1’s Facts
0 Facts
Explanation
Representation
Multiplication & Division Math Strategies
Any fact with 10 as a
factor or a divisor
5’s Facts
Strategy
Any fact with 5 as a
factor or a divisor
Square Facts
Facts
Any fact where the
factors are the same
or the divisor and
quotient are the same
To Drill or Not to Drill Training
Region 13
Any fact with 6 as a
factor or a divisor
Any fact with 3 as a
factor or a divisor
Any fact with 9 as a
factor or a divisor
7’s Facts
6’s Facts
3’s Facts
9’s Facts
Explanation
Representation
Multiplication & Division Math Strategies
Any fact with 7 as a
factor or a divisor
4’s Facts
Strategy
Any fact with 4 as a
factor or a divisor
8’s Facts
Facts
Any fact with 8 as a
factor or a divisor
To Drill or Not to Drill Training
Region 13
Resources
Double ten-frame
0
1 2 3 4
5
6 7
8 9
10
11 12 13 14
15
16 17 18 19
20
Hundreds Chart
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© 2008 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Place Value Chart
thousands
hundreds
tens
ones
References
Van de Walle, John A. (2006). In Teaching Student Centered Mathematics Grades 3 -5.
Boston: Pearson Education, Inc. ISBN 0-205-40844-3
Fosnot, C. (2001). Young Mathematicians At Work. Constructing Number Sense .
Burns, M. (2007). About Teaching Mathematics: A K-8 Resource. Math Solutions
Publications. Sausalito, CA.
O’Connell, S. & SanGiovanni, J. (2011). Mastering the Basic Math Facts in Addition and
Subtraction: Strategies, activities, & interventions to move students beyond
memorization. Heinemann. Portsmouth, NH.
Schielack, J. (2009). Focus in grade 3: teaching with curriculum focal points. (pp. 01-23).
United States of America: National Council of Teachers of Mathematics. DOI:
www.nctm.org
Schielack, J. (2009). Focus in grade 4: teaching with curriculum focal points. (pp. 01-11).
United States of America: National Council of Teachers of Mathematics. DOI:
www.nctm.org
Woodward, John. (2004). Fact Fluency & More: Addition, Subtraction, Multiplication &
Division Computational Skills Practice. Sopris West Education Services.
How can the
FACTastic Math Strategy
System help your students
master the basic math facts?
The FACTastic Math Strategy System creates an engaging
way to teach your students math facts by providing strategies
for solving problems rather than expecting students to rely on
memorization. Each card in the set contains a visual cue around
a strategy for solving math facts.
These cards are also helpful for parents to continue their
children’s learning at home!
The FACTastic Math Strategy system includes:
• over 25 Strategies
• over 400 Strategy Cards
• instructional player’s guides on how to introduce and work
with each strategy
• suggestions for effective practice
Available sets include:
• Addition/Subtraction Edition
• Multiplication/Division Edition
See the FACTastic Math
Strategy Cards in action!
Scan the QR code or view a
video about using the cards in
your classroom.
Complete your FACTastic
Math Strategy System
with the Multiplication/
Division Edition!
To order, visit http://store.esc13.net!
For more information, contact
JC Sanders, 512.919.5420, [email protected]

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