BASIC FACTS
Basic Facts
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What are they?
Why should students memorize basic facts?
Why Basic Facts Instruction?
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Frees up working memory to master algorithms and
math applications.
Cognitive psychology research points to the value
of automatic recall of facts.
Students who do not memorize facts flounder when
more complex math is introduced—progress for
these student can end at elementary school.
Math Wars
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(Strauss, Washington Post, Jan. 05)
Among the topics the NCTM and the mathematicians said
they agreed on:
 Heavy reliance on calculators in the early elementary
grades is a bad idea.
 Elementary school children must have automatic recall of
number facts, meaning that, yes, they have to memorize
multiplication tables.
 Children must master basic algorithms. The meeting
participants spent time defining the word
"algorithm,"which means a set of rules for solving a
problem in a finite number of steps.
Teaching Math Facts
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Three types of instructional activities:
 Understanding
 Relationships
 Memorization
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What are these activities? Why?
Relationship Activities
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Exercises based on a series (e.g., 3x1, 3x2, 3x2)
Exercises based on fact families and inverse
operations (e.g., 5-2=3, 5-3=2, 2+3=5, 3+2=5)
Purpose of these exercises is to make memorization
easier
Preskill for Relationships
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Plus-one Facts—Format 6.1, page 90
 Teaches
facts and relationships.
 Rule: When you plus one you say the next number.
 Model Part A and B.
Plus-one Facts
Part C
8+1
4+1
7+1
5+1
9+1
(Your turn—format practice!)
Series Saying
Prompts students to notice the counting relationship:
6+2=8
5 x 2 = 10
7+2=9
5 x 3 = 15
8 + 2 = 10
5 x 4 = 20
5 x 5 = 25
Series Saying
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Format 6.2 Model and Practice
 Part
A:
 Part B:
Erased
 Part C:
 Part D:
Reading the Statements
Reading the Statements with the Answer
Saying the Statements (No visual prompts)
Random Fact Drill
Series Saying
Format 6.2 Model and Practice
Teaching behaviors:
 3-2 seconds per statement
 Timing for each statement
 Practice, practice, practice and make it fun!
 Correction for slow pace—lead and work on
increasing the pace
 Correction for statement error?
Three Number Fact Families
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Sets of three numbers from which students can
create 4 statements.
Either—addition and subtraction or multiplication
and division.
Teach commutative property of addition (a + b = c
and b + a = c) and multiplication (a x b = c and b
x a = c).
Why is the commutative property important?
Three Number Fact Families
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Format 6.3
Part A—how to construct pairs (big number introduced)
 Part B—oral test on the “reverse” fact
 Part C—worksheet, filling in the big number and
generating the two facts
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Three Number Fact Families
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Format 6.4
Family of Facts for Subtraction and Division. Teaches
students how to generate 4 statements (2 addition and 2
subtractions or 2 multiplication and 2 division).:
 2 x 5 = 10, 5 x 2 = 10, 10/5 = 2, 10/2 = 5
 Students learn the rule: when you subtract (or divide),
you always start with the big number.
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Three Number Fact Families: Model and
Practice
•
____ + ____ = _____
____ + ____ = _____
____ - ____ = _____
____ - ____ = _____
Sequencing Introduction of Facts
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Systematic, cumulatively introduction of facts—
Figures 6.2, 6.3, 6.4, and 6.5.
Separate similar facts
Teach easier facts first
Teach related facts together
Reverse of specific series taught soon after initial
series
Sequencing Introduction of Facts
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Systematic, cumulatively introduction of facts—
Figures 6.2, 6.3, 6.4, and 6.5.
Figures indicate the order in which to teach facts
and the format to use for each set.
A set is presented for several days then included on
memorization worksheets.
Sequencing Introduction of Facts
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Addition facts are introduced first.
Little research is available to guide us regarding
when to introduce subtraction facts—after addition is
completed—after part of addition is mastered and
extend to subtraction?
Recommendation—delay subtraction until students
have learned about half of the addition facts (Sets am addition mastered). Then alternate—Subtraction A,
Addition N, Subtraction B, Addition O, etc.
Sequencing Introduction of Facts
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When to start multiplication?
 Start
in third grade even if students are still working on
addition and subtraction.
 Provide a “double dose” of facts instruction for students
who need it.
Mastery Activities
Programs for Fact Memorization include:
1.
2.
3.
4.
5.
6.
A specific performance criterion
Intensive practice on new facts
Systematic practice on previously introduced facts
Adequate allotted time
A record keeping system
A motivation system
Performance Criterion
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Oral criterion: saying an entire fact every 2 seconds
Written criterion: 2/3 rate at which student is able
to write digits
 How
do you determine students’ writing rate?
Performance Criterion
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40 facts per minute is the low end of fluent
performance.
However, common expectation around the country
is100 facts in five minutes.
Otter Creek Institute
(Don Crawford)
Intensive Practice
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Instruction of new facts using relationship activity
Oral practice on new facts
Written practice on new facts and old facts
Adequate Allotted Time
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Approximately 10-15 minutes per day
Preferably, time in addition to math instructional
time
Before school, during lunch recess, after school etc.
Record Keeping System
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Purpose: monitor student progress
Recommendation: keep paperwork at minimum—
see Student Record Form on page 86
Motivation
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Integrate with record keeping system
Motivation comes with SUCCESS
Teacher’s responsibility to set students up for
success: Must teach facts
Two Fact Mastery Programs
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Homogeneous Group Program
Teacher Led – Group Oral Practice
 Materials
 Pretesting
 Timed test
 Record keeping/Motivation
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Materials
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Written fact practice worksheet divided in half
Smaller number of facts to master at once
One minute timings (more than once?)
Top half: Practice on new facts – current set and two
previously introduced sets
Bottom half: Current fact set presented twice; practice
on previously introduced sets
Pretest
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Develop a written pretest with all 100 facts of one
operation.
Allow the students 2 minutes to work as many
problems as they can.
30 facts per minute—start at set G
45 facts per minute—start at set M
60 facts per minute—start at set R
>85 test on next operation
Oral Group Practice
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Using the worksheets—oral drill of top part saying
the problem and answer in unison
Repeat the first line until students can answer
correctly at with about 2 seconds think time
Model and Practice
Timed Test
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Bottom half of the worksheet
About 1 min. 15 seconds
Mastery Criteria
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If ¾ or more of the students got 28 of 30 facts
correct go on to the next worksheet.
If not, repeat the same worksheet.
Two Fact Mastery Programs
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Heterogeneous Group Program
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Partner Practice
Materials: folders for each student with their level of worksheet (one
folder with answers and one without)
Pretesting: same
Timed Test
Record keeping/Motivation
Modifications
Two Fact Mastery Programs
Heterogeneous Group Program
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Daily Routine:
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Pairs at same level, one with answers
Each student practices the worksheet twice, saying the problem and
the answer
If student makes an error the partner with the answer sheet corrects
Teacher times for 1 ½ minutes on the top and one minute on the
bottom
Written test—Bottom half of worksheet
Compare/Contrast
Traditional Programs
1)
2)
3)
Not teacher-directed
Length of time to
mastery
Not cumulative
Effective Programs
1)
Teacher-directed
(Oral practice)
2)
3)
Quicker mastery of
smaller sets
Cumulative introduction
and review
Resources
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Math facts at: http://depts.washington.edu/facts/
(files are huge but free)
Otter Creek Institute
Mastering Math Fact Families
 http://www.oci-sems.com/home.htm
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