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BASIC FACTS
Basic Facts
What are they? Why should students memorize basic
facts?
Why Basic Facts Instruction? 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 (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
Three types of instructional activities: Understanding Relationships Memorization
What are these activities? Why?
Relationship Activities
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
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 C8 + 1 4 + 17 + 15 + 19 + 1(Your turn—format practice!)
Series Saying
Prompts students to notice the counting relationship:
6 + 2 = 8 5 x 2 = 107 + 2 = 9 5 x 3 = 158 + 2 = 10 5 x 4 = 20
5 x 5 = 25
Series Saying
Format 6.2 Model and Practice Part A: Reading the Statements Part B: Reading the Statements with the
Answer Erased Part C: Saying the Statements (No visual
prompts) Part D: Random Fact Drill
Series Saying
Format 6.2 Model and PracticeTeaching 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
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
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
Three Number Fact Families
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.
Three Number Fact Families: Model and Practice
____ + ____ = _________ + ____ = _________ - ____ = _________ - ____ = _____
Sequencing Introduction of Facts
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
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
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 a-m addition mastered). Then alternate—Subtraction A, Addition N, Subtraction B, Addition O, etc.
Sequencing Introduction of Facts
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. A specific performance criterion2. Intensive practice on new facts3. Systematic practice on previously introduced
facts4. Adequate allotted time5. A record keeping system6. A motivation system
Performance Criterion
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
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
Instruction of new facts using relationship activity
Oral practice on new facts Written practice on new facts and old
facts
Adequate Allotted Time
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
Purpose: monitor student progress Recommendation: keep paperwork at
minimum—see Student Record Form on page 86
Motivation
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
Homogeneous Group Program Teacher Led – Group Oral Practice Materials Pretesting Timed test Record keeping/Motivation
Materials
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
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
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
Bottom half of the worksheet About 1 min. 15 seconds
Mastery Criteria
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
Heterogeneous Group Program 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 Daily Routine:
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) Not teacher-directed
2) Length of time to mastery
3) Not cumulative
Effective Programs
1) Teacher-directed (Oral practice)
2) Quicker mastery of smaller sets
3) Cumulative introduction and review
Resources
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