Basic Facts

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Basic Facts
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Basic Facts

• What are they?
• Why should students memorize basic facts?

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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 introducedprogress for
  these student can end at elementary school.

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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.

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Teaching Math Facts

• Three types of instructional activities
• Understanding
• Relationships
• Memorization
• What are these activities? Why?

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Relationship Activities

• Exercises based on a series (e.g., 3x1, 3x2, 3x2)
• Exercises based on fact families and inverse
  operations (e.g., 5-23, 5-32, 235, 325)
• Purpose of these exercises is to make
  memorization easier

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Preskill for Relationships

• Plus-one FactsFormat 6.1, page 90
• Teaches facts and relationships.
• Rule When you plus one you say the next number.
• Model Part A and B.

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Plus-one Facts

• Part C
• 8 1
• 4 1
• 7 1
• 5 1
• 9 1
• (Your turnformat practice!)

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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

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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

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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 pacelead and work on
  increasing the pace
• Correction for statement error?

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Three Number Fact Families

• Sets of three numbers from which students can
  create 4 statements.
• Eitheraddition 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?

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Three Number Fact Families

• Format 6.3
• Part Ahow to construct pairs (big number
  introduced)
• Part Boral test on the reverse fact
• Part Cworksheet, filling in the big number and
  generating the two facts

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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.

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Three Number Fact Families Model and Practice

• ____ ____ _____
• ____ ____ _____
• ____ - ____ _____
• ____ - ____ _____

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Sequencing Introduction of Facts

• Systematic, cumulatively introduction of
  factsFigures 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

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Sequencing Introduction of Facts

• Systematic, cumulatively introduction of
  factsFigures 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.

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Sequencing Introduction of Facts

• Addition facts are introduced first.
• Little research is available to guide us
  regarding when to introduce subtraction
  factsafter addition is completedafter part of
  addition is mastered and extend to subtraction?
• Recommendationdelay subtraction until students
  have learned about half of the addition facts
  (Sets a-m addition mastered). Then
  alternateSubtraction A, Addition N, Subtraction
  B, Addition O, etc.

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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.

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Mastery Activities

• Programs for Fact Memorization include
• 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

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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?

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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)

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Intensive Practice

• Instruction of new facts using relationship
  activity
• Oral practice on new facts
• Written practice on new facts and old facts

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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.

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Record Keeping System

• Purpose monitor student progress
• Recommendation keep paperwork at minimumsee
  Student Record Form on page 86

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Motivation

• Integrate with record keeping system
• Motivation comes with SUCCESS
• Teachers responsibility to set students up for
  success Must teach facts

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Two Fact Mastery Programs

• Homogeneous Group Program
• Teacher Led Group Oral Practice
• Materials
• Pretesting
• Timed test
• Record keeping/Motivation

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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

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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 minutestart at set G
• 45 facts per minutestart at set M
• 60 facts per minutestart at set R
• 85 test on next operation

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Oral Group Practice

• Using the worksheetsoral 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

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Timed Test

• Bottom half of the worksheet
• About 1 min. 15 seconds

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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.

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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

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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 testBottom half of worksheet

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Compare/Contrast

• Traditional Programs
• Not teacher-directed
• Length of time to mastery
• Not cumulative

• Effective Programs
• Teacher-directed
• (Oral practice)
• Quicker mastery of smaller sets
• Cumulative introduction and review

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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
•