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 FactsPart 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 SayingFormat 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 ActivitiesPrograms 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 ProgramsHeterogeneous 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