basic facts. basic facts what are they? why should students memorize basic facts?

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