*Laws of Arithmetic*

**Laws of Arithmetic** educational software program created for the Texas Instuments TI-99/4 and TI-99/4A home computers helping young students further their education in math education. It was developed and published by Milliken publishing company and is part of several software titles in the Milliken Math Sequences series. It was programmed by John C. Plaster. It was released during the first quarter of 1983 and released on Solid State Software^{TM} Command Module cartridge as part #: PHM 3099. It retailed originally at $39.95 (USD).

Laws of Arithmetic | |
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Laws of Arithmetic (Front Cover) ^{[1]} | |

Publisher(s) | Milliken |

Original Retail Price | $39.95 |

Programmer(s) | John C. Plaster |

Part# | PHM 3099 |

Format(s) |
Solid State Software^{TM} Command Module |

Release | 1983 (1st Quarter) |

Genre(s) | Educational, Mathematics |

## Advertising Blurb

### Manual

A self-paced "tutor" which presents mathematical principles to help your child develop strong math skills. Suitable for children from grades 4 through 8.

## Manual

### A Note to Parents

Children need strong math skills to solve today's and tomorrow's problems. The Milliken Math Sequences, along with the Tl Home Computer, can help your child meet these challenges. The series allows children to work at their own pace and on the skill level at which they need practice. Children find that learning with the computer is fun, challenging, and motivating. The computer never tires of repetition or loses patience-it's like having a private math tutor!

The Milliken Math Sequences, developed for Texas Instruments by Milliken Publishing Company, consists of twelve Solid State Cartridges. Each cartridge concentrates on a different skill area in mathematics, such as addition, subtraction, decimals, or laws of arithmetic. By providing different levels of difficulty, the series is suitable for children from the kindergarten age through grade eight.

The Laws of Arithmetic cartridge is divided into 19 levels of difficulty, covering material generally taught in grades four through eight. The program introduces your child to the basic laws of arithmetic: the property of zero, the principles of identity elements, and the commutative, associative, and the distributive properties.

The program also presents the applications of the laws of arithmetic. For instance, the commutative law, which states that the order of factors may be changed without affecting the resulting product, is applicable for addition and multiplication. The associative law, which states that the grouping of factors may be changed without affecting the resulting product, applies to both addition and multiplication.

Your child learns that multiplication is distributive over addition. The distributive property of multiplication states that multiplying one number (A) by a set of numbers which are to be added (8 + C) can be done in two ways. The numbers (8) and (C) can be added first and then the sum can be multiplied, or they can be multiplied by (A) one by one and then combined. For example,

- A × (B + C) = (A × B) + (A × C).

Your child also encounters the applications of the principles of identity elements and the property of zero in multiplication. For example, zero is the identity element for addition; that is, zero plus a number equals that number. Similarly, this principle applies to multiplication. With multiplication, however, the number 1 is the identity element (one times a number equals that number). The· property of zero in multiplication-zero times a number is zero-is also presented.

The Laws of Arithmetic cartridge offers several special features that increase its motivational and reinforcement value:

- Colorful, rewarding graphics and sound effects that appear in response to correct answers.
- An unintimidating, try-again approach to incorrect answers.
- A progress report posted at the bottom of the screen.
- A feature that allows your child to study the answer to the problem if he or she makes a mistake.
- Advancement to the next level if problems are answered correctly, or automatic return to a lower level if your child needs more practice.
- Report screens personalized with your child's name at the end of each level's activities.
- An "Exit" screen with a complete report on your child's score at the end of the work session.

### Your Child and the Computer

The Texas Instruments computer is a rugged, durable device designed for easy use and care. Teach your child to give the computer the same good care and respect he or she would give a television set, record player, or any piece of electronic equipment:

- Keep snacks and beverages away from the console.
- Don't hammer on the keyboard or place heavy objects on it.
- Don't touch the cartridge contacts. These are recessed in the cartridge to help prevent accidental soiling and/or damage.

The letters and numbers on the keyboard are arranged in the same order found on standard typewriter keyboards. If your child is not familiar with a typewriter or has not used the computer before, take a few minutes to acquaint him or her with the keyboard. Point out the row of number keys at the top and the rows of letter keys below. Show your child how to insert the cartridge and how to select the activities. This brief "tour" of the computer will help reinforce correct procedures and instill confidence as your child starts out in a new world of computers.

Today computers are involved in almost every aspect of life. Working with this cartridge can help your child become familiar with computers and their operation. Since computer-enhanced instruction is more common in the classroom every year, this knowledge can give your child an important advantage.

### A Sample Activity

For easy use, directions are displayed on the screen throughout all the levels. This sample activity, however, can help to illustrate the way the program works.

#### Let's Begin

When the Milliken title screen appears, press any key to begin. The screen then prompts you to enter the Beginning Level. Select any level from 1 to 19 by typing the number and then pressing **ENTER**. For this example, press 1 and then press **ENTER**. Next, the screen asks for Name. Type the child's name (up to ten letters long) and press **ENTER**.

Now a problem is displayed on the screen. Problems at Level 1 involve the application of the commutative property of arithmetic. The principle "ADDITION IS COMMUTATIVE" is displayed on the screen. A flashing question mark shows where the answer goes, and the directions on the screen tell you to "ENTER THE CORRECT NUMBER." Your child computes the problem mentally and types the missing addend in the equation.

A progress report appears across the bottom of the screen, with the following meanings:

- PL = Problem Level
- TC = Total Correct
- TP = Total Problems
- AVG = Average

As your child works through the problems, these figures are updated to report his or her progress. TC, TP, and AVG are reset to zero at the beginning of each level.

#### Entering Answers

Let your child answer a few problems as you observe. He or she simply presses the correct number from the top row of keys.

#### How the Computer Responds

If the problem is answered correctly, an animated picture appears. Your child then presses ENTER to continue to the next problem. If the problem is answered incorrectly, the computer returns a screen message and encourages your child to press **ENTER** to try again. If a second incorrect answer is given, the screen border turns red and flashes. To continue, your child presses **ENTER** again, and the computer gives the answer with a message to "STUDY THE ANSWER." When your child presses **ENTER** again, the next problem appears.

#### Advancing or Moving Back

If your child answers five of the previous six problems correctly, a "Good News" report is displayed. He or she then advances to the next level. If three problems in a row are answered incorrectly, a "Bad News" report appears and your child moves back one level.

#### Changing Levels

You can change levels any time the question mark is flashing. To leave this level, simply press the letter E for "exit." An EXIT screen appears, which reports on your child's progress. Press ENTER to return to the Milliken title screen.

Let's try another level. Press any key to go to the "Beginning Level" screen. This time, enter **14** as the Beginning Level. Then type your child's name again, and press **ENTER** to continue.

Problems at Level 14 involve the application of the distributive law of multiplication over addition. The message "MULTIPLICATION DISTRIBUTES OVER ADDITION" is displayed on the screen. A flashing question mark shows where the answer will go, and the directions on the screen tell you to "ENTER THE CORRECT NUMBER." Using mental computation, your child determines the missing factor in the equation and enters the correct answer.

Continue to observe as your child works through the problems and gains familiarity with the program's operations.

### Skill Levels

This chart can help you find the appropriate starting level for your child. By looking at the sample problems and the skill description, select a level that is not too easy, but also not too difficult, for him or her. If in doubt, start at a lower level and work up from there. A glossary is provided on pages 12-13.

Level Sample Problem Skill Description 1-2 1 + 8 = 8 + ? (2 + 1) + 3 = ? + (2 + 1)

Applying the commutative property of addition to

problems with addends of 0

through 9.

3 (2 + 1) + 4 = ? + (1 + 4) Applying the associative property of addition to

problems with addends of 1

through 9.

4-5 (4 + ?) + 3 = 4 + (3 + 5) (6 + 9) + 5 = 5 + (? + 9)

REVIEW of Levels 1 through 3. Applying both the associative

and commutative properties

of addition to problems with

addends of 1 through 9.

6 7 + 0 = ? Solving addition problems with the identity element O as

an addend. Other addends are

from 0 through 9.

7 6 × 7=? × 6 Applying the commutative property of multiplication to

problems with factors of 1

through 9.

8 (6 × 7) × 8 = ? × (7 × 8) Applying the associative property of multiplication to

problems with factors of 1

through 9.

9-10 ? × 9 = 9 × 8 (8 × 4) × 3 = 8 × (3 × ?)

REVIEW of Levels 7 and 8. Applying both the

commutative and associative

properties of multiplication to

problems with factors of 1

through 9.

11 7 × ? = 7 4 × 1 = ?

Solving multiplication problems with the identity element 1 as

a factor. Other factors are

from 0 through 9.

12 8 × 0 = ? 4 × ? = 0

Solving multiplication problems with the property 0 as a

factor. Other factors are from

0 through 9.

13 3 × ? = 0 1 × 8 = ?

REVIEW of Levels 11 and 12. Solving multiplication

problems with the identity

element 1 and the property 0

as factors. Other factors are

from 0 through 9.

14-15 3 × 14 = (3 × 10) + (3 × ?) 9 × 91 = (? × 43) + (9 × 48)

Applying the distributive property of multiplication over

addition to problems with

factors from 2 through 9.

16-17 ? × 3 = 3 6 + (1 + ?) = (1 + 2) + 6

REVIEW of Levels 1 through 6. Applying properties for

addition and the identity

element, 0, for addition.

18-19 ? × 9 = 9 9 × (8 × 7) = (8 × 9) × ?

REVIEW of Levels 7 through 15. Applying properties for

multiplication and the identity

element, 1, for multiplication.

### Gloassary

**Addend:** A number to be added to another; for example, ADDEND + ADDEND = SUM.

**Associative property:** A basic law of arithmetic which states that when elements are regrouped without changing the order, the result is not affected; for example,

- (A + 8) + C = A + (8 + C) (in addition)

- (A x 8) x C =A x (8 x C) (in multiplication).

**Commutative property:** A basic law of arithmetic which states that the result does not depend on the order in which quantities are combined. This property applies both to addition and to multiplication; for example,

- A + 8 + C = C + A + 8 (in addition)

- A x 8 x C = C x 8 x A (in multiplication).

**Digit:** Any of the numerals O to 9; the number "986" has three digits.

**Distributive property:** A basic law of arithmetic which states that a mathematical operation performed on a whole factor has the same results as when the same operation is performed on parts of that same factor. For example,

- 7 X 25 = (7 X 20) + (7 X 5)

may be expressed as

- 7 X 25 = (7 X 19) + (7 X 6)

with no affect upon the solution of the problem.

**Equation:** A statement in mathematical form in which one quantity is said to be equal to a second quantity. For example, in the equation 4 x 4 = 16, the product of 4 x 4 is said to be equal to 16.

**Factor:** One of two or more numbers which, when multiplied together, produce a given product; for example, FACTOR x FACTOR = PRODUCT.

**Identity element:** A number that, when added to or multiplied by a second number, causes the result to equal the second number. Zero is the identity element for addition (zero plus a number equals that number), and 1 is the identity element for multiplication (1 times a number equals that number).

**Product:** The total or result of multiplying numbers; for example, PRODUCT = FACTOR x FACTOR.

**Property:** A statement which is true in all cases; a basic assumption or law.

**Sum:** Total or result of adding numbers (addends) together; for example, SUM = ADDEND + ADDEND