Genres

For information:

Fred W. Duckworth, Jr.

c/o Jewels Educational Services

1560 East Vernon Avenue

Los Angeles, CA 90011-3839

E-mail: admin@trinitytutors.com

Website: www.trinitytutors.com

Copyright © 2006 by Fred Duckworth. All rights reserved. This publication is copyrighted and may not be linked to directly, reproduced, stored in a retrieval system, transmitted in any form by any means, electronic, mechanical, photocopying, recording, or otherwise without written permission from the publisher.

You may print this entire publication or portions thereof directly from this website, but may neither download to your computer nor store any text or images comprising this work. Moreover, you may not place on any other website for others to access, nor distribute to anyone else in any manner any of the pages comprising this work. This material is to be utilized only for your personal use in a homeschool or tutoring environment, and you may print out any or all of the pages herein only on an individual, one-time basis.

Furthermore, all copyright notifications must be included and you may not alter them in any way. Classroom use and/or use in a public or private school setting is expressly prohibited. Anyone wishing to use this material must come to this website to access it. Any use beyond these terms requires the written permission of the author/publisher. This publication is being provided at no cost and may not be sold under any circumstances.

To the instructor:

The following descriptions have been provided so that you can have your learners compare them with the illustrative selections you have chosen.

For example, given the election you choose to illustrate the characteristics of a fantasy, you might want to have your learner(s) identify what it is about that selection that makes it completely unbelievable, or just what is it that the characters do which they clearly couldn't do in real life, etc.

FANTASY

A fantasy is a completely unbelievable imaginary story in which people, animals, or objects may do things that they can't do in real life. Also, things may happen that could never happen in the real world. The setting may not be a real place or the story may have creatures that do not really exist. And finally, the problem in the story may be one that nobody ever has in the real world.

FAIRY TALE

A fairy tale is a fantasy having a magical quality and written especially for children.

REALISTIC FICTION

Realistic fiction is a made-up story that describes things as they really are. In realistic fiction, things happen that actually could happen in real life. The story has real-life problems, and the setting may include real places.

THE TENS PLACE

A Logical Approach

When multiplying two digits, the first half of the answer will ALWAYS be less than the smaller digit.

The above piece of information is excedingly powerful.

The reason it’s true is that all of the digits are less than 10 (the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9). This means that one digit times another has to be less than either digit. times ten.

Why?

Well, as you know, if you multiply the smaller digit times ten, the resulting product can be derived by simply placing that same digit in the tens place and a zero in the one’s place.

Consequently, if you multiply something less than ten times that digit, you will end up with something less than that digit in the tens place.

For example, since 3 × 6 is less than 3 × 10, the digit in the tens place MUST be less than 3 (since the product will have to be less than 30).

And given 9 × 6, the digit in the tens place MUST be less than 6 (since the product will have to be less than 60), and so on.

(Please note that the above strategy only applies when there are two digits in the answer.)

And with that, we’re off to a decent start. But, how helpful is all this when it comes to a problem like, say . . . 7 × 8 ?

THE 9 × TABLE

We’ve already discovered that, when multiplying any two unequal digits, the first half of the answer will always be exactly one less, or two less, than the smaller digit.

But, while this is very helpful, what we really need is some method of determining which it is -- one less or two less?

Thank goodness, with the 9 × table there’s no mystery about it. It’s ALWAYS one less.

So, to determine the first half of the answer when multiplying a given digit times nine, we simply ask ourselves, “What number comes just before the given digit?”

For example, when multiplying 6 × 9 we ask ourselves, “What number comes just before six?”

Of course, five comes just before six, so we know the answer is going to be fifty-something.

Now, to get the second half of the answer, we have to invent a concept we’ll call partners, which are simply two digits that add up to 10. Hence, the partner of six is four (because 6 + 4 = 10), the partner of eight is two (because 8 + 2 = 10), the partner of five is five (because 5 + 5 = 10), the partner of one is nine (because 1 + 9 = 10), the partner of seven is three (because 7 + 3 = 10), and vice versa.

Anyone that has not yet mastered these five pairs of addition facts will need to do so before being able to use the 9 × table strategy effectively.

THE 8 × TABLE

By now it is hopefully clear that, when multiplying two unequal digits, the first half of the answer will always be exactly one less, or two less, than the smaller digit.

We have also established that, while this is very helpful, what we really need is some method of determining which it is -- one less or two less?

When it comes to multiplying a digit × 8, we can accomplish this by considering the number of hands it takes to represent that same digit on our hands and fingers.

For example, let's pretend we need to find the product of 2 × 8. We begin by representing 2 on our hands and fingers.

We only need one hand to do so. That lets us know that the first half of the product is one less than 2.

When we need two hands to represent a given digit on our hands and fingers, that lets us know that the first half of the answer will be two less than that same digit.

It's quite that simple!

So, our strategy for finding the first half of product when mutiplying a digit × 8 is: "Subtract the hands that came to play . . ."

Let's see how this works in real life . . .

THE 8 × TABLE

Students who don’t already know this sums of digits added to themselves (can’t double digits) can learn them by singing about the Dubba Lupps:

THE DUBBA LUPPS

The only thing you’ll ever see the Dubba Lupps do,

Is double half the cotton picking digits times two.

They double half the cotton picking digit’s they see

Underneath their cotton picking Dubba Lupp tree.

They double up one,

And they get two.

They double up two,

And they get four.

But, now there’s six.

How could that be?

I think I know.

They doubled up three.

It’s all they do,

But man, they’re great.

They double up for,

And they get eight.

They double up five,

And finish with ten.

But, then they start to double up

All over again.

’Cause . . .

The only thing you’ll ever see the Dubba Lupps do,

Is double half the cotton picking digits times two.

THE 7 × TABLE

In Pathmatics we do not duplicate multiplication facts that have already been mastered.

And if you are using this book correctly, your learners have already mastered 0 × 7 = 0, 1 × 7 = 7, 10 × 7, 9 × 7, and 8 × 7.

That leaves 2 × 7, 3 × 7, 4 × 7, 5 × 7, 6 × 7 and 7 × 7.

Logic tells us that when multiplying any of these digits times to seven, the number in the tens place must be less than the smaller digit. But, with 7 × 7, neither digit is smaller. Would we do then?

This is the only time when the number in the tens place will ever be more than two. When multiplying two identical digits (3 × 3, 4 × 4, 5 × 5, 6 × 6, 7 × 7) the tens place will be three less than either digit.

So, 7 × 7 will be forty-something.

The pattern for the 7 × table is:

“7-Up, double up.”

We say “7-Up” because it is the 7 × table.

We say “double up” because you double the standing fingers on any incomplete hand (any hand that has less than all five fingers raised).

But, when representing seven on our hands and fingers, there are only two standing fingers on the incomplete hand. If you double them, you get four, not nine. And yet, we know that 7 × 7 = 49, so what gives?

Unfortunately, when it comes to the middle five digits (3, 4, 5, 6, and 7) our patterns for the units place only work when multiplying times even digits. To make them work with odd digits, we have to apply one more step, which we call “modifiving the results.”

To modifive a result, you reduce it by five. However, if the result is too small to be reduced by five, then you increase it by five.

Since 7 is an odd digit, we need to modifive the result for the units place. After doubling the two standing fingers we have four -- too small to subtract five -- so we add five instead and get nine, exactly what we needed.

This process is too complicated for our taste, so we make an exception here and have our clients learn this multiplication fact through some other approach.

Now, we are left with 2 × 7, 3 × 7, 4 × 7, 5 × 7, and 6 × 7.

Logic tells us that when multiplying any of these digits times to seven, the number in the tens place must be less than the smaller digit, but how much less?

Well, in all but the first two cases, it will be two less, so we will postpone 2 × 7 and 3 × 7 until we get to the 2 × table and 3 × table respectively.

That leaves us with 4 × 7, 5 × 7, 6 × 7 and 7 × 7.

The 5 × table is so easy that we will postpone 5 × 7 until then as well.

Now, all we have is 4 × 7, and 6 × 7.

In both cases, the number in the tens place is two less than the smaller digit. That means that 4 × 7 = twenty-something and 6 × 7 = forty-something.

Both for and six art even digits, so our strategy for the units place will work without having to modifive the results.

Remember our strategy is “7-Up, double up.”

In representing four on our hands and fingers, we have four fingers standing. When we double them, we get eight, so . . .

4 × 7 = 28

In representing six on our hands and fingers, we have one finger standing. When we double it, we get two, so . . .

6 × 7 = 42

In this chapter, the following multiplication facts . . .

7 × 7 = 49

6 × 7 = 42

4 × 7 = 28

. . . are the only ones that need to be mastered. So, let’s go on to the 6 × times table.

THE 6 × TABLE

In Pathmatics we do not duplicate multiplication facts that have already been mastered.

And if you are using this book correctly, 0 × 6, 1 × 6, 10 × 6, 9 × 6, 8 × 6 and 7 × 6.

That leaves 2 × 6, 3 × 6, 4 × 6, 5 × 6, and 6 × 6.

We know from working with the 6 × table that multiplying six times and odd digit will involve a complicated pattern called modifiving, which is more trouble than it is worth. So, we’re not even going to get into that.

We are left with . . .

2 × 6

4 × 6,

6 × 6.

Fortunately, the product of any even digit × 6 has a very simple pattern . . .

“Half of it and all of it.”

When multiplying any even digit times six, you simply place half of that digit’s value in the tens place, and all of the digit in the unit’s place.

For example, half of two is 1, and all of two is 2, so 2 × 6 = 12

Half of four is 2, and all of four is 4, so 4 × 6 = 24

And half of six is 3, while all of six is 6, so 6 × 6 = 36

And we already know that 8 × 6 = 48, though the pattern works just as well with 8.

THE 5 × TABLE

Is multiplication table is another that already has a well-known pattern.

Some like to take half of the digit they are multiplying times five and place a zero after it.

(If they are multiplying 5 times an odd digit, they subtract one from the digit they are multiplying, then take half of the resulting number and place a 5 after that. In other words, they “modifive” a zero.)

The above strategy works just fine. Nonetheless, our favorite approach is as follows:

Our first step is to make sure that our learners know and understand the value of half of every digit -- especially the odd digits:

½ of 1 = ½

½ of 2 = 1

½ of 3 = 1½

½ of 4 = 2

½ of 5 = 2½

½ of 6 = 3

½ of 7 = 3½

½ of 8 = 4

½ of 9 = 4½

Next, we make sure that they know and understand how to write the above values as decimal numbers:

½ of 1 = 0.5

½ of 2 = 1.0

½ of 3 = 1.5

½ of 4 = 2.0

½ of 5 = 2.5

½ of 6 = 3.0

½ of 7 = 3.5

½ of 8 = 4.0

½ of 9 = 4.5

Finally, to derive the value of any given digit × 5, they simply write half of fat digit’s value as a decimal number, then remove the decimal point.

½ of 1 = 0.5 consequently, 1 × 5 = 5

½ of 2 = 1.0 hence, 2 × 5 = 10

½ of 3 = 1.5 therefore, 3 × 5 = 15

½ of 4 = 2.0 so, 4 × 5 = 20

½ of 5 = 2.5 thus, 5 × 5 = 25

½ of 6 = 3.0 consequently, 6 × 5 = 30

½ of 7 = 3.5 hence, 7 × 5 = 35

½ of 8 = 4.0 therefore, 8 × 5 = 40

½ of 9 = 4.5 so, 9 × 5 = 45

THE 4 × TABLE

Virtually all of the multiplication facts from this table are mastered while learning the others, so the only one that we have to worry about is 4 × 4.

When mastering the 7 x table we learned that the only time when the number in the tens place will ever be more than two less than the digits been multiplied is when multiplying two identical digits (3 × 3, 4 × 4, 5 × 5, 6 × 6, 7 × 7).

That means that when multiplying 4 × 4 we place in a 1 in the tens place.

And when multiplying four times an even digit, the pattern for the unit’s place is the same as it was for the 9 × table -- we need the “partner.”

And since the partner of four is 6 . . .

4 × 4 = 16

(Though they have already been learned or will be learned elsewhere, we note that the partner of two is eight, and four times two equals eight. the partner of six is four, and four-times six equals twenty-four. And finally, the partner of eight is two, and four times eight equals thirty-two.)

THE 3 × TABLE

In some ways the 2 × table is quite different from any of the others.

We organize it in this way:

Note that all of the products in the top row have nothing in the tens place. All of the products in the middle row have a 1 in the tens place. And finally, all of the products in the bottom row have a 2 the tens place.

This means that when multiplying 3 × the first set of digits (not counting zero), the answer won’t have any digit in the tens place. When multiplying 3 × the middle three digits (4, 5, and 6) the product will have a 1 in the tens place. And when multiplying 3 × the last three digits (7, 8, and 9) the product will have a 1 in the tens place.

Note also that when you add together the digits in each product, in the first column, they all add up to three. In the second column, they all add up to six are you And in the last column, they all add up to nine.

So, the key to the 3 × table is to remember 3, 6, and 9.

This task is not difficult for those of us that grew up chanting the rhyme . . .

Three, six, nine.

The goose drank wine.

The monkey was swinging from the telephone line.

The line broke.

The monkey got choked.

And they all went to heaven in the little rowboat.

As with the 8 × table, when multiplying three times even digits, the number that goes in the unit’s place can be derived by doubling the fingers that are NOT used when representing a digit on your hands and fingers.

When representing two on your hands and fingers, three fingers are NOT used. Double them and you get six, and indeed 3 × 2 = 6.

When representing four on your hands and fingers, one finger is NOT used. Double it and you get two, and indeed 3 × 4 = 12.

When representing six on your hands and fingers, four fingers are NOT used. Double them and you get eight, and indeed 3 × 6 = 18.

And finally, when representing eight on your hands and fingers, two fingers are NOT used. Double them and you get four, and indeed 3 × 8 = 24.

At any rate, you know that when multiplying digits times three, if you can never have any digit other than one or two in the tens place, and whatever your product, if the digits that comprise it don’t add up to three, six, or nine, something is wrong.

THE 2 × TABLE

Before tackling the 2 × table, you may wish to have your students complete an art activity in which they create a turkey by tracing around one of their hands.

Here is the “secret” to multiplying any digit times two:

1. Tally the turkey, and . . .

2. Double the worms.

First, identify the digit that you’re going to multiply times two.

If, in representing that digit on your hands and fingers, you happened to see a hand with all five fingers raised (a “turkey”) you make a tally mark -- “you tally the turkey.”

This means that you will have to tally the turkey when multiplying 6, 7, 8, and 9 times two. In other words, when multiplying 6, 7, 8, or 9 times two, you place a 1 in the tens place.

Then double the fingers that are raised on any hand that is NOT a turkey (on any hand that does not have all five fingers raised) as we did when multiplying an even digit times seven. In other words, you “double the worms.”

When multiplying 2 × 2, there is no turkey to tally, so the only thing that remains to be done is to double the worms (2 + 2). Hence . . .

2 × 2 = 4

When multiplying 3 × 2, there is no turkey to tally, so the only thing that remains to be done is to double the worms (3 + 3). Hence . . .

3 × 2 = 6

When multiplying 4 × 2, there is no turkey to tally, so the only thing that remains to be done is to double the worms (4 + 4). Hence . . .

4 × 2 = 8

When multiplying 5 × 2, there is one turkey to tally, and there are zero worms that need to be doubled (0 + 0). Hence . . .

5 × 2 = 10

Some students master the preceding process by singing about Tally, the cross eyed Turkey.

Tally, the cross eyed Turkey.

Saw 1 worm crawl in my shoe.

But, because she sees things double,

She thought that she saw two.

Tally, the cross eyed Turkey.

Saw 2 worms crawl on the floor.

But, because she sees things double,

She thought that she saw four.

Tally, the cross eyed Turkey.

Saw 3 worms crawl through the sticks.

But, because she sees things double,

She thought that she saw six.

Tally, the cross eyed Turkey.

Saw 4 worms crawl out the gate.

But, because she sees things double,

She thought that she saw eight.

The bottom line is, when you multiply a digit times two, either one or nothing will go in the tens place -- never anything else.

http://facstaff.uww.edu/collinsj/Syl_BibLit_Sp03.htm

Appreciating the Bible as literature

http://www.ucd.ie/adulted/courses/ln131.htm

http://www.ucd.ie/adulted/courses/ln231.htm

Appreciating Poetry

http://www.upd.edu.ph/~ovcaa/rgep/ah/hum%20I.htm

THE

GENRES

TrinityTutors.com

FEATURES OF LITERATURE

STANDARD 3.1 Literary Response & Analysis w Level 4

The Literary Genres

In the state of California there is an expectation that fourth grade students will not only read and respond to a wide variety of significant works of children's literature, but also be able to described the structural differences of various unimaginative forms of literature, including fantasies, fables, myths, legends, and fairy tales.

In fact, there is much to appreciate in the various literary genres formed down through the ages. In examining literature, one examines mankind and his perception of himself and his environment. Looking at representative texts provides a context in which to examine different world views and expand one's own perspectives in light of the rich elements of artistry that characterize each genre. By studying different forms of writing, readers not only afford themselves an opportunity to develop a sesitivity to the beauty and expressive power of literature, but also to appreciate different approaches to using language while exploring the creative ways in which different writers express a wide variety of experiences.

Other lessons that can be gained in the process are an understanding of the cultural differences in such works, an appreciation of both the unique and shared values and ideals of different societies, recognizing the special uses of (figurative) language in imaginative literature, manifesting increased sensitivity to human needs and social concerns, demonstrating open-mindedness towards differences in race/culture/values, and overcoming grammatical and lexical difficulties.

Hence, one is offered the opportunity to gain a wealth of knowledge while participating in a rich educational experience. We encourage all to take advantage of this opportunity as both teacher and student use the remaing pages to maximize each learner’s educational experience.

There are seven digits that are less than 7 (0, 1, 2, 3, 4, 5, and 6). So, while we know that the first half of the answer must be less than seven, it would be much better if we had some way of determining exactly how much less!

Fortunately, we do.

In analyzing all of the multiplication tables, I was able to establish the following:

When multiplying two unequal digits, the first half of the answer will ALWAYS be exactly one less, or two less, than the smaller digit.

That narrows our choices down quite a bit! For example, when multiplying 7 × 8, we now know that the product will either be sixty-something or fifty-something. There simply are no other choices!

Looking at another example, if we were given 6 × 4, we would know that the answer was either going to be thirty-something or twenty-something. It’s really quite that simple.

Let’s make sure you understand how to apply this rule. Complete the following exercises and then compare your answers to the answer key.

(The answer key can be found at http://www.trinitytutors.com/answerkey.html.)

EXERCISE #1:

1. Given 4 × 9, the digit in the tens place is either a __ or a __.

2. Given 5 × 6, the digit in the tens place is either a __ or a __.

3. Given 8 × 4, the digit in the tens place is either a __ or a __.

4. Given 7 × 3, the digit in the tens place is either a __ or a __.

5. Given 6 × 9, the digit in the tens place is either a __ or a __.

ANSWERS TO EXERCISE #1:

1. Given 4 × 9, the digit in the tens place must either be a 3 or a 2.

2. Given 5 × 6, the digit in the tens place must either be a 4 or a 3.

3. Given 8 × 4, the digit in the tens place must either be a 3 or a 2.

4. Given 7 × 3, the digit in the tens place must either be a 2 or a 1.

5. Given 6 × 9, the digit in the tens place must either be a 5 or a 4.

If you got all of the correct answers, it is time to move on to the 9 × table.

Christianity is the only faith that has a loving God.

MYTH

A myth is a traditional story from long, long ago, usually with supernatural characters, such as gods and goddesses. A myth may give an imaginative explanation for some mystery in life, such as why something occurs in nature, why something looks the way it does, or why people behave in certain ways.

LEGEND

A legend is a myth that is believed to have some historical basis.

FOLK TALE

A folktale is a traditional story from long ago, passed down among common people by word-of-mouth, from generation to generation.

It is an old story that has been told and retold until it was written down. Some folk tales begin with the words "Once upon a Time" or "Long ago and far away."

The characters are sometimes animals or objects that speak, and folk tales often contain a moral, or lesson, about life. Usually, goodness and intelligence win out over evil and ignorance. The story is told from the third-person point of view, with the action building through repetition to a high point at the end of the story.

So, to determine the product of 9 × 3, for example, I simply ask myself, “What comes before three and what’s the partner of three?”

Of course, everybody knows that 2 comes before three, and the partner of three is 7 so . . .

9 × 3 = 27.

By filling in the blanks with whatever digit I’m multiplying times nine and then answering the resulting questions, I can automatically reveal the product of any digit times nine.

What comes before ___?

What’s the partner of ___?

EXAMPLE:

What comes before 6 ? (Five comes before six.)

What’s the partner of 6 ? (The partner of six is four.)

Hence, 9 × 6 = 54

Our strategy is:

What comes before "blank" and what's the partner of "blank?"

Now for the second half.

When representing seven on my hands and fingers, I hold up seven fingers and leave three of them down, saying that the three fingers I'm NOT using are "sleeping all day."

Doubling the fingers that sleep all day automatically produces the second half of the product!

3 + 3 = 6

So, when multiplying 7 × 8, I subtract the two hands that came to play to get 5, and double the fingers that sleep all day to get 6.

Consequently, 8 × 7 = 56

Essentially, what it comes down to is this: When multiplying a given digit times eight, you know that the tens place will have to be one less or two less than that digit. If that digit is greater than five, then the tens place will be two less. But, if that digit is five or less, then the tens place will only be one less than the digit. And in either case, you determine the units place by doubling the number of fingers that are kept down when representing that digit on your hands and fingers.

This "secret" pattern can be used to derive the correct product given any digit times eight, though we won't bother with zero or one. Some students practice the process by singing the following and using hand gestures.

THE 8 × TABLE

Lets say we want to figure out what is the product of 8 × 7.

Since we need two hands to represent seven on our hands and fingers, the first half of the answer will be two less than seven, or fifty-something.

7 – 2 hands = 5 (fifty-something)

Or, lets say we want to figure out what is the product of 4 × 8.

The fact that we need just one hand to represent four on our hands and fingers lets us know that the first half of the answer will be just one less than four, or thirty-something.

4 – 1 hand = 3 (thirty-something)

Do you understand how that works?

When it comes to the 8 × table, the number of hands it takes to represent a given digit on our hands and fingers tells us whether or not the first half of the answer will be one less or two less than that digit.

THE EIGHT STRATEGY

I only need one hand to represent 2 on my hands and

fingers, so I subtract one from two to get the first half

of my answer. To get the second half, I double the

three fingers that are NOT used. This gives me 1 and 6,

so 8 × 2 = 16

I only need one hand to represent 3 on my hands and

fingers, so I subtract one from three to get the first half

of my answer. To get the second half, I double the

two fingers that are NOT used. This gives me 2 and 4,

8 × 3 = 24

I only need one hand to represent 4 on my hands and

fingers, so I subtract one from four to get the first half

of my answer. To get the second half, I double the

only finger that are NOT used. This gives me 3 and 2,

8 × 4 = 32

I only need one hand to represent 5 on my hands and

fingers, so I subtract one from five to get the first half

of my answer. To get the second half, I double the

zero fingers that are NOT used. This gives me 4 and 0,

8 × 5 = 40

HISTORICAL FICTION

Like realistic fiction, historical fiction is a believable imaginary story. The difference between the two is that historical fiction takes place in a different time period from the present (i.e., the past). The characters in historical fiction may include real people, and the plot may include actual historical events

BIOGRAPHY

A biography is a story about a real person's life, but written by someone else.

AUTOBIOGRAPHY

An autobiography is a story that someone wrote about his or her own life.

When 6 comes out to play

We take two hands away

Then double 4 more fingers

That lay in bed all day

6 – 2 = 4

4 + 4 = 8

8 × 6 = 48

When 7 comes out to play

We take two hands away

Then double 3 more fingers

That lay in bed all day

7 – 2 = 5

3 + 3 = 6

8 × 7 = 56

When 8 comes out to play

We take two hands away

Then double 2 more fingers

That lay in bed all day

8 – 2 = 6

2 + 2 = 4

8 × 8 = 64

When 9 comes out to play

We take two hands away

Then double one more finger

That lays in bed all day

9 – 2 = 7

1 + 1 = 2

8 × 9 = 72