Teaching the Three Times Table

Storytelling and Mathematics
The Wholistic and Cross-Curricula Nature of the Lesson
Examples from our Material
Conclusion
Lesson Plan: Multiplying by Three - A mathematics/language arts lesson

Introduction
We begin by examining two areas that influenced the lesson design of "Multiplying by Three" and which are not usually part of teaching mathematics. They are storytelling and a cross-curricula approach and we will indicate why both these ideas are appropriate for teaching mathematics to young elementary school children.

Storytelling
Why does a lesson on mathematics begin with a story?

Stories, more than anything else, engage the child's imagination. They transport children into a world where they can easily create pictures, and visualize a situation.

Part of the task of teachers is to transmit knowledge to students. However, the act of learning is not complete until students have internalized the knowledge and made it their own. This process is far more effective when it is done through storytelling.

We need not be concerned, at present, with the extent to which this occurs or with the influence on hemispheric development (this will occur in a later newsletter). The main point is to establish that storytelling is a way in which we can pass on information to students while at the same time enhancing and optimizing their learning.

Storytelling and Mathematics
We believe that this enhancement and optimization can occur even in subjects like mathematics. For example, in our material for the learning of the multiplication tables each table starts with a story (an overview of our material is available at: http://members.aol.com/WaldorfEdu/Math.html).

When teaching our lessons on the multiplication tables we recommend that, initially, the teacher reads (even better, if the teacher can tell) the story to the class. At this point there is no pressure on children to do anything but listen to the content and create pictorial representations according to their ability to do this.

They will, instinctively, create pictures from the story content, and in so doing they create their own context within which to work. Any information they now receive will be absorbed into this context. Thus the base has been laid for the teacher to move on to the next stage.

In other words, the teacher by reading or telling the story "Ramiro and the Jiwi Fruit" has created a context with which the children can identify, and through which they can absorb information.

Within this context students have a clear visual image of three, for example, Ramiro's paintings of three portions of various foods. This enables children to become familiar with the concept of three.

As far as our approach is concerned this point is crucial. Students start the process of understanding by creating pictures in their imagination. It is only when this has occurred should they move on to work through hands-on experiences with manipulatives. Finally, and only when they have worked through the first two stages, are they ready to work with the abstract and theoretical.

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The Wholistic and Cross-Curricula Nature of the Lesson
An examination of the contents of the lesson indicates its cross-curricula nature. It includes mathematics, language arts, craft, and art.

Why do we believe that we should teach young elementary school children in this way?

We have already described how a child of this age thinks pictorially. This is related to the wholistic nature of the child's thinking. A young child is able to create an image of a situation without observing or having any direct experience of it. In other words a child's thinking is pictorial and unspecialized.

This type of thinking needs continual stimuli of a rich and colorful nature if the inner imaginative activity is to grow and develop.

Unspecialized
We have already shown how subjects and content need to be taught so that they relate to a child's rich inner life where imagination and feeling are the main factors influencing his/her thinking.

However, besides the pictorial element a child's thinking is unspecialized. For the adult it is different. Our thinking is usually compartmentalized and in many instances we find difficulty in looking at the whole.

Whereas adults would usually prefer to receive knowledge that fits comfortably into a particular compartment, a child instinctively views the whole.

Practical Application
This should, of course, influence the teaching process. If we wish to reach the mindset of the child we need, wherever possible, to teach in a wholistic way. For example, a young child does not think, "I am being taught mathematics, English, or whatever," or "What I am learning now belongs to language arts, or this lesson is about art history," and so on.

We need, therefore, to structure content so that it meets the wholistic nature of children's thinking. In other words whereas we, as adults, will talk about the cross-curricula nature of the lesson children only care that the lesson relates to their way of thinking. They do not care that the subject matter is called mathematics.

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Examples from our Material
In the lesson "Multiplying by Three" we not only include mathematics but also language arts, craft, and art.

1. Language Arts/Readability Levels
Children will naturally be involved in decoding as they read the story. Obviously the story needs to be at an appropriate readability level. You will see that in the material we have rewritten the story with a readability level appropriate for young children.

Readability level (including proper nouns) Flesch-Kincaid Grade Level 2.2
Flesch Reading Ease (including proper nouns) 94.4

Readability level (excluding proper nouns) Flesch-Kincaid Grade Level 1.5
Flesch Reading Ease (including proper nouns) 99.8

2. Cross-Curricula
For example, Assignment 1 "Ramiro and Jiwi Fruit" is a craft activity and gives students a hands-on approach. Assignment 2 "Guided Reading" is a language arts activity. Assignment 3 "Creating Patterns" is a pictorial mathematical exercise. Assignment 4 "Table Summary" is a mathematical/language arts activity that introduces and reinforces the language of mathematics.

Assignment 5 "Let's Practice What We Have Learned" is a mathematical/language arts activity which again introduces and reinforces the language of mathematics. However, this time mathematical language has to be used more precisely and the child also works with numbers (symbols) in an abstract way.

Assignment 6 "Patterns-Three Times Table" is an activity where the child visualizes the patterns of numbers. It gives teachers the opportunity to show students a practical application; firstly, in relation to the three times table itself; secondly through all the tables to the twelve times table (see Teacher Notes in "Patterns-Three Times Table" for explanation.)

Conclusion
In order for the teaching of mathematics to be successful we must engage all facets of the child's thinking. This will include the engagement and the development of the affective (in modern jargon "emotional intelligence.")

Introducing content with a story does this successfully for it immediately engages the child's imagination. For young children mathematics should not begin with manipulatives or an exercise in the abstract. Both of these are important but the first task is to relate content to the mindset of the child so optimum learning occurs.

It is important therefore that the design of the lesson is in line with children's thinking and that we do not impose a structure to learning that is foreign to them.

Unfortunately, subject content in mathematics and related areas does not usually take into consideration that content should be so structured for the younger elementary school student. Hence the need for our material and the newsletter.

Note
We have not dealt with personality types or learning styles. These do, however, play a large part in our approach and we write material taking this area (which we call Methodology of Teaching) into consideration. We plan lessons so that different personality types will find activities that are appropriate for their particular learning style.

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Ramiro and the Jiwi Fruit (teacher's version)
I once knew a trader called Ramiro who lived in a village near Mexico City. He was a kind and generous man who loved good food. There was nothing he liked better than to sample food that he had never tried before.

Ramiro would often cook a wonderful meal and invite friends to share it with him. Many of his friends were poor and they loved to have an invitation to Ramiro's home for a meal. He was respected and loved by all who knew him.

Ramiro's Vanity
His only fault was that he was quite a vain person. Ramiro had a long white beard and was very proud of this.

He would often say to me, "I think my friends like me because of my fine beard."

"You are wrong," I would answer. "It has nothing to do with that beard you are so proud of, they like you because you are a kind man." However, I doubt if he believed me.

Ramiro and New Food
Ramiro's work as a trader took him to many new places and every time he visited a new town he would go in search of something new to eat. He always did the same thing; he would buy three portions of the new food.

When he first visited Puebla, he bought three special pineapples; when he visited Toluca, he bought three speckled eggs, and when he visited Veracruz, he bought three silver freshwater fish."This is what I do," he once explained to me."I eat the first serving to get used to the taste, I eat the second serving to enjoy the taste and I eat the third serving to remember the taste."

I knew that if he liked the food a lot, he would paint a picture of the three portions and display it in his house.

The Beard is Gone
The last time I visited him I was surprised to see that he no longer had a beard.

"Tell me," I said, "Why did you shave your beard? Was it a bet? Are you ill? I can't believe that you did it yourself."

Ramiro had a sparkle in his eye that I had not seen before. He certainly looked a lot happier than I had ever seen him.

"I will tell you how I lost my beard," he said, "But you have to hear the whole story."Naturally I was very curious.

He took me through his house showing me his paintings. We started in the porch where there were four paintings.

There were three silver freshwater fish, three mangoes, three guavas and a delightful painting of three pineapples."Those pineapples must have been particularly good," I commented.

We went into the main room and there were paintings of tacos, burritos and tostadas.

There were also drawings of papayas, blue saltwater fish and three eels. Beside the door which led into the last room was a small drawing of three speckled eggs.

The Strange New Fruit
So far Ramiro had shown me eleven drawings - each of three items of food. Before he lifted aside the curtain to the last room, he said, "My friend, I will know if you recognize this drawing because of the expression on your face."

Then he lifted the heavy curtain and led me towards the last picture. The room was dim and it took a moment for my eyes to become adjusted to the darkness.

When I could see, I was face to face with Ramiro's last drawing.

It was of three large, prickly-skinned fruit. I did not recognize the fruit, but looked more closely because they were so unusual.

"What kind of fruit is this?" I asked Ramiro.

"Ahh," sighed Ramiro, "I see you have not seen a Jiwi fruit before. It taught me such a lesson."

"What do you mean?" I asked.

"Let me tell you the story of the Jiwi fruit," he said. We sat on the floor in front of the drawing.

Ramiro Tells His Story
"As you know," my friend began, "I am in the habit of trying new food. One day, my travels took me to Oaxaca de Juarez.

There, I visited a market in search of new tastes. I wandered around that market for a long time and not one piece of food took my fancy.

Finally, I gave up and was on my way home when I came across a dark, little stall, tucked out of the way, behind the other stalls.

At the back of this stall there were three pieces of the Jiwi fruit. Nowhere else were they for sale. I decided that I must have them, so I paid an outlandish price for them and hurried away.

I was so eager to eat them that I didn't even speak to the stall-owner, although he called after me.

When I got home, I went to my room quickly and put the Jiwi fruit on the table. Now the Jiwi fruit is quite a large fruit and three pieces was more than I needed, but that fruit smelled so good that I wanted to taste it all by myself. I didn't even ask my hosts to share it."

I laughed when Ramiro said this because I knew that there were only two things in the world that he was selfish about and those were his beard and his food-tasting.

"Go on, please," I said.

"Well here I was, sitting on my own with three pieces of the most unusual and delicious smelling fruit in the world," said Ramiro, "and you know what I did? I ate all three right up.

I didn't even slow down to try to remember the taste. I ate the pips, and the juice dribbled over my fingers and down my chin. It was so delicious."

A Terrible Shock
"What happened next?" I asked.

"I went to wash the juice off," said Ramiro, "and it was then that I got such a shock. The juice would not come off, and the more I washed, the stickier it became . My hands stuck to my beard and I had a terrible time trying to get them off. I was wailing and tugging at my beard when my hosts came in.

When they saw me, they knew what had happened. 'You have been eating a Jiwi Fruit, haven't you?" they said. I admitted that I had indeed eaten three Jiwi Fruit.

"Three Jiwi fruit. All by yourself," my hosts said. They were very disappointed with me for being so selfish."If only you had shared the Jiwi fruit with us," my hosts said, we could have told you that you must always rub your face and hands with oil before you begin."

"What did you do?" I asked. I was starting to guess what might have happened.

"I left the house in shame and rode back home," Ramiro continued. "All the way back from Oaxaca de Juarez things stuck to my beard. Flies flew in and never came out. Leaves falling to the ground met my beard and stayed there. Bits of it kept getting pulled out and by the time I got home, it was a matted, tangled mess.""You poor man," I said.

"I rushed inside and sat in front of the mirror. I certainly didn't want to draw a picture of that horrible Jiwi fruit.

Ramiro's Great Loss
My beard had lost all of its beauty. I thought that if I had it shaved off nobody would respect me anymore, but I knew I could not keep it the way it was.

So the next day I had my beard shaved off. I walked out of the barber's shop with my head down and hoped I wouldn't see anyone that I knew.

I was so ashamed. I regretted ever being so greedy as to eat so much of the fruit by myself."

Ramiro seemed to be lost in thought. We were silent for a moment and then he continued.

A Surprising Outcome
"Do you know what happened next? As I was walking home with my head down, people started to recognize me. Why, it's the trader, Ramiro,they said, and hello there, they called.

A woman ran up to me with a small basket of fish which she pressed into my hands. A man called me over to his house and asked me to dinner. His little son gave me a huge smile.

I had never had these things happen to me before. I often had people to dine with me, but they always seemed a little afraid of me. Now they greeted me in the street. They were not in the least timid.Now that I no longer had my beard, or the vanity that went with it, I realized that people liked me for who I was.

I went home with a warm feeling inside and had the best night's sleep in years. The next day I drew this picture of the three pieces of Jiwi fruit that had taught me such an important lesson."

Ramiro stood up and stretched. We left the dark little back room and together we went out through the main room and sat on the porch.

We sat quietly in the warm, golden, evening sun.

Before I went home, we sat for a while exchanging stories, but none as good as Ramiro's story of the Jiwi fruit.

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Story - Ramiro and the Jiwi Fruit (student's version)
This is a story about someone who loved good food.

I once knew a trader called Ramiro. He lived in a village near Mexico City.

Ramiro loved to try new food. He would often cook a tasty meal and invite friends to share it. People loved and respected Ramiro.

Ramiro's Vanity
Ramiro had a long white beard. He was very proud of it. He would often say to me,

"I think my friends like me because of my fine beard."

"You are wrong," I would answer. "They like you because you are a kind man."

However, I doubt if he believed me.

Ramiro and New Food
When it came to food, Ramiro had a strange habit. Every time he went to a new town he would sample the food. He would always buy three servings of a new food.

He ate the first serving to get used to the taste. He ate the second serving to enjoy the taste. He ate the third serving to remember the taste.

If he really liked the food he would draw a picture of it. This picture he would hang in his house.

The Beard is Gone
The last time I saw Ramiro I was surprised to see that he no longer had a beard.

"Tell me," I said, "who shaved off your beard? Was it a bet? Are you ill?"

Ramiro had a sparkle in his eye. He looked a lot happier than I had ever seen him.

"I will tell you how I lost my beard," he said, "but you have to hear the whole story."

And so we went into the house.

The Strange New Fruit
Hanging on the walls were his paintings of food. One, however, was larger than all the rest.

"What kind of fruit is this?" I asked.

"Ahh," sighed Ramiro. "I see you have not seen a Jiwi fruit before. It taught me such a lesson."

It was then that Ramiro told me his story.

Ramiro Tells His Story
"One day I went to the market in Oaxaca de Juarez. I wandered for a long time. Not one piece of food took my fancy.

Then, I came across a little stall. At the back of this stall there were three pieces of a strange fruit. I decided that I must have it.

I went to my room and ate the fruit. It was so good. The juice dribbled over my fingers and down my chin.

A Terrible Shock
I then went to wash the juice off and I got a shock. It would not come off. The more I washed the stickier it became.

My hands stuck to my beard. I had a terrible time getting them off. I was wailing and tugging at my beard when my hosts came in."

"You have been eating a Jiwi fruit, haven't you?" they said.

"I admitted that I had indeed eaten three Jiwi fruit."

"Three Jiwi Fruit all by yourself," my hosts said. "If only you had shared the fruit we would have advised you. You must always rub your face and hands with oil before eating a Jiwi fruit."

Ramiro continued his story.

"I rode back home. On the journey, things stuck to my beard. Flies flew in and never came out. Leaves falling to the ground met my beard and stayed there. By the time I got home I was in an awful mess.

Ramiro's Great Loss
I rushed inside and sat in front of the mirror. My beard had lost all its beauty. I knew I could not keep it. Next day I shaved it off.

I hoped I would not see anyone. I was so ashamed."

Ramiro was silent for a moment. Then he continued.

A Surprising Outcome
"Do you know what happened next? As I was walking home with my head down, people started to recognize me."

"Why it is the trader, Ramiro," and "Hello there," they said.

"A woman ran up to me. She pressed a small basket of fish into my hands. A man called me over and asked me to dinner. His little son gave me a huge smile.

These things had never happened to me before. When I had people to dine they always seemed a little afraid of me. Now they greeted me in the street. They were not in the least timid.

I went home with a warm feeling inside. That night I slept well. The next day I drew this picture of the Jiwi Fruit. I had learned such an important lesson."

We went out to sit on the porch. Before I went home we sat for a while exchanging stories. However, none as good as Ramiro's story of the Jiwi Fruit.

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Assignment 1: Ramiro and the Jiwi Fruit
Activity 1 Create a picture for the story "Ramiro and the Jiwi Fruit" with yourself as Ramiro's friend. Activity 2 1. Work in groups 2. Make a model of Ramiro's house. 3. Make the house from cardboard boxes. 4. Cut a door and windows and paint the walls. 5. Perhaps you would like to bring a colorful scrap of material from home to make little rugs.
Activity 3 Making a Framed Picture Make your picture small enough to hang inside the house. What is your favorite food? Draw a small picture of 3 portions of your favorite food. Remember to sign your name at the bottom of the picture. Framing your picture. You will need: lengths of twig, string, and glue 1. Cut 4 pieces of twig, slightly longer than your picture. These are the sides of the frame. 2. Bind each corner of the frame together with string. 3. Start by tying the string around one piece and then lashing the two together as shown. 4. Finish each corner by tying the string tightly. 5. Glue the frame to the picture. 6. When dry, tie a piece of string to the frame so that the picture can be hung.

Assignment 2: Guided Reading
This Guided Reading assignment is designed to be used as a teacher guide for class discussion of the story. It is not intended for the teacher to formally teach about synonyms and antonyms. In other words we do not expect the teacher to teach a formal grammar lesson.

We do expect the teacher, say, to discuss with the children different aspects of the story. For example, helping the children to select words with the same meaning (see "Identifying synonyms"). This is followed with words of the opposite meaning (see "Identifying antonyms").

We would leave to the teacher the point at which he/she would introduce the terms "synonyms" and "antonyms", and whether this would occur. The main point is to get the children to work with similar or opposite words. Similarly, the same principal applies when introducing "defining the word from context", and "selecting a stated concept", and "determining the sequence of events." The total emphasis should be on building the children's confidence to work with language not introducing them to formal grammar.

The headings in each question are for teacher's guidance; they are not for children's work or usage. The questions are designed, therefore, to be used by the teacher for development of oral language. For example, in the group discussion the teacher can embellish these guidelines and "brings the questions to life" when working with the students.

We hope that we have conveyed the type of atmosphere we want established in the classroom. It is not one where children sit at a desk and learn synonyms and antonyms, defining the word from context and selecting a stated concept as if they were headings in a grammar textbook. We want the children to be introduced gradually and gently to working with different aspects of our language through an oral approach.

The last item "identifying nouns, verbs and adjectives" is the first exercise where the children are introduced to any type of formal grammar. However, this is done in a way that is appropriate to their mindset. For example, the exercise is based on children associating color with parts of speech.

1 Identifying synonyms
Ramiro was respected and loved by all who knew him.
Select words from the following that have the same, or almost the same, meaning as respected:
admired, understood, valued, disliked, appreciated

2 Identifying antonyms
If people had not respected Ramiro what words do you think might be used to describe how they felt about him?

3 Defining the word from context
These are statements relating to dribbled. What do you think the word means?
When Ramiro ate the Jiwi fruit the juice dribbled down his fingers and chin.
Even though we turned off the faucet, the water still dribbled out.
There had been no rain for weeks and the water from the stream dribbled into the pond.

4 Selecting a stated concept
Why did Ramiro shave off his beard?
Select one:
He was tired of it
He thought people would like him better
It became tangled and matted
His friends advised him to shave it off

5 Determining the sequence of events
Place these statements in the correct order.
1. Ramiro wandered around the market.
2. The juice from the Jiwi fruit stuck to his hands and beard.
3. There was no food in the market that Ramiro wanted.
4. Ramiro had to shave off his beard.
5. Ramiro saw a stall with some unusual fruit.
6. Ramiro took the fruit home and ate it all.

6 Identifying nouns, verbs and adjectives
For this activity each student will need three colored pencils (red, blue and green), and a copy of the story, Ramiro and the Jiwi Fruit (student version).

Work as a class or in small groups.

Read the story, looking for nouns. As soon as a student identifies a noun, stop and give the students time to gently shade the noun in blue. Repeat this until around 6 nouns have been identified and shaded.

Repeat this activity, this time looking for verbs and shading these in red.

Finally, repeat the activity,but this time identifying adjectives and shading them in green.

The red is used for the verbs because of its quality of warmth and activity, green for adjectives, because of the living quality of green and blue for nouns for its quality of coldness.

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Assignment 3: Creating Patterns

1x3=3

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Remember how Ramiro drew 12 pictures with 3 portions of food on each. In this pattern a symbol has been used instead of the picture with 3 portions of food. The pattern has been started for you. Can you complete the pattern using colored pencils until you reach 12x3 = 36?

2x3=6

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3x3=9

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Assignment 4: Table Summary
Ramiro was a trader from a little village near Mexico City, who loved to try new types of food. Ramiro would travel to new places and buy three portions of a food he had never tried. He would draw the food and hang the drawings on the walls of his house.
The 1st drawing was of 3 silver fish	3	portions of food in all
The 2nd drawing was of 3 mangoes	6	portions of food in all
The 3rd drawing was of 3 guavas		portions of food in all
The 4th drawing was of 3 pineapples	12	portions of food in all
The 5th drawing was of 3 tacos		portions of food in all
The 6th drawing was of 3 burritos		portions of food in all
The 7th drawing was of 3 tostadas		portions of food in all
The 8th drawing was of 3 papayas		portions of food in all
The 9th drawing was of 3 blue fish		portions of food in all
The 10th drawing was of 3 eels		portions of food in all
The 11th drawing was of 3 speckled eggs		portions of food in all
The 12th drawing was of 3 Jiwi fruit		portions of food in all

We can write this in a short form - have a look below.
The 1st drawing was of 3 silver fish	3	portions of food in all	1 x 3 = 3
The 2nd drawing was of 3 mangoes	6	portions of food in all	2 x 3 = 6
The 3rd drawing was of 3 guavas		portions of food in all	3 x 3 =
The 4th drawing was of 3 pineapples	12	portions of food in all	4 x 3 = 12
The 5th drawing was of 3 tacos		portions of food in all	5 x 3 =
The 6th drawing was of 3 burritos		portions of food in all	6 x 3 =
The 7th drawing was of 3 tostadas		portions of food in all	7 x 3 =
The 8th drawing was of 3 papayas		portions of food in all	8 x 3 =
The 9th drawing was of 3 blue fish		portions of food in all	9 x 3 =
The 10th drawing was of 3 eels		portions of food in all	10 x 3 =
The 11th drawing was of 3 speckled eggs		portions of food in all	11 x 3 =
The 12th drawing was of 3 Jiwi fruit		portions of food in all	12 x 3 =

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Go Shopping! - 3 x 3 = 9 Jiwi Fruit A game for up to four players Preparation Divide the class into groups of four. Have each group of players make a set of playing cards. The game requires 36 cards with each of the twelve foods drawn on three cards. (36 cards in all) A pair of factors from the 3 Times Table together with the product should be written above the drawing and the name of the food below it. Aim of the Game The aim of the game is to get as many matching sets of three as possible. Rules of the Game Each player is dealt five cards. The remaining cards are placed face down in the center and the game proceeds as follows: As the players collect sets of three matching cards they should place them face down on the table. If the cards on the center pile run out, the players should continue without picking up. The game ends when the players' cards run out. The winner is the player with the most sets.

Assignment 5: Let's Practice What We Have Learned Do you remember how Ramiro used to draw pictures of the unusual food he would always buy? He would hang the pictures of three portions of his favorite food around his home.
1. Beside the door leading to the last room of the house was a drawing of speckled eggs. How many portions of food were in this drawing?		X		=
2. In the main room of Ramiro's house there were more pictures. On the left-hand wall there were pictures of papayas, blue salt-water fish and eels. How many portions of food had Ramiro drawn?		X		=
3. On the right hand wall there were three more drawings - one of tacos, one of burritos, and one of tostadas. How many portions of food had Ramiro drawn?		X		=
4.Under the porch of Ramiro's house there were four drawings. One of silver fresh-water fish, one of mangoes, one of guavas and one of pineapples. How many portions of food was this.		X		=
5. How many pictures were there if you add together those beside the door, those in the main room, and those under the porch?
6. Can you work out how many portions of food Ramiro had drawn for all these pictures - the ones beside the door, those in the main room, and those under the porch??		X		=

Assignment 5 - Continued
7. When Ramiro drew his picture of the Jiwi Fruit, it was his twelfth picture. How many portions of food had he drawn in total?		X		=
Take care - these problems are a little different!
8. In the main room of the house there were 18 portions of food on the wall. How many pictures were displayed there? Put your answer in this box		X		=
9. Ramiro drew 12 portions of fruit. Can you work out how many pictures of fruit he drew? Put your answer in this box.		X		=
10. Ramiro drew 9 portions of fish and eel. Can you work out how many pictures he drew? Put your answer in this box.		X		=
11. If Ramiro moved his picture of the Jiwi fruit to the porch so that everyone could see it when they came to visit, there would be 15 portions of food displayed. How many pictures is this? Put your answer in this box.		X		=
12. When Ramiro's friends found out about his adventures with the Jiwi fruit, they decided to show him how to eat the sticky fruit. Six of his friends arrived on the same day, each carrying three Jiwi fruit! They all sat around Ramiro's table to share the fruit. Can you work out how many Jiwi Fruit they shared?		X		=

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Assignment 6: Patterns - Three Times Table

Write all the multiples of 3 in these boxes. Start with 3 and carry on until you reach 36. Once you have filled in the boxes see how  many of these numbers you can find in the chart below. Color each one. Be careful - they appear more than once.

1	2	3	4	5	6	7	8	9	10	11	12
2	4	6	8	10	12	14	16	18	20	22	24
3	6	9	12	15	18	21	24	27	30	33	36
4	8	12	16	20	24	28	32	36	40	44	48
5	10	15	20	25	30	35	40	45	50	55	60
6	12	18	24	30	36	42	48	54	60	66	72
7	14	21	28	35	42	49	56	63	70	77	84
8	16	24	32	40	48	56	64	72	80	88	96
9	18	27	36	45	54	63	72	81	90	99	108
10	20	30	40	50	60	70	80	90	100	110	120
11	22	33	44	55	66	77	88	99	110	121	132
12	24	36	48	60	72	84	96	108	120	132	144

Teacher Notes

The following are stages of this activity: 1. The first activity reinforces what students have learned in this lesson and shows them the pattern of the multiplication facts. 2. The teacher may want to extend this activity to include the rest of the numbers in the Multiplication Square; with students coloring the numbers 42, 45, 48, 54, 60, 63 and so on up to 144. 3. Students can be shown how to use the square to check their answers when they solve the multiplication problems in this lesson. The squares they have shaded will help them trace with their fingers the horizontal and vertical lines to check their answers. 4. Some students may be ready to extend this process to check answers to all the multiplication facts to 12 x 12.

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