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Multiplication: Just the Facts, Ma’am

Mary Ebejer

Becki West

EDG 630 - 01

Teaching Mathematics K-8

November 30, 2010

Table of Contents

Introduction ................................................................................................................................. 3

Unit Standards(GLCEs)............................................................................................................... 3

“Big Ideas”.....................................................................................................................................4

Assessments....................................................................................................................................5

Lessons: 1: Kickoff Lesson ...............................................................................................7

2: Multiplication Illustration.........................................................................11

3: Fish Bowl.....................................................................................................19

4: Multiplication Constellations ....................................................................23

5: Array Art.....................................................................................................28

6: Groupings All Around Us..........................................................................31

7: Game: Circle and Stars .............................................................................34

8: Creating Multiplication Tables.................................................................38

9: Multiplication Houses.................................................................................44

10: Beaded Bracelets........................................................................................49

11: Billy Wins a Shopping Spree!....................................................................54

Songs …………………………………………………………………………….. 57

References .................................................................................................................................. 64

2

Introduction

This third and fourth grade math unit explores the various meanings and representations of

multiplication as “repeated addition. The lessons in this unit rely on extensive use of

manipulatives, as well as math songs and games and art activities to help students identify

situations when multiplication would be useful, to reinforce their learning and to improve

recall speed for multiplication facts.

Many of the activities in the unit involve cooperative learning in pairs, small groups and as a class

as a whole. Students should see their classroom as a place where cooperation and collaboration are

valued and expected. It respects the principle that interaction fosters learning and that cooperative

group work is basic the classroom culture.

Unit Standards

3 Multiply and divide whole numbers

3. N.MR.03.09 Use multiplication and division fact families to understand the inverse relationship

of these two operations, e.g., because 3 x 8 = 24, we know that 24 ÷ 8 = 3 or 24 ÷ 3 = 8; express a

multiplication statement as an equivalent division statement.

3.N.MR.03.10 Recognize situations that can be solved using multiplication and division including

finding "How many groups?" and "How many in a group?" and write mathematical statements to

represent those situations.

3. N.FL.03.11 Find products fluently up to 10 x 10; find related quotients using multiplication and

division relationships.

3. N.MR.03.12 Find solutions to open sentences, such as 7 x __ = 42 or 12 ÷ __ = 4, using the

inverse relationship between multiplication and division.

N.FL.04.10 Multiply fluently any whole number by a one-digit number and a three-digit number by

a two-digit number; for a two-digit by one-digit multiplication use distributive property to develop

meaning for the algorithm.

N.FL.04.11 Divide numbers up to four-digits by one-digit numbers and by 10.

3

N.FL.04.12 Find the value of the unknowns in equations such as a ÷ 10 = 25; 125 ÷ b = 25.*

N.MR.04.13 Use the relationship between multiplication and division to simplify computations and

check results.

N.MR.04.14 Solve contextual problems involving whole number multiplication and division.*

“Big Ideas”

Lesson 1: Kick off lesson

Students will discuss and write about their current understanding of multiplication

before we begin the unit of study. Recognize situations that can be solved using

multiplication and division including finding "How many groups?" and "How many

in a group?" and write mathematical statements to represent those situations.

Lesson 2: Multiplication Illustration

Students will demonstrate that they recognize situations that can be solved using

multiplication including: finding “How many groups?” and “How many in a

group?”

Lesson 3: Fish Bowl

Multiplication is repeated addition.

Lesson 4: Multiplication Constellations

Students will create arrays for multiplication fact families 0-12

using the medium of art, to help the students visualize the

meaning of multiplication

Lesson 5: Art Arrays

This lesson has the students using manipulatives to create arrays, and then extends

the lesson into students creating and finding artistic representations of arrays.

Lesson 6: Groupings All Around Us

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Multiplication is a quick way to figure out how many you have

altogether of something when things come in groups

Lesson 7: Circle and Stars Game

Students see multiplication as the combining of equal-size groups that

can be represented with a multiplication equation.

Lesson 8: Creating Multiplication Tables

Students create personal laminated multiplication tables as they

learn to recognize both the geometry and patterns inherent in

multiplication.

Lesson 9: Multiplication Houses

The students will be studying multiplication facts focusing on the multiples

of individual numbers. The multiples of whole numbers 0-12 will be

explored in this lesson as the students create multiplication houses of the

multiples of a given number.

Lesson 10: Beaded Bracelets

Students create beaded bracelets to explore multiplication,

estimation, prediction, charting and graphing, measurement,

and multiplication fact families.

Lesson 11: Billy Wins a Shopping Spree!

We use multiplication everyday to solve real-world problems.

Unit Songs: Multiplication songs

Introduce in morning playing a recording. During transition periods play songs.

Teach song at end of math lesson of the day. Each student has book of songs. Sing

song at closing.

5

Unit Assessments

Teacher observation of class work, combined with evaluation of Student Portfolio and Math Journal

Entries to serve as assessments of student understanding of multiplication, both its meaning and real-

world uses.

Formative:

Periodic Math Journal Entries

Individual daily activities and student work

Group Work and Class Discussion Observations

Summative:

Student Portfolios

The instructor will pass out a journal to each student. The journal will contain copies of

everything that will be used in this unit including handouts, templates, and multiplication

charts. The student journals will also contain blank paper for students to recorded their

observations and thoughts as well as to use to generate any computations that may be

needed. In my classroom this journal is comprised of a two pocket folder that contains

brads for binding papers.

As the students work through this unit their work will be evaluated formatively and

summative. A copy of all student work will be compiled and displayed in their portfolio to

assess the students’ overall understanding and progression throughout the study of this unit.

Final Math Journal Entry

“What I now know about multiplication.”

6

Grade LevelThird and Fourth

Time Needed50 minutes

Materials

Large piece of butcher paper

Marker to record ideas

List of questions to generate discussion

A math journal for each student

A copy of each chart located in the math journal; an instructor copy of a journal would work too.

M&M's, jelly beans, and small candy

Kick-off Lesson: Introduction to Multiplication

Introduction:

Students will be able to use multiplication to solve everyday math problems.

Students will be able to successfully complete their own math problems

using manipulatives.

3.N.MR.03.10 Recognize situations that can be solved using multiplication and

division including finding "How many groups?" and "How many in a group?" and

write mathematical statements to represent those situations.

3. N.MR.03.12 Find solutions to open sentences, such as 7 x __ = 42 or 12 ÷ __ = 4,

using the inverse relationship between multiplication and division.

N.MR.04.14 Solve contextual problems involving whole number multiplication and

division.*

Preparation:

The instructor will pass out a journal to each student. The journal will

contain copies of everything that will be used in this unit including handouts,

templates, and multiplication charts. The student journals will also contain

blank paper for students to recorded their observations and thoughts as well

as to use to generate any computations that may be needed. In my classroom

this journal is comprised of a two pocket folder that contains brads for

binding papers.

You will need bags of M&M's, jelly beans, or some other small

candy.

Engagement (15 minutes):

Teacher led class discussion

“Students open your math journals to an empty page. As we discuss our ideas about

multiplication you may write down your thoughts, ideas, and observations in the

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section titled ‘What I Know’. Write whatever you want to about the multiplication, spelling does

not matter in this part. Please don’t erase anything you write. Who’s ready to begin?”

The instructor is to ask a series of questions that follows. Record the answers on the classroom

KWL chart.

1. Has everyone heard about multiplication?

2. Who thinks they know what multiplication is?

3. Who thinks they could explain multiplication?

4. Who knows any multiplication facts?

5. Does anyone know how to solve a problem using more than one multiplication fact?

Journal Time:

Students will write their ideas about multiplication in their math journals (3min)

Exploration (30 minutes):

M&M multiplication:

Using real world story problems to solve multiplication facts

This is a lesson to help students understand the uses of multiplication and practice

problem solving while having fun. You will need bags of M&M's, jelly beans, or

some other small candy.

Procedure:

Students are divided into groups.

Give each group a bag of candy.

Explain that each group must share their candy with the other groups.

Give each group a different problem to solve. For instance, if you have 5 groups with 4

students in each group tell your first group they must give every group 12 pieces of candy.

8

What is the multiplication problem that would tell them how many pieces of candy they

need? (12 X 5 = 60). Have them write the problem on the board and explain to the class

how they solved their problem.

Each group would be given a different problem.

When each group receives their candy from another group they should write down the

problem needed to show how many pieces of candy each student in the group will receive.

(4 Students X ? = 60). At the end of the lesson let the students eat their candy

Teacher lead class discussion

“Now we will discuss the section titled ‘What We Want to Know’. As we discuss the things we

want to learn about multiplication, you may write down your thoughts and ideas in the section titled

‘What I Want to Know’. Who’s ready to begin?”

The Instructor will ask for volunteers to tell the class what they hope to find out by studying this

unit. Record the answers on the classroom KWL chart.

Journal Time:

Students may record what they hope to learn in their journals. (5 min)

Explanation:

Setting the agenda:

The instructor will explain that we are going to be studying multiplication for the next unit: the

agenda for the unit:

Students will bring home their journals daily and record their observations and discoveries

about multiplication in their journal

Students will locate arrays in real life, and either photograph them, draw them, or bring in

examples of them.

Students will create their own examples of multiplication through literature, music, and art.

As we study certain aspects of multiplication, you will record your data and observations in

your journals.

9

You will occasionally have other assignments that are to be recorded in your journals as

well. I will give you that information when we get to the appropriate lesson.

An instructor led Exploration of the journals:

The instructor will show the students an example of the chart to record multiplication facts.

The instructor will show the students an example of the charts and templates they will use

during this unit. The instructor will remind them that we will not begin the individual

lessons or activities until we have done them as a class.

Students will take time to familiarize themselves with their journals. (5 min)

Instructor is to ask if there are any questions at this time.

10



Materials

Large piece of butcher paper

Marker to record ideas

List of questions to generate discussion

A math journal for each student

A copy of each chart located in the math journal; an instructor copy of a journal would work too.

Each Orange Had 8 Slices, A Counting Book

- 9 X 12 Drawing paper

- Crayons or markers for each student

- Copies of the checklist

- 1 Apple

- A knife

Lesson 2: Multiplication Illustration

Introduction:

Students will demonstrate that they recognize situations that can be solved

using multiplication including: finding “How many groups?” and “How many

in a group?”

Students will write mathematical statements to represent those situations.

Students will illustrate the examples of their mathematical statements to further

demonstrate principals

4th graders will be able to use this model to solve multiplication facts using

three 1-digit factors.

Standards







N.FL.04.10 Multiply fluently any whole number by a one-digit number and a three-

digit number by a two-digit number; for a two-digit by one-digit multiplication use

distributive property to develop meaning for the algorithm.


division.*

Preparation:

Obtain a copy of the book; Each Orange Had 8 Slices, A Counting Book, by

Paul Giganti Jr.

Make a transparency of the story template (refer to attached).

11

Copy the Each Apple Had 6 Seeds story template and checklist/rubric for each student (refer to

attached).

Obtain a knife and an apple.

Prepare 9 X 12 drawing paper, 1 sheet per student

Background:

Students should have knowledge of addition and or multiplication facts as a prerequisite to

teaching this lesson.

Students should know that multiplication is repeated addition.

Students will have knowledge of addition facts

Students will be able to count by 2s, 3s, 4s, 5,s ext…

4th grade students should have knowledge of multiplication facts.

Engagement

Hold up an apple and ask students if they have ever eaten an apple and counted the

seeds inside. Cut the apple into quarters and ask students how many equal pieces

there are. Invoke answers from students that there are four.

Take the seeds out of one of the pieces and count them with the students. Ask

students to determine how many seeds would be in the apple if each piece has the

same number of seeds as the ones just counted. Allow students to determine the

answer by multiplication, counting by numbers, or repeated addition.

Pose the question, If I had six apples just like this one, how many seeds would there

be in all? Have students give the number sentence required to answer this question.

Work the equation on the board with the students.

Exploration

Explanation

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Read the book, Each Orange Had 8 Slices, by Paul Giganti Jr., pausing to allow the

students to answer the questions posed on each page.

o Model the appropriate number sentences and mathematical reasoning behind the

correct answer.

Explain that the students will illustrate their own multiplication stories using 9 X 12

drawing paper, and the story template, which is similar to the format in the book.

Show the template transparency on the overhead projector and demonstrate how students

should write their own stories.

Invoke ideas from the students to fill in the blanks on the story template transparency.

Complete the template with the students and suggest ways it can be illustrated. Encourage

students to think of places, activities, animals, or things that are familiar to them, which

they can draw.

Exploration

Hand out the drawing paper, and clean the story template transparency. Hand out a copy of

the checklist to each student, and explain that this activity will be assessed using the criteria

on the checklist.

Allow at least 60 minutes for the students to write their stories and complete their

illustrations.

Circulate about the room providing feedback to students as they work. Make sure students

write their multiplication story correctly before working on their illustrations.

o 4th graders should work on this activity as individuals or pairs. If they work

together as pairs, they must each produce at least one illustration and story

problem.

o 3rd graders will need to work together in groups to complete this activity. They

should produce one story and illustration per group. Each student must participate

and fill out their own template however.

o The instructor must help with and check their mathematical reasoning before the

students may illustrate their story.

Have students share their stories and illustrations with the class.

Create a class book of multiplications stories created during this lesson for students to read.

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Extension

The students may create a book of multiplications stories using this model for their

portfolios with at least 5 examples.

4th graders can use this model to solve multiplication facts using four or more 1-digit

factors.

4th graders can use this model to solve multiplication facts using three or more multi-digit

factors.

Evaluation

This lesson assesses the multiplication of three or more factors for 4th graders and a

beginning understanding of multiplication for 3rd graders.

Formatively assess students' concepts and illustrations of multiplication factors by teacher

feedback as lesson progresses.

Using a rubric (refer to attached files) and template will allow you to either summatively or

formatively asses the students understandings

This product is formatively assessed using the checklist.

The lesson is intended to introduce multiplication to third graders, and to introduce

multiplication with three or more factors to fourth graders.

Excerpt from Each Orange Had 8 Slices, by Paul Giganti Jr.

14

4th grade Story template for lesson 1

On my way to the _________________,

I saw (1 digit number) ________________, each ___________ had (1 digit number) ____________.

On each _________ was (1 digit number) _________.

How many _________ were there? (Answer here)



Illustrate your story below:

Story book rubric and checklist 4th grade

Each Apple Had 6 Seeds Checklist

15

Story follows the template outline correctly _____

Story uses 1-digit numbers greater than 1 _____

Illustrations depict the story accurately _____

Multiplication applied accurately to determine each answer _____

TOTAL NUMBER OF POINTS _____

4 Points - Demonstrates acceptable understanding of multiplication of three 1-digit factors.

3 Points - Demonstrates partial understanding of multiplication of three 1-digit factors.

2 Points – Demonstrates inadequate understanding of multiplication of three 1-digit factors.

1 Point – Demonstration shows lack of understanding when multiplying three 1-digit factors.

0 Points – Failure to attempt the activity.

3rd grade Story template for lesson 1

On my way to the _________________, I saw (1 digit number) ________, each _________ had

(1 digit number) ____________.



Write the number sentence and answer:

Illustrate your story below:

16

Story book rubric and checklist 3rd grade

Each Apple Had 6 Seeds Checklist

Story follows the template outline correctly _____

Story uses 1-digit numbers greater than 1 _____

Illustrations depict the story accurately _____

Mathematics applied accurately to determine each answer _____

TOTAL NUMBER OF POINTS _____

4 Points - Demonstrates acceptable understanding of mathematics to obtain an answer

3 Points - Demonstrates partial understanding of mathematics to obtain an answer.

2 Points – Demonstrates inadequate understanding of mathematics to obtain an answer

1 Point – Demonstration shows lack of understanding of mathematics to obtain an answer

0 Points – Failure to attempt the activity.

Reference:

17

Christian, Peggy.2005. Multiplication Illustration.BeaconLearningCenter.com Dev.01.30.04 #

http://www.beaconlearningcenter.com/Lessons/11126.htm

Giganti Jr., Paul. 1992. Each Orange Had 8 Slices, A Counting Book. Greenwillow Books,

New York, NY.

18




MaterialsClear container for “fishbowl”

Unifix cube “fish”(One color for each work group, three cubes for each student)

11” x 14” paper

Writing pencils

Colored pencils

Grid paper (For extension)

Lesson 3: Fish Bowl

Introduction: This lesson introduces students to the concept of “multiplication as

repeated addition of equal sets.” First they will work either independently or in pairs

to write and illustrate their solution to a “How many are there altogether?” problem,

taking time to explore their thinking and clarify their understanding. Next, students

will share their ideas with the class so others can try-on alternate ways of visualizing

solutions to the same problem.

Preparation: Prepare ahead of time small “packets” of Unifix cubes, one color for

each work group, three cubes for each student.

GLCE:3.N.MR.03.10 Recognize situations that can be solved using multiplication

and division including finding "How many groups?" and "How many in a group?"

and write mathematical statements to represent those situations.

Engagement (5 minutes): First divide the class up into even groups of 3-5 students

each. Then pass out small bins of Unifix cubes to each group, giving each a single,

unique color. Next, hold up a clear container (bowl, plastic bin, etc.). Tell the

students that it’s a “fishbowl” and you want each of them to put three “fish” from

their group’s bin into the bowl.

Exploration (15 minutes):After discussing how many students put fish into the

bowl, tell the class that you want to see if they can figure out how many are in the

bowl altogether. On the board write:

There are ____ fish in the bowl.

I think this because __________.

Tell them they can work in pairs or independently, but they need to explain their

thinking with numbers and words. They can use pictures too if that would help.

Explanation (30 minutes): Reconvene as a group and ask the students to share their

thinking with the class. Acknowledge the different responses by asking thoughtful

questions that extend their thinking and illuminate fuzzy logic.

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Students might show some of the following examples (24 students, 6 groups of 4):

a) 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 (etc) = 72 fish

b) 3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3 = 72 fish

c) 3+3+3+3 = 12 red fish 3+3+3+3 = 12 blue fish 3+3+3+3 = 12 green fish

3+3+3+3 = 12 yellow fish 3+3+3+3 = 12 brown 3+3+3+3 = 12 orange fis

Then add 12+12+12+12+12+12 and you get 72 fish!

d) 12 red fish + 12 yellow + 12 blue + 12 brown + 12 green + 12 orange = 72 fish

e) 6 groups of kids x 4 kids in each group x 3 fish for each kid = 72 fish

f) 24 kids x 3 fish each = 72 fish

This is the time to explicitly make the connection that:

1) You can make groups of like things and add them together.

“What kinds of groups do we see here? 72 fish 1 time. 3 fish 24 times. 6 groups of three fish

added together. 12 groups of fish 6 times.”

2) Adding up groups of things is quicker and easier than adding up singletons (a and b).

“For those of you who added each fish by itself up to 72 and those who added 3 fish 24 times,

did you have any problems with your strategy? Do any other strategies look easier or faster?”

3) Multiplication is repeated addition of similar sized groups of things (c and d).

“Who can explain what I mean by, ‘multiplication is repeated addition’?”

4) Multiplication is commutative like addition, that is 2x4 = 4x2 = 8.

On the board write:

12 = 3 x 4 = 4 x 3 = 12

“Who can explain what I mean by, ‘multiplication is commutative’?”

5) You can group like numbers of things and add them to groups with larger or smaller numbers.

“Can you figure out how many fish there would be if there were 5 students in the green and

orange fish groups?”

20

Sample answer:

3+3+3+3 = 12 red fish 3+3+3+3 = 12 blue fish 3+3+3+3+3 = 15 green

fish

3+3+3+3 = 12 yellow fish 3+3+3+3 = 12 brown fish 3+3+3+3+3 = 15 orange fish

12x4 = 48 fish and 15x2 = 30 fish

48 fish + 30 fish = 78 fish!

“What if there were 8 students had red and 8 had yellow fish, 5 had blue and 5 had brown fish

and only 3 students had green and 3 had orange?”

Sample answer:

3+3+3+3 = 12 red fish 3+3+3+3+3 = 15 blue fish 3+3+3 = 9 green fish

3+3+3+3 = 12 yellow fish 3+3+3+3+3 = 15 brown fish 3+3+3 = 9 orange fish

12x2 = 24 fish and 15x2 = 30 fish and 9x2 = 18 fish

24 fish + 30 fish + 18 fish =72 fish!

“Hey, that’s interesting. That’s the same amount as we had the first time! Who knows why?”

6) Multiplying groups of things is even quicker and easier when you learn your math facts!

3 red x 4 kids = 12 red fish 3 blue x 4 kids = 12 blue fish 3 green x 4 kids = 12 green fish

3 yellow x 4 kids = 12 yellow fish 3 brown x 4 kids = 12 brown fish 3 orange x 4 kids = 12 orange

fish

And 12 fish x6 groups = 72 fish!

“There’s one way that’s even faster. Can anyone see it? … 3 fish x 24 kids = 72 fish!”

“Do you think you could make similar groups for the other examples? Sure you could.

Who wants to show us how?”

Invite at least two students come to the board and show their thinking. Ask the rest of the

class if they agree. Be sure to ask them to explain their thinking if they head down the

wrong path. Others in the class who may have gone there too will benefit.

21

Extension: Pass out grid paper and ask the students to represent their thinking in colorful arrays.

Ask them to write a number sentence that means the same thing as their array. Ask for volunteers to

explain their work. Ask thoughtful questions that extend their thinking and illuminate fuzzy logic.

Evaluation: Monitor student’s oral and written responses to assess understanding of multiplication

as repeated addition. Collect written responses as formative assessment.

Reference: Burns, M. (1995).Writing in Math Class: A Resource for Grades 2-8. Sausalito, CA: Math

Solutions.

22

Grade LevelThird and fourth


MaterialsKitchen sponges cut into the following shapes:

8 2inch stars

10 1 inch stars

8 ½ inch stars

Gold paint

Silver paint

Copper paint

If not available use white and yellow paint

Construction paper

Yellow crayons, yellow crayons, or chalk

Pencils

Paint pens or chalk

Ruler or straight edge

Sketch paper or

Grid paper

Lesson 4: Multiplication Constellations

Introduction:

In this lesson, students will create arrays for multiplication fact families 0-12

using the medium of art, to help the students visualize the meaning of

multiplication. The final multiplication constellations will be displayed in the

classroom for the students to use as a reference tool.

Standards

N.MR.03.10 Recognize situations that can be solved using multiplication and

division including finding “How many groups?” and “How many in a group?” and



3. N.MR.03.09 Use multiplication and division fact families to understand the

inverse relationship of these two operations, e.g., because 3 x 8 = 24, we know that

24 ÷ 8 = 3 or 24 ÷ 3 = 8; express a multiplication statement as an equivalent division

statement.




3. N.FL.03.11 Find products fluently up to 10 x 10; find related quotients using

multiplication and division relationships.







23

N.FL.04.12 Find the value of the unknowns in equations such as a ÷ 10 = 25; 125 ÷ b = 25.*

N.MR.04.13 Use the relationship between multiplication and division to simplify computations and

check results.

N.MR.04.14 Solve contextual problems involving whole number multiplication and division.*

Preparation:

The instructor will prepare head of time the materials needed for this lesson.

The instructor will have cut the kitchen sponges into star shapes of ½ inch, 1 inch, and 2

inch diameter stars.

Students with number facts 1-30 will receive 2 inch stars

Students with number facts 31-70 will receive 1 inch stars

Students with number facts 71-100 will receive ½ inch stars

The instructor will prepare a large work area for the students and protect the area with

newspaper.

The instructor will pour washable tempura paint into the painting dishes beforehand.

The instructor will place two dishes of each color at each work station. Students will be

working four students to a station.

Background:

The instructor will explain that today we are studying multiplication arrays. The instructor

will divide the multiplication facts represented on the 100s chart into groups of 5. The

instructor will group these problems according to their difficulty level, and pre-assign each

student five problems and arrays to work on based on skill level.

Engagement:

Have the students bring their math notebooks and pencil to the reading circle. The

instructor will begin by explaining the assignment and activity for the day will be

multiplication arrays.

Ask the students to write in their notebooks what they think a multiplication array is.

According to the multiplication facts the instructor chose before hand; the students will be

given a multiplication problem to solve and present for this project.

24

The students are to solve their problems in their notebooks. The students are to share their

work with a partner and ask their partner for help if needed.

The instructor will walk around to check for correct answers.

The instructor will then choose a problem to represent as a constellation array.

The instructor will demonstrate what a 4x5 constellation would look like as well as a 5x4

constellation. The instructor will write the proper number sentence at the bottom of the

page, and then place above it an array illustrating that sentence. The original will be done

on sketch paper or grid paper to demonstrate proper placement. (It is important that the

students know an array is in the form of a grid, not just 20 objects on a page.) Then this

graft will be done in crayon first to show proper placement of stars on construction paper,

using the ruler to space the stars out evenly.

Finally the instructor will demonstrate how to use the sponges with the paint to create the

constellation.

The student will sketch out their multiplication array on a piece of paper before beginning

the project.

Exploration:

The students may begin sketching out their multiplication arrays on a piece of graph paper

or sketch paper before heading to their seats; they may begin this process as the instructor is

demonstrating it. The original will be done on sketch paper or grid paper to demonstrate

proper placement. (It is important that the students know an array is in the form of a grid,

not just 20 objects on a page.)

Once a student has successfully demonstrated their understanding of the array

representations of their number sentence, they may continue to the next step.

The students will write the proper number sentence at the bottom of the page, and then

place above it an array illustrating that sentence.

Then this graft will be done in crayon or chalk first to show proper placement of stars on

construction paper, using the ruler to space the stars out evenly.

The instructor must verify all drawings in chalk or crayon before the students may move to

painting.

Finally the students will use the sponges with the paint to create the constellations.

25

Dip the star sponge in the paint, wipe off any excess paint against the side of the pint dish,

the sponge should be close to dry, with no dripping paint.

Using chalk or a paint pen write over the number sentences when the arrays are complete.

The instructor will collect the individual arrys when they are finished and palce them aside

to dry.

Explanation:

Reconvene as a group and ask the students to write in their notebooks what they think a

multiplication array is now.

Have the students share their thinking with the class.

Help the students to come to the following understandings:

Students can more readily develop an understanding of multiplication concepts if they see

visual representations of the computation process. For example, they can picture students in

a marching band arranged in equal rows or chairs set up in rows in an auditorium. These

arrangements all have something in common; they are all in rows and columns. An

arrangement of objects, pictures, or numbers in columns and rows is called an array. Arrays

are useful representations of multiplication concepts. For example using the instructor’s

demonstration illustrations we can see that this array has 4 rows and 5 columns. It can also

be described as a 4 by 5 array. When the students can see the connection between equal

groups and arrays, they can easily understand how to use arrays to multiply. They will use

arrays again later to divide.

Extension:

We may not finish all of the facts on the 100s chart in one day, this may be extended to two

days.

Extend the arrays to multiplication facts 12x12.

For students who are familiar with multiplication facts: give these students products and ask

them to develop arrays representing the many fact families that create that product. These

students may also help other students when they are finished who may be having difficulty

with the assignment.

26

Evaluation: Monitor student’s written and demonstrated responses to assess understanding

of multiplication facts as an array of objects. Collect the notebook responses and these

arrays as formative assessments.

Reference:

Brunetto, Carolyn. (1997) Math Art Projects and Activities. Scholastic. New York, New York.

27



MaterialsCans

Flashcards

Blank bulletin board

Small bags of

buttons

Grid paper with 1

inch grids

Construction paper

Crayons

Lesson 5: Art Arrays

Introduction:

Students can more readily develop an understanding of multiplication concepts if

they see visual representations or complex mathematical concepts. An arrangement

of objects, pictures, or numbers in columns and rows is called an array. This lesson

has the students using manipulatives to create arrays, and then extends the lesson

into students creating and finding artistic representations of arrays.

Standards






Engagement:

Begin with an array of cans (4 x 6) stacked on the table at the front of the

room.

Ask the students if they have ever seen something similar to this. Ask them

where?

Explain that this is called an 'array': an arrangement of items in a number of

equal-sized rows.

Ask the students where else they have seen arrays of items.

Have the students identify arrays that are in the classroom. (make sure that

there are a number of possibilities before beginning the lesson).

Finally, point out a blank bulletin board and tell the students that they will be

making their own bulletin board with the work they do today.

Exploration:

28

Call the students' attention to the array of cans at the front of the room, again. I will ask

them how many rows across there are of the cans. How many cans in each row? I will write

"4 rows of 6 cans" on the board. How many cans in all? I will write " = 24" next to the

existing sentence. Is there another way that I can write this? I will write "4 x 6 = 24."

Have the students get into pairs and pass out bags of small buttons to each group. Tell the

class that we are going to practice making arrays with the buttons.

Using a set of flashcards (making sure that the "0" facts are taken out), pick multiplication

problems at random. If flashcards are not available use a deck of cards, or dice.

Write the problem in large print on the board, and ask the students how I could make an

array to show this problem. Using buttons on an overhead demonstrate your array to the

students.

Demonstrate how arrays can be drawn on a grid. We will practice doing this together, and I

will be sure to point out the fact that a 2 x 3 array yields covers the same space as a 3 x 2

array. I will also be sure to label each array appropriately.

Continue to pick cards at random, having the pairs of students make arrays with their

buttons. Choose volunteers to demonstrate what they have done at their desks, using the

buttons on the overhead.

Ask for students who may have done the problems in a different way.

Determine if the students may have discovered the Commutative Property on their own.

Turn the page on the overhead so that it is sideways. Ask if this is the same problem. Why

or why not? We will discuss how this problem is written and why it is the same.

Repeat this activity, but each group needs to show the two arrays that yield the same

answer.

Now mix up the flashcards, hold them facedown, and have each child pick two

29

The students are to outline and color each array on the grid paper. Then they should cut out

each array.

Pass out one piece of construction paper to each student. When they are finished, they will

need to glue each array onto the construction paper, making sure to label my array with the

proper number sentence.

Extension:

This extension project uses multiplication and art: we will find pictures of things in the real

world that illustrate and or display multiplication arrays. Pictures may be found in

magazines, or on the internet. If we can’t find pictures we can brainstorm ideas on what

might represent that amount, then find or create that object and photograph it. Once this

project is completed we will have a classroom multiplication table similar to a 100s chart

with the displayed arrays to place on the math bulletin board. Then we will take a

photograph of our board and make a copy for each student to have in their personal journal

as well.

Evaluation:

The formative assessment of this lesson will be watching the students’ progress. The

summative assessment of this lesson will be the finished products. When all of the students

have finished making and labeling their arrays, we will be displaying the arrays on the

bulletin board. Then, I will have the students come up one by one. Each student should

show his/her array to the class, tell us what multiplication sentences that each one

illustrates, and then I will hang it up on the board.

Reference:

Dalke. J. 2010, Commutative Property. Math art. the lesson plan page. Retrieved from.

http://www.lessonplanspage.com/MathArtCommutativeProperty35.htm

30




MaterialsNewsprint (One piece for each work group)Drawing paper (At least one for each student)

11” x 14” paper

Writing pencils

Colored pencils

Lesson 6: Groupings All Around Us

Introduction: This lesson introduces students to the concept of “Multiplication is a

quick way to figure out how many you have altogether of something when things

come in groups.” First the class will work collaboratively brainstorming a list of

objects in the world that always occur in groups of 2, 3, 4 … 12 and solving made

up problems to find “how many?”. Next, students will work in small groups creating

and solving their own made up problems. Finally, each group will share their ideas

with the class so others can try-on alternate ways of visualizing solutions to

multiplication problems.

Preparation: Prior to beginning the lesson, determine how the class will be divided

up into groups of 3-5 students each. Have sufficient newsprint for each group to

have one piece. Also, be prepared to record lists generated by the class as a whole on

newsprint posted on the wall, chart paper on an easel or on the white board. For the

extension activity, each student will also need a piece of paper on which to write and

illustrate a sample multiplication problem.

GLCE:3.N.MR.03.10 Recognize situations that can be solved using multiplication

and division including finding "How many groups?" and "How many in a group?"

and write mathematical statements to represent those situations.

3.N.FL.03.11 Find products fluently up to 10 x 10; find related quotients using


Engagement (10 minutes):“Today we are going to brainstorm what sorts of things

that come in groups of 2s, 3s, 4s, 5s all the way up to 12s. First we’re going to list as

a class together examples of things that come in groups of two. Then,we’re going to

break out into small groups. Each group will continue to brainstorm lists of things

that come in groups of 3s through 12s and record their ideas on a large sheet of

paper.”

Now, together as a class, brainstorm a list of things that always come in twos,

excluding things that sometimes come in twos. If students are unsure about an item,

31

list it off to the side to research later. Once you have a good list of items, break up into the smaller

work groups for the students to continue on their own. Be sure to remind them that since they are

not listing groups of 1s and you have already listed groups of 2s together, each group will be

exploring 10 lists total.

Exploration (20 minutes):The first challenge of this activity will arise as the students figure out

how they will work cooperatively to brainstorm and record their groups’ lists. Resist the urge to step

in, confidently assuring them that they can figure it out for themselves. The next puzzle will be to

figure out how to arrange their thinking on the large sheet of paper. Again, resist the urge to step in.

Use this time to assess the creativity and uniqueness of each student’s thinking, as well as the

students’ ability to cooperatively problem solve in a group setting.

Explanation (20 minutes): Once all the groups have completed their lists, it’s time to discuss them

together as a class.

“Now we’ll go around the room, group by group. Each group will report just one thing from any

one list, without telling us which list it’s on. Then the others in the class will have the chance to

decide where it belongs. Once we agree, I’ll write it on the board under the correct number. Since

you’ll want to report something from your list that has not already been suggested, take a few

minutes now to have an alternative in case the one you chose has already been mentioned.”

This part of the activity will involve group thinking and discernment. Some items will be obvious,

legs on a dog and cans in a six-pack, for example; others may not be, such as legs on a stool or

points on a star. You will need to talk this through problem together. Someone may suggest

something that makes no sense. Others may be very creative, so be sure to ask students to explain

their thinking. For example, a group my say “four holes in a shirt,” then offer they were thinking of

the one for the neck, at the bottom and for each sleeve!

32

Extension: These lists are a rich resource for generating problems that students can solve. Start by

creating problems and linking them to their proper multiplication sentences.

1) For example, ask:“How many cans of Coke are in three six packs?”

If the students are able, have them tell you what sentence to write. If not, you write 3 x 6 = 18

on the board. Then ask: “What does the 6 tell us? What does the 3 tell us? What does the 18 tell

us? How do you know that 18 is correct?”

2) Another activity would be to have students to write and illustrate multiplication problems for

others to solve. They can write the problem out in words with an illustration on one side of the

paper, then turn it over and write the complete multiplication sentence on the other side. That

way, children can read each other’s problem, solve them, and check their solutions. Challenge

students to see how many ways they can figure out the answer. Then ask volunteers to share

their multiplication problems and their thinking for how they solved them.

It’s important that the solution is more than the answer that results from the multiplication; it is the

entire multiplication sentence. The emphasis is on relating the multiplication sentence to the

problem situation to develop children’s understanding.

3) Another extension activity would be to generate charts from the lists of 12 multiples. For

example:

People Eyes Multiplication Sentence

1

2

3

(etc.)

2

4

6

(etc.)

1 x 2 = 2

2 x 2 = 4

3 x 2 = 6

(etc.)

Evaluation: Monitor student’s oral and written responses to assess understanding of multiplication as

a quick way to figure out how many you have altogether of something when things come in groups,

as well as their ability to work in groups effectively together. Collect written responses as formative

assessment. Use extensions to challenge students who already have a basic understanding of

multiplication or to provide additional practice to students who need help clarifying their

understanding.

33



MaterialsOne six-sided die (One die per group of 2-4 students)

Three 8 ½” x 11” sheet of paper for each student

Writing pencils

12-sided dice (For extension)

Reference: Burns, M. (1987). A Collection of Math Lessons: From Grades 3 through 6. Sausalito, CA: Math

Solutions.

Lesson 7: Circles and Stars Game

Introduction: Through this game, students learn to see multiplication as the

combining of equal-size groups that can be represented with a multiplication

equation.

Preparation: Divide the class up into groups of two to four students and distribute

materials accordingly.

GLCE: 3.N.FL.03.11 Find products fluently up to 10 x 10; find related quotients

using multiplication and division relationships.

Engagement (10 minutes): Invite the children to fold their pieces of paper in half,

then in half again, creating four quadrants on each side. Explain the rules of the

game.

1. The first player starts the first round by rolling the die. This number is the amount

of circles he/she will draw in the first square on his/her paper. It is also the first

number in his/her multiplication problem.

2. The player rolls the die again. This number is the amount of stars he/she will draw

in each circle in that first square. It is also the second number in his/her

multiplication problem.

34

3. Now the player writes the two numbers and the answer in a multiplication sentence right below

the circles and stars.

4. Each player takes a turn until the group has repeated filled in all eight squares on their score

sheets (front and back).

5. Add up all of your answers. Whoever has the most wins the game!

Model how to play the game then invite the class to play one round with guided practice.

Exploration (15 minutes):The students play several rounds of Circles and Stars.

Explanation (15 minutes): Pose the following questions for students to discuss in small groups or

as a class.

- What is the fewest number of stars you can get in one round? Explain.

-What is the greater number of stars you can get in one round? Explain.

-What other observations did you make as you were playing this game? Explain.

-What numbers did you represent in different ways? Compare with your partner. Explain.

-I have a die that has a 0. What would you do if your first roll was a zero? Explain.

-What would you do if your first roll was a 5 and your second roll was a zero? Explain.

Create Class Data Chart.(Prepare before the lesson.) List all numbers 1-36 on a chart using

column format. (Thirty-six is the largest product possible using a six-sided die.)

Select one student to bring up one of his/her recording sheet. Together model how to use tally marks

to record the student’s scores for each round on the Class Data Chart. Then invite the groups to

come up and record their scores from all of their games on the Class Data Chart. Suggest that if one

partner reads each score, the other partner can record tally marks.

Discuss the data. After all students have played several games and recorded their products for each

round on the class chart, engage students in conversation about the data chart, asking questions like:

- Why did I write the numbers 1-36 on the chart?

-Are there numbers that are impossible using a 1-6 die? Explain.

- Why do some numbers have more tally marks than other numbers? Explain.

- What are the ways to get 2 as an answer? Ways for 6? Ways for 12? (Students might think

about this with a partner or in small groups. Record equations.)

35

- Which number(s) 1-36 has the most combinations using two 1-6 dice? What numbers can I

skip count by to say this number? (Relate numbers on dice to factors in multiplication

equations.

- You can skip count by both factors to figure out the product. Is this always true? (Ask students

to test this idea. Some may want to test larger numbers.)

-Is there a product that can only be represented one way? Why? Explain.

- What other observations do you notice about the data?

- How might this data be useful for thinking about multiplication combinations (facts)?

Extension: Invite those looking for a challenge to:

1. Change the die to a higher number sided die (e.g. 12 sided) to make the multiplication problems

more difficult.

2. Use two dice at the same time and choose which order to put them in for your circles and stars.

Commutative property of multiplication rule says you get the same answer no matter what order.

3. Write the fact family for each problem you roll to practice multiplication and division sentences.

Example: 3 x 4 = 12 4 x 3 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3

Evaluation: Monitor student’s oral and written responses to assess understanding of multiplication

as repeated addition. Collect score sheets for formative assessment.

Reference: Cleveland County Schools.http://tinyurl.com/circlesandstarsdirections. Accessed November 26,

2010. (Adapted from Math by All Means; Multiplication Grade 3 by Marilyn Burns.)

36

http://tinyurl.com/circlesandstarsdirections

Circles and Stars Multiplication Game

Mary Ebejer and Becki West

Objective

Students will be able to form simple multiplication problems using 1 die by grouping them in circles and using stars to represent the numbers then multiplying them to find the product.

Materials Needed

1 Die (6 sided)PaperPencil

Directions

1. Fold the paper into separate sections, usually four squares on front and four on back.

2. The first player starts the first round by rolling the die. This number is the amount of circles he/she will draw in the first square on his/her score sheet. It is also the first number in his/her multiplication problem.

3. The first player rolls the die again. This number is the amount of stars he/she will draw in each circle in that first square. It is also the second number in his/her multiplication problem.

4. Now the player writes the two numbers and the answer in a multiplication sentence right below the circles and stars.

5. Each player takes a turn until the group has filled in all eight squares on their score sheets (front and back).

6. Add up all of your answers. Whoever has the most wins the game!

Challenges

1. Change the die to a higher number sided die (e.g. 12 sided) to make the multiplication problems more difficult.

2. Use two dice at the same time and choose which order to put them in for your circles and stars. Commutative property of multiplication rule says you get the same answer no matter what order.

3. Write the fact family for each problem you roll to practice multiplication and division sentences.

Example: 3 x 4 = 12 4 x 3 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3

Lesson 8: Creating Multiplication Tables

From: http://tinyurl.com/circlesandstarsgame. Accessed November 26, 2010. (Variation on Marilyn Burn: “Circles and Stars.” Math By All Means. ©1991 The Math Solution Publications.)

**

2 x 4 = 8

37

Grade LevelThird

Time Needed5 days50 minutes/day

MaterialsFor each group:24 1” square tiles

For each student:8 ½” x 11” paper ruled with ½” squares (stack of extras on hand)

Writing pencils

Colored pencils

Scissors

“Rectangles”Worksheet

Introduction: In this 5-day lesson, students will create arrays for multiplication

fact families 0-12 and cleverly transfer them to create a multiplication table to

laminate for their own personal use.

Preparation: Prior to beginning the lesson, ask students to respond to this prompt in

their math journals:

Write what you know about the 0-12 multiplication table.

Their response will serve as a benchmark for their formative assessments.

GLCE: 3.N.FL.03.11 Find products fluently up to 10 x 10; find related quotients

using multiplication and division relationships.

DAY ONE: MAKING RECTANGLES

Engagement (10 minutes): Divide the class up into groups of four students. Invite

one person from each group to come up and count out 25 tiles and bring them back to

their group.

Exploration (40 minutes):“Each group will have 25 tiles. I would like you to work

with a partner in your group for this first task. (A group of three will work if there is

an odd number.) I want you and your partner to take 12 tiles and arrange them into a

solid rectangle. Your rectangle should be all filled in completely. Don’t use the tiles

just to outline a rectangle.”

Students create their rectangles.

“Look at your group’s rectangles. Raise your hand if both the rectangles are the same.”

“Now raise your hand if your rectangles are different.”

Some may not raise their hands at all because they have the same shape but a different

orientation, e.g. 6x2 and 2x6 or 4x3 and 3x4. Ask the students to describe their

rectangles so you can draw them on the board. Show that the rectangles are the same

dimension, just in a different position, so they are the same.

Rectangles that are the same shape and orientation but used different colors are also

the same.

38

Have a member from each group come up and draw their rectangle on the board until all factors of

12 are represented (1x12; 2x6; 3x4). Ask them to write “12” on each rectangle.

“Let’s try another number. This time, work as a group instead of with a partner. See if you can find

all the ways to build rectangles with sixteen tiles. Draw each rectangle you find on the grid paper,

write 16 inside, and cut it out. If you finish that and others are still working, do the same for the

number 7.” (Write 16 and 7 on the board.)

If anyone asks, a 4x4 square counts because a square is a rectangle.

Once you’re sure everyone understands the directions, they can continue making rectangles for each

number 1-25. Suggest that they continue using the tiles if that helps.

“Draw each rectangle you find on the grid paper, write the number on it and cut it out. You will be

cutting out a lot of rectangles so draw them close together to conserve paper. Also, don’t forget the

number 12. We already did it on the board, but you will need to draw and cut out rectangles for that

one too. Also, you will want to figure out a way to keep track of which ones you have finished. So

take a minute to get organized before you begin. Any questions?”

(If the paper isn’t long enough to cut out the longest rectangles, it’s okay to tape two pieces

together.)

As the time for the activity runs out, give each group a legal-size envelope. Ask them to put their

names on it and put all of their rectangles inside, as well as any extra paper and scraps of paper still

big enough for more rectangles. Put their envelopes and tiles on the supply table. Tomorrow, when

it’s time for math, they can get their envelopes, some tiles and paper and continue working.

DAY TWO: FINISH RECTANGLES; BEGIN SUMMARIZING

Engagement (10 minutes):On the board write the numbers 1-12 across the top, with about 6-8”

between each. As the groups finish, ask them to organize their rectangles by number. Then ask one

group at a time to come tape their rectangles to the board under the corresponding number. Be sure

to ask if any other group has any other rectangles after each set of rectangles is posted. If a groupis

missing a set or two of rectangles, this would be a good timeto make them.

Explanation (40 minutes):Distribute “Exploring Our Rectangles” worksheet to each student and

invite groups to investigate the patterns together.

You can leave the rectangles posted on the board for the next day’s lesson.

39

DAY THREE: MAKING OUR MULTIPLICATION TABLES

Engagement (10 minutes): Invite the students to come up to the board to take a good look at al of

the rectangles they have posted. After a few minutes, invite them to sit down on the floor near the

rectangle display and ask them how it went working in groups on their rectangles. (“What worked

well?” “What could have gone better?”)

Exploration (40 minutes): Work through each of the questions on the “Exploring Our Rectangles”

worksheet, listing the answers on the board, discussing the patterns, and giving new vocabulary

when appropriate. For example, for rectangles that have a side with two squares on them, write 2, 4,

6, 8 10. 12, 14, 16, 18, 20, 22, 24.

“What do you notice about these numbers?” (They skip every other one.)

“Who could continue the numbers in this pattern?”

“What is another name for these numbers?” (Even)

“These numbers are also multiples of 2 because each can be written as two times something … 2

times 2 is 4 (write 2 x 2 = 4).”

Other patterns to make note of include multiples of 3, 4 and 5, as well as squares, like 1, 4, 9, 16 and

25. Ones with only one rectangle like 1, 2, 3, 5, 7, 11, 13, 17, 19, 24 are prime.

Next, introduce the idea of transferring their rectangles to a chart.

“Here’s what I want you to do next. I’ll demonstrate on the board; then you’ll each do this

individually. You’ll use your own sheet of squared paper, but you’ll share your group’s rectangles.”

Tape a piece of the squared paper to the board. Take the 3-by-4 rectangle and place it on the squared

paper in the upper left-hand corner. Then lift the lower right-hand corner and write the number 12 in

the square. Explain:

“If I drew a rectangle around the 12, I would outline the 3-by-4 rectangle I used to locate the 12.

Now I’ll use the same rectangle, but in another position.”

Rotate the rectangle and again place it in the upper left-hand corner. Again, lift the lower right-hand

corner and write 12 in the square. Do the same for the 2-by-6 and the 1-by-12 rectangles, writing 12

in the four additional squares.

Demonstrate the process again using the rectangles for the number 9, showing that rotating the 3-

by3 rectangle doesn’t matter since the lower right-hand corner will be the same square either way.

40

Invite the students to return to their seats and follow this process for each of their rectangles that

would fit on the squared paper. They can use the rest of class to finish.

DAY FOUR: INVESTIGATING PATTERNS ON OUR MULTIPLICATION TABLES

Engagement (10 minutes):Ask students to take a look at their squared paper and the chart they are

creating. Does anyone recognize it?

Exploration (40 minutes):Discuss the patterns in what they have done. Look at rows with patterns

they are familiar with … 2s, 5s and 10s. Model how you continue to fill in the rest of each row and

column. Some students may also know the 3s. You can show them how to continue skip counting

using a calculator, pressing 3 then +, then = repeatedly until that row and column are filled in. Invite

the class to go back to their desks and fill in the rest of the numbers themselves. Also tell them that

as they fill in their tables you want them to make note of any special patterns on special 3” x 11”

strips of paper.

Explanation (15 minutes): When everyone has finished, post and compare what the students have

found. Some of the patterns will include:

In even numbered rows and columns, all of the products are even numbers.

In the odd numbered rows and columns, the products are odd, even, odd, even, odd, even.

In the 5 row and column, the products end in 5, 0, 5, 0, 5, 0.

For the 10x column, you just have to add a 0.

Everything in the 11 row and column has a double digit.

In the nines row and column, all of the products add up two nine.

Plus many more!

DAY FIVE: INVESTIGATING MORE PATTERNS ON OUR MULTIPLICATION TABLES

Engagement (10 minutes):Pass out several sheets of multiplication tables to each student and ask

them to get out their colored pencils or crayons. Tell them that today they are going to investigate

even more patterns on the multiplication table.

Begin by modeling the multiples of 6.

41

“First I need to make a list of the multiples of 6. Read them to me from the 6 row or column of your

multiplication table.” (The list will go up to 72.) Now demonstrate how you will cross off the

number 6 wherever it occurs on the chart, then the number 12 wherever it occurs, and so on.

“What is the largest number on the 12-by-12 table?” (144) “So we need to continue the list of

multiples to get as close to 144 as we can. Let’s add 6 to 72 to get the next number (and so on).”

“We could continue adding 6s or we could use a calculator. Do you think we will land exactly on

144? Is 144 a multiple of 6?” Invite students to explore their thinking out loud.

Exploration (40 minutes): Now invite the students complete what you’ve started on the multiples

of 6 chart in their small groups, then the multiples of the ten remaining numbers (2-5 and 7-12) –

making sure to use separate charts for each number.

“As we did here, you’ll want to first list the multiples of the number, then color in all of the

multiples of that number on a fresh multiplication table. Be sure to color in every square for that

multiple. For example, for multiples of 6, we crossed off all four 6s that occurred on the chart and

all six 12s. Continue until you have colored in all of the multiple squares and see what patterns

emerge.”

As the children work, write the numbers 2-12 on the board leaving room underneath each so group

representatives can post sample charts for discussion when everyone is done.

Explanation (15 minutes): Discuss the students’ findings during the last 15 minutes of class.

Example questions for their consideration include: What did you notice? Which of the numbers

have just stripes? We colored in the multiples of only two square numbers, 4 and 9. What did you

notice about them?

Evaluation: Monitor student’s oral and written responses to assess understanding of factor patterns

that emerge on the multiplication table. Also, ask the students to respond to this prompt in their

math journals: What do you know about 7 x 6?

References:

Burns, M. (1987). A Collection of Math Lessons: From Grades 3 Through 6. Sausalito, CA: Math Solutions.

Burns, M. (1991). Math By All Means: Multiplication Grade 3. Sausalito, CA: The Math Solutions

Publications.

Name __________________________________

42

EXPLORING OUR RECTANGLES

1. Which numbers have only one rectangle? List them from smallest to largest.

2. Which rectangles have a side with two squares on them? Write the numbers from smallest to largest.

3. Which rectangles have a side with three squares on them? Write the numbers from smallest to largest.

4. Do the same for rectangles with four squares on a side.

5. Do the same for rectangles with five squares on a side.

6. Which numbers have rectangles that are squares? List them from smallest to largest. How many squares would there be in the net larger square you could make?

7. What is the smallest number that has two different rectangles? Three different rectangles? Four?

Lesson 9: Multiplication Houses

From A Collection of Math Lessons: From Grades 3 through 6. (c)1987 Math Solutions.

43

Grade LevelThird


Materials

Construction paper

Two house templates for each student.

Scissors

Crayons

Markers

Tape

Glue

Stapler

Writing pencils

Colored pencils

Paper for calculating problems

Introduction: In this lesson, students will create multiples houses for

multiplication fact families 0-12 using the medium of art, to help the students

visualize the meaning of multiplication. The final fact houses will be

The multiples of whole numbers 0-12 will be explored in this lesson as the

students create multiplication houses of the multiples of a given number.

Standards




statement.









division.*

Preparation:

The instructor will prepare head of time the materials needed for this lesson.

The instructor will have drawn the template for the houses before hand.

Represent the windows with dotted lines. These will be guide lines for

cutting.

Photocopy this template at least two for each student; prepare extras for

students who may need to redo their work.

44

Write the numbers 0-12 on small pieces of paper, writing each number twice. Place these

slips of paper in a container.

Students will draw a number form the bowl. Pair the students with like numbers together,

they will work as partners.

Background:

The instructor will explain that today we are studying multiplication facts focusing on the

multiples of individual numbers. The multiples of a whole number are found by taking the

product of any counting number and that whole number. For example, to find the multiples

of 3, multiply 3 by 1, 3 by 2, 3 by 3, and so on. To find the multiples of 5, multiply 5 by 1,

5 by 2, 5 by 3, and so on. The multiples are the products of these multiplications. The

multiples of whole numbers 0-12 will be explored in this lesson as the students create

multiplication houses of the multiples of a given number.

Engagement (10 -15 minutes):

Have the students bring their math notebooks and pencil to the reading circle. The

instructor will begin by explaining the assignment and activity for the day will be studying

multiplication facts focusing on the multiples of individual numbers. The multiples of a

whole number are found by taking the product of any counting number and that whole

number. The multiples are the products of these multiplications.

Ask the students to write in their notebooks what they think a multiple is and an example

of one.

The instructor will select a number for example, to find the multiples of 3, multiply 3 by 1,

3 by 2, 3 by 3, and so on. To find the multiples of 5, multiply 5 by 1, 5 by 2, 5 by 3, and so

on.

Using a deck of cards the instructor will select a card and have the students work on the

multiples of that number using facts n x 0-12.

The students are to solve their problems in their notebooks. The students are to share their

work with a partner and ask their partner for help if needed.

The instructor will walk around to check for correct answers.

45

Everyone is working on the same problem and the instructor will as well. When we are

done we will share in the circle our answers.

The students will drw a card 0-12. This will represent the house they will be working on.

There will be two students with the same number 0-12, these studntet pairs will work

together to create their answers.

Exploration (20 minutes):

The students will sit in their pairs at their work stations to create their houses. Before they

begin to construct their houses the students must work collaboratively to find all the

multiples of their number 0-12.

For example if the card I draw is a 5, then my house is all the multiples of 5.

0x5=0

1x5= 5 2x5=10

3x5=15 4x5=20 5x5=25

6x5=30 7x5=35 8x5=40

9x5=45 10x5=50

11x5=55 12x5=60

Once a student has successfully demonstrated their understanding of the multiples of their

number, they may continue to the next step.

The student will take the first house template and cut the windows to make flaps, cut only

on three sides. Do not cut them all the way out, they must open and close.

Next the student will line up both of their houses using the house with the windows open as

the top sheet. Once they have been aligned properly glue, tape, or staple them together.

On the top sheet write on the door the number house the multiples belong to, for example

the house of fives.

Next label the window flaps 0-12 according to the order shown above.

46

Lift the flaps of the individual windows and write the answer to the multiplication fact

represented by the house number and the window. For example in the house of fives the “3”

window will need the answer 15 behind it.

Some examples can be found below. The instructor will have to create their own template

using these as models.

Once the students have finished placing their houses together and assembling them and

their problems, the student may affix the house to a piece of construction paper. The

students may then decorate their houses when they are complete.

Explanation:

Students can more readily develop an understanding of multiplication concepts if they see

visual representations of the computation process. For example, they can now picture the

multiplication houses when they are trying to recover facts. These can be placed and

displayed at a math center so students may use them for future reference..

Extension:

For students who need more challenging problems, they can create houses using larger

numbers including double digit numbers such as 20, 30, 50, ect…

47

Evaluation: Monitor student’s written and demonstrated responses to assess understanding

of multiplication facts as they are arranged in multiples of whole numbers. The students

will present their finished products to the class and share their houses and their multiples.

Collect the notebook responses and these houses as formative and summative assessments.

Reference:

Brunetto, Carolyn. (1997) Math Art Projects and Activities. Scholastic. New York, New York.

48


Time Needed3 50 minute sessions

Materials

Seed beads in a variety of colors

wire (approximately 8 inches per student)

Bead plan worksheet — one for each student.

“Jessie’s Jazzy Bracelet” instructions

Two crimp beads per student.

One bracelet clasp set per student.

Pliers

Wire cutters

Super glue

paper plates for each students’ work area.

Paper to do calculations

Graph paper to sketch out pattern.

Crayons

pens

Calculators

Lesson 10: Beaded Bracelets

Introduction:

This lesson will concentrate on Students create beaded bracelets

to explore multiplication, estimation, prediction, charting and

graphing, measurement, and multiplication fact families.

Standards:




statement.











division.*

Preparation:

Students need to be able to measure in centimeters and millimeters to complete this

project.

Students need to be able to multiply two- or three- digit numbers by one-digit

numbers or need to understand how to use a calculator to solve multiplication

problems. (Some of the real-life problems encountered in creating the bracelets will

49

http://www.learnnc.org/lp/media/lessons/DaylePayne10192002244/Jessie.rtf



http://www.learnnc.org/lp/media/lessons/DaylePayne10192002244/beads2.htm

http://www.learnnc.org/lp/media/lessons/DaylePayne10192002244/beads2.htm

http://www.learnnc.org/lp/media/lessons/DaylePayne10192002244/ttail.jpg

http://www.learnnc.org/lp/media/lessons/DaylePayne10192002244/seedbeads.jpg

involve decimals, and students may need to use calculators to solve these problems. The teacher

created assessment questions should only involve whole numbers.)

Explanation:

In this lesson you will develop fluency with multiplication and division. This will be done in the following ways:

Two-digit by two-digit multiplication will be explored (larger numbers with calculator), up to three-digit by two-digit division (larger numbers with calculator). We will be learning strategies for multiplying and dividing numbers. As well as working with estimation of products and quotients in appropriate situations.

We will also be strengthening our understanding of the relationships between operations by develop flexibility in solving problems through selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

Engagement:

Today we will be planning patterned beaded bracelets using multiplication fact families, estimating the number of beads which will be needed, assembling the beaded bracelets, solve multiplication word problems involving beaded bracelets. You will be assessed on this project by your final product as well as you will write directions for making their bracelets, including the exact number of beads needed.

Exploration:

Measuring Wrists

Working with a partner, each student needs to measure his/her wrist in centimeters. This is easily accomplished by wrapping a piece of string around the wrist; they will mark that measurement with a marker. Before cutting the string remind students that the string should be wrapped as tight or loosely as they want their bracelet to be it should not be cutting off their circulation. Do not have the students cut the string until they have determined their pattern. The pattern will determine the ultimate length of the string as well as the student’s wrist size.

Ex. if the students wrist measures 6 inches or 15.2 cm. assuming one bead measures 1mm it will take 152 beads to cover total length of wrist. Allow another inch of string to attach fasteners. However we must take into account the total number of beads needed for each fact family. In the following example we would need 240 beads total to represent the entire

50

fact family. Therefore to solve the problem we would need to wrap the student’s wrist twice as well as leave the extra inch. Therefore this student will need 13 inches of string.

Have them record this information on their bead plan worksheets. This would be a good time to explain that the measurement they just recorded is the circumference of their wrists.

Planning the Pattern:

Each student will need a plate, a wire and beads. Each work station should have a container of each color of available beads for the students to choose from.

The students will be creating their pattern by using multiplication fact families. Using a number given by the instructor the student will calculate all of the factor combinations of that number. We will not be doing the commutative properties of numbers unless the instructor chooses one with few factors such as a prime number. It is recommended that the instructor chose numbers with many factors.

Ex. 48

1 x 48=48 2x 24=48 3x 16=48 4x12=48 6x8=48

Referring to the problem above, 152 beads would cover the circumference of the wrist, however this fact family contains 240 numerals; therefore to cover the wrist twice we will need 88 extra beads.

My pattern would look as follows:

18 white beads, 1 black bead, 48 red beads, 17 white beads, 2 green beads, 24 yellow beads, 18 white beads, 3 blue beads, 16 purple beads, 17 white beads, 4 red beads, 16 black beads, 18 white beads, 6 yellow beads, 8 green beads.

The white beads separate the fact families, and the color beads represent the facts.

Next, have the students use their paper to figure out the math and the patterns, using calculators if needed. The students will then confer with the instructor to check their math, their measurements, and their patterns. The students will then map out their patterns on graph paper and crayons representing the appropriate color pattern. Once again the instructor will verify before the students begin the bracelets.

Assembling the Bracelets:

Directions:

51

1. Put a crimp bead on one end of the tiger tail. Put the clasp on the tiger tail next. Make a loop of tiger tail. Tuck the end back into the crimp bead. Push the crimp bead up close to the clasp. Crimp the bead with the pliers. (This is easier if you get a friend to help you hold everything.)

2. Pour the beads you need onto the plastic plate. Follow the color pattern you determined to string the beads in the correct order. After you have strung the first five or six beads, make sure the end of the tigertail which is sticking out of the crimp bead is tucked inside the beads so you can’t see it.

3. Put the other crimp bead onto the tiger tail. Loop the tiger tail through the clasp, then through the crimp bead. Tuck the tiger tail back through the last three or four beads. Pull on it until the crimp bead is touching the clasp. Then crimp the bead with the pliers.

4. Cut off the extra tiger tail with the wire cutters. Put a tiny drop of Super Glue on each crimp bead to make sure your bracelet stays together. Let it dry for overnight. Then you can wear it.

*have somebody help me hold the tiger tail when I crimped the bead. The bracelet is slippery and tries to fall apart. A friend makes sure that doesn’t happen.** if you spill your beads on the table, they are hard to pick up. Be careful! If you do have to pick up beads, lick your finger and put it on top of them. They will stick to your finger.

Checking math:After the bracelets are completed, refer once again to the plan sheet to record the actual number of beads needed.

Evaluation:

Writing Directions:

Have each student write step-by-step instructions explaining how to make his/her bracelet. If you wish, compile the students’ directions into a book.

Beaded Bracelet Plan Sheet

Before you make your bracelet:

The string that I put around my wrist was ___________ cm. long.

This is my pattern:

52

My pattern is _________ cm. long.

I think I will need to repeat my pattern _________ times.

To make my bracelet, I think I will need:

This many seed beads: In this color:1. 2. 3. 4. 5.

After you have finished your bracelet:

I repeated my pattern ___________ times.

To make my bracelet I needed:

This many seed beads: In this color:1. 2. 3. 4. 5.

Reference:

Payne, Dayle. 2010. Beaded Bracelet Multiplication. K–12 teaching and learning from the UNC School of Education. Retrieved from http://www.learnnc.org/lp/pages/3885

Lesson 11: Billy Wins a Shopping Spree!

53



MaterialsCopies of “Billy Wins a Shopping Spree” worksheet

Writing pencils

Introduction: In this lesson, students will solve a real-world problem – Billy Wins a

Shopping Spree – using their growing knowledge of multiplication, demonstrating

that they understand both the meaning of and practical use for multiplication.

Preparation: Divide the class up into groups of two to four students and distribute

materials accordingly.

GLCE: 3.N.MR.03.09 Use multiplication and division fact families to understand

the inverse relationship of these two operations, e.g., because 3 x 8 = 24, we know

that 24 ÷ 8 = 3 or 24 ÷ 3 = 8; express a multiplication statement as an equivalent

division statement.

3. N.MR.03.10Recognize situations that can be solved using multiplication and



Engagement (10 minutes):Tell the class that Billy is a fortunate boy who won a

$25 shopping spree at the Science Museum Store. They will find a list of the items

that he can purchase and the price for each item on their worksheet.

Explain that Billy can spend up to $25 on any selection of the listed items. If he

doesn’t spend the entire amount, he can’t keep the change, instead he will have a

store credit that he can use later. He can’t spend more than $25 and cannot use any

other money that he might have … or ask his parents for some. They do not need to

calculate any sales tax.

Draw a model of the receipt on the board:

Science Museum Store

Receipt

___ items @ $3.00

___ items @ $3.00

___ items @ $3.00

Total

Store Credit

$__________

$__________

$__________

$__________

$__________

54

Instead of duplicating blank receipts for the students to fill in, have them prepare their own. This

experience will help them learn how to organize their work on paper.

They need to record Billy’s transaction two different ways:

1) In words, describing what he bought, how much each item cost, the total amount he spent and the

amount of any store credit he can use later; and

2) On the receipt that they prepare.

Exploration (25 minutes): Invite the students to “shop” for Billy, writing their transactions both

ways.

Explanation (15 minutes): Use class discussion to have some of the children present different

ways they found to spend exactly $25. This will reinforce the idea that problems can have more than

one solution.

Extension: Find the different combinations of $3, $4 and $5 items that equal exactly $25. When

students search for solutions by trial and error, they get great deal of number practice. Make sure,

however, that they understand the focus on the number of items at a particular price, not the section

of particular items. For example, buying five Koosh balls is the same solution as buying three

Koosh balls, an inflatable world globe, and a dinosaur model kit. In each case, Billy spends $25 buy

buying five items @ $5.

Evaluation: The students’ written and oral responses will serve as a component of the summative

assessment of their understanding of multiplication, both its meaning and real-world uses.

For their final Math Journal entry for the unit, invite them to respond to the prompt:

“What I now know about multiplication.”

Reference: Burns, M. (1991). Math By All Means: Multiplication Grade 3. Sausalito, CA: The Math

Solutions Publications.

55

SONGS for MULTIPLICATION

All songs, lyrics, and recordings can be found at:

http://gardenofpraise.com/multi.htm

Twos(Four measure introduction)

Count on shoe-s to lear-n th-e TwosThis is some-thing you will al-ways use.

2... 4... 6... 8... 10... 12... 14... 16... 18... 20... (snap... snap) 2... 4... 6... 8... 10... 12... 14... 16... 18... 20... (snap... snap) 2... 4... 6... 8... 10... 12... 14... 16... 18... 20... (snap... snap) 2... 4... 6... 8... 10... 12... 14... 16... 18... 20... (snap... snap)

Threes(Four measure introduction)

Learn the three-s with bir-ds in the trees. You can do it quick-ly and with ease.

Look at the trees and count loudly over and over! Notice that on the answers on the first row of trees are single digit numbers, the second row has teen numbers, the third row twenties numbers, and the last tree has the number 30.


Fours

56


Learn the fo-urs by count-ing on the doors. You'll be prou-d of your-self, of course.

Now look at the doors and count them loudly. On the first row of doors there are single digits and teen numbers, the second row has twenties numbers, the third row thirties ,and the fourth row house is 40.


FivesUse the hi-ves and it will be a breeze.Learn the fi-ves while you count the bees.

Now look at the hives and count by fives over and over again.


Sixes

57

(Two measure introduction)

Super Sixes are easy you see. Come along and learn with me. 6 times 6 is 36. It ends with a 6 which is double the 3.

Interlude

Let's learn a couple more. Now in your brain you'll storeThat 6 times 8 is 48. Yes, it ends with an 8 which is double the 4.

Interlude

There's a domino game to playcalled "42" they say, So 6 times 7 is easy for you. 6 times 7 is 42.

Sevenshttp://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/seven.html

Music & Lyrics: Bob DoroughSung by: Bob Dorough

Now you can call me Lucky 'cause Lucky's my name,Singin' and dancin', that's my game.I never did a whole day's work in my life,Still everything seems to turn out right.Like a grasshopper on a summer's day,I guess I love to play, and pass the time away.'Cause I was born 'neath a lucky star!

They said I'd go far...

Makin' people happy, that's my favorite game,Lucky Seven is my natural name.Slippin' and slidin' my whole life throughStill I get everything done that I got to do.'Cause I was born 'neath a lucky star!

School is where you are? Aww, that's not hard, lemme show yasomething.

58

http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/seven.html

You multiply seven time one,I got seven days to get that problem done.Multiply seven time two,Take 14 laughs when you're feelin' blue.Multiply seven time three,A 21-day vacation, you can play with me.Multiply seven time four,You got 28 days, that's-a one month more,To pay the mortgage on your store, don't worry!

Somethin'll turn up, yeah!

Multiply seven time five,I don't know how you did it, but man alive, that's 35.Multiply seven time six,Grab a stick and make-a 42 clickety-clicks.Multiply seven time seven,Take 49 steps right up to seventh heaven.Multiply seven time eight,They got 56 flavors and I just can't wait...Multiply seven time nine,63 musicians, all friends of mine.Multiply seven time ten,And that brings you right back to 70 again.

You know, I think that's important, there's a trick theresomewhere...

Multiply seven time eleven,Even a rabbit knows that 70 plus 7.Multiply seven time twelve,You got 84, and isn't that swell.I'm gonna try seven times 13 just for fun:70 plus 21.Seven times 14 must be great,Well, exactly that's-a 70 plus 28.Seven times 15, man alive,That's 70 plus 35, a hundred and five!

Man, this stuff is simple, no jive, you got it! Now I gotta fly.'Scuse me folks, I'm sayin' goodbye,I sure do thank you for the huckleberry pie.Take it home, boys!

Remember Lucky Seven Samson, that's my natural born name,If you should ask me again, I'll have to tell you the same.You'll wake up tomorrow, you'll be glad that I came,'Cause you'll be singin one of the songs that I sang.

So keep a happy outlook and be good to your friend,And maybe I'll pass this way again!

59

Maybe... Bye!

Eightshttp://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/eight.html

Music & Lyrics: Bob DoroughSung by: Blossom Dearie

Figure eight, is double four.Figure four, is half of eight.If you skate, you would be great,If you could make a figure eight.That's a circle that turns 'round upon itself.

One times eight is two times four.Four times four is two times eight.If you skate upon thin ice,You'd be wise, if you looked twiceBefore you made another single move. One times eight is eight, two timeseight is 16Three times eight is 24, four times eight is 32And five times eight is 40, you know.

Six times eight is 48, seven times eight is 56,Eight times eight is 64, nine times eight is 72,And ten times eight is 80, that's true.

Eleven times eight is 88, and twelve times eight is 96.Now here's a chance to get off on your new math tricks:'Cause twelve times eight is the same as ten times eightPlus two times eight:80 plus 16, ninety-six!

One times eight is eight, two times eight is 16Three times eight is 24, four times eight is 32And five times eight is 40, you know. Figure eight, as double four.Figure four, as half of eight.If you skate, you would be great,If you could make a figure eight.That's a circle that turns 'round upon itself.

Place it on its side and it's a symbol meaning infinity.

Nines

60

http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/eight.html

(Two measure introduction)

Would you like to learn the nines? Learn this trick and you'll be fine Number down and don't give out,Fol-low me and give a shout! "Number down! 1,2,3,4,5,6,7,8, Halfway through!"

"Number up! 1,2,3,4,5,6,7,8,Good for you!"

Tens(Four measure introduction)

Add a ze-ro to the end You have mul-ti-plied by 10 Add two 0's. Use your head, Mul-ti-ply by one hun-dred.

Interlude

Add three 0's. This is fun. Mul-ti-ply by one thou-sand.How much fur-ther can you go? There's no lim-it, you should know.

Elevenshttp://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/eleven.html


Good, good, good, good... the good elevenIt's almost as easy as multiplying by one.Good, good, good, good elevenYes, eleven almost makes multiplication fun.

Some people get up at a quarter till sevenOther people I've met, till 8:45 or nine.But I'm happy just a-hanging there till eleven.Cause eleven has always been a friend of mine.

Good, good, good, good elevenNever gave me any trouble till after nine.

61

http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/eleven.html

Good, good, good, good elevenEleven will always be a friend of mine.

Now when you get a change to multiply by eleven,It's almost as easy as multiplying by one.You don't even have to use a pencil when you use eleven.And eleven almost makes multiplication fun.You know why?

Because you get those funny-looking double-digit-doojies as an answer.Like 22, 33, 44 and 55.66, 77, 88, and 99 is your answerWhen you multiply 11 by 2, 3, 4, 5, 6, 7, 8 and 9.

Good, good, good, good elevenNever gave me any trouble till after nine.Good, good, good, good elevenI can always get the answer easy every time.

Now eleven times ten is the same is ten times eleven.It's 110, no matter what you do.And 121 is the answer to eleven times eleven.And eleven times twelve is 132.

Eleven thirteens are 143 now (that's-a 1-4-3).Eleven fourteens are 154 (dig it, that's 1-5-4),1-6-5 and 1-7-6 are fifteen and sixteen.You'd better pick up on the latter 'cause I ain't got time to tell you any more.

I've got a date with the good eleven...She never gave me any trouble till after nine.Good, good, good, good elevenYes, eleven will always be a friend of mine!

Twelveshttp://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/twelve.html


Now if man had been born with 6 fingers on each hand, he'd also have12 toes or so the theory goes. Well, with twelve digits, I meanfingers, he probably would have invented two more digits when heinvented his number system. Then, if he saved the zero for the end,he could count and multiply by twelve just as easily as you and I doby ten.

Now if man had been born with 6 fingers on each hand, he'd probablycount: one, two, three, four, five, six, seven, eight, nine, dek, el,

62

http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/twelve.html

doh. "Dek" and "el" being two entirely new signs meaning ten andeleven. Single digits! And his twelve, "doh", would be written 1-0.Get it? That'd be swell, for multiplying by 12.

Hey little twelvetoes, I hope you're well.Must be some far-flung planet where you dwell.If we were together, you could be my cousin,Down here we call it a dozen.Hey little twelvetoes, please come back home.

Now if man had been born with 6 fingers on each hand, his childrenwould have 'em too. And when they played hide-and-go-seek they'dcount by sixes fast. And when they studied piano, they'd do theirsix-finger exercises. And when they went to school, they'd learn thegolden rule, and how to multiply by twelve easy: just put down azero. But me, I have to learn it the hard way.

Lemme see now:One times 12 is twelve, two times 12 is 24.Three times 12 is 36, four times 12 is 48, five times 12 is 60.Six times 12 is 72, seven times 12 is 84.Eight times 12 is 96, nine times 12 is 108, ten times 12 is 120.Eleven times 12 is 132, and 12 times 12 is 144. WOW!

Hey little twelvetoes, I hope you're thriving.Some of us ten-toed folks are still surviving.If you help me with my twelves, I'll help you with your tens.And we could all be friends.Little twelvetoes, please come back home.

Zeros

63

(Four measure introduction)

Zero, zero, you're my hero. How many eggs now do you see? If I have an empty nest,How many eggs can there be? (Spoken)" Zero!"

Interlude

If I have 10 empty nests, Having no eggs at all, you see.How many eggs in these 10 nests? Please, what can the answer be? (Spoken)" Zero!"

Interlude

100 nests, 1,000 nests,10,000 nests and on we go. All are empty. How many eggs? (Spoken) "That's easy!"Zero!

References

Brunetto, C. 1997. Math art projects and activities grades 3-5. Scholastic Inc. New York. New

York. 1997.

Burns, M. (1987). A Collection of Math Lessons: From Grades 3 through 6. Sausalito, CA: Math

Solutions.

64

Burns, M. (1991). Math By All Means: Multiplication Grade 3. Sausalito, CA: The Math Solutions

Publications.

Burns, M. (1995). Writing in Math class: A Resource for Grades 2-8. Sausalito, CA: Math Solutions.

Christian, Peggy.2005. Multiplication Illustration.BeaconLearningCenter.com Dev.01.30.04 #


Cleveland County Schools. http://tinyurl.com/circlesandstarsdirections. Accessed November 26, 2010.

(Adapted from Marilyn Burn: Math by All Means: Multiplication Grade 3. ©1991 The Math

Solution Publications.)

Dalke. J. 2010, Commutative Property. Math art. the lesson plan page. Retrieved from.


Giganti Jr., Paul. 1992. Each Orange Had 8 Slices, A Counting Book. Greenwillow Books,

New York, NY.

Payne, Dayle. 2010. Beaded Bracelet Multiplication. K–12 teaching and learning from the UNC School of Education. Retrieved from http://www.learnnc.org/lp/pages/3885

R.S. Schaffer Math Department.2010. Kutztown University. Retrieved from

http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/multrock.html

San Marco Unified School District. http://tinyurl.com/circlesandstarsgame. Accessed November 26,

2010. (Adapted from Marilyn Burn: “Circles and Stars.”Math by All Means: Multiplication

Grade 3. ©1991 The Math Solution Publications.)

Stevens. P. 2010. Musical Multiplication. Garden Of Praise. retrieved from

http://gardenofpraise.com/multi.htm http://gardenofpraise.com/multi.htm

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http://tinyurl.com/circlesandstarsgame

http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/multrock.html


http://tinyurl.com/circlesandstarsdirections


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