Unit Plan

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the formatting. Roberts, T. (2010). Multiplication Concepts and Facts Unit. (Unpublished unit plan). University of Phoenix, Phoenix, AZ. Reprinted with permission.

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Multiplication Concepts and Facts Unit Author: Teresa Roberts based on unit by: teresa roberts 08/31/2010 09:58:00 AM UMST

VITAL INFORMATION

Subject(s): Mathematics, Reading

Grade/Level: 3

Time Required: 1 week/1 one hour math lesson per day

Objective(s): Mathematics Instructional Objectives:

• Students will represent and use the concept of repeated addition. • Students will solve multiplication sentences using the factors: 2 and

5. • Students will determine that the product when multiplying using a

factor of 2 will give a product with an even number in the ones place. • Students will determine that the product when they multiply using 5

as a factor will result in a product that always ends in a 0 or 5 in the ones place.

• Students will use models of multiplication (equal sized groups, arrays, equal jumps on number lines, and hundreds charts).

• Students will solve multiplication sentences using the factor: 3 • Students will use the Order Property of Multiplication to solve

problems. • Students will apply models of multiplication by using number lines • Students will be represent, analyze, and extend number patterns

using rules that involve multiplication • Students will understand and use the Zero Property for Multiplication

and the Property of One as a factor in multiplication • Students will develop fluency in their computational skills by

exploring patterns in one digit multiplication.

Reading Instructional Objectives:

• Students will develop listening comprehension of more complex text through discussions

• Students will draw upon the comprehension strategies; group and class discussions, and responding to essential questions.

• Students will listen to and understand grade level informational text and children's literature.

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Summary: The students will learn to connect multiplication sentences with addition sentences and draw arrays to represent multiplication sentences. Students will write multiplication facts with products by using the Order of Property of Multiplication.

IMPLEMENTATION

Learning Activities: 1. Algebra: Connect Addition and Multiplication

2. Multiply with Two and Five

3. Arrays to Show Multiplication Concepts

4. Multiply with Three

5. Multiply with 0 and 1

Resources and Unit Handouts:

• Materials and resources: The book, Amanda Bean's Amazing Dream (1998). by Marilyn Burns The book, Each Orange Had 8 Slices (1992) by Paul Giganti, Jr. Various student worksheets and quizzes given throughout lessons. (attached in each individual lesson) End of Unit Review Test (attached at end of unit) Rubric to Grade Student's understanding (attached at end of unit) Overhead projector or document camera white board/markers crayons/markers paper/pencil

ASSESSMENT & STANDARDS

Standards addressed by unit:

OR- Oregon Standards

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• Subject : Mathematics

• Grade : Third Grade

• Content Standard: 3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.

Performance Standard: 3.2.1 Represent and apply the concept of multiplication as repeated addition.

Performance Standard: 3.2.6 Represent, analyze and extend number patterns using rules that involve multiplication and/or addition (e.g., {3, 6, 9, 12, …}, .{1, 2, 4, 8, …} ).

Performance Standard : 3.2.3 Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems.

Performance Standard : 3.2.4 Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts.

• Subject : English Language Arts

• Grade : Third Grade

• Area : Reading

• Content Standard: Listen to and Read Informational and Narrative Text: Listen to, read, and understand a wide variety of informational and narrative text across the subject areas at school and on own, applying comprehension strategies as needed.

Performance Standard : EL.03.RE.07 Listen to, read, and understand a wide variety of grade-level informational and narrative (story) text including children’s magazines and newspapers, dictionaries, other reference materials, online information, classic and contemporary literature, and poetry.

Performance Standard: EL.03.RE.08 Demonstrate listening comprehension of more complex text through discussions.

Performance Standard: EL.03.RE.09 Draw upon a variety of comprehension strategies as needed--re-reading, self-correcting, summarizing, class and group discussions, generating and responding to essential questions, making predictions, and comparing information from several sources.

• Content Standard: Vocabulary: Increase word knowledge through systematic vocabulary development; determine the meaning of new words by applying knowledge of word origins, word relationships, and context clues; verify the meaning of new words; and use those new words accurately across the subject areas.

Performance Standard: EL.03.RE.12 Understand, learn, and use new vocabulary that is introduced and taught directly through orally-read stories and informational text as well as student-read stories and informational text.

Assessment/Rubrics: Assess students understanding of concepts by using attached review test. Add this review test to student's portfolios.

Use scoring rubric to grade students.

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Rubrics

1. Multiplication Concepts and Facts

Attachments 1. Review/Test

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Multiplication Concepts and Facts

Attached Standards:

1 2 3 Score/ Level

Demonstrates a complete understanding of the problem and chooses and appropriate strategy to determine the solution.

Demonstrates a partial understanding of the problem and chooses a strategy that does not lead to a complete and accurate solution.

Demonstrates little understanding of the problem and shows little evidence of using any strategy to determine a solution.

Standards

OR- Oregon Standards

Subject : Mathematics

Grade : Third Grade

Content Standard : 3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.

Performance Standard : 3.2.1 Represent and apply the concept of multiplication as repeated addition.

Performance Standard : 3.2.3 Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems.

Performance Standard : 3.2.4 Apply increasingly sophisticated strategies based on the number properties (e.g., place value,

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commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts.

Performance Standard : 3.2.6 Represent, analyze and extend number patterns using rules that involve multiplication and/or addition (e.g., {3, 6, 9, 12, …}, .{1, 2, 4, 8, …} ).

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Review/Test Check Vocabulary and Concepts

Choose the best term from the box.

1. When groups have the same number, you can __________

to find how many in all?

2. The numbers you multiply are ________________

3. The answer to a multiplication problem is the ____________

Find the product. You may wish to draw an array.

4. 4 x 5 = ____ 5. 3 x 2 = ____ 6. 3 x 6 = ____ 7. 7 x 3 = _____

Check Skills

For 8-9, choose the letter of the number sentence that matches.

8. 3 + 3 + 3 + 3 = ______

9. 4 + 4 + 4 + 4 + 4 = ______

Find the Product.

10. 3 x 8 = ____ 11. 7 x 3 = ____ 12. 5 x 6 = ____ 13. 4 x 2 = ____

14. 5 x 1 = ____ 15. 2 x 0 = ____ 16. 3 x 2 = ____ 17. 10 x 1 = ____

18. 6 x 2 = ____ 19. 5 x 4 = ____ 20. 24 x 1 = ____

Array

Factors

Multiply

Product

a. 5 x 4 = 20

b. 6 x 2 = 12

c. 4 x 3 = 12

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Answer Key

Review/Test Check Vocabulary and Concepts

Choose the best term from the box.

1. When groups have the same number, you can multiply

to find how many in all?

2. The numbers you multiply are factors

3. The answer to a multiplication problem is the product

Find the product. You may wish to draw an array.

4. 4 x 5 = 20 5. 3 x 2 = 6 6. 3 x 6 = 18 7. 7 x 3 = 21

Check Skills

For 8-9, choose the letter of the number sentence that matches.

8. 3 + 3 + 3 + 3 = c

9. 4 + 4 + 4 + 4 + 4 = a

Find the Product.

10. 3 x 8 = 24 11. 7 x 3 = 21 12. 5 x 6 = 30 13. 4 x 2 = 8

14. 5 x 1 = 5 15. 2 x 0 = 0 16. 3 x 2 = 6 17. 10 x 1 = 10

18. 6 x 2 = 12 19. 5 x 4 = 20 20. 24 x 1 = 24

Array

Factors

Multiply

Product

a. 5 x 4 = 20

b. 6 x 2 = 12

c. 4 x 3 = 12

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Algebra: Connect Addition and Multiplication Author: Teresa Roberts based on lesson by: teresa roberts 08/31/2010 12:07:00 PM UMST

VITAL INFORMATION

Subject(s): Mathematics, Reading

Topic or Unit of Study: Multiplication Concepts and Facts Unit

Grade/Level: 3

Objective: Mathematics Instructional Objectives:

• Students will be represent and use the concept of repeated addition.

Reading Instructional Objectives:

• Students will develop listening comprehension of more complex text through discussions

• Students will draw upon the comprehension strategies; group and class discussions, and responding to essential questions.

• Students will listen to and understand grade level informational text and children's literature.

Summary: Students will be able to use equal groups of objects to see that multiplication is another way to find the total number of objects in equal groups. The teacher will Introduce the word "multiply." The teacher will define the word multiply as a way to find how many in all, when groups have the same number of items. Teacher will have students add it to their math vocabulary sheet.

IMPLEMENTATION

Learning Context: This is the first lesson in a unit on understanding multiplication concepts and facts. Students will learn to use equal groups to count objects using various methods such as repeated addition, skip counting, and finally multiplication.

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Procedure: Instructional Strategy - Directed Reading/Thinking Activity

Assess Prior Knowledge - Hand out Check What You Know worksheet to asses student's knowledge. (See attached in materials and resources)

Anticipatory Set - "Today we will be learning a faster way to count objects. This is called multiplying. Has anyone ever heard of multiplication?" Ask students what they know about it. Explain to the students that you will be reading the book, Amanda Bean's Amazing Dream (1998) by Marilyn Burns. Tell students it is a book about a girl who likes to count everything and she has found a faster way to count objects and that is by multiplying. Show students the pictures as you read and tell them to look at the various groups of objects on each page.

Lesson - After reading the story go back and show the illustrations to the students in more detail. Talk to students about different ways to count objects. Have them look at the various groups of objects and have them count them. Show them that they can count objects by adding them or they can use multiplication to figure out the total number of objects. For instance, on the first page there is a picture of a building with six large windows. In each window there is a six by three array of smaller panes. Ask students how many panes are in each window? You may have to explain the word pane to your students.

Ask for volunteers to share their answers with the class and explain how they got their answer. Continue until everyone who wants to has had a chance to share their thinking. This shows students there is more than one correct way to solve. Plus, it is good for children to hear other's way of thinking.

As students give you their ideas write them on the board. There may be several suggestions or ideas such as addition; 3 + 3 + 3 = 18 or 6 + 6 + 6 + 6 + 6 + 6 = 18; Skip counting; 6, 12, 18 or 3, 6, 9, 12, 15, 18; multiplying; 6 x 3 = 18 or 3 x 6 = 18.

Next continue with the other questions from the same page. For example, ask:

• How many windows are there on the second building from the left?

• How many windowpanes are in each? • How many windowpanes are there altogether in that building?

Go to the page where Amanda is in the bakery. Ask these questions:

• How many brownies or cookies are on the bakery shelves? • How many cakes are in the display case? • How many stripes are there on all the loaves of bread?

Next go to the page where Amanda is counting objects in the kitchen. Ask these questions:

• How many tiles are on the counter? • How many pickles are in the jar?

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• How many pieces of popcorn are in the bowl? (Point out that the popcorn is not organized in a way that makes multiplication useful because it is not organized into equal groups. Talk about how the popcorn can be organized into groups of twos, fives, or other ways to make for a faster, easier way of counting.

Each page will give students an opportunity to count objects in various ways.

Independent practice: Write ten problems which students will use repeated addition on the board.

Closure: At the end of the lesson, students will review the concept of repeated addition by answering 3 + 3 + 3 or 3 x 2.

Differentiated Instruction: For special needs students: Have them connect addition and multiplication by having them arrange objects into 3 sets with two objects in each set. Have students count the total number of objects and write an addition sentence and a multiplication sentence.

For ELL students: Have them make a math dictionary which will enable students to look up unfamiliar words.

For gifted students: Have these students make story problems using multiplication facts. Let their peers try and solve the problems.

Sample Student Products: No student sample available.

Collaboration: Students will work individually.

Time Allotment: 1 class period. 1 Hr per class.

Author's Comments & Reflections:

Before introducing this unit assess prior knowledge by giving students a worksheet with some of the required skills needed to understand the new concepts you will be introducing. If after evaluating you find that your students need further review practice skip counting, review equal groups, and review column addition.

MATERIALS AND RESOURCES

Instructional Materials: The book, Amanda Bean's Amazing Dream (1998) by Marilyn Burns Attachments 1. Check What You Know.doc

Resources: • Materials and resources: White board and markers.

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STANDARDS & ASSESSMENT

Standards:

OR- Oregon Standards

• Subject : Mathematics

• Grade : Third Grade

• Content Standard : 3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.

Performance Standard : 3.2.1 Represent and apply the concept of multiplication as repeated addition.

• Subject : English Language Arts

• Grade : Third Grade

• Area : Reading

• Content Standard : Listen to and Read Informational and Narrative Text: Listen to, read, and understand a wide variety of informational and narrative text across the subject areas at school and on own, applying comprehension strategies as needed.

Performance Standard : EL.03.RE.07 Listen to, read, and understand a wide variety of grade-level informational and narrative (story) text including children’s magazines and newspapers, dictionaries, other reference materials, online information, classic and contemporary literature, and poetry.

Performance Standard : EL.03.RE.08 Demonstrate listening comprehension of more complex text through discussions.

Performance Standard : EL.03.RE.09 Draw upon a variety of comprehension strategies as needed--re-reading, self-correcting, summarizing, class and group discussions, generating and responding to essential questions, making predictions, and comparing information from several sources.

• Content Standard : Vocabulary: Increase word knowledge through systematic vocabulary development; determine the meaning of new words by applying knowledge of word origins, word relationships, and context clues; verify the meaning of new words; and use those new words accurately across the subject areas.

Performance Standard : EL.03.RE.12 Understand, learn, and use new vocabulary that is introduced and taught directly through orally-read stories and informational text as well as student-read stories and informational text.

Assessment/Rubrics: Summarize the lesson by having students solve this story problem:

Paul and three friends want to buy enough cookies so that each can have 5 cookies. Show two ways to solve this problem. 5 + 5 + 5 + 5

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= 20 and 4 x 5 = 20.

Have students tell you when you can use multiplication to solve a problem. Have them give examples.

Lesson Quiz (see attached) Attachments 1. Lesson Quiz.doc

Lesson Quiz

Name: ________________ Date: __________________

1. 2 + 2 + 2 = 6 A. 4 x 3 = 12

2. 3 + 3 + 3 + 3 = 12 B. 2 x 5 = 10

3. 8 + 8 + 8 + 8 = 32 C. 3 x 2 = 6

4. 5 + 5 = 10 D. 4 x 8 = 32

Lesson Quiz Answer Key

1. C

2. A

3. D

4. B

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Multiply with Two and Five Author: Teresa Roberts based on lesson by: teresa roberts 08/31/2010 09:30:00 PM UMST

VITAL INFORMATION

Subject(s): Mathematics

Topic or Unit of Study: Multiplication Concepts and Facts Unit

Grade/Level: 3

Objective: • Students will solve multiplication sentences using these factors: 2 and 5.

• Students will determine that the product when multiplying using a factor of 2 will give a product with an even number in the ones place.

• Students will determine that the product when they multiply using 5 as a factor will result in a product that always ends in a 0 or 5 in the ones place.

Summary: Students will learn that when you multiply with 2 the product is always even. Students will learn that when you multiply with 5 the product always has a 5 or 0 in the ones place.

Vocabulary: Have students add to their math dictionary

• Product: The answer to a multiplication problem • Factors: Numbers that are multiplied to find a product

IMPLEMENTATION

Learning Context: This is the second lesson in the Multiplication Concepts and Facts Unit. Students have learned that equal numbers of groups can be quickly totaled by using multiplication. Students will learn multiplication facts 2 and 5 during this lesson by using equal groups of objects.

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Procedure: Instructional Strategy - Direct/Explicit Instruction and group work.

Anticipatory Set - "Remember yesterday when we read the book, Amanda Bean's Amazing Dream and learned that you can group objects into equal groups and find the total quickly by multiplying? Well, today we are going to learn how to multiply by 2 and 5. There are a couple of clues to help you know if you have the answer correct when multiplying by 2 and 5. When multiplying by 2 the number in the ones place will always be an even number, like 0, 2, 4, 6, etc. and when multiplying by 5 the number in the ones place will always be a 0 or a 5."

Lesson - After reviewing yesterday's lesson tell students they will be using counters to help them learn the multiplication facts, 2 and 5. First, introduce the new vocabulary words, factors and product. Have them write the new words and their definitions in their math dictionary. Then have students split into pairs. Have one student from each pair come up and get a handful of counters. Show students an example on the overhead projector or document camera how they will be using counters to help them count. Show 3 groups of 2 counters. Ask if anyone knows the total number of counters? Then write the multiplication problem on the board. 3 x 2 = 6. Point out that this was a multiplication problem with one factor of 2 and notice how the answer or product is an even number. Next. show an example of 3 groups of 5. Write the multiplication problem of the board, ask students if they know what the product of 3 x 5 is. Point out that the product or answer is 15 and that there is a 5 in the ones place.

Student Activity:

• Have one student from each pair get a cupful of counters • Instruct the other student in the pair to get out a piece of

paper and pencil. • Write a multiplication problem on the board, 2 x 2. • Have them use their counters to make 2 groups of 2 • Students will write the multiplication sentence on the paper

and give the product • Continue doing this with ten more multiplication facts using 2's

and 5's only. • As students are working in pairs walk around the room and

ask questions like; what are the factors you used in this sentence? or What is the product of this multiplication sentence? to check for understanding. Have a computer workstation (http://www.ixl.com/math/grade-2/multiplication-tables-up-to-5 ) where students go over and answer multiplication questions using 1s through 5s).

Independent Practice: - Hand out a worksheet for students to complete individually so that you may check for each student's understanding. Tell them they can still use their counters to complete this worksheet. See attached worksheet.

Closure: At the end of the lesson, students will review the concept of multiplying by 2 and 5 by answering several questions.

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Differentiated Instruction: Special Needs Students - provide the reteach worksheet. See attached. Allow the use of counters during worksheet time.

ELL students - Make sure they write the vocabulary words in their math dictionary correctly. Have a math word wall visible to ELL students.

Gifted Students - provide extra challenge worksheet. See attached.

Sample Student Products: No student work available

Collaboration: Students will work collaboratively & individually. Students will work in groups of 2.

Time Allotment: 1 class period. 1 Hr per class.

Author's Comments & Reflections:

Walk around the room checking for understanding when group work is being done. Ask questions to check for understanding and allow children the opportunity to use math language.

MATERIALS AND RESOURCES

Instructional Materials: Attachments

1. Challenge Worksheet with answer key 2. Reteach Worksheet with answer key

3. http://www.ixl.com/math/grade-2/multiplication-tables-up-to-5

Resources: • Materials and resources: White board and markers Document camera or overhead projector counters paper and pencil for each student

STANDARDS & ASSESSMENT

Standards:

OR- Oregon Standards

• Subject : Mathematics

• Grade : Third Grade

• Content Standard : 3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.

Performance Standard : 3.2.3 Apply models of multiplication (e.g.,

equal-sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and

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sharing) to solve problems.

Performance Standard : 3.2.6 Represent, analyze and extend number patterns using rules that involve multiplication and/or addition (e.g., {3, 6, 9, 12, …}, .{1, 2, 4, 8, …} ).

Assessment/Rubrics: Assess students by discussing as a group how you would find the product of 10 x 5. Ask students what two numbers are the factor.

Give lesson quiz See attached. Attachments 1. lesson quiz

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Challenge Worksheet Name: _______________________ Date: _________________

Pattern Plot Find the next three numbers.

Write the rule used to make the pattern

1. 22, 24, 26, 28, ____ , ____ , ____ Rule: __________________________

2. 80, 85, 90, 95, ____ , ____ , ____ Rule: ___________________________

3. 117, 122, 127, 132, ____, ____, ____ Rule: ___________________________

4. 211, 213, 215, 217, ____, ____, ____ Rule: __________________________

5. 317, 319, 324, 326, 331, 333, 338, 340, 345, ____, ____, ____ Rule: __________________________

Make up your own pattern suing differences of 2 or 5. Write the rule under your pattern.

6. _____, _____, _____, _____, _____, _____ Rule: ___________________________________

7. _____, _____, _____, _____, _____, _____

Rule: ___________________________________

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Answer Key

Pattern Plot Find the next three numbers.

Write the rule used to make the pattern

1. 22, 24, 26, 28, 30, 32, 34 Rule: add 2

2. 80, 85, 90, 95, 100, 105, 110 Rule: add 5

3. 117, 122, 127, 132, 137, 142, 147 Rule: add 5

4. 211, 213, 215, 217, 219, 221, 223 Rule: add 2

5. 317, 319, 324, 326, 331, 333, 338, 340, 345, 347, 352, 354 Rule: add 2, then add 5

Make up your own pattern suing differences of 2 or 5. Write the rule under your pattern. Answers will vary. Check each student’s work.

6. _____, _____, _____, _____, _____, _____ Rule: ___________________________________

7. _____, _____, _____, _____, _____, _____

Rule: ___________________________________

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Re-teach Worksheet

Name: _________________________ Date: __________________

Multiply with 2 and 5

Eric packs 5 pairs of socks. How many socks does he pack in all?

He can solve the problem in 3 ways.

He can add:

2 + 2 + 2 + 2 + 2 = ____

He can skip count:

2 4 6 8 ____

He can multiply:

2 x 5 = _____

Solve each problem by adding, then by skip-counting, and then by multiplying. You can use counters to help you solve.

1. Four houses each have five windows. 2. How many wings do 7 birds have? How many windows are there in all? __________________________ __________________________ __________________________ __________________________ __________________________ __________________________

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Answer Key

Multiply with 2 and 5

Eric packs 5 pairs of socks. How many socks does he pack in all?

He can solve the problem in 3 ways.

He can add:

2 + 2 + 2 + 2 + 2 = 10

He can skip count:

2 4 6 8 10

He can multiply:

2 x 5 = 10

Solve each problem by adding, then by skip-counting, and then by multiplying. You can use counters to help you solve.

1. Four houses each have five windows. 2. How many wings do 7 birds have? How many windows are there in all? 5 + 5 + 5 + 5 = 20 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14 5, 10, 15, 20 2, 4, 6, 8, 10, 12, 14 4 x 5 = 20 7 x 2 = 14

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Lesson 2 Quiz

Name: ____________________________ Date: ______________________

Complete:

1. 7 x 2 = 6. 8 x 2 =

2. 5 x 7 = 7. 2 x 5 =

3. 2 x 9 = 8. 6 x 2 =

4. 5 x 5 = 9. 4 x 5 =

5. 3 x 2 = 10. 9 x 2 =

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Answer Key

1. 7 x 2 = 14 6. 8 x 2 = 16

2. 5 x 7 = 35 7. 2 x 5 = 10

3. 2 x 9 = 18 8. 6 x 2 = 12

4. 5 x 5 = 25 9. 4 x 5 = 20

5. 3 x 2 = 6 10. 9 x 2 = 18

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Arrays to Show Multiplication Concepts Author: Teresa Roberts based on lesson by: teresa roberts 12/18/2009 02:36:00 PM UMST

VITAL INFORMATION

Subject(s): Mathematics, Reading

Topic or Unit of Study: Using arrays to show Multiplication concepts

Grade/Level: 3

Objective: Students will use models of multiplication (equal sized groups, arrays, equal jumps on number lines, and hundreds charts).

Reading Instructional Objectives:

• Listen to and understand grade-level literature. • Student will draw upon comprehension strategies such as;

class and group discussions, and responding to questions.

Summary: Arrays are a useful way to show multiplication concepts. The student will use arrays and the commutative property to explore the concept of multiplication.

IMPLEMENTATION

Learning Context: The student has learned the concept of using equal groups to multiply. Now the student will apply this concept to experience and explore how to use arrays to multiply. Learning about arrays will teach students about the Commutative Property of Multiplication. In the future students will use arrays to show division.

Instructional Strategy - Direct/Explicit Instruction

Anticipatory Set - "We have been working so hard on learning our multiplication facts and today we are going to use arrays to show multiplication." Explain to the students that an array is a cool way to solve multiplication problems. Have the students then join you in the reading area to listen to a book that helps explore multiplication. The book is Each Orange Had 8 Slices, by Paul Giganti,

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Jr. It is an awesome book that explains how to count in equal groups.

Lesson - After reading the book have students go back to their seats. Tell the students that they will be learning how to build their own arrays by using various objects. Show the students an example of an array by using square tiles on the Smart Board or an overhead projector. Explain to the class that multiplication can be represented by rectangular arrays with equal numbers in each row and in each column. Also, numbers that can be represented in square arrays have the same number of rows and columns. Later you will learn that these arrays can be identified as perfect squares. You will also learn the commutative property of multiplication; a x b = c then b x a = c.

• Review with students what a row is. Tell them a row goes across the page and point to the row on the example array.

• Then tell them that a column goes down the page and show them the column on the example array.

Student Activity:

• Have student helpers pass out the square tiles to each student.

• After each student has 20 or so tiles have them make an array on their desk. Instruct them to make a row of three tiles with a five in each column.

• Have them count the total number of tiles. • Ask the students, "How many tiles are in the 3 rows of 5?" 15

tiles • Ask student, "What multiplication sentence can you write to

find the number of tiles?" Ask for volunteers to come up to the white board to write the number sentence, 3 x 5 = 15. Tell them that 3 rows of 5 is like saying 3 x 5

• Tell them to then form 5 rows and 3 columns. 5 x 3 • Ask them, "How many tiles do you have now?" Still 15 tiles. • Have them write the multiplication sentence, 5 x 3 = 15 • Explain that in the commutative property the arrangement can

be switched and still equal the same amount. • Then have the students make an array with 3 rows and 3

columns. • Ask, "What shape does this array form?" • Ask, "What multiplication sentence can you write to find the

number of tiles?" Have more volunteers go to the board and write the sentence. Check students' arrays. They should be square; 3 x 3 = 9 remind them that 3 rows of 3 is the same as 3 x 3.

• Ask students, "How would you form an array in the shape of a rectangle?" Make an array with different numbers of rows and columns.

• Have students use their square tiles to form an array in the shape of a rectangle. Have them write the multiplication sentence. Walk around and check.

• Ask students, "How would you form an array in the shape of a square? Make an array with equal numbers of row and columns.

• Have students form an array in the shape of a square and

26

write down the multiplication sentence. Walk around and check for understanding.

• After having the students form various arrays with the tiles, have helper students hand out large squared graph paper.

• Split class into groups of two. • Instruct students to get out their colored pencils. • Show them an example of an array formed on the graph paper

by coloring in equal rows and columns. • Have each student replicate the example array on their own

graph paper. • Walk around the room checking for understanding. • Tell the students that they are going to form 5 different arrays

on their graph paper and under each array they will need to write the appropriate multiplication sentence.

• As the students form their arrays walk around the room to make sure they are doing it correctly.

• Tell them do their nicest work when coloring in the arrays because you want to put them up on the bulletin board.

Remedial Activity - Give each student only 8 tiles and tell them to arrange them into 4 rows of 2, and then 2 rows of 4. Have them write 4 x 2 = 8 under the 4 rows of 2 and 2 x 4 = 8 under the 2 rows of 4. Then give them 10 tiles and have them form 5 rows of 2 and then 2 rows of 5. Have them write those multiplication sentences on their paper.

Independent Practice: - Have students look around the classroom to find arrays. As they find them write them on the white board and count how many arrays they found in the classroom.

Closure: At the end of the lesson, students will review the concept of arrays by demonstrating the array 4 x 2 and 2 x 4.

Task Analysis/Procedure: Arrays are a useful way to show multiplication concepts. By using arrays students have an easier time understanding the concept of multiplication.

Collaboration: Students will work collaboratively & individually. Students will work in groups of 2.

Time Allotment: 1 class period. 1 Hr per class.

Author's Comments: It is important to walk around the room while individual and group work is being done. This way you can make sure the students are doing it correctly.

MATERIALS AND RESOURCES

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Instructional Materials (handouts, etc.):

square tiles

large squared graph paper

colored pencils

Resources: • Materials and resources: Smart Board or overhead projector White board

STANDARDS & ASSESSMENT

Standards:

OR- Oregon Standards

• Subject : Mathematics

• Grade : Third Grade

• Content Standard : 3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.

Performance Standard : 3.2.3 Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal 'jumps' on number lines and hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems.

Performance Standard : 3.2.4 Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts.

• Subject : English Language Arts

• Grade : Third Grade

• Area : Reading

• Content Standard : Listen to and Read Informational and Narrative Text: Listen to, read, and understand a wide variety of informational and narrative text across the subject areas at school and on own, applying comprehension strategies as needed.

Performance Standard : EL.03.RE.07 Listen to, read, and understand a wide variety of grade-level informational and narrative (story) text including children’s magazines and newspapers, dictionaries, other reference materials, online information, classic and contemporary literature, and poetry.

Performance Standard : EL.03.RE.09 Draw upon a variety of comprehension strategies as needed--re-reading, self-correcting, summarizing, class and group discussions, generating and responding to essential questions, making predictions, and comparing information from several sources.

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Assessment/Rubrics: As an informal assessment give each student a blank piece of paper. Have them write problems 1-4. Then show different arrays on the smart board or overhead projector. Have students write down the multiplication sentence on their paper with the product.

Multiply with Three Author: Teresa Roberts based on lesson by: teresa roberts 09/01/2010 12:59:00 PM UMST

VITAL INFORMATION

Subject(s): Mathematics

Topic or Unit of Study: Multiplication Concepts and Facts Unit

Grade/Level: 3

Objective: • Students will solve multiplication sentences using the factor: 3.

• Students will use the Order Property of Multiplication to solve problems.

• Students will apply models of multiplication by using number lines

• Students will be represent, analyze, and extend number patterns using rules that involve multiplication

Summary: In this lesson the students will learn to use the Order Property of Multiplication to solve multiplication problems. They will also learn to use a number line to skip count by threes.

IMPLEMENTATION

Learning Context: This is the 4th lesson in the multiplication concepts and facts unit. First, the teacher will review skip counting and equal groups. In this lesson the teacher will introduce the Order Property of Multiplication. The teacher will explain that the Order Property says you can multiply two factors in any order and the product will always be the same. The teacher will explain that when you multiply 3 by an even number, the product is even. When you multiply 3 by an odd number the product is odd. Have the students add the new vocabulary, Order Property of Multiplication to their math dictionary.

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Procedure: Instructional Strategy - Direct Instruction/Individual work

Anticipatory Set - "Now that we have learned the multiplication facts of 2 and 5 we will be learning the facts of 3." Then ask, "Has anyone heard of a number line?" Show a number line on the overhead projector. "Today we will be using a number line to help us learn how to multiply by 3."

Lesson - Show students how to use the number line using your document camera, white board, or overhead projector. Use this story problem: Nick practiced basketball 2 hours each day for 3 days. How many hours did he practice in all? Show how to use the number line by moving 2 spaces for 3 days. Show the multiplication sentence: 3 x 2 = 6. Then ask what if he practiced basketball for 3 hours each day for 2 days? How many hours did he practice then? Show on the number line moving 3 spaces for 2 days. Write the sentence on the board; 2 x 3 = 6. Ask students if they see any similarities with these two multiplication sentences. Explain that it doesn't matter if it is 3 x 2 or 2 x 3 he still practiced a total of 6 hours. Tell students this is the Order Property of Multiplication and it will help them learn their multiplication facts.

After introducing the concept and giving examples tell students they will be using a number line to solve various multiplication problems using 3 as a factor. See attached. Have a student volunteer pass out the worksheets. Go over the first number line together. Allow students to work in pairs to find products using factors from 1s to 5s at http://www.ixl.com/math/grade-2/multiplication-tables-up-to-5.

Independent practice: Have students complete the attached worksheet on their own. Walk around the room to check student's work and be available to help.

Closure: At the end of the lesson, students will review the concept of multiplying by 3s by finding the product for 3 x 3 or 3 x 5.

Differentiated Instruction: Special Needs Students - Have them only complete the even numbered problems or give them a reteach worksheet with less problems. Allow them to use manipulatives if needed.

ELL students - Check often for understanding. Allow them to work with a English speaking partner. To help ELL understand the Order Property of Multiplication have them write three multiplication sentences and draw arrays to model each. Below each number sentence have them reverse the order of the factors. Have them draw arrays to model the new sentence to show that the product remains the same.

Gifted Students - Have students use a number line to multiply. Draw a large number line on the board from 0 to 25. Have students make jumps of 2, 3, and 5 on the number line. Have them show where they will land if the make:

3 jumps of 8

4 jumps 5

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6 jumps of 2

8 jumps of 3

2 jumps of 9

5 jumps of 5

Sample Student Products: No student work available

Collaboration: Students will work individually.

Time Allotment: 1 class period. 1 Hr per class.

Author's Comments & Reflections:

Provide assistance when needed. Walk around room checking student's work and making sure they stay on task.

MATERIALS AND RESOURCES

Instructional Materials: Attachments

1. AllMultiplication-AS-NumberLines.pdf

2. http://www.ixl.com/math/grade-2/multiplication-tables-up-to-5

Resources: • Materials and resources: Number line Worksheets and pencils white board and markers overhead projector or document camera

STANDARDS & ASSESSMENT

Standards:

OR- Oregon Standards

• Subject : Mathematics

• Grade : Third Grade

• Content Standard : 3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.

Performance Standard : 3.2.4 Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts.

Performance Standard : 3.2.3 Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal 'jumps' on number lines and

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hundreds charts) and division (e.g., repeated subtraction, partitioning, and sharing) to solve problems.

Performance Standard : 3.2.6 Represent, analyze and extend number patterns using rules that involve multiplication and/or addition (e.g., {3, 6, 9, 12, …}, .{1, 2, 4, 8, …} ).

Assessment/Rubrics: Assess students comprehension of the Order Property of Multiplication by asking, "How does knowing the Order Property help you learn multiplication facts more easily?"

Give student's number line worksheet and various story problems using 3 as a factor. Check for understanding by grading each student's paper.

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Multiply with 0 and 1 Author: Teresa Roberts based on lesson by: teresa roberts 09/01/2010 03:47:00 PM UMST

VITAL INFORMATION

Subject(s): Mathematics, Reading

Topic or Unit of Study: Multiplication Concepts and Facts Unit

Grade/Level: 3

Objective: Mathematics Instructional Objectives:

• Students will understand and use the Zero Property for Multiplication and the Property of One as a factor in multiplication

• Students will develop fluency in their computational skills by exploring patterns in one digit multiplication.

Reading Instructional Objectives:

• Students will understand, learn and use new math vocabulary that is taught through informational text.

Summary: This is the fifth and final lesson in the unit of multiplication concepts and facts. Students will understand how to multiply with 0 and 1. Students will learn the number of groups multiplied by the number in each group equals the number in all. They will also learn that the product of 1 and any number equals that number and that the product of 0 and any number equals 0.

IMPLEMENTATION

Learning Context: Student will use what they know to apply strategies based on number properties specifically the Zero Property and Property of One when multiplying. Before this activity students learned about the Order Property and how it is helpful in learning multiplication facts.

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Procedure: Instructional Strategy - Direct/Explicit Instruction

Anticipatory Set - "Today we will be learning more multiplication facts. Does anyone know what 1 x 0 is? How about 1 x 2? Well, there is a rule or property for multiplying by 0 and 1 and today you will be learning about this rule and how it will help you remember your multiplication facts."

Procedures -

• Introduce key vocabulary; multiple, Zero Property, and Property of One and have students add them to their math dictionary. Remind students the meaning of factor and product.

• Display the Hundreds Chart using an overhead projector or document camera

• Have a student hand out copies of the Hundreds Chart to students (See attached)

• Have students count by 2's as you shade in the multiples of 2 with a yellow pen.

• Have students shade in multiples of 2 on their hundreds chart. Ask students if they notice any patterns? (The multiples of two are even and always end in 0, 2, 4, 6, or 8).

• Have students count by 5's. Circle the multiples of 5 with a blue marker. Have students also circle on their chart. Ask students if they see a pattern. What patterns do you see here? (The multiples of 5 end in either 0 or 5).

• Have students count by 3's on the number chart. Have them color in lightly with red.

• Ask students what would happen if they shaded in all the multiples of 1. (They would soon realize they would be shading in all the numbers). Talk about the Property of One. Explain to them that the product of a number and 1 is that same number and that every number is a multiple of 1 and itself.

• Ask several easy questions at this point. What is 8 x 1? What is 9 x 1? What is 53 x 1? What about 1 million x 1?

• Ask students to think about multiplying with zero in terms of repeated addition. Remind students that multiplication is a faster way to add up numbers. Write on the board 0 + 0. Ask students what the answer would be. Then write 2 x 0. Remind them that 2 x 0 would be just like saying 0 + 0. They both equal 0.

• Talk about the Zero Property as being the product of a number and 0 is always 0.

Independent Practice: Students complete a multiplication facts worksheet.

Closure: At the end of the lesson, students will review the concept of multiplying with zero and one by giving the product of 4 x 0 and 1 x 10.

Differentiated Instruction: Special Needs Students - Hand out reteach worksheet. (see attached) Allow extra time and check for understanding.

ELL Students - Review math vocabulary in their math dictionary. Add

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new words to the word wall. Let ELL students work with English speaking students.

Gifted Students - Have students make story problems using 1 and 0 as factors.

Sample Student Products: No student sample available

Collaboration: Students will work individually.

Time Allotment: 1 class period. 1.25 Hrs per class.

Author's Comments & Reflections:

Check for understanding by asking questions. Check student's hundred charts to make sure they are filling in the correct boxes.

MATERIALS AND RESOURCES

Instructional Materials: student: crayons and/or markers

hundreds chart (see attached)

reteach worksheet (see attached)

lesson 5 quiz Attachments 1. Hundreds Chart 2. Reteach Worksheet

Resources: • Materials and resources: Overhead projector visa pens white board/markers document camera worksheets/ hundreds chart and reteach worksheet markers and crayons quiz

STANDARDS & ASSESSMENT

Standards:

OR- Oregon Standards

• Subject : Mathematics

• Grade : Third Grade

• Content Standard : 3.2 Number and Operations, Algebra, and Data Analysis: Develop understandings of multiplication and division, and strategies for basic multiplication facts and related division facts.

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Performance Standard : 3.2.4 Apply increasingly sophisticated strategies based on the number properties (e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts.

• Subject : English Language Arts

• Grade : Third Grade

• Area : Reading

• Content Standard : Vocabulary: Increase word knowledge through systematic vocabulary development; determine the meaning of new words by applying knowledge of word origins, word relationships, and context clues; verify the meaning of new words; and use those new words accurately across the subject areas.

Performance Standard : EL.03.RE.12 Understand, learn, and use new vocabulary that is introduced and taught directly through orally-read stories and informational text as well as student-read stories and informational text.

Assessment/Rubrics: Lesson Quiz (see attached)

Discuss: How does knowing rules for multiplying with 0 and 1 help you find the product more easily? Attachments 1. lesson 5 quiz

Reteach Worksheet Multiply with 0 and 1

Teresa put one muffin in each of 6 bags. How many muffins did she put in each bag? You can draw a picture to find the answer.

Draw 6 bags with 1 muffin in each bag.

1. What multiplication sentence can you write for 6 bags with 1 muffin in each bag? _________________________________

2. What happens when you multiply any number by 1?

______________________________________________________________

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Teresa gave each bag that had a muffin in it to a friend. Each friend ate the muffin. Now how many muffins are there?

You can draw another picture to find the answer.

Draw 6 empty bags with 0 muffins in each bag.

3. What is the multiplication sentence you can write for 6 bags with 0 muffins in each bag? __________________________________

4. What happens when you multiply any number by 0?

______________________________________________________________

Find the Product.

5. 1 x 9 = _____ 11. 8 x 0 = _____ 17. 8 x 1 = _____ 6. 7 x 1 = _____ 12. 3 x 1 = _____ 18.10 x 1 = _____ 7. 1 x 4 = _____ 13. 5 x 1 = _____ 19. 2 x 1 = _____ 8. 0 x 6 = _____ 14. 9 x 0 = _____ 20. 4 x 0 = _____

Answer Key Multiply with 0 and 1

Teresa put one muffin in each of 6 bags. How many muffins did she put in each bag? You can draw a picture to find the answer.

Draw 6 bags with 1 muffin in each bag.

Accept any drawing that represents the problem.

1. What multiplication sentence can you write for 6 bags with 1 muffin in each bag? 6 x 1 = 6

2. What happens when you multiply any number by 1?

The product is the number being multiplied.

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Teresa gave each bag that had a muffin in it to a friend. Each friend ate the muffin. Now how many muffins are there?

You can draw another picture to find the answer.

Draw 6 empty bags with 0 muffins in each bag.

Accept any drawing that represents the problem.

3. What is the multiplication sentence you can write for 6 bags with 0 muffins in each bag? 6 x 0 = 0

4. What happens when you multiply any number by 0?

The product is 0.

Find the Product.

5. 1 x 9 = 9 11. 8 x 0 = 0 17. 8 x 1 = 8 6. 7 x 1 = 7 12. 3 x 1 = 3 18.10 x 1 = 10 7. 1 x 4 = 4 13. 5 x 1 = 5 19. 2 x 1 = 2 8. 0 x 6 = 0 14. 9 x 0 = 0 20. 4 x 0 = 0

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Lesson 5 Quiz

1. 0 x 5 = ____ 6. 100 x 1 = ____

2. 1 x 7 = ____ 7. 0 x 9 = _____

3. 1 x 1 = ____ 8. 52 x 1 = _____

4. 23 x 0 = ____ 9. 0 x 0 = _____

5. 8 x 1 = _____ 10. 2 x 1 = _____

Answer Key

1. 0 x 5 = 0 6. 100 x 1 = 100

2. 1 x 7 = 7 7. 0 x 9 = 0

3. 1 x 1 = 1 8. 52 x 1 = 52

4. 23 x 0 = 0 9. 0 x 0 = 0

5. 8 x 1 = 8 10. 2 x 1 = 2

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Annotated Bibliography

Giganti, P. (1992). Each Orange Had 8 Slices. Harper Collins Publisher.

I used this book as an anticipatory set for the multiplication lesson on arrays. This is a

wonderful book to use in patterning, multiplication, and creative thinking.

Learning. (2011). IXL – Math grade 2 multiplication. Retrieved from http://www.ixl.com/math/

grade-2/multiplication-tables-up-to-5

The IXL site allows students to practice multiplication tables from 1s to 5s. It will give

students a chance to be exposed to finding products.

Maletsky, E. M. (2002). Harcourt Math. Harcourt School Publishers.

This is a teacher’s lesson plan book that I used to help me come up with lessons for my

Multiplication Concepts and Facts Unit.

Neuschwander, C. (1998). Amanda Bean’s Amazing Dream. Scholastic Press Publisher.

This is a book where a mathematical concept is revealed to the main character in a dream.

This book is a great way to integrate literature with mathematics and is a useful to aid in

the introduction of multiplication to students in my 3rd grade.

Oregon Department of Education. (2010). Standards by Design. Third Grade for Mathematics.

This is where I got all the standards I used in my math lessons.

Oregon Department of Education. (2010). Standards by Design. Third Grade for English Language Arts.

This is where I got all my standards for reading for my lesson plans.

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References

Giganti, P. (1992). Each Orange Had 8 Slices. Harper Collins Publisher.

Learning. (2011). IXL – Math grade 2 multiplication. Retrieved from http://www.ixl.com/math/

grade-2/multiplication-tables-up-to-5

Maletsky, E. M. (2002). Harcourt Math. Harcourt School Publishers.

Neuschwander, C. (1998). Amanda Bean’s Amazing Dream. Scholastic Press Publisher.

Oregon Department of Education. (2010). Standards by Design. Third Grade for Mathematics.

Oregon Department of Education. (2010). Standards by Design. Third Grade for English Language Arts.

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