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Teachers: Alexis Mayer, Sarah Gorski, Kimberly FrazierTopic: MultiplicationUnit: OperationsTarget Grade: 4th Grade

Unit Overview:

Multiplication skills are important for real-world problems that students may need to solve. Instead of having to solve problems using repeated addition, they need to know more flexible and efficient ways to solve problems of multiplication.

We are teaching several methods for students to refer to when solving multiplication problems. Students need a variety of representations to solve multiplication problems. Students learn in different ways and may have a preference for one method over another, which may differ from student to student. Some students may be processing in the concrete stage, while others are in the abstract stage of mathematical thinking, and as teachers we must accommodate for student differences.

In Wisconsin, 4th Grade mathematics focuses of multiplication.

Students must first understand addition and subtraction.

Learning Objectives- see each lesson

Lessons Overview

Lesson 1: Multiplication as Repeated AdditionThroughout the lesson students will be given opportunities to develop an

understanding of the relationship between repeated addition and multiplication. Students need to understand the relationship between repeated addition and multiplication because repeated addition is the foundation of multiplication. The students will be able to manipulate objects to learn the repeated grouping algorithm of multiplication. The beginning of the lesson will consist of a review of the basic algorithm of multiplication. The lesson will then move on to learning about the repeated grouping algorithm.

Lesson 2: Multiplication Using ArraysStudents are introduced to arrays through a class discussion. The teacher uses

physical manipulatives to first demonstrate arrays, then the students are paired up and create arrays with each others’ help. The students are then given the opportunity to create arrays by drawing items of their choice, such as basketballs. They accompany their drawing with the multiplication problem. This lesson also introduces the commutative property of multiplication.

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Lesson 3: Properties of MultiplicationDuring activity, students must first comprehend the four properties. The teacher

explains them to the class by incorporating technology. Then, the students perform a class activity to get the students moving around and collaborating with each other. Students record their understandings in their math journal and, if time permits, play an interactive game on the computer using the Smart board.

Lesson 4: Area and Perimeter Using MultiplicationThe students will be able to learn about area and perimeter throughout this lesson

while integrating multiplication. They will be given opportunities to explore area and perimeter of actually objects. The beginning of the lesson will start off with teaching the students about the vocabulary that goes along with area and perimeter. The students then will learn about the area and perimeter of a 2-D rectangle. The end of the lesson will be completed by the students measuring rectangles in the classroom and finding the area and perimeter of them.

Lesson 5: Multiplication with MoneyI would read The Coin Counting Book in order to set up background knowledge

for working with varies coins. After reading the book I would review the basic multiplication facts with my students. I would ask for volunteers to come up to the Smart Board and solve a variety of multiplication problems showing their work and using any manipulatives if needed.

During this unit I would set up a store in the classroom where the children could make real products to sell using real money. The students would be given an opportunity to participate in being both a cashier and a customer of the classroom store. I would take my students on a field trip to a store, and give them the opportunity to work with the cashiers at that store to see what their job is like. Students would have the chance to handle real money, and work with real customers.

During the entire lesson I would check the students understanding of solving money multiplication problems based on student’s answers to the money problems.

Lesson 6: Word Problems and MultiplicationRead the books Too Many Kangaroo Things to Do, and Divide and Ride to the

classroom in order to help the children think of real-life word problems using the operations discussed earlier in class. As the books are read, have each student think of the connections between multiplication and addition, and division and subtraction. Then ask them to come up with real-world problems that include addition, subtraction, multiplication, and/or division. Have students work alone or in groups in order to solve the real-life problems they came up with in class. Students will use manipulatives on the SMART board in order to help solve the problems they came up with. After students have answered the questions, they will come up to the SMART board in order to demonstrate how they solved the word problems.

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Extension: Have each student think of at least one real-life word problem they come across over the weekend. Tell them to write down the problem, how to solve it, and the manipulatives they used to solve it. Have each student bring in their problem the next week, and teach the class the real-life problem they came up with using the appropriate manipulatives to solve the problem.

During the entire lesson we will be checking for understanding based on student’s answers to the word problems. The homework sheet will also let us know how much of the lesson the students understood.

Standards

Mathematics Performance Standards - Grade 4

A.4.1 Use reasoning abilities to

perceive patterns identify relationships formulate questions for further exploration justify strategies test reasonableness of results

A.4.2 Communicate mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models

A.4.4 Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work

A.4.5 Explain solutions to problems clearly and logically in oral and written work and support solutions with evidence

B.4.1 Represent and explain whole numbers, decimals, and fractions with

physical materials number lines and other pictorial models verbal descriptions place-value concepts and notation symbolic renaming (e.g., 43=40+3=30+13)

B.4.2 Determine the number of things in a set by

grouping and counting (e.g., by threes, fives, hundreds) combining and arranging (e.g., all possible coin combinations amounting to thirty

cents) estimation, including rounding

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B.4.5 In problem-solving situations involving whole numbers, select and efficiently use appropriate computational procedures such as

recalling the basic facts of addition, subtraction, multiplication, and division using mental math (e.g., 37+25, 40x7) estimation selecting and applying algorithms for addition, subtraction, multiplication, and

division using a calculator

F.4.6 Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity of addition, inverse relationship of multiplication and division)

Wisconsin Language Arts Standard C: Oral Language PerformanceC.4.3 Participate effectively in discussion by volunteering relevant information, asking relevant questions, answering questions directly, reflecting on the ideas and opinions of others and respond thoughtfully, and asking for clarification and explanation of unfamiliar words and ideas.

Wisconsin Technology Standard A: Media and TechnologyA.4.1 Use common media and technology terminology and equipment.A.4.5 Use media and technology to create and present information

VocabularyMultiplication, array, area, perimeter, factor, product, commutative property, associative property, distributive property, zero property, identity property

Pre-Assessment Questions

What is multiplication? What does it look like?

What words are associated with multiplication and division?

What is division? What does it look like?

How are multiplication and division related?

How many groups of 8 are in 32?

Mike’s kitchen floor is five tiles long by seven tiles wide. How many tiles are in his kitchen total?

If Mollie has four cookies and puts three M&Ms on each cookie, how many M&Ms does she need total?

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A classroom has six rows of desks. There are four desks in each row. How many desks are in the classroom?

Dr. McGee sees three patients every hour. How many patients does he see in five hours?

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Lesson Plan Lesson Topic: Multiplication Repeated grouping Grade: 4thLesson duration: 45-60 minutes

State Standard (s): By the end of fourth grade students will be able to A.4.2 Communicate mathematical ideas in a variety of ways, including words,

numbers, symbols, pictures, charts, graphs, tables, diagrams, and models

B.4.2 Determine the number of things in a set by

grouping and counting (e.g., by threes, fives, hundreds) combining and arranging (e.g., all possible coin combinations amounting to

thirty cents) estimation, including rounding

Learning Objective(s):The students will be able to represent single digit multiplication problems using the repeated grouping algorithm.The students will be able to correctly answer single digit multiplication problems.The students will be able to make the relationships between repeated addition and multiplication.

Rationale and Strategies:Throughout the lesson students will be given opportunities to develop an

understanding of the relationship between repeated addition and multiplication. Students need to understand the relationship between repeated addition and multiplication because repeated addition is the foundation of multiplication. The students will be able to manipulate objects to learn the repeated grouping algorithm of multiplication. The beginning of the lesson will consist of a review of the basic algorithm of multiplication. The lesson will then move on to learning about the repeated grouping algorithm.

Materials/Equipment needed:Circle worksheet White board and markersScissorsPaper and pencilsPaper clips

Introduction to lesson/Engage/ Launch/Anticipatory Set:The teacher will write the following multiplication problems on the board.

5 X 7 = 7 X 3 = 8 X 9 = 5 X 2 =4 X 6 = 3 X 4 =

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The students will copy them onto their paper and solve them. The teacher will then call on students to write the answer on the board, and then ask the student how he/she arrived at the answer.

Lesson- The body/Content/Explain/Elaboration/Extensions:

The teacher will pass out the circle worksheet (students will need multiple worksheet) and scissors to each student, and have the students cut out the circles. The teacher will then explain the repeated grouping algorithm. For example, in the problem 5 X 7 there would be 5 circles with 7 dots in each circle (figure 1). The dots could then be counted to find the answer. The teacher will point out that the grouping algorithm works because it is stating that 5 X 7 = 5 groups of 7 or 7 +7 + 7+ 7+ 7. The students will use their circles and draw dots in them to solve the problems on the board. While the students are solving the problems on the bored the teacher will be walking around answering questions and making sure the student understand the repeated grouping algorithm. After all of the students have solved the problems on the board, the teacher will pass out the paper clips, and have the students turn in their circles with the multiplication problems written on the back of them.

Once everything is turned in and put away, the class will split into two groups and play a game. The students will come up to the board, one at a time from each time, and the teacher will call out a problem. For instance, the teacher could call out 6 X 7. The students will have to write the multiplication problem on the board and solve the problem using the repeated grouping algorithm. The first person to solve the problem wins a point for their team.

Extensions, Adaptations and Accommodations:

An accommodation for this lesson could be instead of the person who answers the question the fastest wins a point, the person who answers the question correctly wins a point which allows both teams to possible win points at the same time. By focusing on correct answer the time factor is taken out of the game, and students can concentrate on the answer rather than speed. For a student that is unable to come to the board he/she can write on a piece of paper.

Closure:

The teacher will close the lesson by ending the game and reminding the students that multiplication is repeated addition.Assessment/Evaluation strategies:

The assessment for this lesson is based on the dots that the students drew in each circle for the multiplication problems and turned in. The students will also be assessed base on the answer given during the game.

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Figure 1: 5 X 7 = 35

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Circle Worksheet

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Multiplication Using Arrays

Name &Date: Kimberly FrazierLesson Topic: Multiplication, Arrays, and the Commutative Grade:Grade 3-4Lesson duration: 1 hour

1.1. State standard(s):WMAS A: Mathematical ProcessesA.4.1 Use reasoning abilities to

perceive patterns identify relationships formulate questions for further exploration justify strategies test reasonableness of results

A.4.2 Communicate mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models*

WMAS F: Algebraic RelationshipsF.4.6 Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity* of addition, inverse relationship of multiplication and division)

2.2. Learning objective(s): Students will develop an understanding of the multiplication by using arrays. They will also learn about the commutative property of multiplication.

3. Rationale and Strategies: During activity, students must first comprehend the four properties. The teacher explains them to the class by incorporating technology. Then, the students perform a class activity to get the students moving around and collaborating with each other. Students record their understandings in their math journal and, if time permits, play an interactive game on the computer using the Smartboard.

4.4. Materials/Equipment needed: -- Cans-- Flashcards-- Blank bulletin board-- Small bags of buttons-- Grid paper-- Visualizer or Projector-- Crayons-- Student’s Imaginations!

5. Introduction to lesson/Engage/Launch/Anticipatory Set:Begin by placing cans on the front table in an array (such as 4 x 6). Ask students

if they have ever seen something like this. Explain that this is an array. Ask students where else they have seen arrays. Have them identify arrays in the classroom. Show

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students the blank bulletin board and tell them they will be filling it with an array of their work.

6.6. Lesson-the Body/Content/Explore/Explain/Elaboration/Extension: Ask students how many rows of cans there are on the table. Write on the board,

“4 rows of 6 cans = 24”. Ask how this can be written in a multiplication equation: “4 x 6 = 24”. Pair up the students. Give each pair a bag of buttons. Tell students that we will be making arrays with the buttons. Use the flashcards to draw a multiplication problem for each pair to do. Once they have one, see if they can make another that looks slightly different. Go around and help groups that may be struggling. Once it appears that all groups understand the concept, explain to them that you can turn the array sideways to yield a different appearing array that represents a similar equation. In the equation, the two factors are simply reversed. Explain that this is the commutative property of multiplication. Repeat the button activity by redistributing the flashcards as many times as you feel is necessary.

Transition the students: hand out a sheet of blank white paper to each student. Explain to them that they will be making arrays. They get to choose what items are in their array. For an example, prepare an array beforehand.

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Have students pick their equations from the flashcard stack at random. Encourage them to use their imaginations and make an array of anything they choose, and if they have any questions or an idea but need some help, they should ask you.

Adaptations and Accommodations: You may find it necessary to partner some students up. A student struggling with multiplication may find this activity more engaging with a partner who is willing to teach them and share their understanding of the properties with them.Some students may also need additional practice. The teacher can spend more time working with this student as the rest of the students work independently.

Extensions: Have the students visit http://demonstrations.wolfram.com/TheCommutativePropertyOfMultiplication/ . Let them play around with the array maker.

7. Closure: Once all students have finished their arrays, hang them on the bulletin board. Ask the students how many pictures they have in all. How can this be made into an array? This has them beginning to think about division. As students bring their creations to you to place on the board, have them share their arrays with the class.

8.8. Assessment/Evaluation strategies: Observe students during the lesson. Check to see that they are actively engaging in the lesson and correctly making the arrays. Check the student work. Are the arrays correct? Do they recognize the commutative property by turning the page sideways?

Reflection considerations: Did students engage in the discussion? The activity?Were all students actively involved in learning?What problems were brought up in this lesson?Would you change anything for next time?Do students have a better understanding of multiplication, arrays, and the commutative property?

Lesson adapted from: http://www.lessonplanspage.com/MathArtCommutativeProperty35.htm

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Properties of Multiplication

Name &Date: Kimberly FrazierLesson Topic: Multiplication PropertiesGrade:Grade 3-4Lesson duration: 1 hour

1.1. State standard(s):WMAS A: Mathematical ProcessesA.4.4 Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work

WMAS F: Algebraic RelationshipsF.4.6 Recognize and use generalized properties and relationships of arithmetic (e.g., commutativity* of addition, inverse relationship of multiplication and division)

2.2. Learning objective(s): Students will develop an understanding of the multiplication properties: the identity property, the commutative property, the associative property, and the distributive property.

3. Rationale and Strategies: During activity, students must first comprehend the four properties. The teacher explains them to the class by incorporating technology. Then, the students perform a class activity to get the students moving around and collaborating with each other. Students record their understandings in their math journal and, if time permits, play an interactive game on the computer using the Smartboard.

4.4. Materials/Equipment needed: Pencils Math Journal (for each student) Index cards with string attached to form a name tag (one per student): place an

equation demonstrating one of the properties on each card Four signs (8.5 x 11 paper); put the name of one property on each and place

around room Computer with internet access’ Smartboard Mrs. Steward’s Powerpoint Presentation Evaluation sheet

5. Introduction to lesson/Engage/Launch/Anticipatory Set:Go to http://teachertube.com/viewVideo.php?video_id=54172&title=4th_grade_podcast___multiplication_properties_ . Show the students the video, made by fourth grade students. Pause the video after each property is discussed and re-explain the ideas to the students. Ask students questions to foster a brief discussion.

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6.6. Lesson-the Body/Content/Explore/Explain/Elaboration/Extension: Following the discussion, use the Powerpoint (see slides below). Have students figure out which property is being demonstrated on the slides. Involve all students.Give each student a name tag with an equation. Ask the students to go to the sign hanging in the room where their property on their nametag is. Encourage the students to discuss their equations and help each other figure it out. (Example: if the student’s nametag says “4 x 3 = 3 x 4”, then they should go to the area in the room that says “commutative property”) When students find their places, have them discuss in their groups why they belong there. If a student chooses an incorrect area, have the class help the student find the correct area.

Adaptations and Accommodations: You may find it necessary to partner some students up. A student struggling with multiplication may find this activity more engaging with a partner who is willing to teach them and share their understanding of the properties with them.Some students may want to use a reference to help them decide which property is being demonstrated. Supplying students with a sheet of paper that gives students the definitions and examples of these properties will help students recognize the properties.

Extensions: Have the students visit http://www.aaaknow.com/mul74bx2.htm . Play the game either as a class using the Smartboard or individually in the computer lab or laptops.

7. Closure: Have the students bring their math journals to the groups. Ask them to record their equation and the equations of others in their groups, as well as the name of the property they demonstrate. Collect the nametags and redistribute them to repeat. If a student is in the same group twice, ask them to join another group so they can learn about another property.

8.8. Assessment/Evaluation strategies: Observe students during the lesson. Check to see if they identified the correct property and worked cooperatively with other group members. Check the student journals to make sure they also correctly identified the property. (See the attached checklist)

Reflection considerations: Did students engage in the video? The activity?Were all students actively involved in learning?What problems were brought up in this lesson?Would you change anything for next time?Do students have a better understanding of properties?

Lesson Adapted from: http://alex.state.al.us/lesson_view.php?id=26430Checklist for the Properties of Multiplication

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Students Correctly identified the

given property

Worked cooperatively with others

Math JournalListed each equation under

the correct property heading.

1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.

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Presented by,Mrs. Kem Steward

4 x 3 = 3 x 4

The Commutative Property

(5 x 6) x 4 = 5 x (6 x 4)

Associative Property

10 x 1 = 10

The Identity Property

12 x 1 = 12

The Identity Property

(6 x 2) x 5 = 6 x (2 x 5)

The Associative Property

7 x 5 = 5 x 7

The Commutative Property

2 x (1 x 8) = (2 x 1) x 8

The Associative Property

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11 x 4 = 4 x 11

The Commutative Property

5 x 1 = 5

The Identity Property

4 x (3 x 2) = (4 x 3) x 2

The Associative Property

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Lesson Plan Lesson Topic: Area and Perimeter Grade: 4thLesson duration: 45-60 minutes

State Standard (s): By the end of fourth grade students will be able to A.4.2 Communicate mathematical ideas in a variety of ways, including words,

numbers, symbols, pictures, charts, graphs, tables, diagrams, and models* D.4.1 Recognize and describe measurable attributes*, such as length, liquid

capacity, time, weight (mass), temperature, volume, monetary value, and angle size, and identify the appropriate units to measure them

D.4.3 Read and interpret measuring instruments (e.g., rulers, clocks, thermometers)

Learning Objective(s): The students will be able to correctly identify the area and perimeter of a

rectangle. The students will learn the vocabulary that goes along with area and rectangle. The students will be able to measure objects in the classroom.

Rationale and Strategies:The students will be able to learn about area and perimeter throughout this lesson

while integrating multiplication. They will be given opportunities to explore area and perimeter of actually objects. The beginning of the lesson will start off with teaching the students about the vocabulary that goes along with area and perimeter. The students then will learn about the area and perimeter of a 2-D rectangle. The end of the lesson will be completed by the students measuring rectangles in the classroom and finding the area and perimeter of them.

Materials/Equipment needed: White board and markers Paper and pencil Rulers

Introduction to lesson/Engage/ Launch/Anticipatory Set:The teacher will have the following words written on the board:

Area, perimeter, length, width, and rectangle

The teacher will then ask each student to write down what he/she believes each word means and how they are in common. The students then will get in groups of three and pick one answer to share with the class.

Lesson- The body/Content/Explain/Elaboration/Extensions:The teacher will draw a rectangle on the board and label the width 6 and the

length 4. Then, the teacher will explain that perimeter is the distance around the rectangle. The formula for the perimeter of a rectangle is length + width X 2. So the answer would be 6 + 4 = 10 X 2 = 20 units. After that the teacher explains the perimeter

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he/she will explain the area. The area is the amount of space inside the 2-D object. The formula for the area of a rectangle is length X width. So, the answer would be 6 X 4 =24 units square. The teacher will write the following problems on the board for the students to further practice :

Rectangle with the length of 7 and width of 8 Rectangle with the length of 3 and width of 6 Rectangle with the length of 2 and width of 9 Rectangle with the length of 6and width of 5

Once the students understand the area of the rectangle, they will form partners and measure rectangles in the classroom and figure out the area and perimeter of them.

Extensions, Adaptations and Accommodations:

When the teacher is drawing the rectangles on the board he/she can use graph paper, so the students could count the rectangle if needed. The students who excel at area and perimeter can work alone measuring rectangles in the classroom.

Closure:The teacher will regroup the class and have a discussion about what objects the

students found in the room and the area and perimeter of them. The teacher will have the students turn in their sheets.

Assessment/Evaluation strategies:The assessment of the students is based on the answers that are given during

discussion and throughout the lesson. The students will also turn in their sheet of the rectangles found in class with their mathematical work.

Math Lesson Plan

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Student: Alexis Mayer University Teacher: Dr. KosiakDate: 11/27/09 Title of Lesson: MultiplicationSubject/Topic: Math/ Multiplication

I. State Standards: Mathematics WMAS B: Number, Operations and Relationships

o B.4.2 Determine the number of things in a set by grouping and counting (e.g., by threes, fives, hundreds), combining and arranging (e.g., all possible coin combinations amounting to thirty cents), and estimation, including rounding.

o B.4.5 In problem-solving situations involving whole numbers, select and efficiently use appropriate computational procedures such as recalling the basic facts of addition, subtraction, multiplication, and division; using mental math (e.g., 37+25, 40x7); estimation; and selecting and applying algorithms for addition, subtraction, multiplication, and division

Technology WMAS A: Media and Technologyo A.4.1 Use common media and technology terminology and

equipment.o A.4.5 Use media and technology to create and present information.

II. Rationale: WMAS B: Number, Operations, and Relationships Rationale:

oPeople use numbers to quantify, describe, and label things in the world around them. It is important to know the many uses of numbers and various ways of representing them. Number sense is a matter of necessity, not only in one's occupation but also in the conduct of daily life, such as shopping, cooking, planning a budget, or analyzing information reported in the media. When computing, an educated person needs to know which operations (e.g., addition, multiplication), which procedures (e.g., mental techniques, algorithms*), or which technological aids (e.g., calculator, spreadsheet) are appropriate.

III. Objectives: Students will participate in group discussion about multiplication. Students will use multiplication to figure out how many pennies, nickels,

dimes, quarters, and dollars they need to make another value and/or to buy a product from the classroom store.

Students will use the Smart Board to manipulate coins to find the exact coins and number of each coin they will need to make a certain value.

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Students will recognize important math vocabulary needed to successfully run the classroom store.

IV. Materials: Computer with Smart Board Paper and pencils Calculators Williams, R. (2001) The Coin Counting Book. Watertown, MA:

Charlesbridge Publishing.

V. Procedures:

Pre-Instruction (10 minutes):Shut the lights off to grab students’ attention. I would ask the students to

gather around the front of the room and sit on the rug in a half-circle. I would explain that today we are learning about multiplication with coin manipulatives. Next, I would read The Coin Counting Book in order to set up background knowledge for working with varies coins. After reading the book I would review the basic multiplication facts with my students. I would ask for volunteers to come up to the Smart Board and solve a variety of multiplication problems showing their work and using any manipulatives if needed.

Direction-Instruction (20 minutes):I would explain how multiplication is repeated addition, and I would put a

variety of strategies to solve multiplication problems on the board as a reference for students to use. Next, I would introduce a variety of multiplication problems involving money. I would explain how one quarter times four equals one dollar (.25 X 4 = $1.00), how one dime times ten equals one dollar (.10 X 10 = $1.00), etc.

Adaptations and Accommodations:In order to differentiate this lesson to the needs of all learners in the

classroom, I would include a variety of money multiplication problems from easy to difficult. If the multiplication money problems are too advanced for some students, I would provide those students with addition and subtraction money problems. I would have students volunteer to come up to the SMART board to show how they solved the money problems they were given. By providing students with the opportunity to visualize a variety of strategies to solve a certain problem, I would be accommodating to their needs because the student is able to choose which strategy works best for him or her. Coin

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manipulatives would help more concrete learners solve the money problems they are given.

Extensions:

In order to extend money solving problems to the real world, I would send a letter home asking parents to take their child grocery shopping with them. I would ask the parents to discuss the different products they are purchasing, to tell the child how much each product costs, and to have the child use real money to pay for the products they are purchasing. During this unit I would set up a store in the classroom where the children could make real products to sell using real money. The students would be given an opportunity to participate in being both a cashier and a customer of the classroom store.

I would take my students on a field trip to a store, and give them the opportunity to work with the cashiers at that store to see what their job is like. Students would have the chance to handle real money, and work with real customers.

Closure:After the students had the opportunity to solve the money problems in

groups or alone and demonstrate how they solve the money problems with use of the SMART board, I would discuss any other methods or important concepts that the students should be aware of and answer any questions the students still had. After all questions are answered, I would work with my students to summarize the important concepts that were introduced throughout the lesson.

Post-Instruction/Closure (15 minutes):I would give the students an opportunity to come up with money

multiplication problems that came up while they were either a cashier or a customer in the classroom store.

Check for Understanding (Assessment/Evaluation Strategies):

During the entire lesson I would check the students understanding of solving money multiplication problems based on student’s answers to the money problems.

Math Lesson Plan

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Clinical Students: Alexis Mayer and Sarah Gorski Cooperating Teacher: Mrs. McKinneyDate/Time of the Lesson: 11/20/09; 1:45-2:30 Title of Lesson: Mixed Word ProblemsSubject/Topic: Math/ Word Problems

VI. State Standards: WMAS A: Mathematical Processes

oA.4.3 Connect mathematical learning with other subjects, personal experiences, current events, and personal interests

oA.4.4 Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work

WMAS B: Number, Operations and RelationshipsoB.4.5 In problem-solving situations involving whole numbers,

select and efficiently use appropriate computational procedures such as recalling the basic facts of addition, subtraction, multiplication, and division; using mental math (e.g., 37+25, 40x7); estimation; and selecting and applying algorithms for addition, subtraction, multiplication, and division

WMAS C: Oral Language Performanceo C.4.3 Participate effectively in discussion by volunteering

relevant information, asking relevant questions, answering questions directly, reflecting on the ideas and opinions of others and respond thoughtfully, and asking for clarification and explanation of unfamiliar words and ideas.

WMAS A: Media and TechnologyoA.4.1 Use common media and technology terminology and

equipment.oA.4.5 Use media and technology to create and present information

VII. Rationale: WMAS A: Mathematical Processes Rationale

o In order to participate fully as a citizen and a worker in our contemporary world, a person should be mathematically powerful. Mathematical power is the ability to explore, to conjecture, to reason logically and to apply a wide repertoire of methods to solve problems. Because no one lives and works in isolation, it is also important to have the ability to communicate mathematical ideas clearly and effectively.

WMAS B: Number, Operations, and Relationships Rationale:

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oPeople use numbers to quantify, describe, and label things in the world around them. It is important to know the many uses of numbers and various ways of representing them. Number sense is a matter of necessity, not only in one's occupation but also in the conduct of daily life, such as shopping, cooking, planning a budget, or analyzing information reported in the media. When computing, an educated person needs to know which operations (e.g., addition, multiplication), which procedures (e.g., mental techniques, algorithms*), or which technological aids (e.g., calculator, spreadsheet) are appropriate.

VIII. Objectives: Students will participate in group discussion about mixed word problems. Students will identify the operation of the word problems. Students will use the Smart Board to manipulate objects to solve the word

problems. Students will recognize important math vocabulary to successfully

complete mixed word problems.

IX. Materials: Computer with Smart Board Math Expressions fourth grade A workbook and homework book Paper and pencils Murphy, S. (1996). Too Many Kangaroo Things to Do! New York, NY:

Harper Collins Publishers, Inc. Murphy, S. (1997). Divide and Ride. New York, NY: HarperCollins Publishers

Inc.

X. Procedures:

Pre-Instruction (10 minutes):Shut the lights off to grab students’ attention. Tell the students to get out

their math notebooks. Write the review problems on the Smart Board. Tell the students to answer the word problems on a sheet of paper. Once all of the students have solved most of the answers, ask for volunteers to come up to the Smart Board and solve the problem showing work and using any manipulatives if needed.

Direction-Instruction (25 minutes):Tell the students to open to page 137. Read the introductory sentence to

the class. Discuss how “addend and total” are related to each other in addition and subtraction situations. Remind students that “more” does not

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always mean addition. Read problem one on page 137 to the class. Have the students find the “addend and total” within the word problem. Ask the students whether the problem is addition or subtraction. Then solve the problem. Repeat this process for problems 1-4.

For problems 5 and 6 discuss how multiplication and division are inverses of each other. We explained how multiplication is repeated addition, while division is repeated subtraction. Read the word problem aloud and ask the students what operations are needed to solve the problem. Have the students solve the problems by themselves or in pairs. Once everyone has had a chance to solve the problems regroup as a class and discuss the last two problems as a class. Invite a couple volunteers to demonstrate how they solved the last two problems by using manipulatives on the SMART board. We explained the standard algorithms for solving the multiplication and division problems, while exploring other alternative methods such as factor triangles.

Read the books Too Many Kangaroo Things to Do, and Divide and Ride to the classroom in order to help the children think of real-life word problems using the operations discussed earlier in class. As the books are read, have each student think of the connections between multiplication and addition, and division and subtraction. Then ask them to come up with real-world problems that include addition, subtraction, multiplication, and/or division. Have students work alone or in groups in order to solve the real-life problems they came up with in class. Students will use manipulatives on the SMART board in order to help solve the problems they came up with. After students have answered the questions, they will come up to the SMART board in order to demonstrate how they solved the word problems.

Extension: Have each student think of at least one real-life word problem they come across over the weekend. Tell them to write down the problem, how to solve it, and the manipulatives they used to solve it. Have each student bring in their problem the next week, and teach the class the real-life problem they came up with using the appropriate manipulatives to solve the problem.*This section was not included in the actual lesson I conducted in my clinical experience, but I thought it would have been a great addition. I think the combination of these children literature books and the mixed word problem lesson creates a solid lesson on the important concepts of the operations used by incorporating real-life experiences and word problems.

Adaptations and Accommodations:

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In order to differentiate this lesson to meet the needs of all learners in the classroom, we had more than one student come up to the SMART board to show how they solved each problem. By providing students with the opportunity to visualize a variety of strategies to solve a certain problem, we are accommodating to their needs because the student is able to choose which strategy works best for him or her. We included the use of math workbooks, the SMART board, pencil and paper, manipulatives, and the choice to work alone or in a group. By providing students with choices, they can choose which method works best for them in a particular subject.

Extensions:In order to extend this activity, we provided a worksheet with word

problems that students could chose to take home and complete if they wished to do so.

Closure:After the students had the opportunity to solve the problems in groups or

alone and demonstrate how they solve the problems with use of the SMART board, we discussed any other methods or important concepts that the students should be aware of and answered any questions the students still had. After all questions were answered, we summarized the important concepts we taught throughout the lesson.

Post-Instruction/Closure (10 minutes):Have each student solve the rest of the word problems provided by us in

groups and if there is time let them start on their homework.

Check for Understanding (Assessment/Evaluation Strategies):During the entire lesson we will be checking for understanding based on

student’s answers to the word problems. The homework sheet will also let us know how much of the lesson the students understood.

XI. Reflection/Evaluation of the Experience:The students responded well to the materials and activities. The students liked

having choices and a variety of strategies to use while solving the word problems.

What we would do differently would be to collaborate with the students in order to come up with real-life word problems from the students’ everyday life at school and at home.

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All the students in the classroom participated in the activity by reading the questions, working alone or in groups to solve the problem, using the SMART board to demonstrate how they solved a particular problem, and by being involves in a discussion about the important concepts taught.

We were surprised at the variety of methods students used in order to solve the word problems. The students enjoyed getting to demonstrate how they solved the word problems with use of the SMART board.