**Title:** A Math and Language Arts lesson: Introduction to Division

**Description:**
The lesson will help students develop an initial understanding of division and clarify how the four operations of addition, subtraction, multiplication, and division relate to and are separate from each other. The lesson begins with a brainstorming discussion which builds background and fosters comprehension. A big book, The Doorbell Rang, by Pat Hutchins, is used along with manipulatives to provide instruction at concrete and pictorial levels. Students will demonstrate what they have learned by writing a short story incorporating simple division.
**Standard(s): **

[MA2015] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3-OA5]

**Subject:**English Language Arts (3), or Mathematics (3)

**Title:**A Math and Language Arts lesson: Introduction to Division

**Description:**The lesson will help students develop an initial understanding of division and clarify how the four operations of addition, subtraction, multiplication, and division relate to and are separate from each other. The lesson begins with a brainstorming discussion which builds background and fosters comprehension. A big book, The Doorbell Rang, by Pat Hutchins, is used along with manipulatives to provide instruction at concrete and pictorial levels. Students will demonstrate what they have learned by writing a short story incorporating simple division.

**Title:** Let's Go Shopping!

**Description:**
This technology-based lesson provides students practice in collecting and organizing data through the use of grocery store circulars.
**Standard(s): **

[MA2015] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3-OA3]

**Subject:**Mathematics (3 - 5), or Technology Education (3 - 5)

**Title:**Let's Go Shopping!

**Description:**This technology-based lesson provides students practice in collecting and organizing data through the use of grocery store circulars.

**Title:** It’s My Party!

**Description:**
Students will learn the value of money by planning their own birthday party. By using the Internet and a calculator, students will be given the opportunity for a practical real-life opportunity to solve a problem related to money exchange.
**Standard(s): **

[MA2015] (5) 16: Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5-NF6]

**Subject:**Mathematics (3 - 5), or Technology Education (3 - 5)

**Title:**It’s My Party!

**Description:**Students will learn the value of money by planning their own birthday party. By using the Internet and a calculator, students will be given the opportunity for a practical real-life opportunity to solve a problem related to money exchange.

**Title:** Budgeting for the Oregon Trail

**Description:**
As a part of the online collaborative unit, Westward Ho!, students will work in cooperative groups of 4-5 students to decide what items they need to take on the Oregon Trail, determine the cost of the items, and complete a ledger to inventory (keep up with) items used on the trail. Information will then be used as part of a multimedia slideshow journal describing the journey.
**Standard(s): **

[MA2015] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4-OA2]

**Subject:**Mathematics (3 - 4)

**Title:**Budgeting for the Oregon Trail

**Description:**As a part of the online collaborative unit, Westward Ho!, students will work in cooperative groups of 4-5 students to decide what items they need to take on the Oregon Trail, determine the cost of the items, and complete a ledger to inventory (keep up with) items used on the trail. Information will then be used as part of a multimedia slideshow journal describing the journey.

**Title:** Multiplying Meanings

**Description:**
In this eight-lesson unit, from Illuminations, students explore the many meanings of multiplication (skip counting, repeated addition, sets, arrays, number line, cross products of sets and balanced equations). They also learn about the order property, the multiplicative inverse and the results of multiplying by 1 and by 0. In addition, students write story problems in which the operation of multiplication is required. Opportunities to connect with literature are presented in four of the lessons.
**Standard(s): **

[MA2015] (3) 7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. [3-OA7]

**Subject:**Language Arts,Mathematics

**Title:**Multiplying Meanings

**Description:**In this eight-lesson unit, from Illuminations, students explore the many meanings of multiplication (skip counting, repeated addition, sets, arrays, number line, cross products of sets and balanced equations). They also learn about the order property, the multiplicative inverse and the results of multiplying by 1 and by 0. In addition, students write story problems in which the operation of multiplication is required. Opportunities to connect with literature are presented in four of the lessons.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Bag the Beans

**Description:**
In this Science NetLinks lesson, students work with manipulatives (beans) to create and solve math problems, some of which have more than one correct answer. This lesson addresses the common misconception that there is only one correct way to solve any math problem.
**Standard(s): **

[MA2015] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3-OA3]

**Subject:**Mathematics

**Title:**Bag the Beans

**Description:**In this Science NetLinks lesson, students work with manipulatives (beans) to create and solve math problems, some of which have more than one correct answer. This lesson addresses the common misconception that there is only one correct way to solve any math problem.

**Thinkfinity Partner:**Science NetLinks

**Grade Span:**3,4,5

**Title:** Modeling Multiplication with Rows and Columns

**Description:**
This lesson, one of a multi-part unit from Illuminations, encourages students to explore the array model of multiplication. Students make arrays with counters and then create a second concrete example of the array model using toothpicks. They also write problems that involve multiplication. A children s book is suggested to connect multiplication with children s literature. Several pieces of literature appropriate for use with this lesson are suggested.
**Standard(s): **

[MA2015] (4) 10: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4-NBT5]

**Subject:**Language Arts,Mathematics

**Title:**Modeling Multiplication with Rows and Columns

**Description:**This lesson, one of a multi-part unit from Illuminations, encourages students to explore the array model of multiplication. Students make arrays with counters and then create a second concrete example of the array model using toothpicks. They also write problems that involve multiplication. A children s book is suggested to connect multiplication with children s literature. Several pieces of literature appropriate for use with this lesson are suggested.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Multiplication Stories

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students practice memorization of multiplication facts where one factor is 6 or 7. They create multiplication stories, play a multiplication game, and then record their current level of mastery of the multiplication facts.
**Standard(s): **

[MA2015] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3-OA4]

**Subject:**Mathematics

**Title:**Multiplication Stories

**Description:**In this lesson, one of a multi-part unit from Illuminations, students practice memorization of multiplication facts where one factor is 6 or 7. They create multiplication stories, play a multiplication game, and then record their current level of mastery of the multiplication facts.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Times Six, Times Seven

**Description:**
In this six-lesson unit, from Illuminations, students who have previously studied the meanings of multiplication use its properties to help them memorize the products to 70, where 6 or 7 is a factor. Retention is fostered through class discussions, preparation of a personal multiplication chart, and game playing. The unit is most appropriate for students who understand the process of multiplication and have mastered the multiplication facts through the 5 table.
**Standard(s): **

[MA2015] (4) 2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4-OA2]

**Subject:**Mathematics

**Title:**Times Six, Times Seven

**Description:**In this six-lesson unit, from Illuminations, students who have previously studied the meanings of multiplication use its properties to help them memorize the products to 70, where 6 or 7 is a factor. Retention is fostered through class discussions, preparation of a personal multiplication chart, and game playing. The unit is most appropriate for students who understand the process of multiplication and have mastered the multiplication facts through the 5 table.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Clothing Sizes

**Description:**
This reproducible worksheet, from an Illuminations lesson, prompts students to analyze measurements of their body, specifically as they relate to clothing sizes.
**Standard(s): **

[MA2015] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5-MD3]

**Subject:**Mathematics

**Title:**Clothing Sizes

**Description:**This reproducible worksheet, from an Illuminations lesson, prompts students to analyze measurements of their body, specifically as they relate to clothing sizes.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** A Brownie Bake

**Description:**
This lesson, one of a multi-part unit from Illuminations, focuses on student organization, preparation, and presentation of some simple foods as a way to apply various mathematical concepts, with problem-solving techniques being a central theme. Students prepare, after determining minimum amounts of ingredients required, a commercial brownie mix and serve equal portions to all class members.
**Standard(s): **

[MA2015] (5) 12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5-NF2]

**Subject:**Mathematics

**Title:**A Brownie Bake

**Description:**This lesson, one of a multi-part unit from Illuminations, focuses on student organization, preparation, and presentation of some simple foods as a way to apply various mathematical concepts, with problem-solving techniques being a central theme. Students prepare, after determining minimum amounts of ingredients required, a commercial brownie mix and serve equal portions to all class members.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** The Variable Machine

**Description:**
This Illuminations lesson provides an introduction to the use of variables. Students explore the idea of variable as a symbol that can stand for any member of a set of numbers, and they substitute numbers for variables (letters) to discover unknown values.
**Standard(s): **

[MA2015] (5) 6: Read, write, and compare decimals to thousandths. [5-NBT3]

**Subject:**Mathematics

**Title:**The Variable Machine

**Description:**This Illuminations lesson provides an introduction to the use of variables. Students explore the idea of variable as a symbol that can stand for any member of a set of numbers, and they substitute numbers for variables (letters) to discover unknown values.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Making Your First Million

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students attempt to identify the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition until a million is reached. Additionally, they use critical thinking to analyze situations and to identify mathematical patterns that enable them to develop the concept of very large numbers.
**Standard(s): **

[MA2015] (8) 6: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. [8-EE4]

**Subject:**Mathematics

**Title:**Making Your First Million

**Description:**In this lesson, one of a multi-part unit from Illuminations, students attempt to identify the concept of a million by working with smaller numerical units, such as blocks of 10 or 100, and then expanding the idea by multiplication or repeated addition until a million is reached. Additionally, they use critical thinking to analyze situations and to identify mathematical patterns that enable them to develop the concept of very large numbers.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Multiplying Turtle

**Digital Tool:**
Online Video **Web Address URL:**
http://www.teachertube.com/viewVideo.php?video_id=77588 **Standard(s): **

[MA2015] (4) 10: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4-NBT5]**Digital Tool Description:** A woman narrates the steps of two digit by two digit multiplication. It is a slideshow. This turtle method is an interesting and fun method for kids to learn double digit multiplication.

**Title:**Multiplying Turtle

**Digital Tool:**Online Video

**Digital Tool Description:**A woman narrates the steps of two digit by two digit multiplication. It is a slideshow. This turtle method is an interesting and fun method for kids to learn double digit multiplication.

**Title:** Kids Teaching Kids

**Digital Tool:**
MathTrain **Web Address URL:**
http://www.mathtrain.com **Standard(s): **

[MA2015] (3) 3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (See Appendix A, Table 2.) [3-OA3]**Digital Tool Description:** Mathtrain.TV is a free, educational "kids teaching kids" project. There are different video channels for every subject. You can make an account for the class for free but you do not need an account just to view videos. You can upload a video once you make an account. There are teacher-created videos and student-created videos. Students and teachers can create these through their computers or iPads. Children love watching other children's work. Watching other kids' projects helps students better understand the content.

**Title:**Kids Teaching Kids

**Digital Tool:**MathTrain

**Digital Tool Description:**Mathtrain.TV is a free, educational "kids teaching kids" project. There are different video channels for every subject. You can make an account for the class for free but you do not need an account just to view videos. You can upload a video once you make an account. There are teacher-created videos and student-created videos. Students and teachers can create these through their computers or iPads. Children love watching other children's work. Watching other kids' projects helps students better understand the content.

**Title:** Number and Operations Web Links

**Description:**
This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.
**Standard(s): **

[MA2015] (5) 26: Classify two-dimensional figures in a hierarchy based on properties. [5-G4]

**Subject:**Mathematics

**Title:**Number and Operations Web Links

**Description:**This collection of Web links, reviewed and presented by Illuminations, offers teachers and students information about and practice in concepts related to arithmetic. Users can read the Illuminations Editorial Board's review of each Web site, or choose to link directly to the sites.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,1,2,3,4,5,6,7,8,9,10,11,12

**Title:** Communicating about Mathematics Using Games: Playing Fraction Tracks

**Description:**
Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This e-example from Illuminations contains an interactive version of a game that can be used in the grades 3-5 classroom to support students' learning about fractions. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.
**Standard(s): **

[MA2015] (5) 26: Classify two-dimensional figures in a hierarchy based on properties. [5-G4]

**Subject:**Mathematics

**Title:**Communicating about Mathematics Using Games: Playing Fraction Tracks

**Description:**Mathematical games can foster mathematical communication as students explain and justify their moves to one another. In addition, games can motivate students and engage them in thinking about and applying concepts and skills. This e-example from Illuminations contains an interactive version of a game that can be used in the grades 3-5 classroom to support students' learning about fractions. e-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5

**Title:** Concentration

**Description:**
This student interactive from Illuminations allows students to play the classic game of Concentration by themselves or against a friend. The interactive can be used to review numbers, shapes, multiplication facts, fractions, decimals, and percents.
**Standard(s): **

[MA2015] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4-MD5]

**Subject:**Mathematics

**Title:**Concentration

**Description:**This student interactive from Illuminations allows students to play the classic game of Concentration by themselves or against a friend. The interactive can be used to review numbers, shapes, multiplication facts, fractions, decimals, and percents.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2,3,4,5

**Title:** Product Game

**Description:**
This interactive game, from Illuminations, exercises students skills with factors and multiples. Players take turns moving a marker along a number line to create products, which are then colored in on the game board. The object of the game is to get four squares in a row.
**Standard(s): **

[MA2015] (4) 1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. [4-OA1]

**Subject:**Mathematics

**Title:**Product Game

**Description:**This interactive game, from Illuminations, exercises students skills with factors and multiples. Players take turns moving a marker along a number line to create products, which are then colored in on the game board. The object of the game is to get four squares in a row.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Factorize

**Description:**
This student interactive, from Illuminations, allows students to visually explore the concept of factors by creating rectangular arrays with an area equal to the product of the factors. They can choose whether or not to use the commutative property when identifying factors.
**Standard(s): **

[MA2015] (6) 5: Fluently divide multi-digit numbers using the standard algorithm. [6-NS2]

**Subject:**Mathematics

**Title:**Factorize

**Description:**This student interactive, from Illuminations, allows students to visually explore the concept of factors by creating rectangular arrays with an area equal to the product of the factors. They can choose whether or not to use the commutative property when identifying factors.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8