ALEX Lesson Plans
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Title: Decimal Dilemma: Carlos the Centipede needs to buy tennis shoes!
Description:
In this lesson, Carlos the Centipede must buy new baseball shoes. His dilemma will be how to multiply decimals (money) by multiples of 10. To add to the dilemma, Carlos' baseball team needs to buy shoes too! Students will multiply decimals by 100. Students will investigate what is happening to the decimal point each time a decimal is multiplied by a multiple of 10.
Standard(s): [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3]
Subject: Mathematics (5  6)
Title: Decimal Dilemma: Carlos the Centipede needs to buy tennis shoes!
Description: In this lesson, Carlos the Centipede must buy new baseball shoes. His dilemma will be how to multiply decimals (money) by multiples of 10. To add to the dilemma, Carlos' baseball team needs to buy shoes too! Students will multiply decimals by 100. Students will investigate what is happening to the decimal point each time a decimal is multiplied by a multiple of 10.
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Title: Pacaderms, Pennies, and Pasta
Description:
After learning of a historical event in which elephants were used to test out the Brooklyn Bridge, students construct their own bridge using very basic materials. Students weigh different items to determine the weight their bridge can withstand without collapsing.
Standard(s): [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7]
Subject: Mathematics (4  5)
Title: Pacaderms, Pennies, and Pasta
Description: After learning of a historical event in which elephants were used to test out the Brooklyn Bridge, students construct their own bridge using very basic materials. Students weigh different items to determine the weight their bridge can withstand without collapsing.
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Title: Decimal Dilemmas: Carlos the Centipede is Adding Decimals!
Description:
In this lesson, students will work in collaborative/cooperative groups to understand adding decimals. Students will use decimal grids to represent the sum of decimals. Emphasis is on using placevalue, lining up the decimals and bringing the decimal down. Students will understand how important estimation of decimals is in reallife situations.
Standard(s): [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3]
Subject: Mathematics (5  6)
Title: Decimal Dilemmas: Carlos the Centipede is Adding Decimals!
Description: In this lesson, students will work in collaborative/cooperative groups to understand adding decimals. Students will use decimal grids to represent the sum of decimals. Emphasis is on using placevalue, lining up the decimals and bringing the decimal down. Students will understand how important estimation of decimals is in reallife situations.
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Title: Decimal Dilemma: Carlos the Centipede is Subtracting Decimals!
Description:
In this lesson, students will work in collaborative/cooperative groups to understand subtracting decimals. Students will use decimal grids to represent the difference of decimals. Emphasis is on using placevalue, lining up the decimals and bringing the decimal down. Students will understand how important estimation of decimals is in reallife situations
Standard(s): [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3]
Subject: Mathematics (5  6)
Title: Decimal Dilemma: Carlos the Centipede is Subtracting Decimals!
Description: In this lesson, students will work in collaborative/cooperative groups to understand subtracting decimals. Students will use decimal grids to represent the difference of decimals. Emphasis is on using placevalue, lining up the decimals and bringing the decimal down. Students will understand how important estimation of decimals is in reallife situations
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Title: Sky High
Description:
Students will work together, implementing problemsolving strategies to complete a building challenge. The group will be given a budget and materials to construct a structurally sound skyscraper. The students will purchase materials, build, and measure their structure.
Standard(s): [MA2013] (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. [4OA1] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7]
Subject: Mathematics (4  5)
Title: Sky High
Description: Students will work together, implementing problemsolving strategies to complete a building challenge. The group will be given a budget and materials to construct a structurally sound skyscraper. The students will purchase materials, build, and measure their structure.
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Title: Satisfy Your Vacation Hunger!
Description:
Students will prepare and present a group project detailing the menu for a 5 day vacation. Each group will select a vacation destination and describe activities involved in the vacation and the meals that will be served. Groups will be given a budget of $200 for the 5 days of meals for 4 people. Students will use various forms of technology to research needed information, prepare the budget, and to present the final product. Projects will be turned in as a binder with required information and as a multimedia presentation to be shared with the class.
Standard(s): [TC2] (68) 2: Publish digital products that communicate curriculum concepts. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3]
Subject: Mathematics (5  6), or Technology Education (6  8)
Title: Satisfy Your Vacation Hunger!
Description: Students will prepare and present a group project detailing the menu for a 5 day vacation. Each group will select a vacation destination and describe activities involved in the vacation and the meals that will be served. Groups will be given a budget of $200 for the 5 days of meals for 4 people. Students will use various forms of technology to research needed information, prepare the budget, and to present the final product. Projects will be turned in as a binder with required information and as a multimedia presentation to be shared with the class.
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Title: Get it Straight Mr. Decimal!
Description:
Students will review addition and subtraction of decimals with a handson, cooperative small group experience. They will be placed in small groups and solve problems on individual white boards. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [CE] (012) 21: Patience [CE] (012) 13: Tolerance [CE] (012) 11: Courtesy [CE] (012) 10: Selfcontrol [CE] (012) 8: Cooperation [CE] (012) 23: Sportsmanship [CE] (012) 8: Cooperation [CE] (012) 10: Selfcontrol [CE] (012) 11: Courtesy [CE] (012) 13: Tolerance [CE] (012) 21: Patience [CE] (012) 23: Sportsmanship [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4]
Subject: Character Education (K  12), or Mathematics (5)
Title: Get it Straight Mr. Decimal!
Description: Students will review addition and subtraction of decimals with a handson, cooperative small group experience. They will be placed in small groups and solve problems on individual white boards. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Pizza! Pizza! Pizza!
Description:
This lesson provides students practical situations using money. It also allows them to practice the skills of adding and subtracting decimals.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [CE] (012) 8: Cooperation [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4]
Subject: Character Education (K  12), or Mathematics (5)
Title: Pizza! Pizza! Pizza!
Description: This lesson provides students practical situations using money. It also allows them to practice the skills of adding and subtracting decimals.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: "All in the Family"
Description:
A cooperative unit where students work together and use a variety of math skills to establish budgets and compare and compute the best buys. Students will continue practicing their writing skills by writing thank you notes to local merchants.
Standard(s): [ELA2013] (6) 38: Demonstrate command of the conventions of Standard English capitalization, punctuation, and spelling when writing. [L.6.2] [ELA2013] (6) 37: Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking. [L.6.1] [ELA2013] (6) 27: Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate. [W.6.7] [ELA] (5) 7: Compose expository texts using an introductory paragraph that includes a main idea; supporting paragraphs with a minimum of three reasons, explanations, or steps in a process; and a conclusion. [ELA] (5) 9: Apply mechanics in writing, including capitalization of first word in a direct quotation and use of punctuation, including quotation marks and comma with direct quotations, colon to introduce a list, and commas after introductory words, with a noun of direct address, and in a compound sentence. [ELA] (5) 10: Demonstrate knowledge of grammar and usage concepts, including subjectverb agreement with a compound subject; present, past, and future verb tenses; forms of adjectives; forms of nouns; and subject, object, and possessive pronouns. [ELA] (6) 9: Utilize vocabulary and spelling skills, including using homonyms, synonyms, and antonyms in writing. [ELA] (6) 10: Use punctuation correctly in writing, including apostrophes to show possession and semicolons joining two independent clauses. [ELA] (6) 11: Apply the rules governing capitalization of proper adjectives, map directions and regions of the country, seasons, titles, words showing family relationships, subjects and courses, and divided quotations. [ELA] (6) 12: Apply grammar conventions in writing with consistent verb tense; nominative, objective, and possessive pronouns; and subjectverb agreement when interrupted by a prepositional phrase. [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7]
Subject: English Language Arts (5  6), or English Language Arts (6), or Mathematics (3  5)
Title: "All in the Family"
Description: A cooperative unit where students work together and use a variety of math skills to establish budgets and compare and compute the best buys. Students will continue practicing their writing skills by writing thank you notes to local merchants.
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Title: Watch That Plant Grow
Description:
This lesson allows students to explore horticulture within a controlled environment, a greenhouse. Students engage in handson activities as they grow their own plants and chart data concerning the conditions related to plant growth in a greenhouse. The data collected is recorded on a spreadsheet to aid in growth prediction over a specified amount of time. This lesson should precede other lessons regarding research on plants grown in a greenhouse.
Standard(s): [S1] (8) 1: Identify steps within the scientific process. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [TC2] (68) 6: Select specific digital tools for completing curriculumrelated tasks. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (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. [5NF2] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3] [MA2013] (6) 28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [6SP4] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5]
Subject: Mathematics (5  6), or Science (8), or Technology Education (6  8)
Title: Watch That Plant Grow
Description: This lesson allows students to explore horticulture within a controlled environment, a greenhouse. Students engage in handson activities as they grow their own plants and chart data concerning the conditions related to plant growth in a greenhouse. The data collected is recorded on a spreadsheet to aid in growth prediction over a specified amount of time. This lesson should precede other lessons regarding research on plants grown in a greenhouse.
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Title: Dream Vacation
Description:
This unit teaches students to plan a trip with an itinerary, remain within a budget, and work cooperatively. It is a technologybased project that combines a study of mathematics, economics, geography, and social studies.
Standard(s): [IL] (012) 2: The student who is information literate evaluates information critically and competently. [IL] (012) 3: The student who is information literate uses information accurately and creatively. [IL] (012) 4: The student who is an independent learner is information literate and pursues information related to personal interests. [IL] (012) 6: The student who is an independent learner is information literate and strives for excellence in information seeking and knowledge generation. [IL] (012) 9: The student who contributes positively to the learning community and to society is information literate and participates effectively in groups to pursue and generate information. [TC2] (35) 2: Use various technology applications, including word processing and multimedia software. [TC2] (35) 5: Practice safe use of technology systems and applications. [TC2] (35) 8: Collect information from a variety of digital sources. [TC2] (35) 9: Use technology tools to organize, interpret, and display data. [TC2] (35) 10: Use digital environments to collaborate and communicate. [TC2] (35) 12: Create a product using digital tools. [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4]
Subject: Information Literacy (K  12), or Mathematics (4  5), or Technology Education (3  5)
Title: Dream Vacation
Description: This unit teaches students to plan a trip with an itinerary, remain within a budget, and work cooperatively. It is a technologybased project that combines a study of mathematics, economics, geography, and social studies.
Thinkfinity Lesson Plans
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Title: Finding Products
Description:
In this lesson, one of a multipart unit from Illuminations, students examine the role of commutativity and the multiplicative identity, play a multiplication game, and explore products where one of the factors is 6. They also create a personal multiplication chart.
Standard(s): [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (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 onedigit numbers. [3OA7] [MA2013] (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.) [4OA2] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit 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. [4NBT5] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5]
Subject: Mathematics Title: Finding Products
Description: In this lesson, one of a multipart unit from Illuminations, students examine the role of commutativity and the multiplicative identity, play a multiplication game, and explore products where one of the factors is 6. They also create a personal multiplication chart. Thinkfinity Partner: Illuminations Grade Span: 3,4,5
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Title: Numbers and Language
Description:
In this fivelesson unit, from Illuminations, students participate in activities in which they focus on the role of numbers and language in realworld situations. Students discuss, describe, read, and write about numbers they find in familiar realworld situations. An emphasis on using components of language helps students build a broader vocabulary of numbers than the traditional symbolic representation of numbers.
Standard(s): [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (6) 4: Interpret and compute quotients of fractions, and solve word problems involving division of fractions, e.g., by using visual fraction models and equations to represent the problem. [6NS1] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3] [MA2013] (7) 1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7RP1] [MA2013] (7) 5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7NS2] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (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. [8EE4] [ELA2013] (3) 28: Conduct short research projects that build knowledge about a topic. [W.3.7] [ELA2013] (4) 28: Conduct short research projects that build knowledge through investigation of different aspects of a topic. [W.4.7] [ELA2013] (5) 28: Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. [W.5.7] [ELA2013] (6) 14: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings. [RI.6.4] [ELA2013] (6) 17: Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. [RI.6.7] [ELA2013] (6) 18: Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not. [RI.6.8] [ELA2013] (6) 20: By the end of the year, read and comprehend literary nonfiction in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RI.6.10] [ELA2013] (7) 13: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone. [RI.7.4] [ELA2013] (7) 19: By the end of the year, read and comprehend literary nonfiction in the Grades 68 text complexity band proficiently, with scaffolding as needed at the high end of the range. [RI.7.10] [ELA2013] (8) 10: Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. [RI.8.1] [ELA2013] (8) 19: By the end of the year, read and comprehend literary nonfiction at the high end of the
Grades 68 text complexity band independently and proficiently. [RI.8.10]
Subject: Language Arts,Mathematics Title: Numbers and Language
Description: In this fivelesson unit, from Illuminations, students participate in activities in which they focus on the role of numbers and language in realworld situations. Students discuss, describe, read, and write about numbers they find in familiar realworld situations. An emphasis on using components of language helps students build a broader vocabulary of numbers than the traditional symbolic representation of numbers. Thinkfinity Partner: Illuminations Grade Span: K,PreK,1,2,3,4,5,6,7,8
ALEX Podcasts
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Title: Percents 5: Percents & Money
Overview:
This podcast is part of a series on operations with percents. Designed with the middle school student in mind, it is a refresher on the basics of solving word problems including money and percents. The lesson uses the bar method to solve the problems. The podcast can be used as a lesson or as a supplement to a lesson. A suggestion would be to stop the lesson as it goes along and allow the students to work problems out themselves. Standard(s):
[MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (6) 5: Fluently divide multidigit numbers using the standard algorithm. [6NS2] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3] [MA2013] (7) 4: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7NS1] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3]
Percents 5: Percents & Money Overview: This podcast is part of a series on operations with percents. Designed with the middle school student in mind, it is a refresher on the basics of solving word problems including money and percents. The lesson uses the bar method to solve the problems. The podcast can be used as a lesson or as a supplement to a lesson. A suggestion would be to stop the lesson as it goes along and allow the students to work problems out themselves.
Web Resources
Interactives/Games
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Title: Divisibility Rules
Description:
This is an interactive game requiring students to choose which integers are evenly divisible.
Standard(s): [MA2013] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 6: Understand division as an unknownfactor problem. [3OA6] [MA2013] (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 onedigit numbers. [3OA7] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [MA2013] (5) 9: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5NBT6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (7) 5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. [7NS2]
Divisibility Rules
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This is an interactive game requiring students to choose which integers are evenly divisible.
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Title: Matching Math Decimals: Addition
Description:
Students practice adding decimals in a game type format. The students may chose a relaxed mode or a fast timed mode.
Standard(s): [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2]
Matching Math Decimals: Addition
http://www.sheppards...
Students practice adding decimals in a game type format. The students may chose a relaxed mode or a fast timed mode.
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Title: Decimals Jeopardy
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An interactive game where the students play the game Jeopardy to review adding, subtracting, and multiplying decimals. The students will need a bell or buzzer to be able to ring in and answer the questions. The game has singleplayer and multiplayer modes.
Standard(s): [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (6) 6: Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. [6NS3]
Decimals Jeopardy
http://www.mathplay...
An interactive game where the students play the game Jeopardy to review adding, subtracting, and multiplying decimals. The students will need a bell or buzzer to be able to ring in and answer the questions. The game has singleplayer and multiplayer modes.
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Title: Everything Math for 5
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The website 1XL has an extensive list of skills students learn in 5th grade. They are organized into categories (ex. place value, problem solving, geometry, etc.)where you can move your mouse over any skill to view a sample question before going to the link. 1XL will track the score and questions will become increasingly difficult. Great to use with SmartBoards!
Standard(s): [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (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. [5NF2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 18: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. [5MD1] [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3]
Everything Math for 5
http://www.ixl.com/m...
The website 1XL has an extensive list of skills students learn in 5th grade. They are organized into categories (ex. place value, problem solving, geometry, etc.)where you can move your mouse over any skill to view a sample question before going to the link. 1XL will track the score and questions will become increasingly difficult. Great to use with SmartBoards!
Thinkfinity Informational Materials
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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): [MA2013] (0) 1: Count to 100 by ones and by tens. [KCC1] [MA2013] (0) 2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). [KCC2] [MA2013] (0) 3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). [KCC3] [MA2013] (0) 4: Understand the relationship between numbers and quantities; connect counting to cardinality. [KCC4] [MA2013] (0) 5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects. [KCC5] [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (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.) [3OA3] [MA2013] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 6: Understand division as an unknownfactor problem. [3OA6] [MA2013] (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 onedigit numbers. [3OA7] [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (3) 10: Use place value understanding to round whole numbers to the nearest 10 or 100. [3NBT1] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (3) 12: Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 14: Understand a fraction as a number on the number line; represent fractions on a number line diagram. [3NF2] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (3) 16: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. [3MD1] [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (3) 20: Recognize area as an attribute of plane figures, and understand concepts of area measurement. [3MD5] [MA2013] (3) 21: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (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. [4OA1] [MA2013] (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.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. [4OA4] [MA2013] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4OA5] [MA2013] (4) 6: Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. [4NBT1] [MA2013] (4) 7: Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4NBT2] [MA2013] (4) 8: Use place value understanding to round multidigit whole numbers to any place. [4NBT3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit 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. [4NBT5] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 14: Understand a fraction ^{a}/_{b} with a > 1 as a sum of fractions ^{1}/_{b}. [4NF3] [MA2013] (4) 15: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4NF4] [MA2013] (4) 16: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) [4NF5] [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (4) 18: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. [4NF7] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [MA2013] (5) 1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5OA1] [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5OA3] [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 9: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5NBT6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (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. [5NF2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 15: Interpret multiplication as scaling (resizing), by: [5NF5] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 18: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. [5MD1] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4]
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
Thinkfinity Interactive Games
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Title: Communicating about Mathematics Using Games: Playing Fraction Tracks
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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 eexample from Illuminations contains an interactive version of a game that can be used in the grades 35 classroom to support students' learning about fractions. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations.
Standard(s): [MA2013] (3) 1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. [3OA1] [MA2013] (3) 2: Interpret wholenumber quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. [3OA2] [MA2013] (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.) [3OA3] [MA2013] (3) 4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. [3OA4] [MA2013] (3) 5: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) [3OA5] [MA2013] (3) 6: Understand division as an unknownfactor problem. [3OA6] [MA2013] (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 onedigit numbers. [3OA7] [MA2013] (3) 8: Solve twostep word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) [3OA8] [MA2013] (3) 9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. [3OA9] [MA2013] (3) 10: Use place value understanding to round whole numbers to the nearest 10 or 100. [3NBT1] [MA2013] (3) 11: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. [3NBT2] [MA2013] (3) 12: Multiply onedigit whole numbers by multiples of 10 in the range 10  90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. [3NBT3] [MA2013] (3) 13: Understand a fraction ^{1}/_{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction ^{a}/_{b} as the quantity formed by a parts and size ^{1}/_{b}. [3NF1] [MA2013] (3) 14: Understand a fraction as a number on the number line; represent fractions on a number line diagram. [3NF2] [MA2013] (3) 15: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. [3NF3] [MA2013] (3) 16: Tell and write time to the nearest minute, and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. [3MD1] [MA2013] (3) 17: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^{3} and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve onestep word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of "times as much").) (See Appendix A, Table 2.) [3MD2] [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [MA2013] (3) 19: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units — whole numbers, halves, or quarters. [3MD4] [MA2013] (3) 21: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). [3MD6] [MA2013] (3) 22: Relate area to the operations of multiplication and addition. [3MD7] [MA2013] (3) 23: Solve realworld and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. [3MD8] [MA2013] (3) 24: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. [3G1] [MA2013] (3) 25: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [3G2] [MA2013] (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. [4OA1] [MA2013] (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.) [4OA2] [MA2013] (4) 3: Solve multistep word problems posed with whole numbers and having wholenumber answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4OA3] [MA2013] (4) 4: Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1100 is prime or composite. [4OA4] [MA2013] (4) 5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. [4OA5] [MA2013] (4) 6: Recognize that in a multidigit whole number, a digit in one place represents ten times what it represents in the place to its right. [4NBT1] [MA2013] (4) 7: Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. [4NBT2] [MA2013] (4) 8: Use place value understanding to round multidigit whole numbers to any place. [4NBT3] [MA2013] (4) 9: Fluently add and subtract multidigit whole numbers using the standard algorithm. [4NBT4] [MA2013] (4) 10: Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit 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. [4NBT5] [MA2013] (4) 11: Find wholenumber quotients and remainders with up to fourdigit dividends and onedigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4NBT6] [MA2013] (4) 12: Explain why a fraction ^{a}/_{b} is equivalent to a fraction ^{nxa}/_{nxb} by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4NF1] [MA2013] (4) 13: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators or by comparing to a benchmark fraction such as ^{1}/_{2}. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. [4NF2] [MA2013] (4) 14: Understand a fraction ^{a}/_{b} with a > 1 as a sum of fractions ^{1}/_{b}. [4NF3] [MA2013] (4) 15: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4NF4] [MA2013] (4) 16: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) [4NF5] [MA2013] (4) 17: Use decimal notation for fractions with denominators 10 or 100. [4NF6] [MA2013] (4) 18: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. [4NF7] [MA2013] (4) 19: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. [4MD1] [MA2013] (4) 20: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. [4MD2] [MA2013] (4) 21: Apply the area and perimeter formulas for rectangles in realworld and mathematical problems. [4MD3] [MA2013] (4) 22: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}). Solve problems involving addition and subtraction of fractions by using information presented in line plots. [4MD4] [MA2013] (4) 23: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4MD5] [MA2013] (4) 24: Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. [4MD6] [MA2013] (4) 25: Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in realworld or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4MD7] [MA2013] (4) 26: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. [4G1] [MA2013] (4) 27: Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4G2] [MA2013] (4) 28: Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. [4G3] [MA2013] (5) 1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [5OA1] [MA2013] (5) 2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. [5OA2] [MA2013] (5) 3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. [5OA3] [MA2013] (5) 4: Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and ^{1}/_{10} of what it represents in the place to its left. [5NBT1] [MA2013] (5) 5: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. [5NBT2] [MA2013] (5) 6: Read, write, and compare decimals to thousandths. [5NBT3] [MA2013] (5) 7: Use place value understanding to round decimals to any place. [5NBT4] [MA2013] (5) 8: Fluently multiply multidigit whole numbers using the standard algorithm. [5NBT5] [MA2013] (5) 9: Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5NBT6] [MA2013] (5) 10: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method, and explain the reasoning used. [5NBT7] [MA2013] (5) 11: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. [5NF1] [MA2013] (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. [5NF2] [MA2013] (5) 13: Interpret a fraction as division of the numerator by the denominator (^{a}/_{b} = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF3] [MA2013] (5) 14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [5NF4] [MA2013] (5) 15: Interpret multiplication as scaling (resizing), by: [5NF5] [MA2013] (5) 16: Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. [5NF6] [MA2013] (5) 17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the relationship between multiplication and division. However, division of a fraction by a fraction is not a requirement at this grade.)
[5NF7] [MA2013] (5) 18: Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. [5MD1] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (5) 20: Recognize volume as an attribute of solid figures, and understand concepts of volume measurement. [5MD3] [MA2013] (5) 21: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. [5MD4] [MA2013] (5) 22: Relate volume to the operations of multiplication and addition, and solve realworld and mathematical problems involving volume. [5MD5] [MA2013] (5) 23: Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [5G1] [MA2013] (5) 24: Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. [5G2] [MA2013] (5) 25: Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. [5G3] [MA2013] (5) 26: Classify twodimensional figures in a hierarchy based on properties. [5G4]
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 eexample from Illuminations contains an interactive version of a game that can be used in the grades 35 classroom to support students' learning about fractions. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 3,4,5

