MS Math GRADE: 6. Credits:

Transcription

1 MS Math GRADE: 6 Credits: ABSTRACT Mathematics at the sixth grade level provides the opportunity for students to apply the rules, properties, and theorems of mathematics to real-world applications. Student knowledge of the number system extends to the use of positive exponents for representing very large numbers. Graphing includes coordinate points in all quadrants of the Cartesian plane. Students (a) apply geometric formulas and properties, (b) convert among operations, fractions, decimals, and percent, (c) examine probabilities of events, and (d) use iterative formulas. The algebraic techniques of solving equations and determining rules from collected or represented data assist students in the development of communicating and predicting trends and events.

2 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days ESTABLISHED GOALS: (NJ CCCS and/or CCS) ENDURING UNDERSTANDINGS: (Students will Understand that...) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? The Number System The Number System 6.NS.2, 6.NS.3 6.NS.1, 6.NS.4 Expressions and Equations Technology 6.EE.1, 6.EE.2b 8.1, 8.2 Technology 21 st Life & Careers 8.1, , 9.2, 9.3, st Life & Careers 9.1, 9.2, 9.3, 9.4 Students will estimate the product Students will estimate products of and quotient of decimals and judge fractions using compatible the reasonableness of the results. numbers and rounding. Students will estimate and find the Students will multiply fractions product and quotient of decimals and whole numbers, fractions and and whole numbers. fractions, and fractions and mixed Students will multiply and divide numbers. 2 Ratios and Proportional Relationships 6.RP.1, 6.RP.2, 6.RP.3, 6.RP.3a, 6.RP.3d Technology 8.1, st Life & Careers 9.1, 9.2, 9.3, 9.4 Students will express ratios and rates in fraction form. Students will determine unit rates. Students will use ratio tables to represent and solve problems involving equivalent ratios. Student will use technology to

3 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days decimals by decimals. Student will represent numbers using exponents. Students will multiply decimals mentally by powers by ten. Students will divide decimals mentally by powers of ten. Students will determine reasonable answers to solve problems. Students will solve problems by drawing a diagram. Students will divide whole numbers by fractions, fractions by fractions, and fractions and mixed numbers. compare output/input ratios for functions. Students will determine if two ratios are equivalent. Students will solve problems using ratios and rates. ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) What kind of result do you expect when you multiply or divide a whole number by a decimal? How is multiplying a decimals by a decimal different than multiplying a decimal by a whole number? How is it smaller? How is dividing decimals similar to and different from dividing whole numbers? How is the placement of the decimal point determined when multiplying and dividing by powers of ten? 3 What is the result when you multiply or divide a number by a fraction? How can rounding help you determine if the product of a whole numbers and a fraction is reasonable? How is multiplying two fractions similar to and different from adding two fractions? How is multiplying two fractions similar to and different from multiplying two whole numbers? How is dividing two fractions similar to and different from dividing two whole numbers? How are ratios, rate, and equivalent ratios used in the real world? How are fractions, ratios, and rates related? How are ratio tables like other tables? How are they different? Describe a real-world situation when it would be helpful to find an equivalent rate.

4 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc. PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 4

5 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days structure. 8. Look for and express regularity in repeated reasoning. structure. 8. Look for and express regularity in repeated reasoning. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) Rubrics Tests/Quizzes Homework Supplemental materials Rubrics Tests/Quizzes Homework Supplemental materials Rubrics Tests/Quizzes Homework Supplemental materials RESOURCES: Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6 5 Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6 Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6

6 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems My.hrw.com Renaissance(hosted.363.renlearn.c om/15027) IXL.com NJASK preparation problems STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) CROSS-CURRICULAR / DIFFERENTIATION: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this Warm-up activities Exploratory activities Student participation Formative and/or summative assessments Use graphic organizers for vocabulary development. Respond to open-ended responses, conclusions, and analysis of exploratory activities in writing. 6 Warm-up activities Exploratory activities Student participation Formative and/or summative assessments Use graphic organizers for vocabulary development. Respond to open-ended responses, conclusions, and analysis of exploratory activities in writing. Warm-up activities Exploratory activities Student participation Formative and/or summative assessments Use graphic organizers for vocabulary development. Respond to open-ended responses, conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for

7 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days unit that will help achieve the desired results?) (What type of differentiated instruction will be used for ELL, SP.ED. and G&T students?) Utilize graphic organizers for comprehension. With exponents, discuss the distance from the sun to each planet. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments LEP plan Use a translation dictionary or Utilize graphic organizers for comprehension. Explore the career of a pastry chef. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments LEP plan Use a translation dictionary or software comprehension. Explore the career of a cosmetics chemist. Special Education: Modify/reduce assignments and tests Provide modifications and IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments LEP plan Use a translation dictionary or software Provide text-to-speech for math problems 7

8 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days software Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday life situations in which whole number, decimal, and fraction operations are 8 Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday life situations in which whole number, decimal, and fraction operations are used). *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday life situations in which whole number, decimal, and fraction operations are used). Products should be modified (evaluations, audiences, real-world problems)

9 Multiply and Divide Decimals 14 Days Multiply and Divide Fractions 12 Days Ratios and Rates 20 Days used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. Learning environment should be modified: student-centered learning, independence, complexity, groups varied. *WHERETO W = Help the students know WHERE the unit is going and WHAT is expected. Help the teacher know WHERE the students are coming from (prior knowledge, interests). H = HOOK all students and HOLD their interest. E = EQUIP students, help them EXPERIENCE the key ideas and EXPLORE the issue. R = Provide opportunities to RETHINK and REVISE their understandings and work. E = Allow students to EVALUATE their work and its implications. T = TAILORED to the different needs, interests, and abilities of learners. O = ORGANIZE to maximize initial and sustained engagement as well as effective learning. 9

10 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days ESTABLISHED GOALS: (NJ CCCS and/or CCS) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Ratios and Proportional Expressions and Equations Relationships 6.EE.1, 6.EE.2a, 6.EE.2c, 6.EE.3 6.RP.3c, 6.RP.3 The Number System Technology 6.NS.6 8.1, 8.2 Technology 21 st Life & Careers 8.1, , 9.2, 9.3, st Life & Careers 9.1, 9.2, 9.3, 9.4 Expressions and Equations 6.Ee.5, 6.EE.7, 6.EE.8, 6.EE.9 The Number System 6.NS.6, 6.NS.7, 6.NS.6 Expressions and Equations 6.EE.2b Technology 8.1, st Life & Careers 9.1, 9.2, 9.3, 9.4 ENDURING UNDERSTANDINGS: (Students will Understand that...) Students will write decimals as fractions or mixed numbers in simplest form. Students will write fractions as decimals. Students will write percents as fractions. Students will write fractions as percents. Students will express percents as decimals and decimals as Students will find the value of expressions using the order of operations. Students will evaluate algebraic expressions. Students will write verbal phrases as simple algebraic expressions. Students will solve problems by acting them out. Students will explore the distributive property and other Students will solve equations by using mental math, and the guess, check, and revise strategy. Students will solve problems by working backward. Students will solve and write addition, subtractions, multiplication, and division equations. 10

11 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) percents. Students will write percents greater than 100% and percents less than 1% as fractions and as decimals, and vice versa. Students will compare and order fractions. Students compare and order fractions, decimals, and percents. Students will estimate the percent of a number. Students will find the percent of a number using fractions and decimals. Student will solve problems by solving a simpler problem. How can the relationship between fractions, decimals, and percents be used to solve mathematical and real-world problems? How are fractions and decimals similar? How are they different? How are percents related to fractions and decimals? Describe a real-world situation in which it is useful to compare 11 mathematical properties. What are mathematical expressions and how are they used to solve problems? Why is it important to have a set of rules, such as the order of operations, for simplifying or evaluating expressions? How do properties and number patterns assist in simplifying expressions? What do you need to know in order to write and solve algebraic equations? How is solving equations similar to simplifying expressions? How is it different? Why is it necessary to multiply or divide by the same number on both sides of the equal sign when solving a multiplication or division

12 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days fractions, decimals, and percents. How can fraction equivalents be helpful in estimating percents? equation? STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] PERFORMANCE TASKS: Mathematical Practices Mathematical Practices Mathematical Practices (Through what authentic performance 1. Make sense of problems and 1. Make sense of problems and 1. Make sense of problems and tasks will students demonstrate the persevere in solving them. persevere in solving them. persevere in solving them. desired understandings?) 2. Reason abstractly and 2. Reason abstractly and 2. Reason abstractly and quantitatively. quantitatively. quantitatively. (By what criteria will performances of 3. Construct viable arguments 3. Construct viable arguments 3. Construct viable arguments understanding be judged?) and critique the reasoning of and critique the reasoning of and critique the reasoning of others. others. others. 4. Model with mathematics. 4. Model with mathematics. 4. Model with mathematics. 5. Use appropriate tools 5. Use appropriate tools 5. Use appropriate tools strategically. strategically. strategically. 6. Attend to precision. 6. Attend to precision. 6. Attend to precision. 7. Look for and make use of 7. Look for and make use of 7. Look for and make use of 12

13 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days structure. 8. Look for and express regularity in repeated reasoning. structure. 8. Look for and express regularity in repeated reasoning. structure. 8. Look for and express regularity in repeated reasoning. OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) Rubrics Tests/Quizzes Homework Supplemental materials Rubrics Tests/Quizzes Homework Supplemental materials Rubrics Tests/Quizzes Homework Supplemental materials RESOURCES: Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6 13 Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6 Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6

14 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems IXL.com My.hrw.com Renaissance(hosted.363.renlearn.c om/15027) NJASK preparation problems STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) Warm-up activities Exploratory activities Student participation Formative and/or summative assessments Warm-up activities Exploratory activities Student participation Formative and/or summative assessments Warm-up activities Exploratory activities Student participation Formative and/or summative assessments CROSS-CURRICULAR: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st Use graphic organizers for vocabulary development. Respond to open-ended Use graphic organizers for vocabulary development. Respond to open-ended Use graphic organizers for vocabulary development. Respond to open-ended responses, 14

15 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) responses, conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for comprehension. Explore the career as a special effects animator. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments 15 responses, conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for comprehension. Explore the career as a water slide engineer. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for comprehension. Explore the career as a sound engineer. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments

16 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days LEP plan Use a translation dictionary or software Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday 16 LEP plan Use a translation dictionary or software Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday LEP plan Use a translation dictionary or software Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday life situations in which whole number, decimal, and fraction operations are

17 Fractions, Decimals, and Percents 10 Days Algebraic Expressions 20 Days Equations 26 Days life situations in which whole number, decimal, and fraction operations are used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. life situations in which whole number, decimal, and fraction operations are used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. Numbers Perimeter, Area, and Volume 26 Days 17 Days 17

18 Numbers 26 Days Perimeter, Area, and Volume 17 Days ESTABLISHED GOALS: (NJ CCCS and/or CCS) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? The Number System Geometry 6.NS.4, 6.NS.5, 6.NS.6, 6.NS.6c, 6.G.1, 6.G.3, 6.NS.8 6.NS.7a, 6.NS.7b, 6.NS.7c Technology Technology 8.1, , st Life & Careers 21 st Life & Careers 9.1, 9.2, 9.3, , 9.2, 9.3, 9.4 ENDURING UNDERSTANDINGS: (Students will Understand that...) Students will use ordered pairs to graph relations. Students will complete function tables and find function rules. Students will extend and describe arithmetic sequences using algebraic expressions. Students will solve inequalities by using mental math and the guess, check, and revise strategy. Students will read and write integers and find the absolute value of an integer. Students will locate and graph ordered pairs on a coordinate 18 Students will find the areas and missing dimensions of parallelograms and triangles. Students will find the areas of trapezoids. Students will estimate and find the circumference of circles. Students will find the area of circles. Students will find the perimeter of a composite figure. Students will find the areas of composite figures. Students will solve problems by making a model.

19 plane. Numbers 26 Days Perimeter, Area, and Volume 17 Days Students will find the volume of rectangular prisms. Students will find the surface areas of rectangular prisms. ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) How do we use functions, inequalities, and integers to describe situations and solve problems? How are function tables related to the coordinate plane? How is solving an inequality similar to solving an equation? How is it different? What is the significance of absolute value? Compare and contrast perimeter, area, and volume. How is the area of a triangle related to the area of a parallelogram? Describe the relationship between a circle s radius, diameter, circumference, and area. How is finding the area of a composite figure similar to the problem-solving strategy of solving a simpler problem? Compare and contrast the volume and surface area of a rectangular prism. STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, observations, etc.] 19

20 PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Numbers 26 Days Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Perimeter, Area, and Volume 17 Days Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their Rubrics Tests/Quizzes Homework Supplemental materials 20 Rubrics Tests/Quizzes Homework Supplemental materials

21 learning?) RESOURCES: Numbers 26 Days Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6 IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems Perimeter, Area, and Volume 17 Days Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6 IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. 21

22 SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) Numbers 26 Days Warm-up activities Exploratory activities Student participation Formative and/or summative assessments Perimeter, Area, and Volume 17 Days Warm-up activities Exploratory activities Student participation Formative and/or summative assessments CROSS-CURRICULAR: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) Use graphic organizers for vocabulary development. Respond to open-ended responses, conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for comprehension. Explore the career as a meteorologist. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians 22 Use graphic organizers for vocabulary development. Respond to open-ended responses, conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for comprehension. Explore the career as a landscape architect. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians

23 Numbers 26 Days ELL: Use Go Math Spanish Resources for assessments and assignments LEP plan Use a translation dictionary or software Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice 23 Perimeter, Area, and Volume 17 Days ELL: Use Go Math Spanish Resources for assessments and assignments LEP plan Use a translation dictionary or software Provide text-to-speech for math problems. *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Tier groups along with tiered assignments (assignments provided by GO MATH that differ based on number and/or complexity of problems and Use online textbook for additional practice

24 Numbers 26 Days Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday life situations in which whole number, decimal, and fraction operations are used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. Perimeter, Area, and Volume 17 Days Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday life situations in which whole number, decimal, and fraction operations are used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. UNIT: Volume and Surface Area 9 Days Analyze Data and Graphs 15 Days 24

25 Volume and Surface Area 9 Days Analyze Data and Graphs 15 Days ESTABLISHED GOALS: (NJ CCCS and/or CCS) STAGE 1: DESIRED RESULTS What will students understand as a result of the unit? What are the BIG ideas? Geometry Statistics and Probability 6.G.2, 6.G.4 6.SP.4, 6.SP.5c, 6.SP.5 Technology Technology 8.1, , st Life & Careers 21 st Life & Careers 9.1, 9.2, 9.3, , 9.2, 9.3, 9.4 ENDURING UNDERSTANDINGS: (Students will Understand that...) Students will find the volume of prisms. Students will find the volume of pyramids. Students will find the volume of cylinders and cones. Students will solve problems by drawing a diagram. 25 Students will find the mean, median, mode, and range of a data set. Students will interpret the median, mode, and range of a set of data. Students make and interpret frequency tables and stem-andleaf-plots. Students will collect, organize, analyze, and display data to solve problems with histograms, and use these data displays to show frequency distribution. Students will construct and

26 ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) Volume and Surface Area 9 Days Why is it important to know how to find the volume and surface area of three-dimensional figures? How is the volume of a triangular prism related to the volume of a rectangular prism? How is the volume of a cylinder related to the volume of a cone? Compare and contrast the surface area and volume of a cylinder. Analyze Data and Graphs 15 Days analyze circle graphs. Students will select an appropriate display for a set of data. Students will recognize when statistics and graphs are misleading. Students will use logical reasoning to solve a problem. How can we use data to become more informed about the world around us? How are measures of central tendency helpful in describing a data set? How are tables helpful in solving problems? How can circle graphs be used to analyze data? How can misleading statistics affect actual data? STAGE 2: ASSESSMENT EVIDENCE What evidence will be collected to determine whether or not the understandings have been developed, the knowledge and skills attained, and the state standards met? [Anchor the work in performance tasks that involve application, supplemented as needed by prompted work, quizzes, 26

27 Volume and Surface Area 9 Days Analyze Data and Graphs 15 Days PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) observations, etc.] Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 9. Students will find the volume of prisms, pyramids, cylinders, and cones. 27 Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning Students will find and interpret the mean, median, mode, and range. 11. Students will collect, organize, analyze, and display data in an

28 OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) RESOURCES: Volume and Surface Area 9 Days Rubrics Tests/Quizzes Homework Supplemental materials Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6 28 Analyze Data and Graphs 15 Days appropriate graph. 12. Students will construct and analyze circle graphs. 13. Students will identify misleading graphs. Rubrics Tests/Quizzes Homework Supplemental materials Graphic Organizers Manipulatives Leveled worksheets ipads Go Math Differentiated Instruction Middle School Grade 6 workbook Go Math Assessment Resources Middle School Grade 6

29 Volume and Surface Area 9 Days IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems Analyze Data and Graphs 15 Days IXL.com My.hrw.com Renaissance(hosted.363.renlearn. com/15027) NJASK preparation problems STAGE 3: LEARNING PLAN What learning experiences and instruction will enable students to achieve the desired results? Utilize the WHERETO* acronym to consider key design elements. SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) Warm-up activities Exploratory activities Student participation Formative and/or summative assessments Warm-up activities Exploratory activities Student participation Formative and/or summative assessments CROSS-CURRICULAR: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st Use graphic organizers for vocabulary development. Respond to open-ended 29 Use graphic organizers for vocabulary development. Respond to open-ended

30 century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) Volume and Surface Area 9 Days responses, conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for comprehension. Explore the career as an interior designer. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments 30 Analyze Data and Graphs 15 Days responses, conclusions, and analysis of exploratory activities in writing. Utilize graphic organizers for comprehension. Explore the career as a marine biologist. Special Education: Modify/reduce assignments and tests IEP Open communication with parents/guardians ELL: Use Go Math Spanish Resources for assessments and assignments

31 Volume and Surface Area 9 Days LEP plan Use a translation dictionary or software Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday 31 Analyze Data and Graphs 15 Days LEP plan Use a translation dictionary or software Provide text-to-speech for math problems *ELL Students- Instruction will be based on language proficiency. At-Risk Students: Use online textbook for additional practice Gifted Students Process should be modified: higher order thinking skills, open-ended thinking, discovery. Assignment and assessment contents should be modified (an example of an assignment would be students creating word problems that connect to everyday

32 Volume and Surface Area 9 Days life situations in which whole number, decimal, and fraction operations are used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. Analyze Data and Graphs 15 Days life situations in which whole number, decimal, and fraction operations are used). Products should be modified (evaluations, audiences, real-world problems) Learning environment should be modified: student-centered learning, independence, complexity, groups varied. 32