Unit: Topic 1: Variables and Expressions. Grade Level: 6 th Grade

Transcription

1 Unit: Topic 1: Variables and Expressions Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day sixteen Topic Test Total Instructional Time: 16 days Anchor Standard(s): Apply and extend previous understandings of arithmetic to algebraic expressions. Unit Essential Questions: What are expressions and how can they be written and evaluated? What arithmetic relationships, called properties, are always true? Student Learning Goals: Students write and evaluate powers as products, write expressions in exponential form, and write numbers in expanded form using exponents. Students give missing addends and factors in equations and state the property used. Students evaluate numeric or algebraic expressions with three or more numbers and up to three variables. (Expressions may include parentheses and exponents). Students use the Distributive Property to evaluate expressions and to compute mentally. Students use the order of operations to evaluate expressions with whole numbers and decimals. Students write numerical expressions with variables to represent relations expressed verbally. Students identify parts of an expression. Students evaluate algebraic expressions using substitution. Students identify missing numbers in a pattern and write an algebraic expression to describe the pattern. Students simplify algebraic expression. Students write equivalent expressions. Students identify equivalent expressions. Students make and use organized lists to solve word problems.

2 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 1 Variables and Expressions Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Variables & Expressions I can use exponential form. I can use the properties of addition and multiplication. I can use order of operations. I can use the Distributive Property. I can write algebraic expressions. I can identify the parts of an expression. I can evaluate algebraic expressions. I can write an algebraic expression to describe a pattern. I can simplify algebraic expressions. I can write equivalent expressions. I can use the Distributive Property and other properties of operations to identify equivalent expressions. I can make an organized list or table to solve word problems Date:

3 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: Place value (10, 100 1,000 and so on) can be represented using exponents. Numbers can be broken apart using place value and represented in different ways. Lesson 2: You can add (or multiply) two numbers in any order. Three numbers can be grouped and added (or multiplied) in any order. 0 + a = a and 1 x a = a for any number. Lesson 3: There is an agreed upon order in which operations are carried out in a numerical expression. Lesson 4: The Distributive Property of Multiplication over Addition lets you multiply a sum by multiplying each addend separately and then adding the sum of the products. Lesson 5: There is an agreed upon order for which operations in a numerical expression are performed. Lesson 6: Some mathematical phrases can be represented using a variable in an algebraic expression. Lesson 7: You can identify parts of numerical and algebraic expressions using words such as term, coefficient, product, and factor. Lesson 8: The value of an algebraic expression can be found by replacing the variable(s) with given number(s) and doing the calculation that results. Lesson 9: Some quantities have a mathematical relationship, the value of one quantity can be found if you know the value of the other quantity. Patterns can sometimes be used to identify a relationship between two quantities. Academic Vocabulary: Base, exponent, power, exponential form Commutative Property of Addition Commutative Property of Multiplication Associative Property of Addition Associative Property of Multiplication Identity Property of Addition Identity Property of Multiplication Order of operations Distributive Property Variable, algebraic, expression, coefficient Term Evaluate, substitution Input/output table Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities

4 Lesson 10: You can simplify algebraic expressions by combining like terms. Like terms are terms with the same variable, such as 4x and 2x, or with no variable at all, such as 10 and 3. Lesson 11: You can apply the Distributive Property and other properties of operations to write equivalent expressions. Lesson 12: Two expressions are equivalent if they have the same value regardless of which number is substituted for the variable. Lesson 13: Some problems can be solved by recording and organizing data in an organized list or a table and by finding and using numerical patterns in the organized list or table. Like terms Equivalent, expressions No new vocabulary Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives: Alaska Standards Addressed & Assessed: 6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. Evaluate expressions and formulas. Include formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order with or without parentheses. (Order of Operations) 6.EE.3. Apply the properties of operations to generate equivalent expressions. Model (e.g., manipulatives, graph paper) and apply the distributive, commutative, identity, and inverse properties with integers and variables by writing equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x.

5 Unit: Topic 2: Equations and Inequalities Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day twelve Topic Test Total Instructional Time: 12 days Anchor Standard(s): Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Unit Essential Question: What procedures can be used to solve equations and inequalities? Student Learning Goals: Students find the solutions to equations. Students use the properties of equality to balance equations. Students use inverse operations to isolate the variable and solve one-step addition and subtraction equations. Students draw pictures that represent information given in problems. Students solve one-step multiplication and division equations. Students solve equations involving fractions and mixed numbers. Students write inequalities to describe situations. Students will solve an inequality by finding all the values that make it true. Students draw pictures that represent information given in problems.

6 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 2 Equations and Inequalities Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Equations and Inequalities I can find solutions to equations. I can use properties of equality to balance equations. I can solve addition and subtraction equations. I can draw a picture and write an equation. I can solve multiplication and division equations. I can solve equations involving fractions and mixed numbers. I can write inequalities. I can solve inequalities. I can draw a picture and write an equation. Date:

7 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: A value is the solution to an equation if the value makes the equation true. An equation is true when both sides of the equation are equal. Lesson 2: The same number can be added or subtracted from both sides of an equation and not change the equality. Multiplying or diving both sides of an equation by the same nonzero number does not change the equality. Lesson 3: Solving an equation involves finding the value of the unknown that makes the equation true. There is more than one way to solve an equation. Lesson 4: Information in a problem can often be shown using a picture and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation. Lesson 5:: Solving an equation involves finding the value of the unknown that makes the equation true. There is more than one way to solve an equation. Lesson 6: You can use inverse relationships and properties of equality to solve equations with fractions and mixed numbers. Lesson 7: An inequality is a mathematical sentence that contains the inequality symbol < (is less than), > (is greater than) and symbols for is greater than or equal and symbols for less than or equal. Lesson 8: A solution to an inequality is a value that makes the inequality true. Lesson 9: Information in a problem can often be shown using a picture and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence or equation. Academic Vocabulary: equation Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality inverse relationship reciprocal inequality No new vocabulary Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities

8 Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives: Alaska Standards Addressed & Assessed: 6.EE.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. 6.EE.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. For example: does 5 make 3x > 7 true? 6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

9 Unit: Topic 3: Patterns and Equations Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day seven Topic Test Total Instructional Time: 7 days Anchor Standard(s): Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables. Unit Essential Questions: How can equations be written? What patterns can be found in tables of values? Student Learning Goals: Students identify independent and dependent variables. Students use rules and functions to find missing values in tables, and they write a rule and an equation that tells how to find one value of a function when another value is known. Equations involve one operation. Students use rules and functions to find missing values in tables, and they write a rule and an equation that tells how to find one value of a function when another value is known. Equations involve two operations. Students solve problems by using objects to model the problem and draw conclusions.

10 Scale/Rubric for Student Learning Goals: 6 th Grade: Math Unit 3 Patterns and Equations Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Patterns and Equations I can identify dependent and independent variable in equations. I can use a table of values to write and solve an equation. I can complete a table of values for equations with more than one operation. I can use logical reasoning to solve problems. Date:

11 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: Variables can be used to represent two quantities that change in relationship to one another. The dependent variable changes in response to the independent variable. Lesson 2 and 3: Patterns can sometimes help identify the relationship between quantities, and an equation can be written describing the relationship Lesson 4: Some problems can be solved by reasoning about the conditions in the problem. Academic Vocabulary: dependent variable independent variable Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives: Alaska Standards Addressed & Assessed: 6.EE.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 6.EE.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time

12 Unit: Topic 4: Achieving Fluency: Adding, Subtracting, and Multiplying Decimals Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day ten Topic Test Total Instructional Time: 10 days Anchor Standard(s): Compute fluently with multi-digit numbers and find common factors and multiples. Unit Essential Question: How are adding, subtracting, and multiplying decimals the same as and different than using the same operations with whole numbers? Student Learning Goals: Students estimate the sums as differences of addition and subtraction expressions that involve decimals. Students evaluate addition and subtraction expressions with decimals and whole numbers. Students use inverse operations to solve addition and subtraction equations. Students estimate products of whole numbers and decimals in a variety of ways. Students find products of whole numbers and decimals to ten thousandths. Students make and use tables to solve word problems.

13 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 4 Achieving Fluency: Adding, Subtracting, and Multiplying Decimals Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Adding, Subtracting, and Multiplying Decimals I can estimate sums or differences of addition and subtraction expressions that involve decimals. I can evaluate addition and subtraction expressions with decimals and whole numbers. I can use inverse operations to solve addition and subtraction equations. I can estimate products of whole numbers and decimals. I can multiply whole numbers and decimals. I can make tables and use patterns and equations to solve word problems. Date:

14 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: Rounding is a process for finding the multiple of 10, 100,etc., or of 0.1, 0.01, etc., closest to a given number. There is more than one way to estimate a sum or difference. Lesson 2: Standard addition and subtraction algorithm break calculations into simpler calculations using place value. Answers to the simpler calculations are used to give the final sum or difference. Lesson 3: Addition and subtraction equations can be solved by using inverse operations. Lesson 4: Rounding is a process for finding the multiple of 10, 100, etc., or of 0.1, 001 etc., closest to a given number. There is more than one way to estimate a product. Lesson 5: The standard multiplication algorithm involving decimals is an extension of the standard algorithm for multiplying whole numbers. Lesson 6: Recording information in a table can help you understand and solve some problems. Academic Vocabulary: estimate compatible numbers Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives: Alaska Standards Addressed & Assessed: 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Express the remainder as a terminating decimal, or a repeating decimal, or rounded to a designated place value. 6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

15 Unit: Topic 5 Achieving Fluency: Dividing Whole Numbers and Decimals Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day eleven Topic Test Total Instructional Time: 11 days Anchor Standard(s): Compute fluently with multi-digit numbers and find common factors and multiples. Unit Essential Question: How are quotients involving whole numbers and decimals estimated and found? Student Learning Goals: Students use estimation to find approximate solutions to division problems with two-digit divisors using compatible numbers Students divide a four-digit number by a two-digit number. Students solve problems involving division of numbers with 4-digits by 2-digit divisors by estimating, dividing, and analyzing the remainder. Students find quotients where the dividend is a decimal. Students find quotients of two decimals. Students evaluate algebraic expressions that include decimals. Students solve multiplication and division equations that include decimals. Students solve multiple-step word problems.

16 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 5 Achieving Fluency: Dividing Whole Numbers and Decimals Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Dividing Whole Numbers & Decimals I can use compatible numbers to estimate quotients with 2- digit divisors. I can divide 4- digit whole numbers by 2- digit whole numbers. I can divide decimals by whole numbers. I can divide by a decimal number. I can evaluate algebraic expressions with decimals for a given value of the variable. I can solve multiplication and division equations involving decimals... I can solve multiple- step word problems. Date:

17 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients. Lesson 2: Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient. Lesson 3: Dividing with 2-digit divisors is an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient. Lesson 4: The standard division algorithm involving decimals is an extension of the standard algorithm for dividing whole numbers. Lesson 5: A number divided by a decimal can be represented as an equivalent calculation using place value to change the divisor to a whole number. Lesson 6: The value of an algebraic expression can be found by replacing the variable(s) with given number(s) and doing the calculation that results. Lesson 7: Division equations can be solved by using the inverse operation. Lesson 8: Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem. Academic Vocabulary: Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities

18 Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives: Alaska Standards Addressed & Assessed: 6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.. 6.NS.2. Fluently multiply and divide multi-digit whole numbers using the standard algorithm. Express the remainder as a whole number, decimal, or simplified fraction; explain or justify your choice based on the context of the problem. 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Express the remainder as a terminating decimal, or a repeating decimal, or rounded to a designated place value.

19 Unit: Topic 6: Dividing Fractions Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day fourteen Topic Test Total Instructional Time: 14 days Anchor Standard(s): Compute fluently with multi-digit numbers and find common factors and multiples Unit Essential Question: What are standard procedures for estimating and finding quotients of fractions and missed numbers? Student Learning Goals: Students find common factors and the greatest common factor of numbers. Students find common multiples and the least common multiple (LCM) of a set of numbers. Students make and use models to divide my fractions and to divide fractions. Students use the inverse relationship between multiplication and division to help them understand how to divide by a fraction. Students make and use models to divide fractions. Students can use multiplication to divide by a fraction. Students estimate quotients of mixed numbers using compatible numbers and rounding. Students find the quotients involving mixed numbers. Students evaluate algebraic expressions containing fractions using substitution. Students solve equations involving division of fractions and mixed numbers. Students solve problems by looking for a pattern.

20 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 6 Dividing Fractions Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Dividing Fractions I can find the greatest common factor. I can find the least common multiple. I can divide fractions using models. I can divide a whole number by a fraction. I can use multiplication to divide fractions. I can estimate quotients of mixed numbers. I can divide missed numbers. I can evaluate expressions involving fractions and mixed numbers. I can solve equations involving fractions and mixed numbers. I can find a pattern to solve a problem. Date:

21 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: There is always a greatest number that divides evenly each of two whole numbers. Sometimes it is 1. Lesson 2: All non-zero whole numbers have common multiples including a least one. Sometimes the least common multiple of two numbers is one of the numbers. Lesson 3: When dividing by a fraction that is less than 1, the quotient is greater than the dividend. The division of a whole number by a fraction can be interpreted in different ways Lesson 4: A division expression with a fraction divisor can be changed to an equivalent multiplication expression. Lesson 5: When dividing by a fraction that is less than 1 the quotient is greater than the dividend. The division of a fraction by a fraction can be interpreted in different ways Lesson 6: A division expression with a fraction divisor can be changed to an equivalent multiplication expression. Lesson 7: Rounding and compatible numbers can be used to estimate the quotient of mixed numbers. Lesson 8: The quotient of two mixed numbers can be found by changing the mixed numbers to improper fractions, then changing the division expression to an equivalent multiplication expression. Lesson 9: The value of an algebraic expression can be found by replacing the variable(s) with given number(s) and doing the calculation that results. Lesson 10: Equations with fractions and mixed numbers can be solved using properties of equality and inverse operations. Academic Vocabulary: greatest common factor (GCF) common multiple least common multiple (LCM) No new vocabulary Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities

22 Lesson 11: Some problems can be solved by identifying elements that repeat in a predicable way Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives: Alaska Standards Addressed & Assessed: 6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2).

23 Unit: Topic 7: Integers and Other Rational Numbers Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day nine Topic Test Total Instructional Time: 9 days Anchor Standard(s): Apply and extend previous understandings of numbers to the system of rational numbers. Unit Essential Question: What are integers? Student Learning Goals: Students read, write, and use positive and negative integers. Students compare and order integers Students will compare and order absolute values. Students locate compare, and order rational numbers on a number line. Students compare and order rational numbers. Students will use reasoning to solve problems.

24 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 7 Integers and Other Rational Numbers Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Integers and Other Rational Numbers I can understand, read, and write integers. I can compare and order integers. I can understand and apply absolute value. I can compare and order rational numbers on a number line. I can solve problems using reasoning. Date:

25 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: Numbers that are the same distance from 0 on the number line are opposites. Integers are the counting numbers, their opposites, and zero. Lesson 2: Numbers to the right of 0 are positive and the numbers to the left of 0 are negative. A number to the right of another on the number line is the greater number. Lesson 3: Absolute value is used to define the distance from a number to zero, regardless of whether the number is positive or negative. Lesson 4: Each rational number can be associated with a unique point on the number line. Lesson 5: Numbers to the right of 0 are positive and the numbers to the left of 0 are negative. A number to the right of another on the number line is the greater number Lesson 6: Some problems can be solved by reasoning about the conditions in the problem. Academic Vocabulary: opposites integers absolute value rational number Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives:

26 Alaska Standards Addressed & Assessed: 6.NS.5 Understand that positive and negative numbers describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explain the meaning of 0 in each situation 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; Recognize that the opposite of the opposite of a number is the number itself [e.g., ( 3) = 3] and that 0 is its own opposite. 6.NS.7. Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3 o C > 7 o C to express the fact that 3 o C is warmer than 7 o C. c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

27 Unit: Topic 8: Coordinate Geometry Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day ten Topic Test Total Instructional Time: 10 days Anchor Standard(s): Apply and extend previous understandings of numbers to the system of rational numbers. Unit Essential Questions: How are points graphed on a coordinate plane? How are equations that can relate real-world quantities graphed? Student Learning Goals: Students identify and graph point with integer coordinates on the coordinate plane. Students identify and graph points with rational number coordinates on the coordinate plane. Students use coordinates and absolute value to find distances between points with the same second coordinate on the coordinate plane. Students find the vertices and perimeters of rectangles and polygons composed of rectangles on the coordinate plane. Students graph simple linear equations on the coordinate plane. Students graph linear relationships involving more than one operation (y = ax + b) Students solve multiple-step word problems.

28 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 8 Coordinate Geometry Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Coordinate Geometry I can identify and graph points with integer coordinates on the coordinate plane. I can identify and graph points with rational number coordinates on the coordinate plane. I can use coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate on the coordinate plane. I can find the vertices and perimeters of polygons on the coordinate plane. I can graph simple linear equations. I can graph linear relationships involving more than one operation (y = x + a) I can solve multiple- step word problems. Date:

29 ESSENTIAL SKILLS/CONCEPTS: Lesson 1 and 2: The Cartesian Coordinate System is a scheme that uses two perpendicular number lines, intersecting at zero to tell the location of points in the plane. Lesson 3 and 4: The distance between two points in the coordinate plane with the same first coordinate or the same second coordinate is found by adding or subtracting the absolute values of the coordinates that are not the same. Lesson 5: Graphs of relationships in the form of y = ax and y = x + a (a is a real number) are straight lines. The graph of y = ax passes through the origin. The graph of y = x + a does not pass through the origin, unless a equals zero. Lesson 6: Graphs of relationships in the form y = ax + b (a and b are real numbers) are straight lines. If b is not zero, they do not pass through the origin. Lesson 7: Some problems can be solved by first finding and solving a sub-problems(s) and then using that answer(s) to solve the original problem. Academic Vocabulary: coordinate plane, x-axis, y-axis quadrants, ordered pair origin T-table linear equation No new vocabulary Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives:

30 Alaska Standards Addressed & Assessed: 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; Recognize that the opposite of the opposite of a number is the number itself [e.g., ( 3) = 3] and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

31 Unit: Topic 9: Ratios Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day nine Topic Test Total Instructional Time: 9 days Anchor Standard(s): Understand ratio concepts and use ratio reasoning to solve problems. Unit Essential Question: What are ratios and how are they used in solving problems? Student Learning Goals: Students express comparisons as ratios in three ways (a/b, a to b, a:b). Students find equivalent ratios and determine if two ratios form a proportion. Students will use tape diagrams and double number line diagrams to solve ratio problems. Students use ration tables and common factors to solve proportions. Students will use tables and graphs to represent equivalent ratios. Students draw pictures that represent information given in problems.

32 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 9 Ratios Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Ratios I can use ratios to compare quantities. I can find equivalent ratios. I can use diagrams to solve ratio problems. I can use ratio tables to solve proportions. I can use tables and coordinate graphs to represent equivalent ratios. I can draw a picture to solve a problem. Date:

33 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: A ratio is a special relationship between two quantities where for every x units of one quantity there are y units of another quantity. The quantities being compared in a ratio are called terms. Lesson 2: In a proportional relationship there are an infinite number of ratios equal to the lowest terms or constant ratio. Equal ratios can be found by multiplying both terms by the same nonzero number. Lesson 3: Tape diagrams and double number line diagrams can show ratio relationships and be used to reason about solutions to problems. Lesson 4: Some proportion problems can be solved by generating equal ratios using multiplication or division. Some proportions can be solved by finding and using the common factor that relates the terms. Lesson 5: Equivalent ratios can be represented in a table, and the pairs of values can be plotted on a coordinate plane. Lesson 6: Information in a problem can often be shown using a picture to understand and solve the problem. Academic Vocabulary: Ratio Terms proportion Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives:

34 Alaska Standards Addressed & Assessed: 6.RP.1. Write and describe the relationship in real life context between two quantities using ratio language. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios, and understand equivalencies.

35 Unit: Topic 10: Rates Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day eleven Topic Test Total Instructional Time: 11 days Anchor Standard(s): Understand ratio concepts and use ratio reasoning to solve problems. Unit Essential Questions: What are ratios and rates and how are they used in solving problems? How can customary and Metric measurements be converted to other units? Student Learning Goals: Students find the unit rate for a given rate. Students use rates to make comparisons. Students find unit rates to solve proportions. Students find the unit price of items to compare costs. Students use a formula to solve problems involving distance, rate, and time. Students change between customary units of length, weight, and capacity. Students change between metric units of length, mass, and capacity. Students explain solutions to word problems.

36 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 10 Rates Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Rates I can find unit rates. I can compare rates. I can use rates to solve proportions. I can find unit price. I can solve problems involving distance, rate, and time. I can convert customary units. I can convert metric units. I can explain solutions to word problems. Date:

37 ESSENTIAL SKILLS/CONCEPTS: Lesson 1: A rate is a special ratio that compares two quantities with different units of measure. A unit rate is a rate that compares a quantity to one unit of another quantity. Lesson 2: Rates are easily compared when each is expressed as a unit rate. Lesson 3 and 4: Some proportions can be solved by finding and using the unit amount. Lesson 5: A formula is a common relationship between quantities expressed as an equation. A special proportional relationship involves distance (d), rate (r), and time (t). The formula showing this relationship is d = r x t. Lesson 6 and 7: Measurements can be represented in equivalent ways using different units. Relationships exist that enable you to convert between units by multiplying or dividing. Lesson 8: Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand. Academic Vocabulary: rate unit rate No new vocabulary unit price constant speed formula capacity, meter, gram, liter, kilo-, centi-, milli- No new vocabulary Interventions/Extensions: Intervention: - Small group reteach - RTI Intervention System Enrichment: - Pearson Realize Game Center - Show/explain the concept/skill on ipad - On-level & advanced center activities Anchor Text(s)/Additional Instructional Resources: envision Math: Pearson realize 2015 Edition Online Subscription: Manipulatives:

38 Alaska Standards Addressed & Assessed: 6.RP.2. Understand the concept of a unit rate (a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship) and apply it to solve real-world problems (e.g., unit pricing, constant speed). For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units between given measurement systems (e.g., convert kilometers to miles); manipulate and transform units appropriately when multiplying or dividing quantities.

39 Unit: Topic 11: Percentages Grade Level: 6 th Grade CRITICAL DATES/TIMELINE: Diagnostic Performance Task(s)- day one Alternate Topic Assessment Unit Common Assessment day ten Topic Test Total Instructional Time: 10 days Anchor Standard(s): Understand ratio concepts and use ratio reasoning to solve problems. Unit Essential Questions: What is the meaning of percent? How can percent be estimated and found? Student Learning Goals: Students interpret percents as parts of a hundred. Students find equivalent forms of fractions, decimals, and percents. Students interpret percents greater than 100 and less than 1 as part of a hundred and express the in equivalent decimal and fraction forms. Students use compatible numbers to estimate percents of numbers and to determine what percent one number is of another. Students find a percent of a number and determine what percent one number is of another. Students will find the whole in problems where they are given the percent and a corresponding part. Students check to see if their answers are reasonable.

40 Scale/Rubric for Student Learning Goals: The 1, 2, 3, 4, Learning Scale will be used daily throughout the lesson for the student and teacher to gauge student comprehension and confidence with the skills and concepts (students will show with fingers on their hand). Students will complete the following Self-Assessment at the beginning, middle and end of the unit. 6 th Grade: Math Unit 11 Percentages Student Self- Assessment Rating Scale 4= I m an expert. I can do it without mistakes and I can help others. 3= I understand it. I can do it by myself with few mistakes. 2= Sometimes I need help. I am starting to understand. 1= I can t do it by myself. I don t understand yet. Percentages I can interpret percents as parts of a hundred. I can find equivalent forms of fractions, decimals, and percents. I can convert percents greater than 100 or less than 1 to decimals and fractions. I can estimate a given percent of a number. I can calculate the percent of a number and what percent one number is of another. I can find the whole given the percent and a corresponding part. I can determine if a solution is reasonable. Date: