Unit:
Topic 1: Variables and Expressions
Grade Level:
6th 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.
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.
6th 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: 4 3 2 1 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.
Academic Vocabulary:
Base, exponent, power,
exponential form
Interventions/Extensions:
Intervention:
- Small group reteach
- RTI Intervention System
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Identity Property of Addition
Identity Property of Multiplication
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
Lesson 3: There is an agreed upon order in which operations
are carried out in a numerical expression.
Order of operations
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.
Distributive Property
Lesson 5: There is an agreed upon order for which operations
in a numerical expression are performed.
No new vocabulary.
Lesson 6: Some mathematical phrases can be represented
using a variable in an algebraic expression.
Variable, algebraic, expression,
coefficient
Lesson 7: You can identify parts of numerical and algebraic
Term
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.
Evaluate, substitution
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.
Input/output table
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.
Like terms
Lesson 11: You can apply the Distributive Property and other
properties of operations to write equivalent expressions.
Equivalent, expressions
Lesson 12: Two expressions are equivalent if they have the
same value regardless of which number is substituted for the
variable.
No new vocabulary
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.
No new vocabulary.
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
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.
Unit:
Topic 2: Equations and Inequalities
Grade Level:
6th 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.
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.
6th 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 4 3 2 1 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: 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.
Academic Vocabulary:
equation
Interventions/Extensions:
Intervention:
- Small group reteach
- RTI Intervention System
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.
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
Lesson 3: Solving an equation involves finding the value of the inverse relationship
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 No new vocabulary.
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 No new vocabulary.
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.
reciprocal
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.
inequality
Lesson 8: A solution to an inequality is a value that makes the
inequality true.
No new vocabulary
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.
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
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.
Unit:
Topic 3: Patterns and Equations
Grade Level:
6th 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.
Scale/Rubric for Student Learning Goals:
6th 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: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
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.
dependent variable
independent variable
Intervention:
- Small group reteach
- RTI Intervention System
Lesson 2 and 3: Patterns can sometimes help identify the
relationship between quantities, and an equation can be written
describing the relationship
No new vocabulary.
Lesson 4: Some problems can be solved by reasoning about
the conditions in the problem.
No new vocabulary.
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:
www.pearsonrealize.com
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
Unit:
Topic 4: Achieving Fluency: Adding, Subtracting, and
Multiplying Decimals
Grade Level:
6th 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.
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.
6th 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 4 3 2 1 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: ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
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.
estimate
Intervention:
- Small group reteach
- RTI Intervention System
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.
No new vocabulary.
Lesson 3: Addition and subtraction equations can be solved by
using inverse operations.
No new vocabulary.
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
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.
compatible numbers
Lesson 5: The standard multiplication algorithm involving
decimals is an extension of the standard algorithm for
multiplying whole numbers.
No new vocabulary.
Lesson 6: Recording information in a table can help you
understand and solve some problems.
No new vocabulary.
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription: www.pearsonrealize.com
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.
Unit:
Topic 5 Achieving Fluency:
Dividing Whole Numbers and Decimals
Grade Level:
6th 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.
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.
6th 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 4 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: 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
Lesson 1: There is more than one way to estimate a quotient.
Substituting compatible numbers is an efficient technique for
estimating quotients.
No new vocabulary.
Intervention:
- Small group reteach
- RTI Intervention System
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.
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:
www.pearsonrealize.com
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.
Unit:
Topic 6: Dividing Fractions
Grade Level:
6th 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.
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.
6th 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: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
Lesson 1: There is always a greatest number that divides
evenly each of two whole numbers. Sometimes it is 1.
greatest common factor (GCF)
Intervention:
- Small group reteach
- RTI Intervention System
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.
common multiple
least common multiple (LCM)
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
No new vocabulary.
Lesson 4: A division expression with a fraction divisor can be
changed to an equivalent multiplication expression.
No new vocabulary.
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
No new vocabulary.
Lesson 6: A division expression with a fraction divisor can be
changed to an equivalent multiplication expression.
No new vocabulary.
Lesson 7: Rounding and compatible numbers can be used to
estimate the quotient of mixed numbers.
No new vocabulary.
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.
No new vocabulary.
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.
No new vocabulary.
Lesson 10: Equations with fractions and mixed numbers can be
solved using properties of equality and inverse operations.
No new vocabulary
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
Lesson 11: Some problems can be solved by identifying
elements that repeat in a predicable way
No new vocabulary.
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
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 1–100 with a common factor
as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Unit:
Topic 7: Integers and Other Rational Numbers
Grade Level:
6th 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.
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.
6th 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: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
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.
opposites
integers
absolute value
Intervention:
- Small group reteach
- RTI Intervention System
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.
No new vocabulary.
Lesson 3: Absolute value is used to define the distance from a
number to zero, regardless of whether the number is positive or
negative.
No new vocabulary.
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
Lesson 4: Each rational number can be associated with a
unique point on the number line.
rational number
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
No new vocabulary.
Lesson 6: Some problems can be solved by reasoning about
the conditions in the problem.
No new vocabulary.
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
Manipulatives:
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 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.
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.
Unit:
Topic 8: Coordinate Geometry
Grade Level:
6th 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.
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.
6th 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 4 3 2 1 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: ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
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.
coordinate plane, x-axis, y-axis
quadrants, ordered pair
origin
Intervention:
- Small group reteach
- RTI Intervention System
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.
No new vocabulary.
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.
T-table
linear equation
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
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.
No new vocabulary
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.
No new vocabulary.
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
Manipulatives:
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.
Unit:
Topic 9: Ratios
Grade Level:
6th 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.
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.
6th 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: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
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.
Ratio
Terms
Intervention:
- Small group reteach
- RTI Intervention System
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.
proportion
Lesson 3: Tape diagrams and double number line diagrams
can show ratio relationships and be used to reason about
solutions to problems.
No new vocabulary.
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.
No new vocabulary.
Lesson 5: Equivalent ratios can be represented in a table, and
the pairs of values can be plotted on a coordinate plane.
No new vocabulary.
Lesson 6: Information in a problem can often be shown using a
picture to understand and solve the problem.
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
Manipulatives:
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
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.
Unit:
Topic 10: Rates
Grade Level:
6th 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.
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.
6th 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: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
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.
rate
unit rate
Intervention:
- Small group reteach
- RTI Intervention System
Lesson 2: Rates are easily compared when each is expressed
as a unit rate.
No new vocabulary
Lesson 3 and 4: Some proportions can be solved by finding
and using the unit amount.
unit price
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.
constant speed
formula
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
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.
capacity,
meter, gram, liter, kilo-, centi-,
milli-
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.
No new vocabulary
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
Manipulatives:
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.
Unit:
Topic 11: Percentages
Grade Level:
6th 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.
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.
6th 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: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
Lesson 1: A percent is a special kind of ratio in which a part is
compared to a whole with 100 parts. The whole is 100%.
Percent is relative to the size of the whole.
percent
Intervention:
- Small group reteach
- RTI Intervention System
Lesson 2: A part of a whole or a part of a set can be
represented by a fraction, a decimal, and a percent.
No new vocabulary
Lesson 3: A percent is a special kind of ratio in which a part is
compared to a whole with 100 parts. The whole is 100%.
Percent is relative to the size of the whole
No new vocabulary
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
Lesson 4: Some percents can be approximated by simple
fractions and used to estimate the percent of a number.
No new vocabulary
No new vocabulary
Lesson 5: Finding a percent of a whole is like finding a
fractional part of a whole. You can find the percent of a number
by changing the percent to a decimal and multiplying or using a
proportion.
Lesson 6: The whole can be found when you are given a
percent and a part. A number line and a proportion can be
used to help solve for the missing whole.
No new vocabulary
Lesson 7: Answers to problems should always be checked for
reasonableness, and this can be done in different ways.
No new vocabulary
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
Manipulatives:
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.”
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.
Unit:
Topic 12: Area
Grade Level:
6th 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):
Solve real-world and mathematical problems involving area, surface area, and volume.
Unit Essential Question:
How can the area of certain shapes be found?
Student Learning Goals:
•
Students find the area of rectangles.
•
Students develop and use the formulas for the areas of parallelograms and rhombuses.
•
Students develop and use the formula for the area of triangles.
•
Students find the area of trapezoids and kites.
•
Students find the areas of polygons.
•
Students solve problems by finding the areas of polygons on a coordinate plane.
•
Students use objects to solve problems that focus on geometric relationships.
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.
6th Grade: Math Unit 12 Area 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. Area I can find the area of rectangles. I can find the area of parallelograms and rhombuses. I can find the area of triangles. I can find the area of special quadrilaterals. I can find the areas of polygons including those on the coordinate plane. I can use objects to solve problems. Date: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
Lesson 1: The measure of a region inside a shape is its area,
and area can be found using square units.
area
Intervention:
- Small group reteach
- RTI Intervention System
Lesson 2: The formula for area of a parallelogram is derived
from the formula for area of a rectangle. The formula for area
of a rhombus is derived from the formula for area of a
parallelogram.
No new vocabulary
Lesson 3: The formula for area of a triangle is derived from the
formula for area of a parallelogram.
No new vocabulary
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
Lesson 4, 5, and 6: The measure of a region inside a shape is trapezoid
its area, and area can be found using square units. The area of kite
some irregular shapes can be found by decomposing the shape
into polygons for which formulas exist for finding area.
Lesson 7: Some problems can be solved by using objects to
act out the actions in the problems.
No new vocabulary
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
Manipulatives:
Alaska Standards Addressed & Assessed:
6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing or decomposing into other
polygons (e.g., rectangles and triangles). Apply these techniques in the context of solving real-world and mathematical problems.
Unit:
Topic 13: Surface Area and Volume
Grade Level:
6th Grade
CRITICAL DATES/TIMELINE:
• Diagnostic Performance Task(s)- day one
Alternate Topic Assessment
• Unit Common Assessment— day eight
Topic Test
• Total Instructional Time: 8 days
Anchor Standard(s):
Solve real-world and mathematical problems involving area, surface area, and volume.
Unit Essential Questions:
What is the meaning of surface area and how can surface area be found?
What is the meaning of volume and how can volume be found?
Student Learning Goals:
•
Students classify polyhedrons and identify vertices, edges, and faces, identify a polyhedron from its net.
•
Students find the surface area of a rectangular prism, a triangular prism, and a square pyramid by adding areas of faces or by
using a formula.
•
Students find the volume of a rectangular prism by using a formula.
•
Students will find the volume of a rectangular prism with fractional edge lengths.
•
Students use objects and reasoning to find the surface area and volume of solid figures.
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.
6th Grade: Math Unit 13 Surface Area and Volume 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. Surface Area and Volume I can classify a polyhedron and other solids and identify a solid from its net. I can find the surface area of solid figures. I can find the surface area of rectangular prisms. I can find the volume of rectangular prisms with fractional edge lengths. I can use objects and reasoning to solve problems. Date: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
Lesson 1: A polyhedron is a three-dimensional figure made of
flat surfaces. The shapes of these flat surfaces and the way
they are connected at edges and vertices determine the
characteristics of the polyhedron.
cone, cylinder, edge, faces, net,
polyhedron, prism, pyramid,
sphere, vertex
Intervention:
- Small group reteach
- RTI Intervention System
Lesson 2: Formulas for finding the area of polygons can be
used to find the surface area of some solids.
No new vocabulary
Lesson 3: Volume is a measure of the amount of space inside
a solid figure. Volume can be measured by counting the
number of cubic units needed to fill a three-dimensional object.
volume
Lesson 4: The volume of rectangular prisms with fractional
edge lengths can be determined in the same way as the
volume of rectangular prisms with whole-number edge lengths.
No new vocabulary
Lesson 5: Some problems can be solved by using objects to
act out the actions in the problems. Some problems can be
solved by reasoning about the conditions in the problems.
No new vocabulary
Anchor Text(s)/Additional Instructional Resources:
enVision Math: Pearson realize 2015 Edition
Online Subscription:
www.pearsonrealize.com
Manipulatives:
Enrichment:
- Pearson Realize Game
Center
- Show/explain the concept/skill
on iPad
- On-level & advanced center
activities
Alaska Standards Addressed & Assessed:
6.G.2. Apply the standard formulas to find volumes of prisms. Use the attributes and properties (including shapes of bases) of prisms
to identify, compare or describe three-dimensional figures including prisms and cylinders.
6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; determine the length of a side joining the coordinates
of vertices with the same first or the same second coordinate. Apply these techniques in the context of solving real-world and
mathematical problems.
6.G.4. Represent three-dimensional figures (e.g., prisms) using nets made up of rectangles and triangles, and use the nets to find the
surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Unit:
Topic 14: Statistics
Grade Level:
6th Grade
CRITICAL DATES/TIMELINE:
• Diagnostic Performance Task(s)- day one
Alternate Topic Assessment
• Unit Common Assessment— day thirteen
Topic Test
• Total Instructional Time: 13 days
Anchor Standard(s):
Summarize and describe distributions.
Develop understanding of statistical variability.
Unit Essential Question:
How can graphs be used to represent data and answer questions?
Student Learning Goals:
• Students determine whether a question is a statistical question or not, and display data sets using dot plots and bar graphs.
•
Students will describe data distributions by looking at their center, spread, and overall shape.
•
Students find the mean of data sets.
•
Students find the median, mode, and range of data sets,
•
Students make and use frequency tables and histograms.
•
Students learn how to interpret and make a box plot.
•
Students will use mean absolute deviation and interquartile range (IQR) to measure variability within a data distribution.
•
Students decide which measure of central tendency most accurately describes a given data set, and they recognize
inappropriate uses of statistical measures.
•
Students will summarize data based on its center, spread, and overall shape.
•
Students solve problems using the Try, Check, and Revise strategy.
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.
6th Grade: Math Unit 14 Statistics 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. Statastics I can determine whether a question is statistical or not, and display data sets using dot plots and bar graphs. I can describe data distributions by looking at their center, spread and overall shape. I can find the mean of data sets. I can find the mode, median, and range of data set. I can make and use frequency tables and histograms.. I can interpret and make a box plot. I can use mean absolute deviation and interquartile range to measure variability. I can decide which measure of central tendency most accurately describes a given data set. I can summarize data based on its center, spread, and overall shape. I can solve problems using the Try, Check, and Revise strategy. Date: 4 3 2 1 ESSENTIAL SKILLS/CONCEPTS:
Academic Vocabulary:
Interventions/Extensions:
Lesson 1: Statistical questions anticipate variability in the data.
These questions can be answered by .collecting and analyzing
data. The question to be answered determines the data that
needs to be collected.
statistical question
Intervention:
- Small group reteach
- RTI Intervention System
Lesson 2: A set of data collected to answer a statistical
question has a distribution, which can be described by its
center, spread, and overall shape.
data distribution
outlier
Lesson 3 and 4: Different measures can be used to describe
the center of a numerical data set. Each measure is most
appropriate depending on characteristics of the data.
mean, average, median, mode,
range
Lesson 5: Each type of graph is most appropriate for certain
kinds of data. A histogram uses bars to compare continuous
numerical data grouped into intervals.
frequency table, histogram
Lesson 6: Box plots are useful for plotting data over a number
line. Box plots show the spread for each quarter of the data
box plot, quartiles
Lesson 7: A measure of variability describes how the values in
a data set vary using a single number.
absolute deviation. interquartile
range (IQR)., mean absolute
deviation
Lesson 8: The best descriptor of the center of numerical data
is determined by the nature of the data and the question to be
answered. Organizing data makes it easier to find measures of
central tendency.
No new vocabulary
Lesson 9: A set of data collected to answer a statistical
question has a distribution which can be described by its
center, spread and overall shape
No new vocabulary
Lesson 10: Some problems can be solved by using reasoning
first to arrive at what the answer might be. Then through
additional reasoning, the correct answer can be found.
No new vocabulary
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:
www.pearsonrealize.com
Manipulatives:
Alaska Standards Addressed & Assessed:
6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the
answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical
question because one anticipates variability in students’ ages.
6.SP.2. Understand that a set of data has a distribution that can be described by its center (mean, median, or mode), spread (range),
and overall shape and can be used to answer a statistical question.
6.SP.3. Recognize that a measure of center (mean, median, or mode) for a numerical data set summarizes all of its values with a
single number, while a measure of variation (range) describes how its values vary with a single number.
6.SP.4. Display numerical data in plots on a number line, including dot or line plots, histograms and box (box and whisker) plots.