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Math Unit 1 Overview
MATH
Grade 5
Unit 1 : Addition and Subtraction with Fractions
Time Frame: 20 Days
Key Vocabulary: denominator, fraction, numerator, unit fraction, equivalent fractions, multiplier, n-split, simplify, unsimplify, benchmark, common denominator, common factor, greater than >, less than <, mixed number, add on, regroup, ungroup, line plot, estimate, round, situation equation, solution equation
Essential Questions:
Why do we need to add and subtract fractions?
What is the relationship between fractions and whole numbers?
Big Ideas:
Equivalent Fractions
Addition and Subtraction with Fractions
Suggested Mentor Texts:
Polar Bear Math: Learning About Fractions with Klondike and Snow, by Ann Whitehead and Cindy Bickel
Working with Fractions, by David A. Adler
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike
denominators (including mixed numbers) by
replacing given fractions with equivalent fractions
in such a way as to produce an equivalent sum or
difference of fractions with like denominators.
Introduce the MathBoard: Use the MathBoard fraction bars to discuss basic fraction ideas.
Explain Equivalent Fractions: Generate and explain simple equivalent fractions.
Equivalent Fractions and Multipliers: Understand the role of the multiplier in equivalent fractions.
Initial Assessment – Form A pre-test
Formative Assessments–Quick quizzes
p. 4, 14, 22, 32, 40, 48, 58, 64, 72, 78, 84, 90, 96
CCSS.MATH.CONTENT.5.NF.A.2
Solve word problems involving addition and
subtraction of fractions referring to the same
whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations
to represent the problem. Use benchmark
fractions and number sense of fractions to
estimate mentally and assess the
reasonableness of answers.
CCSS.MATH.CONTENT.5.MD.B.2
Make a line plot to display a data set of
measurements in fractions of a unit (1/2, 1/4,
1/8). Use operations on fractions for this grade to
solve problems involving information presented in
line plots.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
Strategies for Comparing Fractions: Use a variety of strategies to compare fractions.
Fractions Greater than One: Convert between fractions and mixed numbers
Add and Subtract Like Mixed Numbers: Add and subtract mixed numbers with like denominators
Add Unlike Fractions: Add fractions with different denominators
Subtract Unlike Fractions: Subtract fractions with different denominators
Solve with Unlike Mixed Numbers: Add and subtract mixed numbers with unlike denominators
Practice with Unlike Mixed Numbers: Add and subtract mixed numbers with unlike denominators
Reasonable Answers: Estimate sums and differences of fractions and mixed numbers, and decide whether answers are reasonable
Real World Problems: Use estimates to determine whether answers to word problems are reasonable
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
CC.K-12.MP.7 Look for and make use of structure
CC.K-12.MP.8 Look for and express regularity in repeated reasoning
Math Unit 2 Overview
MATH
Grade 5
Unit 2 : Addition and Subtraction with Decimals
Time Frame: 17 Days
Key Vocabulary: decimal, tenth, hundredth, thousandth, notation, standard form, word form, expanded form, power of ten, equivalent decimal, meter (m), decimeter (dm), centimeter (cm), millimeter (mm), grouping, ungrouping, break apart drawing, ungroup, Commutative Property of Addition, Associative Property of Addition, Distributive Property of Multiplication over Addition, round, estimate
Essential Questions:
Why are decimals necessary in everyday situations?
How are decimals related to whole numbers?
Why is place value important when representing and computing whole numbers and
decimals?
How do we record and interpret numerical expressions?
Big Ideas:
Read and Write Whole Numbers and Decimals
Addition and Subtraction
Round and Estimate with Decimals
Suggested Mentor Texts:
Sold! A Mathematics Adventure by Nathan Nimelman
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it
Decimals as Equal Divisions: Understand decimals as equal divisions of a whole.
Initial Assessment – Form A pre-test
represents in the place to its right and 1/10 of what it represents in the place to its left.
CCSS.MATH.CONTENT.5.NBT.A.3
Read, write, and compare decimals to
thousandths.
CCSS.MATH.CONTENT.5.NBT.A.3.A
Read and write decimals to thousandths using
base-ten numerals, number names, and
expanded form, e.g., 347.392 = 3 × 100 + 4 × 10
+ 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
CCSS.MATH.CONTENT.5.NBT.A.3.B
Compare two decimals to thousandths based on
meanings of the digits in each place, using >, =,
and < symbols to record the results of
comparisons.
CCSS.MATH.CONTENT.5.NBT.A.4
Use place value understanding to round decimals
to any place.
CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Thousands to Thousandths: Read, write, and model whole and decimal numbers.
Equate and Compare Thousandths: Model and identify equivalent fractions.
Adding and Subtracting Decimals: Model adding and subtracting decimals.
Add Whole Numbers and Decimals: Add whole numbers and decimals to hundredths.
Subtract Whole and Decimal Numbers: Subtract whole and decimal numbers to hundredths.
Properties and Strategies: Use the Commutative, Associative, and Distributive Properties to compute mentally.
Round and Estimate with Decimals: Estimate decimal sums and differences.
Graph with Decimal Numbers: Read and construct graphs with decimal scales and decimal numbers.
Focus on Mathematical Practices: Use the Common Core State Standards and Practices in a variety of real world problem solving situations.
Formative Assessments–Quick quizzes
p. 108, 118, 130, 138, 144, 152, 158, 168, 174, 180
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of structure
CC.K-12.MP.8 Look for and express regularity in repeated reasoning
Math Unit 3 Overview
MATH
Grade 5
Unit 3 : Multiplication and Division with Fractions
Time Frame: 23 Days
Key Vocabulary: comparison bars, multiplicative comparison, factor, product, area model for multiplication, fraction-bar model for multiplication, Multiply and Simply Method, Simplify and Multiply Method, Unit Fraction Method, Associative Property, Commutative Property, Distributive Property, decimal fraction, dividend, divisor, quotient
Essential Questions:
How do you multiply fractions?
Why do you multiply fractions?
How do you divide fractions?
Why do you divide fractions?
What is the relationship between multiplication & division of fractions?
Big Ideas:
Multiplication with Fractions
Multiplication Links
Division with Fractions
Suggested Mentor Texts:
Go, Fractions! by Judith Stamper
Parting is Such Sweet Sorrow: Fractions and Decimals (Adventures in Mathopolis) by Linda Powley and Catherine Weiskopf
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike
Basic Multiplication Concepts: Connect multiplying by (1/n) to dividing by n, and use this idea to make multiplicative comparisons
Initial Assessment – Form A pre-test
denominators (including mixed numbers) by
replacing given fractions with equivalent fractions
in such a way as to produce an equivalent sum or
difference of fractions with like denominators.
CCSS.MATH.CONTENT.5.NF.A.2
Solve word problems involving addition and
subtraction of fractions referring to the same
whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations
to represent the problem. Use benchmark
fractions and number sense of fractions to
estimate mentally and assess the
reasonableness of answers.
CCSS.MATH.CONTENT.5.NF.B.3
Interpret a fraction as division of the numerator
by the denominator (a/b = a ÷ b). Solve word
problems involving division of whole numbers
leading to answers in the form of fractions or
mixed numbers, e.g., by using visual fraction
models or equations to represent the problem.
CCSS.MATH.CONTENT.5.NF.B.4
Apply and extend previous understandings of
multiplication to multiply a fraction or whole
number by a fraction.
CCSS.MATH.CONTENT.5.NF.B.4.A
Interpret the product (a/b) × q as a parts of a
Multiplication with Non-Unit Fractions: Interpret a/b times a quantity as a of b equal parts of that quantity.
Multiplication with Fractional Solutions: Multiply a whole number by a fraction to produce a fraction.
Multiply a Fraction by a Fraction: Multiply any two fractions.
Multiplication Strategies: Compare and apply strategies for multiplying fractions.
Multiply Mixed Numbers: Multiply with mixed numbers.
Relate Fraction Operations: Relate operations with fractions and whole numbers, and discuss properties of arithmetic.
Solve Real World Problems: Add, subtract, compare, and multiply fractions to solve word problems.
Make Generalizations: Predict the size of a product relative to the size of one factor based on the size of the other factor.
When Dividing Is Also Multiplying: Relate division by a unit fraction or whole number to multiplication.
Solve Division Problems: Write and solve division word problems.
Distinguish Multiplication from Division: Determine whether solving a word problem requires multiplication or division.
Review Operations with Fractions: Solve numerical and word problems involving all four operations with fractions.
Focus on Mathematical Practices: Use the Common Core Standards and Practices in a variety of real world problem solving situations.
Formative Assessments–Quick quizzes
p. 192, 198, 206, 216, 224, 232, 240, 246, 252, 260, 266, 274, 280, 286
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
partition of q into b equal parts; equivalently, as
the result of a sequence of operations a × q ÷ b.
CCSS.MATH.CONTENT.5.NF.B.4.B
Find the area of a rectangle with fractional side
lengths by tiling it with unit squares of the
appropriate unit fraction side lengths, and show
that the area is the same as would be found by
multiplying the side lengths. Multiply fractional
side lengths to find areas of rectangles, and
represent fraction products as rectangular areas.
CCSS.MATH.CONTENT.5.NF.B.5
Interpret multiplication as scaling (resizing), by:
CCSS.MATH.CONTENT.5.NF.B.5.A
Comparing the size of a product to the size of
one factor on the basis of the size of the other
factor, without performing the indicated
multiplication.
CCSS.MATH.CONTENT.5.NF.B.5.B
Explaining why multiplying a given number by a
fraction greater than 1 results in a product greater
than the given number (recognizing multiplication
by whole numbers greater than 1 as a familiar
case); explaining why multiplying a given number
by a fraction less than 1 results in a product
smaller than the given number; and relating the
principle of fraction equivalence a/b =
(n × a)/(n × b) to the effect of multiplying a/b by 1.
CCSS.MATH.CONTENT.5.NF.B.6
Solve real world problems involving multiplication
of fractions and mixed numbers, e.g., by using
visual fraction models or equations to represent
the problem.
CCSS.MATH.CONTENT.5.NF.B.7
Apply and extend previous understandings of
division to divide unit fractions by whole numbers
and whole numbers by unit fractions.1
CCSS.MATH.CONTENT.5.NF.B.7.A
Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients.
CCSS.MATH.CONTENT.5.NF.B.7.B
Interpret division of a whole number by a unit
fraction, and compute such quotients.
CCSS.MATH.CONTENT.5.NF.B.7.C
Solve real world problems involving division of
unit fractions by non-zero whole numbers and
division of whole numbers by unit fractions, e.g.,
by using visual fraction models and equations to
represent the problem.
CCSS.MATH.CONTENT.5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to
solve problems involving information presented in line plots.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of structure
CC.K-12.MP.8 Look for and express regularity in repeated reasoning
Math Unit 4 Overview
MATH
Grade 5
Unit 4: Multiplication with Whole Numbers and Decimals
Time Frame: 18 Days
Key Vocabulary: shift, base, exponent, exponential form, power of ten, even, odd, partial products, Place Value Sections, Expanded Notation, New Groups Below, Place Value Rows, Short Cut, Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property of Multiplication over Addition,
Essential Questions:
Why are decimals necessary in everyday situations? How are decimals related to whole numbers? Why is place value important when representing and computing whole numbers and
decimals? How do we record and interpret numerical expressions?
Big Ideas:
Multiplication with Whole Numbers
Multiplication with Decimal Numbers
Suggested Mentor Texts:
The Amazing Impossible Erie Canal by Cheryl Harness
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.NF.B.5
Interpret multiplication as scaling (resizing), by:
CCSS.MATH.CONTENT.5.NF.B.5.A
Comparing the size of a product to the size of
Shift Patterns in Multiplication: Understand the shift patterns when multiplying by 10, 100, or 1,000.
Patterns with Fives and Zeros: Understand that multiples of 5 need extra attention in the zeros pattern.
Initial Assessment – Form A pre-test
Formative Assessments–Quick quizzes
one factor on the basis of the size of the other
factor, without performing the indicated
multiplication.
CCSS.MATH.CONTENT.5.NF.B.5.B
Explaining why multiplying a given number by a
fraction greater than 1 results in a product greater
than the given number (recognizing multiplication
by whole numbers greater than 1 as a familiar
case); explaining why multiplying a given number
by a fraction less than 1 results in a product
smaller than the given number; and relating the
principle of fraction equivalence a/b =
(n × a)/(n × b) to the effect of multiplying a/b by 1.
CCSS.MATH.CONTENT.5.NBT.A.1
Recognize that in a multi-digit number, a digit in
one place represents 10 times as much as it
represents in the place to its right and 1/10 of
what it represents in the place to its left.
CCSS.MATH.CONTENT.5.NBT.A.2
Explain patterns in the number of zeros of the
product when multiplying a number by powers of
10, and explain patterns in the placement of the
decimal point when a decimal is multiplied or
divided by a power of 10. Use whole-number
exponents to denote powers of 10.
Sharing Methods for Multiplication: Understand how a place value model can be used to solve multidigit multiplication problems.
Multiply Two-Digit Numbers: Solve two-digit multiplication problems using various methods.
Practice Multiplication: Practice multiplying mulitidigit numbers.
Multiply Decimals by Whole Numbers: Solve multiplication problems in which one factor is a decimal number.
Multiply by Decimals: Solve multiplication problems in which at least one factor is a decimal number.
Multiply with Decimals Greater Than 1: Multiply with decimal numbers greater than 1.
Compare Shift Patterns: Understand and apply shift patterns when multiplying by 10, 100, 1,000, 0.1, or 0.01.
Estimate Products: Round whole numbers and decimal numbers to estimate the product in a multiplication problem.
Multiplication Practice: Perform multidigit multiplication with decimal numbers.
Focus on Mathematical Practices: Use the Common Core State Standards and Practices in a variety of real world problem solving situations.
p. 302, 308, 314, 322, 326, 334, 344, 350, 358, 366, 372, 378
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
CCSS.MATH.CONTENT.5.NBT.A.3
Read, write, and compare decimals to
thousandths.
CCSS.MATH.CONTENT.5.NBT.A.3.A
Read and write decimals to thousandths using
base-ten numerals, number names, and
expanded form, e.g., 347.392 = 3 × 100 + 4 × 10
+ 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
CCSS.MATH.CONTENT.5.NBT.A.3.B
Compare two decimals to thousandths based on
meanings of the digits in each place, using >, =,
and < symbols to record the results of
comparisons.
CCSS.MATH.CONTENT.5.NBT.A.4
Use place value understanding to round decimals
to any place.
CCSS.MATH.CONTENT.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of structure
CC.K-12.MP.8 Look for and express regularity in repeated reasoning
Math Unit 5 Overview
MATH
Grade 5
Unit 5 : Division with Whole Numbers and Decimals
Time Frame: 16 Days
Key Vocabulary: Digit-by-Digit method, dividend, divisor, Expanded Notation method, Place Value Sections method, quotient, remainder, overestimate, underestimate
Essential Questions:
How and why do you divide decimals?
What is the relationship between multiplication & division of decimals?
Why is place value important when representing and computing whole numbers and
decimals?
Big Ideas:
Division with Whole Numbers
Division with Decimal Numbers
Suggested Mentor Texts:
A Remainder of One by Elinor J. Pinczes
The Everything Kids’ Money Book: Earn it, save it, watch it grow! By Brette McWhorter Sember
The Great Divide: A Mathematical Marathon by Dayle Ann Dodds
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the
Divide Whole Numbers by One Digit: Divide multidigit numbers by single-digit divisors.
Explore Dividing by Two-Digit Whole Numbers: Solve division problems having two-digit divisors.
Initial Assessment – Form A pre-test
Formative Assessments–Quick quizzes
decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
CCSS.MATH.CONTENT.5.NBT.A.3.B Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
CCSS.MATH.CONTENT.5.NBT.B.5
Fluently multiply multi-digit whole numbers using
the standard algorithm.
CCSS.MATH.CONTENT.5.NBT.B.6
Find whole-number quotients of whole numbers
with up to four-digit dividends and two-digit
divisors, using strategies based on place value,
the properties of operations, and/or the
relationship between multiplication and division.
Illustrate and explain the calculation by using
equations, rectangular arrays, and/or area
models.
CCSS.MATH.CONTENT.5.NBT.B.7
Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings
and strategies based on place value, properties
of operations, and/or the relationship between
addition and subtraction; relate the strategy to a
written method and explain the reasoning used.
Too Large, Too Small, or Just Right?: Understand several ways to adjust the estimated divisor when it is too small.
Interpret Remainders: Express and interpret remainders for a variety of problem types.
Division Practice: Practice dividing whole numbers.
Divide Decimal Numbers by Whole Numbers: Divide decimal numbers by one- and two-digit whole numbers.
Divide Whole Numbers by Decimal Numbers: Solve division problems that have decimal divisors.
Divide with Two Decimal Numbers: Solve division problems in which both numbers are decimals.
Division Practice: Solve division problems that require multiplying or dividing whole numbers and decimal numbers.
Focus on Mathematical Practices: Use the Common Core Content Standards and Practices in a variety of real world problem solving situations.
p. 394, 400, 406, 414, 420, 428, 438, 446, 452, 460, 466
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
CCSS.MATH.CONTENT.5.NF.B.5
Interpret multiplication as scaling (resizing), by:
CCSS.MATH.CONTENT.5.NF.B.5.A
Comparing the size of a product to the size of
one factor on the basis of the size of the other
factor, without performing the indicated
multiplication.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of structure
CC.K-12.MP.8 Look for and express regularity in repeated reasoning
Math Unit 6 Overview
MATH
Grade 5
Unit 6 : Operations and Word Problems
Time Frame: 18 Days
Key Vocabulary: situation equation, solution equation, break apart drawing, rectangle model, benchmark, comparison, leading language, misleading language, scaling, additive, multiplicative, parentheses, equation
Essential Questions:
Leave this section blank. Nicole will complete.
Big Ideas:
Equations and Problem Solving
Comparison Word Problems
Problems with More Than One Step
Suggested Mentor Texts:
O, Say Can You See? by Shelia Keenan and Ann Boyajian
Time for Kids Almanac, by Time for Kids Editors
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.NBT.A.4 Use place value understanding to round decimals to any place.
Situation and Solution Equations for Addition and Subtraction: Write situation and solution equations to solve addition and subtraction problems.
Situation and Solution Equations for Multiplication and Division: Write situation and solution equations to multiplication and division problems.
Write Word Problems: Write word problems for equations involving fractions and decimals and model the product.
Initial Assessment – Form A pre-test
Formative Assessments–Quick quizzes
p. 478, 486, 492, 500, 508, 516, 524, 532, 538, 544, 550
CCSS.MATH.CONTENT.5.NBT.B.5
Fluently multiply multi-digit whole numbers using
the standard algorithm.
CCSS.MATH.CONTENT.5.NBT.B.6
Find whole-number quotients of whole numbers
with up to four-digit dividends and two-digit
divisors, using strategies based on place value,
the properties of operations, and/or the
relationship between multiplication and division.
Illustrate and explain the calculation by using
equations, rectangular arrays, and/or area
models.
CCSS.MATH.CONTENT.5.NBT.B.7
Add, subtract, multiply, and divide decimals to
hundredths, using concrete models or drawings
and strategies based on place value, properties
of operations, and/or the relationship between
addition and subtraction; relate the strategy to a
written method and explain the reasoning used.
CCSS.MATH.CONTENT.5.NF.A.1
Add and subtract fractions with unlike
denominators (including mixed numbers) by
replacing given fractions with equivalent fractions
in such a way as to produce an equivalent sum or
difference of fractions with like denominators. For
example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In
general, a/b + c/d = (ad + bc)/bd.)
Determine Reasonable Answers: Use a variety of methods to determine reasonable answers.
Language of Comparison Problems: Understand and apply comparison language.
Multiplicative Comparison Problems: Model and solve multiplicative comparison problems.
Types of Comparison Problems: Solve comparison problems.
Equations and Parentheses: Solve two-step problems.
Multistep Word Problems: Solve multistep problems.
Practice Problem Solving: Practice solving multistep problems.
Focus on Mathematical Practices: Use the Common Core Content Standards and Practices in a variety of real world problem solving situations.
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
CCSS.MATH.CONTENT.5.NF.A.2
Solve word problems involving addition and
subtraction of fractions referring to the same
whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations
to represent the problem. Use benchmark
fractions and number sense of fractions to
estimate mentally and assess the
reasonableness of answers.
CCSS.MATH.CONTENT.5.NF.B.3
Interpret a fraction as division of the numerator
by the denominator (a/b = a ÷ b). Solve word
problems involving division of whole numbers
leading to answers in the form of fractions or
mixed numbers, e.g., by using visual fraction
models or equations to represent the problem.
CCSS.MATH.CONTENT.5.NF.B.4
Apply and extend previous understandings of
multiplication to multiply a fraction or whole
number by a fraction.
CCSS.MATH.CONTENT.5.NF.B.4.A
Interpret the product (a/b) × q as a parts of a
partition of q into b equal parts; equivalently, as
the result of a sequence of operations a × q ÷ b.
CCSS.MATH.CONTENT.5.NF.B.4.B
Find the area of a rectangle with fractional side
lengths by tiling it with unit squares of the
appropriate unit fraction side lengths, and show
that the area is the same as would be found by
multiplying the side lengths. Multiply fractional
side lengths to find areas of rectangles, and
represent fraction products as rectangular areas.
CCSS.MATH.CONTENT.5.NF.B.5
Interpret multiplication as scaling (resizing), by:
CCSS.MATH.CONTENT.5.NF.B.5.A
Comparing the size of a product to the size of
one factor on the basis of the size of the other
factor, without performing the indicated
multiplication.
CCSS.MATH.CONTENT.5.NF.B.5.B
Explaining why multiplying a given number by a
fraction greater than 1 results in a product greater
than the given number (recognizing multiplication
by whole numbers greater than 1 as a familiar
case); explaining why multiplying a given number
by a fraction less than 1 results in a product
smaller than the given number; and relating the
principle of fraction equivalence a/b =
(n × a)/(n × b) to the effect of multiplying a/b by 1.
CCSS.MATH.CONTENT.5.NF.B.6
Solve real world problems involving multiplication
of fractions and mixed numbers, e.g., by using
visual fraction models or equations to represent
the problem.
CCSS.MATH.CONTENT.5.NF.B.7
Apply and extend previous understandings of
division to divide unit fractions by whole numbers
and whole numbers by unit fractions.1
CCSS.MATH.CONTENT.5.NF.B.7.A
Interpret division of a unit fraction by a non-zero
whole number, and compute such quotients.
CCSS.MATH.CONTENT.5.NF.B.7.B
Interpret division of a whole number by a unit
fraction, and compute such quotients.
CCSS.MATH.CONTENT.5.NF.B.7.C
Solve real world problems involving division of
unit fractions by non-zero whole numbers and
division of whole numbers by unit fractions, e.g.,
by using visual fraction models and equations to
represent the problem.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of structure
CC.K-12.MP.8 Look for and express regularity in repeated reasoning
Math Unit 7Overview
MATH
Grade 5
Unit 7 : Algebra, Patterns, and Coordinate Graphs
Time Frame: 12 Days
Key Vocabulary: expression, Order of Operations, simplify, evaluate, variable, numerical pattern, term, coordinate plane, ordered pair, origin, x-coordinate, y-coordinate, x-axis, y-axis
Essential Questions:
How can identifying patterns help determine multiple solutions?
In what ways can we represent real world and mathematical problems using rules?
When can coordinate grids help you organize information?
What relationships can be determined by analyzing two sets of given rules?
Big Ideas:
Algebraic Reasoning and Expressions
Patterns and Graphs
Suggested Mentor Texts:
The Fly on the Ceiling, by Julie Glass
Find the Constellations, by H.A. Rey
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.OA.A.1
Use parentheses, brackets, or braces in
Read and Write Expressions: Read and write expressions.
Simplify Expressions: Simplify numerical expressions.
Evaluate Expressions: Write and evaluate expressions that contain variables.
Initial Assessment – Form A pre-test
Formative Assessments–Quick quizzes
numerical expressions, and evaluate expressions
with these symbols.
CCSS.MATH.CONTENT.5.OA.A.2
Write simple expressions that record calculations
with numbers, and interpret numerical
expressions without evaluating them.
CCSS.MATH.CONTENT.5.OA.B.3
Generate two numerical patterns using two given
rules. Identify apparent relationships between
corresponding terms. Form ordered pairs
consisting of corresponding terms from the two
patterns, and graph the ordered pairs on a
coordinate plane.
CCSS.MATH.CONTENT.5.G.A.1
Use a pair of perpendicular number lines, called
axes, to define a coordinate system, with the
intersection of the lines (the origin) arranged to
coincide with the 0 on each line and a given point
in the plane located by using an ordered pair of
numbers, called its coordinates. Understand that
the first number indicates how far to travel from
the origin in the direction of one axis, and the
second number indicates how far to travel in the
direction of the second axis, with the convention
that the names of the two axes and the
coordinates correspond (e.g.,x-axis and x-
coordinate, y-axis and y-coordinate).
Patterns and Relationships: Generate and extend numerical patterns and identify relationships of corresponding terms.
The Coordinate Plane: Locate and plot points in the first quadrant of the coordinate plane.
Graph Ordered Pairs: Graph ordered pairs and use them to represent and solve real world problems.
Focus on Mathematical Practices: Use the Common Core Standards and Practices in a variety of real world problem solving situations.
p. 560, 566, 572, 580, 590, 596, 602
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
CCSS.MATH.CONTENT.5.G.A.2
Represent real world and mathematical problems
by graphing points in the first quadrant of the
coordinate plane, and interpret coordinate values
of points in the context of the situation.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of structure
CC.K-12.MP.8 Look for and express regularity in repeated reasoning
Math Unit 8 Overview
MATH
Grade 5
Unit 8 : Measurement and Geometry
Time Frame: 26 Days
Key Vocabulary: meter, millimeter, centimeter, decimeter, decameter, hectometer, kilometer, liter, milliliter, centiliter, deciliter, dekaliter, hectoliter, kiloliter, mass, gram, milligram, centigram, decigram, dekagram, hectogram, kilogram, mile (mi), ton, frequency table, line plot, perimeter, area, square centimeter, square unit, face, edge, rectangular prism, cube, unit cube, volume, cubic unit, rectangular prism, volume, cubic unit, one-dimensional, two-dimensional, three-dimensional, composite, acute angle, adjacent angles, adjacent sides, congruent, counterexample, line of symmetry, opposite angles, opposite sides, parallel, parallelogram, perpendicular, quadrilateral, rectangle, rhombus, right angle, square, trapezoid, acute angle, acute triangle, adjacent sides, congruent angles, congruent sides, equilateral triangle, isosceles triangle, obtuse angle, obtuse triangle, perpendicular sides, right angle, right triangle, scalene triangle, closed, concave, convex, open, polygon, reflex angle, regular polygon
Essential Questions:
Where and when can you find a 2 dimensional figure in life?
Why do you need to know the volume of something?
Why is the formula for volume important?
Big Ideas:
Measurements and Data
Area and Volume
Classify Geometric Figures
Suggested Mentor Texts:
The Math Chef: Over 60 Math Activities and Recipes for Kids, by Joan D’Amico and Karen Eich Drummond
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
CCSS.MATH.CONTENT.5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
CCSS.MATH.CONTENT.5.MD.C.3
Recognize volume as an attribute of solid figures
and understand concepts of volume
measurement.
CCSS.MATH.CONTENT.5.MD.C.3.A
A cube with side length 1 unit, called a "unit
cube," is said to have "one cubic unit" of volume,
and can be used to measure volume.
CCSS.MATH.CONTENT.5.MD.C.3.B
A solid figure which can be packed without gaps
or overlaps using n unit cubes is said to have a
volume of n cubic units.
Convert Metric Units of Length: Convert among metric units of length.
Metric Units of Liquid Volume: Convert among metric units of liquid volume.
Metric Units of Mass: Convert among metric units of mass.
Customary Units of Length: Convert among customary units of length.
Customary Measures of Liquid Volumes: Convert among customary measures of liquid volume.
Customary Units of Weight: Convert among customary measures of weight.
Read and Make Line Plots: Make and analyze line plots.
Perimeter and Area of Rectangles: Use a formula to find the perimeter and area of a rectangle with fractional side lengths.
Cubic Units and Volume: Use a formula to find the volume of a rectangular prism.
Visualize Volume: Compute the volume of a rectangular prism.
Introduce Volume Formulas: Use a formula to find the volume of a rectangular prism.
Relate Length, Area, and Volume: Identify whether a situation involves length, area, or volume.
Volume of Composite Solid Figures: Find the volume of a composite solid figure.
Attributes of Quadrilaterals: Understand attributes of different types of quadrilaterals.
Initial Assessment – Form A pre-test
Formative Assessments–Quick quizzes
p. 614, 620, 626, 632, 638, 644, 650, 660, 668, 674, 680, 686, 692, 702, 710, 718, 724
Math Writing Prompts
End of Unit Assessment – Form A assessment
Performance Task if created.
CCSS.MATH.CONTENT.5.MD.C.4
Measure volumes by counting unit cubes, using
cubic cm, cubic in, cubic ft, and improvised units.
CCSS.MATH.CONTENT.5.MD.C.5
Relate volume to the operations of multiplication
and addition and solve real world and
mathematical problems involving volume.
CCSS.MATH.CONTENT.5.MD.C.5.A
Find the volume of a right rectangular prism with
whole-number side lengths by packing it with unit
cubes, and show that the volume is the same as
would be found by multiplying the edge lengths,
equivalently by multiplying the height by the area
of the base. Represent threefold whole-number
products as volumes, e.g., to represent the
associative property of multiplication.
CCSS.MATH.CONTENT.5.MD.C.5.B
Apply the formulas V = l × w × h and V = b × h for
rectangular prisms to find volumes of right
rectangular prisms with whole-number edge
lengths in the context of solving real world and
mathematical problems.
CCSS.MATH.CONTENT.5.MD.C.5.C
Recognize volume as additive. Find volumes of
solid figures composed of two non-overlapping
right rectangular prisms by adding the volumes of
Attributes of Triangles: Understand the attributes of different types of triangles.
Attributes of Two-Dimensional Shapes: Understand attributes of polygons and other two-dimensional shapes.
Focus on Mathematical Practices: Use the Common Core State Standards and Practices in a variety of real world problem solving situations.
the non-overlapping parts, applying this
technique to solve real world problems.
CCSS.MATH.CONTENT.5.G.B.3
Understand that attributes belonging to a
category of two-dimensional figures also belong
to all subcategories of that category. For
example, all rectangles have four right angles
and squares are rectangles, so all squares have
four right angles.
CCSS.MATH.CONTENT.5.G.B.4
Classify two-dimensional figures in a hierarchy
based on properties.
CCSS.MATH.CONTENT.5.NF.B.4.B Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Mathematical Practice
CC.K-12.MP.1 Make sense of problems and persevere in solving them
CC.K-12.MP.2 Reason abstractly and quantitatively
CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others
CC.K-12.MP.4 Model with mathematics