White Oak Elementary
Fifth Grade
Mathematics at a Glance
Mathematics Fifth Grade – Year at a Glance Numbers and Operations in Base Ten
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Place Value
Multiply Whole
Numbers
Divide by a OneDigit Divisor
Divide by a TwoDigit Number
Add and Subtract
Decimals
Multiply and Divide
Decimals
3 Weeks
5.NBT.1
5.NBT.3
5.NBT.3a
5.NBT.3b
3 Weeks
5.NBT.2
5.NBT.5
4 Weeks
5.NBT.6
2 weeks
5.NBT.6
3 weeks
5.NBT.4
5.NBT.7
4 weeks
5.NBT.2
5.NBT.4
5.NBT.5
5.NBT.7
Vocabulary
Vocabulary
Vocabulary
Vocabulary
Vocabulary
Vocabulary
place-value chart;
period; place; place
value; standard
form; expanded
form; decimal;
decimal point;
equivalent decimals
Assessment
•
prime factorization;
exponent; base;
power; squared;
cubed; powers of
10; Distributive
Property; compatible
numbers
Assessment
•
Fact family;
unknown; variable;
dividend; divisor;
quotient; remainder;
partial quotients
All vocabulary in this
chapter are review
words.
Commutative
Property of Addition;
Associative Property
of Addition; Identity
Property of Addition;
inverse operations
Assessment
•
Assessment
•
Assessment
•
Associative Property
of Multiplication;
Commutative
Property of
Multiplication;
Identity Property of
Multiplication
Assessment
•
Page 2 Mathematics Fifth Grade – Year at a Glance OA Thinking
Numbers and Operations - Fractions
Measurement and Data
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Expressions and
Patterns
Fractions and
Decimals
Add and Subtract
Fractions
Multiply and Divide
Fractions
Measurement
Geometry
2 Weeks
5.OA.1
5.OA.2
5.OA.3
5.G.1
5.G.2
2 Weeks
5.NF.2
5.NF.3
5.NF.5
5.NF.5b
3 Weeks
5.NF.1
5.NF.2
3 Weeks
5.NF.4
5.NF.6
5.NF.4a
5.NF.7
5.NF.4b
5.NF.7a
5.NF.5
5.NF.7b
5.NF.5a
5.NF.7c
5.NF.5b
4 Weeks
5.MD.1
5.MD.2
3 Weeks
5.G.3
5.MD.5
5.G.4
5.MD.5a
5.MD.3
5.MD.5b
5.MD.3a 5.MD.5c
5.MD.3b
5.MD.4
Vocabulary
Vocabulary
Vocabulary
Vocabulary
Numerical
expression;
evaluate; order of
operations;
sequence; term;
coordinate plane;
origin; ordered pair;
x-coordinate; ycoordinate
Fraction; numerator;
denominator;
common factors;
greatest common
factor (GCF);
simplest form;
equivalent fractions;
multiple; common
multiples; least
common multiple
(LCM); least
common
denominator (LCD)
Like fractions; unlike
fractions
Scaling; unit fraction
Length; inch;
customary system;
foot; yard; convert;
inches; mile; weight;
ounces; pounds;
ton; capacity; pints;
cups; gallons; quart;
fluid ounce; fair
share; centimeter;
millimeter; metric
system; meter;
kilometer; mass;
gram; liter
Hexagon; pentagon;
polygon; octagon;
congruent angles;
congruent sides;
regular polygon;
attribute; equilateral;
isosceles; scalene;
acute; obtuse; right;
trapezoid;
parallelogram;
rhombus; square;
rectangle; 3d figure;
net; cube; congruent
figures; rectangular
prism; face;
triangular prism;
Page 3 Mathematics Fifth Grade – Year at a Glance OA Thinking
Measurement and Data
Numbers and Operations - Fractions
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Expressions and
Patterns
Fractions and
Decimals
Add and Subtract
Fractions
Multiply and Divide
Fractions
Measurement
Geometry
edge; vertex; base;
cube; volume; unit
cube; cubic unit;
composite figure
Assessment
Assessment
Assessment
Assessment
•
•
•
•
•
•
Page 4 Mathematics Fifth Grade – Year in Detail Summary of Year for Fifth Grade Mathematics In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding
of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions);
(2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to
hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.
1. Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent
calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also
use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures
for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit
fractions.)
2. Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize
fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties
of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students
use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an
appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute
products and quotients of decimals to hundredths efficiently and accurately.
3. Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size
units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring
volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose threedimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes.
Mathematical Practices 1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Page 5 Mathematics Fifth Grade – Year in Detail Fifth Grade Overview Operations and Algebraic Thinking
Numbers and Operations in Base Ten
Measurement and Data
• Write and interpret numerical
expressions.
• Analyze patterns and relationships.
• Understand the place value system.
• Perform operations with multi-digit
whole numbers and with decimals to
hundredths.
• Convert like measurement units
within a given measurement system.
• Represent and interpret data.
• Geometric measurement:
understand concepts of volume and
relate volume to multiplication and
to addition.
Numbers and Operations - Fractions
• Use equivalent fractions as a
strategy to add and subtract
fractions.
• Apply and extend previous
understandings of multiplication and
division to multiply and divide
fractions.
Geometry
• Graph points on the coordinate
plane to solve real-world and
mathematical problems.
• Classify two-dimensional figures
into categories based on their
properties.
Page 6 Mathematics Fifth Grade – Year in Detail Chapter 1: Place Value All of the lesson in Chapter 1 will connect with the theme of Let’s Go Outdoors! , which centers around activities such as sports,
camping, swimming, hiking, and biking. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How does the position of Essential Question: a digit in a number relate to it’s value?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
Common Core State Standard Descriptor
5.NBT.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.
5.NBT.3
Read, write, and compare decimals to thousandths.
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).
Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record
5NBT.3b
the results of comparisons.
5NBT.3a
Standards For Mathematical Practice •
•
•
•
•
•
•
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and express regularity in repeated reasoning. Anchor Texts Anchor Text
If You Made a Million
Millions to Measure
Alexander Who Used to Be Rich Last Sunday
Little Numbers and Pictures That Show Just
How Little They Are!
Math Man
The Toothpaste Millionaire
Author
David M. Schwartz
David M. Schwartz
Judith Viorst
Edward Packard
Teri Daniels
Jean Merrill
Page 7 What Students Should Understand
Place Value Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.1 How to use a place value chart. • A digit in each place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left. • A digit in the millions place has a value of 1,000,000 times the digit, a digit in the hundred thousands place has a value of 100,000 times the digit, and so on. Page 8 What Students Should Understand
Represent Decimals Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT3; 5.NBT.3a How to represent fractions with denominators of 10, 100, or 1,000 as decimals. • Use models. • Write decimals using words and numbers. Expanded Form of Decimals 5.NBT.1; 5.NBT.3; 5.NBT.3a How to use place value to write decimals in expanded form. • A digit in each place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left. • Expanded form shows the sum of the value of digits. Page 9 What Students Should Understand
Four-Step Plan Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.3; 5.NBT.3a; 5.NBT.3b How to use place value and the four-­‐step plan to solve problems. • Use place-­‐value charts. • Write numbers in different forms and then compare. Page 10 Mathematics Fifth Grade – Year in Detail Chapter 2: Multiply Whole Numbers All of the lessons in Chapter 2 will connect with the theme of Taking Care of My Pets!, which centers around feeding pets, cost
associated with pets, and facts about pets. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “What strategies can be used to multiply whole numbers?” Possible Time Frame: 3 weeks Essential Question: Major Cluster Standards CCSS
5.NBT.2
5.NBT.5
Common Core State Standard Descriptor
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.
Fluently multiply multi-digit whole numbers using the standard algorithm.
Standards For Mathematical Practice •
•
•
•
•
•
•
•
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Anchor Texts Anchor Text
Author
The Best of Times
Greg Tang
Ten Times Better
Richard Michaelson
Among the Odds and Evens: A Tale of
Adventure
King’s Chessboard
Priscilla Turner
Pigs Will be Pigs: Fun With Math and
Money
Amanda Bean’s Amazing Dream
Amy Axelrod
David Birch
Cindy Neuschwander
Page 11 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Multiply by Powers of Ten What Students Should Be Able to Do
5.NBT.2 How to use patterns to multiply a number by a power of 10. • When multiplying by a power of 10, the number of zeros in the product depends on the exponent of the power. Partial Products 5.NBT.5 How to use partial products to multiply two numbers. • Area models can be used to show partial products. • To multiply two numbers, find each partial product and then add. Page 12 What Students Should Understand
Distributive Property Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.5 How to use the Distributive Property to multiply whole numbers. • The Distributive Property combines multiplication and addition. Page 13 What Students Should Understand
Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Estimation 5.NBT.5 How to estimate the product of two whole numbers. • Compatible numbers are numbers that are easy to compute mentally. • Products can be estimated by using compatible numbers or by rounding. Page 14 What Students Should Understand
Multiply by Two-Digit Numbers Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.5 How to use the standard algorithm to multiply by two-­‐digit numbers. • Multiply by the ones of the two-­‐digit number, then multiply by the tens of the two-­‐digit number, and then add the partial products. Page 15 Mathematics Fifth Grade – Year in Detail Chapter 3: Divide by a One-­‐Digit Divisor All of the lessons in Chapter 3 will connect with the theme of Let’s Help Others!, which centers around activities such as volunteering,
helping neighbors, recycling, and charity events. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “What strategies can be Essential Question: used to divide whole numbers?” Possible Time Frame: 4 weeks Major Cluster Standards CCSS
Common Core State Standard Descriptor
5.NBT.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. Standards For Mathematical Practice •
•
•
•
•
•
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Attend to precision.
Use appropriate tools strategically.
Anchor Texts Anchor Text
A Place for Zero: A Math Adventure
Betcha!
A Remainder of One
17 Kings and 42 Elephants
Author
Angeline Sparagna
Stuart J. Murphy
Elinor J. Pinczes
Margaret Mahy
Page 16 What Students Should Understand
Model Division Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.6 How to make a model for division. • Divide by forming equal groups. Page 17 What Students Should Understand
Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Division and Mental Math 5.NBT.6 How to divide mentally. • Use basic facts and patterns. • Connect multiplication and division using fact families and inverse operations. Page 18 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Estimate Quotients 5.NBT.6 How to estimate quotients. • Use compatible numbers. • Use fact families. What Students Should Be Able to Do
Page 19 What Students Should Understand
Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Distributive Property 5.NBT.6 How to use the Distributive Property to find quotients of three-­‐digit dividends and one-­‐
digit divisors. • Use a bar diagram. • Add the partial quotients. Page 20 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Multi-Digit Division What Students Should Be Able to Do
5.NBT.6 How to solve division problems that result in two-­‐, three-­‐, and four-­‐digit quotients. • The algorithm used to find one-­‐digit quotients can be used to find larger quotients. Page 21 Mathematics Fifth Grade – Year in Detail Chapter 4: Divide by a Two-­‐Digit Number All of the lessons in Chapter 4 will connect with the theme of Around My School!, which centers around activities such as sports,
clubs, plays and performances, and classroom items. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “What strategies can I Essential Question: use to divide by a two-­‐digit divisor?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
Common Core State Standard Descriptor
5.NBT.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. Standards For Mathematical Practice •
•
•
•
•
•
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Attend to precision.
Use appropriate tools strategically.
Anchor Texts Anchor Text
Cut Down to Size at High Noon: A Math
Adventure
If You Hopped Like a Frog
Pigs Will Be Pigs
City Planning
Author
Scott Sundby
David M. Schwartz
Amy Axelrod
My Math Classroom Library
Page 22 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Multi-Digit Division What Students Should Be Able to Do
5.NBT.6 How to divide by a two-­‐digit divisor. • The algorithm used to find quotients with one-­‐digit divisors can be used to find quotients with two-­‐digit divisors. Page 23 What Students Should Understand Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do Division and Mental Math
5.NBT.6 How to adjust quotients. • Use estimation. • Adjust the quotient higher or lower as needed. Page 24 What Students Should Understand
Model Division Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.6 How to use models for division. • Use base-­‐ten blocks. • Divide by forming equal groups. Page 25 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Estimate Quotients What Students Should Be Able to Do
5.NBT.6 How to estimate quotients. • Use compatible numbers. • Use rounding. Page 26 Mathematics Fifth Grade – Year in Detail Chapter 5: Add and Subtract Decimals All of the lessons in Chapter 5 will connect with the theme of Let’s Explore Technology!, which centers around technology, such as
MP3 players, video games, cell phones, and computers. This is reflected in problem solving and the visuals used throughout the
chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How can I use place Essential Question: value and properties to add and subtract decimals?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
5.NBT.4
5.NBT.7
Common Core State Standard Descriptor
Use place value understanding to round decimals to any place.
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.
Standards For Mathematical Practice •
•
•
•
•
•
•
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Anchor Texts Anchor Text
Coyotes All Around
Sold! A Mathematics Adventure
If You Hopped Like a Frog
Pigs Will Be Pigs
Math Man
Spaghetti and Meatballs for All
Author
Stuart J. Murphy
Nathan Zimelman
David M. Schwartz
Amy Axelrod
Teri Daniels
Marilyn Burns and Gordan Silveria
Page 27 What Students Should Understand
Rounding Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.4 How to use place value to round numbers. • There are different ways to round numbers. • Rounding can be used to estimate sums and differences. Page 28 What Students Should Understand
Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Model Addition 5.NBT.7 How to use models to add decimals. • Models and place value can be used to add decimals to the tenths or hundredths. Page 29 What Students Should Understand
Add Decimals Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.7 How to add decimals. • Line up the decimal points and add the digits in the same place-­‐value position. • Bring the decimal point straight down in the sum. Page 30 Mathematics Fifth Grade – Year in Detail What Students Should Understand
What Students Should Be Able to Do
Properties of Addition 5.NBT.7 How to use properties of addition to add decimals. • The Commutative and Associative Properties of Addition can be used to add decimals mentally. • It is helpful to group decimals together that add to whole numbers. Page 31 What Students Should Understand
Model Subtraction Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.7 How to use models to subtract decimals. • Models and place value can be used to subtract decimals to the tenths or hundredths. Page 32 Mathematics Fifth Grade – Year in Detail Chapter 6: Multiply and Divide Decimals All of the lessons in Chapter 6 will connect with the theme of My Summer Fun!, which centers around fun activities to do in the
summer such as going to the beach, playing sports, going swimming, and flying kites. This is reflected in problem solving and the
visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How is multiplying and Essential Question: dividing decimals similar to multiplying and dividing whole numbers?” Possible Time Frame: 4 weeks Major Cluster Standards CCSS
5.NBT.2
5.NBT.4
5.NBT.5
5.NBT.7
Common Core State Standard Descriptor
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.
Use place value understanding to round decimals to any place.
Fluently multiply multi-digit whole numbers using the standard algorithm.
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.
Page 33 Mathematics Fifth Grade – Year in Detail Standards For Mathematical Practice •
•
•
•
•
•
•
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and express regularity in repeated reasoning.
Anchor Texts Anchor Text
Coyotes All Around
Sold! A Mathematics Adventure
If You Hopped Like a Frog
Pigs Will Be Pigs
Math Man
Spaghetti and Meatballs for All
Author
Stuart J. Murphy
Nathan Zimmerman
David M. Schwartz
Amy Axelrod
Teri Daniels
Marilyn Burns and Gordan Silveria
Page 34 What Students Should Understand
Model Multiplication Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.7 How to use models to multiply decimals. • Models and place value can be used to multiply decimals in the tenths or hundredths position. Page 35 Mathematics Fifth Grade – Year in Detail What Students Should Understand
What Students Should Be Able to Do
Multiply Decimals 5.NBT.7 How to multiply decimals. • Multiply as with whole numbers. • Add the decimal point based on the sum of the decimal places in the factors. Page 36 What Students Should Understand
Properties of Multiplication Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NBT.7 How to use the properties of multiplication to multiply whole numbers and decimals. • The Commutative and Associative Properties of Multiplication can be used to multiply numbers mentally. • Numbers can be multiplied in any order. • The way in which numbers are grouped when they are multiplied does not matter. Page 37 What Students Should Understand
Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Estimate Quotients 5.NBT.7 How to estimate quotients involving decimals. • Round the decimal so that both numbers are compatible, or easy to divide mentally. Page 38 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Divide Decimals What Students Should Be Able to Do
5.NBT.7 How to divide a decimal by a whole number. • Use rounding and compatible numbers to first estimate the quotient. • Place the decimal point directly above the decimal point in the divisor, and then divide as with whole numbers. Page 39 Mathematics Fifth Grade – Year in Detail Chapter 7: Expressions and Patterns All of the lessons in Chapter 7 will connect with the theme of Fun with My Friends, which centers around fun activities with friends
such as going out to dinner, attending sporting events, and riding bicycles. This is reflected in problem solving and the visuals used
throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How are patterns used Essential Question: to solve problems?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
5.OA.1
5.OA.2
5.OA.3
5.G.1
Common Core State Standard Descriptor
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating
them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 +
921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
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.
For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0,
generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms
in the other sequence. Explain informally why this is so.
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).
Page 40 Mathematics Fifth Grade – Year in Detail 5.G.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.
Standards For Mathematical Practice •
•
•
•
•
•
•
•
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Anchor Texts Anchor Text
Amanda Bean’s Amazing Dream
The Fly on the Ceiling: A Math Myth
The Warlord’s Puzzle
Incredible Comparisons
Author
Cindy Neuschwander
Dr. Julie Glass
Virginia Walton Pilegard
Russell Ash
Page 41 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Order of Operations What Students Should Be Able to Do
5.OA.1 How to use the order of operations to simplify expressions. • The order of operations is a set of rules to follow when simplifying an expression with more than one operation. Page 42 What Students Should Understand
Numerical Expressions Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.OA.2 How to write verbal phrases as mathematical expressions. • Use numbers and operation symbols. • Write a phrase in parts. Write verbal phrases as numerical expressions. • Phrase: Subtract 2 from 8, then divide by 3 • Expression: (8 – 2) / 3 Page 43 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Number Patterns What Students Should Be Able to Do
5.OA.3 How to use addition and subtraction to describe and extend a number pattern. • Find a rule that describes the relationship between the numbers in a pattern. • Use the rule to extend the pattern. Page 44 What Students Should Understand
Ordered Pairs Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.G.1; 5.G.2 How to name ordered pairs for points on a coordinate plane. • In (x,y), x tells how far to travel along the horizontal axis. • In (x,y), y tells how far to travel along the vertical axis. Page 45 What Students Should Understand
Patterns in Graphs Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.OA.3; 5.G.2 How to compare numerical patterns graphically. • Use rules to generate patterns. • Graph patterns on a coordinate plane and compare. Page 46 Mathematics Fifth Grade – Year in Detail Chapter 8: Fractions and Decimals All of the lessons in Chapter 8 will connect with the theme of Let’s Play Games and Sports!, which centers around games such as
chess and sports such as basketball. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How are factors and Essential Question: multiples helpful in solving problems?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
5.NF.2
5.NF.3
5.NF.5b
5.NBT.5
Common Core State Standard Descriptor
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. For example, recognize an
incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4
equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want
to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two
whole numbers does your answer lie?
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.
Fluently multiply multi-digit whole numbers using the standard algorithm.
Page 47 Mathematics Fifth Grade – Year in Detail Standards For Mathematical Practice •
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Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Anchor Texts Anchor Text
Give Me Half!
Polar Bear Math: Learning About Fractions
from Klondike and Snow
Fraction Fun
Author
Stuart J. Murphy
Ann White Nagda and Cindy Bickel
David A. Adler
Page 48 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Fractions as Division What Students Should Be Able to Do
5.NF.3 How to use a fraction to represent division. • A fraction represents division of the numerator by the denominator. Page 49 What Students Should Understand
Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Models 5.NF.3 How to use models to represent division. • Models can be used to represent division problems in which the answer is a fraction or a mixed number. Page 50 What Students Should Understand
Simplest Form Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NF.5b How to write a fraction in simplest form. • A fraction is in simplest form when the GCF of the numerator and the denominator is 1. • The simplest form of a fraction is equivalent to the fraction. Page 51 What Students Should Understand
Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Compare Fractions 5.NF.5b How to compare fractions with unlike denominators. • Write equivalent fractions so the denominators of the fractions are the same. • Compare the numerators. Page 52 Mathematics Fifth Grade – Year in Detail What Students Should Understand Use Models What Students Should Be Able to Do 5.NF.5b
How to use models to write a fraction as a decimal. • Use a tenth grid to show tenths. • Use a hundredths grid to show hundreths. Page 53 Mathematics Fifth Grade – Year in Detail Chapter 9: Add and Subtract Fractions All of the lessons in Chapter 9 will connect with the theme of Our Oceans, which centers around animal life and facts related to the
world’s oceans. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How can equivalent Essential Question: fractions help me add and subtract fractions?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
5.NF.1
5.NF.2
Common Core State Standard Descriptor
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.)
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. For example, recognize an
incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 <1/2.
Standards For Mathematical Practice •
•
•
•
•
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Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Anchor Texts Anchor Text
Pizza Counting
How Pizza Came to Queens
Fraction Fun
Minnie’s Diner: A Multiplying Menu
The Missing Piece
Author
Christina Dobson
Dayla Kaur Khalsa
David A. Adler
Dayle Ann Dodds
Shel Silverstein
Page 54 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Model Addition 5.NF.2 How to use fraction tiles to model the sum of fractions. • Fractions that have the same denominators are called like fractions. • Fraction tiles can be used to model the addition of like fractions. What Students Should Be Able to Do
Page 55 Mathematics Fifth Grade – Year in Detail What Students Should Understand
What Students Should Be Able to Do
Like Fractions 5.NF.2 How to add and subtract like fractions. • Add or subtract the numerators and keep the denominator. Page 56 What Students Should Understand
Unlike Fractions Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NF.1 How to add and subtract unlike fractions. • Fractions that have different denominators are called unlike fractions. • Rewrite unlike fractions as equivalent fractions that have the same denominator. Page 57 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Estimate 5.NF.2 How to estimate the sum and difference of mixed numbers. • If the fractional part of a mixed number is less than ½, round the mixed number down to the nearest whole number. • If the fractional part is greater than or equal to ½, round the mixed number up to the nearest whole number. What Students Should Be Able to Do
Page 58 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Mixed Number 5.NF.1 How to add and subtract mixed numbers. • Write equivalent fractions so that the fraction parts of the mixed numbers have the same denominator. • Add or subtract the wholes, and then add or subtract the fractions. What Students Should Be Able to Do
Page 59 Mathematics Fifth Grade – Year in Detail Chapter 10: Multiply and Divide Fractions All of the lessons in Chapter 10 will connect with the theme of In My Kitchen, which centers around cooking, recipes, and baking. This
is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “What strategies can be Essential Question: used to multiply and divide fractions?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
5.NF.4a
5.NF.4b
5.NF.5a
5.NF.5b
5.NF.6
5.NF.7a
5.NF.7b
5.NF.7c
Common Core State Standard Descriptor
Interpret the product (a/b) × q as a part of a partition of q into b equal parts; equivalently, as the result of a sequence of
operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this
equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
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.
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.
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.
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or
equations to represent the problem.
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story
context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and
division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4
÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to
explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
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. For example, how much chocolate
will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Page 60 Mathematics Fifth Grade – Year in Detail Standards For Mathematical Practice •
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Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Anchor Texts Anchor Text
Tiger Math: Learning to Graph from Baby
Tiger
Weather
Mathematics
Nature’s Delicate Balance
Author
Ann Whitehead Nadga and Cindy
Bickel
Seymour Simon
Irving Adler
My Math Classroom Library
Page 61 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Partition a Whole What Students Should Be Able to Do
5.NF.4a How to multiply a whole number and a fraction. • Model the whole number. • Partition the whole into equal parts. Page 62 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Use Models to Multiply 5.NF.4b How to multiply fractions. • Use rectangle with fractional side lengths. • Find the area of a rectangle. What Students Should Be Able to Do
Page 63 What Students Should Understand
Multiply Mixed Numbers Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NF.6 How to solve word problems involving mixed numbers. • Write an equation to represent the problem. • Write the mixed numbers as improper fractions. • Multiply as with fractions. • Simplify before or after multiplying. Page 64 What Students Should Understand
Use Models to Divide Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.NF.7b How to divide a whole number by a unit fraction. • Model the whole number. • Partition the whole into equal parts, labeling each part with a unit fraction. Page 65 Mathematics Fifth Grade – Year in Detail Chapter 11: Measurement All of the lessons in Chapter 9 will connect with the theme of My Favorite Animals, which centers around popular animals, such as
dogs, cats, horses, and elephants. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How can I use Essential Question: measurement conversions to solve real-­‐world problems?” Possible Time Frame: 4 weeks Major Cluster Standards CCSS
5.MD.1
5.MD.2
Common Core State Standard Descriptor
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.
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. For example, given different measurements of
liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were
redistributed equally.
Standards For Mathematical Practice •
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Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Anchor Texts Anchor Text
Measuring Penny
Zachary Zormer: Shape Transformer
Measuring Up!
How Big is the Solar System?
Author
Loreen Leedy
Joanne Reisberg
Sandra Markle
My Math Classroom Library
Page 66 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Customary Units of Length What Students Should Be Able to Do
5.MD.1 How to convert customary units of length. • Inch, foot, and yard are units of length in the customary system. • To convert larger units to smaller units, multiply; to convert smaller units to larger units, divide. Page 67 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Customary Units of Weight What Students Should Be Able to Do
5.MD.1 How to convert customary units of weight. • Ounces, pounds, and tons are units of weight in the customary system. Page 68 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Customary Units of Capacity What Students Should Be Able to Do
5.MD.1 How to convert customary units of capacity. • Capacity is the amount of liquid that a container can hold. • Fluid ounces, cups, pints, quarts, and gallons are units of capacity in the customary system. Page 69 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Graph Measurement Data 5.MD.2 How to use a line plot to represent measurement data. • Make a line plot to display measurements given in fractions of a unit. • Use a line plot to find the fair share, or the amount of each if the total amount were redistributed equally. What Students Should Be Able to Do
Page 70 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Convert Metric Units What Students Should Be Able to Do
5.MD.1 How to convert metric units of measurement. • The metric system is a decimal system of measurement. • To convert metric units, multiply or divide by powers of 10. Page 71 Mathematics Fifth Grade – Year in Detail Chapter 12: Geometry All of the lessons in Chapter 9 will connect with the theme of Let’s Travel, which centers around traveling on vacation, weekend trips,
or to visit family friends. This is reflected in problem solving and the visuals used throughout the chapter.
Once students have completed this chapter they should be able to answer the Essential Question “How does geometry help Essential Question: me solve problems in everyday life?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
5.G.3
5.G.4
Common Core State Standard Descriptor
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.
Classify two-dimensional figures in a hierarchy based on properties.
5.MD.3a
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.
5.MD.3b
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.
5.MD.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
5.MD.5a
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.
5.MD.5b
Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems.
5.MD.5c
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by
adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Page 72 Mathematics Fifth Grade – Year in Detail Standards For Mathematical Practice •
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Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Anchor Texts Anchor Text
Sir Cumference and the Sword in the Cone
Measure with Metric
Million to Measure
How Tall, How Short, How Far Away?
Geometry
Matter All Around
Author
Cindy Neuschwander
Franklin Mansfield Branley
David M. Schwartz
David A. Adler
Lucille Caron and Phillip M. St.
Jacques
My Math Classroom Library
Page 73 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Polygons What Students Should Be Able to Do
5.G.4 How to classify polygons. • By the number of sides and the number of angles. • If sides are congruent and angles are congruent, a polygon is regular. Page 74 What Students Should Understand
Triangles Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
5.G.3; 5.G.4 How to classify triangles. • Use side measures to classify triangles, as isosceles, equilateral, or scalene. • Use angle measures to classify triangles as acute, right, or obtuse. Page 75 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Quadrilaterals 5.G.4 How to classify quadrilaterals. • Determine if there are any right angles. • Determine if sides are parallel or congruent. What Students Should Be Able to Do
Page 76 What Students Should Understand
Shared Attributes 5.G.3 How to use attributes to describe two-­‐
dimensional figures. • All the attributes of a parallelogram also belong to rectangles, rhombi, and squares. • All the attributes of a rectangle and a rhombus also belong to squares. Mathematics Fifth Grade – Year in Detail What Students Should Be Able to Do
Page 77 Mathematics Fifth Grade – Year in Detail What Students Should Understand
Volumes 5.MD.5 How to find the volume of prisms. • Use unit cubes. • Apply formulas. What Students Should Be Able to Do
Page 78