White Oak Elementary School
Third Grade
Traditional Pathway
Mathematics at a Glance
Numbers and Operations in Base Ten
Mathematics Third Grade Traditional Pathway – Year at a Glance Operations and Algebraic Thinking
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Place Value
Addition
Subtraction
Understanding
Multiplication
Understand
Division
Multiplication and
Division Patterns
2 Weeks
3.NBT.1
3.NBT.2
3.NBT.3
3 Weeks
3.NBT.2
3.OA.9
2 Weeks
3.NBT.2
3.OA.8
2 weeks
3.OA.1
3.OA.3
3.OA.5
3.OA.8
2 weeks
3.OA.2
3.OA.4
3.OA.6
3.OA.7
3 weeks
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
3.OA.9
Vocabulary
Vocabulary
Vocabulary
Vocabulary
Vocabulary
Vocabulary
digit; expanded
form; place value;
standard form; word
form; round
Properties of
addition:
Associative,
Commutative;
Identity; pattern;
estimate;
reasonable; regroup;
unknown; bar
diagram
regroup; inverse
operation
division; divide;
partition; division
sentence; repeated
subtraction;
dividend; divisor;
quotient; inverse
operations; related
facts; fact family
multiple
Assessment
•
Assessment
•
Assessment
•
equal groups;
multiplication;
multiplication
sentence; multiply;
factors; product;
array;
Communicative
Property of
Multiplication;
combination; tree
diagram
Assessment
•
Assessment
•
Assessment
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Page 2 Mathematics Third Grade Traditional Pathway – Year at a Glance Operations and Algebraic Thinking
Measurement and Data
N/O - Fractions
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Multiplication and
Division
Apply
Multiplication and
Division
Properties and
Equations
Fractions
Measurement
Represent and
Interpret Data
3 Weeks
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
3.OA.9
3 Weeks
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
3.OA.9
3 Weeks
3.OA.5
3.OA.7
3.OA.8
3 Weeks
3.NF.1
3.NF.2
3.NF.2a
3.NF.2b
3.NF.3
3.NF.3a
3.NF.3b
3.NF.3c
3.NF.3d
3.G.2
2 Weeks
3.MD.1
3.MD.2
3.OA.3
3 Weeks
3.MD.3
3.MD.4
3.OA.3
Vocabulary
Vocabulary
Vocabulary
Vocabulary
Known fact;
decompose; Identity
Property of
Multiplication; Zero
Property Of
Multiplication
review vocabulary
for chapters 1-7
Distributive
Property;
Associative Property
of Multiplication;
operations;
expression;
evaluate; variable;
equation
fraction; unit
fraction; numerator;
denominator;
equivalent fractions
Capacity; liquid
volume; liter; metric
unit; milliliter; unit;
gram; kilogram;
mass; analog clock;
digital clock; time
interval
Data; frequency
table; survey; tally
marks; tally chart;
picture graph;
analyze; pictograph;
interpret; key; bar
graph; scale; line
plot; half inch;
quarter inch
Assessment
Assessment
Assessment
Assessment
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•
•
•
•
•
Page 3 M/D (continued)
Geometry
Chapter 13
Chapter14
Perimeter and Area
Geometry
3 Weeks
3.MD.5
3.MD.5a
3.MD.5b
3.MD.6
3.MD.7
3.MD.7a
3.MD.7b
3.MD.7c
3.MD.7d
3.MD.8
Vocabulary
perimeter; area; unit
square; square unit;
area; formula;
composite figure
2 Weeks
3.G.1
3.G.2
Assessment
•
Mathematics Third Grade Traditional Pathway – Year at a Glance Vocabulary
Angle; vertex; right
angle; ray; endpoint;
polygon; pentagon;
hexagon; octagon;
triangle; attribute;
right triangle;
parallelogram;
parallel; square;
rectangle; rhombus;
trapezoid
Assessment
•
Page 4 Mathematics Third Grade Traditional Pathway – Year in Detail Summary of Year for Third Grade Mathematics In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and
division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of
rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.
Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups,
arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group
situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of
whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By
comparing a variety of solution strategies, students learn the relationship between multiplication and division.
Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use
fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole.
For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon
because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to
represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies
based on noticing equal numerators or denominators.
Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area
required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that
rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students
connect area to multiplication, and justify using multiplication to determine the area of a rectangle.
Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these
with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.
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 Third Grade Traditional Pathway – Year in Detail Third Grade Overview Operations and Algebraic Thinking
Numbers and Operations in Base Ten
Measurement and Data
• Represent and solve problems
involving multiplication and division.
• Understand properties of
multiplication and the relationship
between multiplication and division.
• Multiply and divide within 100.
• Solve problems involving the four
operations and identify and explain
patterns in arithmetic.
• Use place value understanding and
properties of operations to perform
multi-digit arithmetic.
• Solve problems involving
measurement and estimation of
intervals of time, liquid volumes, and
masses of objects
• Represent and interpret data.
• Geometric measurement;
understand concepts of area and
relate area to multiplication and to
addition.
Numbers and Operations - Fractions
• Develop understanding of fractions
as numbers.
Geometry
• Reason with shapes and their
attributes.
Page 6 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 1: Addition Concepts All of the lesson in Chapter 1 will connect with the theme of Let’s Travel!, which centers around means of travel and travel
destinations. 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 numbers be Essential Question: expressed, ordered, and compared.?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
Common Core State Standard Descriptor
3.NBT.1
Use place value understanding to round whole numbers to the nearest 10 or 100.
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or
the relationship between addition and subtraction.
Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place
value and properties of operations.
3.NBT.2
3.NBT.3
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
Author
The Magic School Bus Lost in the Solar System
Earth Day – Hooray!
Betcha!
Pigs Will Be Pigs
Joanna Cole
Stuart J. Murphy
Stuart J. Murphy
Amy Axelrod
Animal Habitats
My Math Classroom Library
Page 7 What Students Should Understand
Place Value Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.NBT.1; 3.NBT.2; 3.NBT.3 How to use a place value chart. • The value of a digit in the thousands place is 1,000 times the digit. • The value of a digit in the hundreds place is 100 times the digit. • The value of a digit in the tens place is 10 times the digit. Write Multi-Digit Numbers 3.NBT.1; 3.NBT.2; 3.NBT.3 How to use place value to write different forms of numbers. • Standard form shows only digits. • Expanded form show the sum of the value of the digits. • Word form uses words. Page 8 What Students Should Understand
Compare and Order Numbers Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.NBT.1; 3.NBT.2; 3.NBT.3 How to use place value to compare and order numbers. • Use the symbols <, >, and = to compare two numbers. • Use a place-­‐value chart or number line to compare and order numbers. Rounding 3.NBT.1 How to use place value to round numbers. • Use a place-­‐value chart, number line, or rounding rules to round numbers. • Rounded numbers are easier to work with when solving problems. Page 9 What Students Should Understand
Four-Step Plan Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.NBT.1 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 Third Grade Traditional Pathway – Year in Detail Chapter 2: Addition All of the lessons in Chapter 2 will connect with the theme of My Transportation!, which centers around all modes of transportation,
such as a subway, school bus, or pogo stick. 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 place value help me add larger numbers?" Possible Time Frame: 3 weeks Essential Question: Major Cluster Standards CCSS
3.NBT.2
3.OA.9
Common Core State Standard Descriptor
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or
the relationship between addition and subtraction.
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties
of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be
decomposed into two equal addends.
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
Betcha!
The Smushy Bus
Zero: Is It Something? Is It Nothing?
Ecosystems All Around
Author
Stuart J. Murphy
Leslie Helakowski
Claudia Zaslavsky
My Math Classroom Library
Page 11 What Students Should Understand
Properties of Addition Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.NBT.2 How to use properties of addition to solve problems. • The order in which numbers are added does not change the sum. • The way in which addends are grouped does not change the sum. Estimate Sums 3.NBT.2 How to use place value to estimate sums. • An estimate is a number close to the actual number. • When estimating sums, addends can be rounded to any place value. • When estimating sums, round both addends to the same place value. • Round to the greatest place value that is shared by both addends when unsure which place to round to. Page 12 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Three- and Four-Digit Addition What Students Should Be Able to Do
3.NBT.2 How to use place value to add three-­‐ and four-­‐digit numbers. • Begin by adding the ones, then the tens, and so on. • Regroup if necessary. Reasonable Answers 3.NBT.2 How to determine whether an answer is reasonable. • Estimation strategies and mental math can be used to check the reasonableness of answers. Page 13 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Arithmetic Patterns What Students Should Be Able to Do
3.OA.9 How to identify and explain number patterns involving addition. • A place-­‐value chart can be used to identify arithmetic patterns. • The properties of addition rely on patterns to add. Page 14 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 3: Subtraction All of the lessons in Chapter 3 will connect with the theme of Activities I Do For Fun!, which centers around enjoyable activies and
games, such as riding a scooter, playing soccer, and picking apples. 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 the operations Essential Question: of subtraction and addition related?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
3.NBT.2
3.OA.8
Common Core State Standard Descriptor
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction
Solve two-­‐step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Standards For Mathematical Practice •
•
•
•
•
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. Use appropriate tools strategically. Anchor Texts Anchor Text
Math Curse
Subtraction Made Easy
The Action of Subtraction
Food, Energy, and You
Author
John Scieszka
Rebecca Wingard-Nelson
Loreen Leedy
My Math Classroom Library
Page 15 What Students Should Understand
Use Mental Computation to Subtract Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.8 How to use mental math to solve subtraction problems. • One way to subtract mentally is to break up the smaller numbers into parts. • Another way to subtract mentally is to make one number a 10 or 100. Estimate Differences 3.OA.8 How to estimate differences. • Rounding can be used to estimate differences. • There are different places to round numbers. Page 16 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Use Addition to Check 3.NBT.2 How to use addition to check a subtraction problem. • Addition and subtraction are inverse operations because they undo each other. • All subtraction problems can be checked by using addition. What Students Should Be Able to Do
Page 17 What Students Should Understand
Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
Subtract with Regrouping 3.NBT.2 How to subtract numbers with regrouping. • Begin by subtracting the ones, then the tens, and so on, regrouping if needed. • Check by adding. Page 18 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Subtract Four-Digit Numbers What Students Should Be Able to Do
3.NBT.2 How to subtract with greater numbers. • First, estimate the difference by rounding. • Subtract the ones and tens, and then the hundreds and thousands, regrouping as needed. Page 19 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 4: Understand Multiplication All of the lessons in Chapter 4 will connect with the theme of My Favorite Foods!, which centers around some of children’s healthy food
favorites, such as “ants on a log,” spaghetti, and frozen yogurt. 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 does multiplication Essential Question: mean?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
3.OA.1
3.OA.3
3.OA.5
3.OA.8
Common Core State Standard Descriptor
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects can be expressed as 5 × 7.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem.
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also
known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10,
then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5
+ 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for
the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including
rounding.
Page 20 Mathematics Third Grade Traditional Pathway – 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 tool strategically. Attend to precision. Look for and make use of structure. Anchor Texts Anchor Text
Author
One Hundred Angry Ants
Mooove Over! About Counting by Twos
Two of Everything
A Grain of Rice
Elinor J. Pinczes
Karen Magnuson Beil
Lily Toy Hong
Helena Clare Pittman
Making a Budget
My Math Classroom Library
Page 21 What Students Should Understand
Repeated Addition Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.1 How to interpret the product of whole numbers. • Multiply by using a set of equal groups. • Multiply by using repeated addition. Page 22 What Students Should Understand Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do Arrays and Multiplication
3.OA.3 How to use arrays to represent multiplication. • Arrays can be used to model the multiplication of two numbers. • The number of objects in each row and the number of objects in each column represent the numbers that are being multiplied. Page 23 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Commutative Property What Students Should Be Able to Do
3.OA.5 How to use the Commutative Property of Multiplication to solve problems. • The order in which factors are multiplied does not change the product. Multiplication Number Sentences 3.OA.8 How to solve word problems by writing multiplication number sentences. • Two number sentences can be written to represent a situation that involves the multiplication of two numbers. Page 24 What Students Should Understand
Combinations Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.3 How to use multiplication to solve real-­‐life problems. • Multiplication is used to solve word problems involving combinations. • A table or tree diagram can be used to show all the combinations in a situation. Page 25 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 5: Understand Division All of the lessons in Chapter 5 will connect with the theme of Careers in Our World!, which centers around jobs students may hold,
such as dog grooming, or careers they may develop as adults. 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 does division Essential Question: mean?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
3.OA.2
3.OA.4
3.OA.6
3.OA.7
Common Core State Standard Descriptor
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56
objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of
8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as
56 ÷ 8.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example,
determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when
multiplied by 8.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.
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
A Grain of Rice
Animal Habitats
Author
Helena Clare Pittman
My Math Classroom Library
Page 26 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Model Division What Students Should Be Able to Do
3.OA.2 How to model division problems. • Objects separated, one at a time, into equal groups can be used to show division. • Making equal groups of certain quantity can be used to find the number of groups. Equal Sharing 3.OA.2 How to write a division sentence that describes equal sharing. • A quotient describes how many equal groups there are or how many objects are in each group. Page 27 What Students Should Understand
Repeated Subtraction Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.7 How to use repeated subtraction to find the quotient of a division problem. • The operations of subtraction and division are related. • One way to divide numbers is to use repeated subtraction. Page 28 What Students Should Understand
Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
Inverse Operations 3.OA.7 How to write related multiplication and division sentences. • Multiplication and division are inverse operations because they undo each other. • One type of fact family usually contains two multiplication sentences and two division sentences using the same numbers. Page 29 What Students Should Understand
Find the Unknown Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.4 How to find the unknown in a division problem. • Use models. • Use multiplication facts. Page 30 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 6: Multiplication and Division Patterns All of the lessons in Chapter 6 will connect with the theme of Let’s Collect!, which centers around collections and groups of objects,
such as toy cars, stamps, and trading cards. 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 is the importance Essential Question: of patterns in learning multiplication and division?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
Common Core State Standard Descriptor
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects can be expressed as 5 × 7.
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56
objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of
8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as
56 ÷ 8.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example,
determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also
known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10,
then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 ×
(5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when
multiplied by 8.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.
Page 31 3.OA.9
Mathematics Third Grade Traditional Pathway – Year in Detail Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties
of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be
decomposed into two equal addends.
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
Annie and the Old One
How Many Feet in the Bed
A Remainder of One
Minnie’s Diner
Miska Miles
Diane Johnston
Elinos Princzes
Dayle Ann Dodds
Sea Squares
Craft Store Supplies
Joy N. Hulme
My Math Classroom Library
Page 32 What Students Should Understand
Arrays and Drawings Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.3; 3.OA.5 How to multiply using arrays, bar diagrams, and drawings. • The number of columns and rows in an array represents the two factors being multiplied. • Draw bar diagrams. • An array is a model for two related multiplication facts. Inverse Operations 3.OA.6; 3.OA.7 How to solve division problems by using multiplication facts. • Use multiplication facts to find the unknown number in a division problem. Page 33 What Students Should Understand
Equal Groups Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.1; 3.OA.2; 3.OA.3 How to divide using equal groups. • Use counters divided into equal groups. • Write a related multiplication fact. Skip Counting 3.OA.9 How to use skip counting and repeated addition to multiply. • Multiplying by a number is the same as skip counting by that number. • Patterns in numbers can be observed by skip counting. Page 34 What Students Should Understand
Multiples of 10 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.4 How to mentally multiply a one-­‐digit number by multiples of ten. • Use basic facts and patterns of zeros. • Use place value. • Use properties. Page 35 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 7: Multiplication and Division All of the lessons in Chapter 7 will connect with the theme of My Fun Friends!, which centers around activities friends enjoy doing
together, such as climbing trees, playing soccer, and riding skateboards. 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 “Which strategies can be Essential Question: used to learn multiplication and division facts?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
Common Core State Standard Descriptor
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects can be expressed as 5 × 7.
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56
objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of
8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as
56 ÷ 8.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example,
determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also
known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10,
then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 ×
(5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when
multiplied by 8.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.
Page 36 3.OA.9
Mathematics Third Grade Traditional Pathway – Year in Detail Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties
of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be
decomposed into two equal addends.
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
The Great Divide
A Remainder of One
Craft Store Supplies
Author
Dayle Ann Dodds
Elinos Princzes
My Math Classroom Library
Page 37 What Students Should Understand
Find Unknown Numbers 3.OA.4 How to find the unknown number in a multiplication sentence. • Use models. • Use related multiplication facts and properties. Skip Count Backwards Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.3 How to use a number line to divide numbers. • On a number line, start at the dividend and skip count backward to 0, by the number of the divisor. Page 38 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Use Known Facts What Students Should Be Able to Do
3.OA.4 How to multiply by using a known fact and doubling. • To multiply a number by 4, multiply the number by 2 and double the product. Page 39 What Students Should Understand
Repeated Subtraction Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.7 How to use subtraction to solve a division problem. • The operations of subtraction and division are related. • One way to divide numbers is to use repeated subtraction. Multiplication Properties 3.OA.5 How to use properties of multiplication to solve problems. • The Identity Property of Multiplication states that when a number is multiplied by 1, the product is that number. • The Zero Property of Multiplication state that when a number is multiplied by 0, the product is 0. Page 40 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 8: Apply Multiplication and Division All of the lessons in Chapter 8 will connect with the theme of Small Creatures of our World!, which centers around small animals,
birds, and insects, and the places they inhabit. 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 multiplication Essential Question: and division facts with smaller numbers be applied to larger numbers?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
Common Core State Standard Descriptor
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects can be expressed as 5 × 7.
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56
objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of
8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as
56 ÷ 8.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example,
determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also
known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10,
then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 ×
(5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when
multiplied by 8.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.
Page 41 3.OA.9
Mathematics Third Grade Traditional Pathway – Year in Detail Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties
of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be
decomposed into two equal addends.
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
Math Appeal
How Hungry are You?
A Remainder of One
Populations on the Rise
Author
Greg Tang
Donna Jo Napoli
Elinos Princzes
My Math Classroom Library
Page 42 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Find Unknown Numbers What Students Should Be Able to Do
3.OA.1; 3.OA.3; 3.OA.4 How to find the unknown number in a multiplication or division problem. • Use models. • Use related facts and properties of operation. Number Lines 3.OA.7 How to use a number line to divide numbers. • On a number line, start at the dividend and skip count by the number of the divisor. • Skip count backward to 0. • The number of jumps is the quotient. Page 43 What Students Should Understand
Doubling Known Facts 3.OA.4; 3:OA.9 How to multiply by using a known fact and doubling. • To multiply a number by 6, multiply the other factor by 3 and double the product. Use Properties 3.OA.5; 3.OA.7 How to use properties of operations to solve a multiplication problem. • Use known facts and properties. • The Commutative Property of Multiplication states that factors can be multiplied in any order. Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
Page 44 What Students Should Understand Model Division
Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do 3.OA.3; 3.OA.6
How to use models and arrays to solve multiplication and division problems. • Partition objects into equal groups or use arrays. • Use inverse operations. Page 45 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 9: Properties and Equations All of the lessons in Chapter 9 will connect with the theme of Let’s Work With Tools!, which centers around materials, and tools
needed for building, such as pliers, nails, and springs. 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 properties and Essential Question: equations used to group numbers?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.OA.5
3.OA.7
3.OA.8
Common Core State Standard Descriptor
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also
known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10,
then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 ×
(5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all
products of two one-digit numbers.
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing
for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies
including rounding.
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. Look for and make use of structure. Anchor Texts Anchor Text
Six-Dinner Sid
Ecosystems All Around
Author
Igna Moore
My Math Classroom Library
Page 46 What Students Should Understand
Decompose Factors Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.7 How to use models to decompose factors and find products. • Whole numbers can be decomposed, or taken apart, to make them easier to work with. • After decomposing a number, the products of both parts can be found and added. Distributive Property 3.OA.5 How to use the Distributive Property to multiply two whole numbers. • The Distributive Property combines the operations of multiplication and addition. Page 47 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Associative Property 3.OA.5 How to use the Associative Property of Multiplication to multiply three numbers more easily. • The Associative Property of Multiplication states that the way in which numbers are grouped should not change the product. • Parentheses are used to group numbers when multiplying. • Group numbers that you find easier to multiply. Expressions What Students Should Be Able to Do
3.OA.8 How to evaluate an expression. • A variable is a letter that stands for an unknown quantity in an expression or equation. • To evaluate an expression, replace the variable with a number and then find its value. Page 48 What Students Should Understand
Equations Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.OA.8 How to write an equation to represent a real-­‐world problem. • An equation shows that two expressions are equal. • Words and phrases can suggest which operations to use in an equation. • When finding the unknown, perform the operations in the parentheses first. • If there are no parentheses, perform operations from left to right, multiplying and dividing first. Page 49 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 10: Three-­‐Dimensional Shapes All of the lessons in Chapter 10 will connect with the theme of A Day at My School!, which centers around classroom objects, school
supplies, and daily routines. 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 fractions be Essential Question: used to represent numbers and their parts?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.NF.1
3.NF.2
3.NF.2a
3.NF.2b
3.NF.3
3.NF.3a
3.NF.3b
3.NF.3c
3.NF.3d
3.G.2
Common Core State Standard Descriptor
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a
fraction a/b as the quantity formed by a parts of size 1/b.
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b
equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on
the number line.
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval
has size a/b and that its endpoint locates the number a/b on the number line.
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent,
e.g., by using a visual fraction model.
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in
the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that
comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the
symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example,
partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
Page 50 Mathematics Third Grade Traditional Pathway – 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. Anchor Texts Anchor Text
Eating Fractions
A Fair Share
MATH-terpieces
The Pizza Book
Moon Gazing
Author
Bruce McMillan
Anne Bowman
Greg Tang
Stephen Krensky
My Math Classroom Library
Page 51 What Students Should Understand
Unit Fractions Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.G.2 How to model unit fractions. • Partition a shape into equal parts. • A unit fraction represents the area of each part. How to Model Fractions 3.NF.1 How to model fractions. • In a fraction, the numerator tells the number of equal parts being represented and the denominator tells the total number of equal parts. • Fractions can be used to name part of a whole or part of a set. Page 52 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Fractions on a Number Line What Students Should Be Able to Do
3.NF.2b How to represent fractions on a number line. • Let the interval from 0 to 1 represent the whole. • Partition the number line into equal parts. Equivalent Fractions 3.NF.3b How to model equivalent fractions. • Fractions that name the same part of a whole are equivalent. • Equivalent fractions are the same point on a number line. Page 53 What Students Should Understand
Compare Fractions Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.NF.3d How to compare two fractions. • Use models. • Use the symbols <,>, and = Page 54 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 11: Measurement All of the lessons in Chapter 9 will connect with the theme of Around My House!, which centers around familiar objects found in the
home, time, and home activities. This is reflected in problem solving and the visuals used throughout the chapter.
Essential Question: Once students have completed this chapter they should be able to answer the Essential Question “How do we measure?” Possible Time Frame: 2 weeks Major Cluster Standards CCSS
3.MD.1
3.MD.2
3.MD.3
Common Core State Standard Descriptor
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and
subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).1
Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same
units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and twostep “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw
a bar graph in which each square in the bar graph might represent 5 pets.
Standards For Mathematical Practice •
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•
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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
Why We Measure
The Moon
Clockwise: A Time-Telling Tale
Just in Time
Think About It
Author
Janine Scott
Margaret W. Carruthers
Sara Pinto
Kathryn Cave
My Math Classroom Library
Page 55 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Estimate Capacity What Students Should Be Able to Do
3.MD.2 How to estimate metric units of capacity. • Capacity is the amount of liquid that a container can hold. • Liter and milliliter are units of capacity in the metric system. Estimate Mass 3.MD.2 How to estimate metric units of mass. • Mass is the amount of matter that an object has. • Mass is different than weight. Page 56 What Students Should Understand
Measurement Problems 3.MD.2 How to solve word problems involving capacity and mass. • If necessary, convert so that all measurements in a problem have the same units. • Use the four operations to solve. Telling Time Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.MD.1 How to tell and write time to the nearest minute. • A digital clock shows the time in numbers. • An analog clock has an hour hand and a minute hand. Page 57 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Time Intervals 3.MD.1 How to measure time intervals in minutes. • Add or subtract minutes. • Use number lines. What Students Should Be Able to Do
Page 58 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 12: Represent and Interpret Data All of the lessons in Chapter 9 will connect with the theme of My Outdoor Adventures!, which centers around favorite outdoor
activities of students, such as watching birds and fishing. 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 do we obtain useful Essential Question: information from a set of data?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.MD.3
3.MD.4
3.OA.3
Common Core State Standard Descriptor
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and twostep “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw
a bar graph in which each square in the bar graph might represent 5 pets.
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data
by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the
problem.
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. Anchor Texts Anchor Text
The War Between the Vowels and the
Consonants
The Great Graph Contest
The Best Vacation Ever
Students at Work
Author
Priscilla Turner
Loreen Leedy
Stuart J. Murphy
My Math Classroom Library
Page 59 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Scaled Graphs What Students Should Be Able to Do
3.MD.3 How to represent data using scaled graphs. • A pictograph uses a symbol to represent more than one tally from a tally chart. • A bar graph uses bars of different lengths or heights to show data. Analyze Data 3.MD.3 How to interpret data in graphs. • Find “how many less” and “how many more.” • Find the difference between the greatest and the least values. Page 60 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Draw Line Plots What Students Should Be Able to Do
3.MD.4 How to use a line plot to represent data. • The horizontal scale is marked off in appropriate units. • Xs are drawn above the number line to represent data values. Measurement Data 3.MD.4 How to use a ruler to measure to the nearest half-­‐inch or quarter inch. • There are two half inches in one inch and four quarter inches in one inch. • Fractional parts of an inch can be used for more precise measurements. Page 61 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Display Measurement Data What Students Should Be Able to Do
3.MD.4 How to graph measurement data on a line plot. • The horizontal scale is marked off in appropriate units, including halves and fourths of an inch. • Xs are drawn above the number line to represent data values. Page 62 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 13: Perimeter and Area All of the lessons in Chapter 13 will connect with the theme of Let’s Build Something!, which centers around building projects, such as
building a sandbox, fence, and garden. 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 perimeter and Essential Question: area related and how are they different?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.MD.5
3.MD.5a
3.MD.5b
3.MD.6
3.MD.7
3.MD.7a
3.MD.7b
3.MD.7c
3.MD.7d
3.MD.8
Common Core State Standard Descriptor
Recognize area as an attribute of plane figures and understand concepts of area measurement.
A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to
measure area.
A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Relate area to the operations of multiplication and addition.
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be
found by multiplying the side lengths.
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and
mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a
× b and a × c. Use area models to represent the distributive property in mathematical reasoning.
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and
adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side
lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the
same area and different perimeters.
Page 63 Mathematics Third Grade Traditional Pathway – 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 make use of structure. Look for and express regularity in repeated reasoning. Anchor Texts Anchor Text
Racing Around
The Places We Live
Author
Stuart J. Murphy
My Math Classroom Library
Page 64 What Students Should Understand
Perimeter 3.MD.8 How to find the perimeter of a figure. • Add side lengths. Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
Area 3.MD.5; 3.MD.5a; 3.MD.5b; 3.MD.6; 3.MD.7; 3.MD.8 How to find the area of a figure. • Area is measured in square units. • A figure can be covered by n unit squares with no gaps or overlaps has an area of n square inches. Page 65 Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Understand
Area and Tiling What Students Should Be Able to Do
3.MD.5; 3.MD.5a; 3:MD.5b; 3.MD.6; 3.MD.7; 3.MD.7a; 3.MD.7b How to tile rectangles to find the area. • If a rectangle is not on a grid, the area can be found by tiling it. • The dimensions of a rectangle are called its length and width. Area of Rectangles 3.MD.5; 3.MD.5a; 3.MD.5b; 3.MD.6; 3.MD.7; 3.MD.7a; 3.MD.7b How to use a formula to find the area of a rectangle. • To find the area of a rectangle, multiply the length by the width. • The formula is A = l x w. Page 66 What Students Should Understand
Area of Composite Figures 3.MD.5; 3.MD.7; 3.MD.7b; 3.MD.7d How to decompose a composite figure to find the area. • A composite figure is made up of two or more figures. • Find the area of a composite figure by decomposing it into smaller rectangles and then adding the area of each rectangle. Perimeter and Area Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.MD.5; 3.MD.7; 3.MD.7b; 3.MD.8 How to relate perimeter and area of rectangles. • Two rectangles can have the same perimeter and different areas, or have the same area and different perimeters. Page 67 Mathematics Third Grade Traditional Pathway – Year in Detail Chapter 14: Geometry All of the lessons in Chapter 9 will connect with the theme of Shapes in Our World!, which centers around favorite outdoor activities of
students, such as watching birds and fishing. 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 geometric Essential Question: shapes help me solve real-­‐world problems?” Possible Time Frame: 3 weeks Major Cluster Standards CCSS
3.MD.3
3.MD.4
3.OA.3
Common Core State Standard Descriptor
Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width
of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation
with an unknown factor.
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition
and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the
difference in length between the longest and shortest specimens in an insect collection.
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations,
including problems in which remainders must be interpreted. Represent these problems using equations with a letter
standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation
strategies including rounding.
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
Shape Up! Fun with Triangles and Other
Polygons
Light, Sight, and Colors So Bright
Author
David A. Adler
My Math Classroom Library
Page 68 What Students Should Understand
Polygons Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.G.1 How to classify polygons. • A polygon is a closed two-­‐
dimensional figure made up of three or more sides. • Polygons can be classified by the number of sides and angles. Triangles 3.G.1 How to describe a triangle using its angles and sides. • A triangle may have one right angle, one angle that is greater than a right angle, or two or three angles less than a right angle. • A triangle may have 0, 2, or 3 sides of equal length. Page 69 What Students Should Understand
Quadrilaterals Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
3.G.1 How to classify quadrilaterals. • Determine if opposite angles are the same or if there are any right angles. • Determine if opposite sides are parallel or of equal length. Page 70 What Students Should Understand
Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
Shared Attributes 3.G.1 How to categorize quadrilaterals according to attributes. • Different quadrilaterals share attributes. • Quadrilaterals can be placed in categories based on their attributes. Page 71 What Students Should Understand
Partition Shapes 3.G.2 How to separate a shape into parts with equal areas. • There are different ways to partition shapes into equal parts. • The area of each part can be expressed as a unit fraction of the whole. Mathematics Third Grade Traditional Pathway – Year in Detail What Students Should Be Able to Do
Page 72