



Grade 3, Quarter 2 Unit 3: Problem Solving, Properties of Operations, and Area
Common Core Standards:
Represent and solve problems involving multiplication and division.
3.OA.A.1 Interpret products of whole numbers, (e.g., interpret 5 x 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 x 7.
3.OA.A.2 Interpret wholenumber 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.
3.OA.A.3 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.1
1See CCSS Mathematics Glossary, Table 2 (Also the Instructional Notes)
3.OA.A.4 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 x ? = 48, 5 = __ ÷ 3, 6 x 6 =?
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.B.5 Apply properties of operations as strategies to multiply and divide. 2 Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive property.)
2 Students need not use formal terms for these properties.
3.OA.B.6 Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Multiply and divide within 100.
3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties or operations. By the end of Grade 3, know from memory all products of two onedigit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.D.8 Solve twostep 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.
3.OA.D.9 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.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
3.MD.5.a 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.
3.MD.5.b 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.
addend 
addition 
additive 
area 
area measurement 
area model 
arithmetic patterns 
arrays 
columns 
compose 
decomose 
difference 
decrease 
digit 
divide 
dividend 
division 
divisor 
equal groups/parts 
eqution 
expression 
factor 
fluently 
gap 
increase 
inverse operations 
length 
mental computation 
minuens 
multiplication 
multiply 
product 
properties of operations 
quotient 
reasonableness 
rectilinear 
relationship 
rounding 
square units 
strategies 
subtraction 
subtrahend 
sum 
unknown factor 
unknown quantity 
variable 
width 

Enduring Understandings (Big Ideas):
Enduring understandings go beyond discrete facts or skills. They focus on larger concepts, principles, or processes. They are transferable and apply to new situations within or beyond the subject.
 Multiplication and division are inverse; they undo each other.
 An equal sign represents balance or equivalence.
 When adding or multiplying two numbers, the order in which the two numbers are added or multiplied does not change the sum or product (Commutative Property).
 You can add or multiply numbers regardless of how they are grouped (Associative Property).
 Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products (Distributive Property).
 The commutative, associative, and distributive properties can be used to develop efficient strategies to multiply.
 The region inside a shape is its area and can be measured using square units.
 Area can be found by counting the square units or by multiplying.
 Area is additive when rectilinear figures are broken into parts.
 Area is an attribute used to describe and measure twodimensional figures.
 Interpret measurement of rectangular regions as a multiplicative relationship of the number of square units in a row and the number of rows.
Prior knowledge:
What should my child already know before starting Unit 3???
 Counting on, counting by 5?s,10?s, and 100?s
 Knowledge of strategies for solving word problems
 Composing and decomposing whole numbers.
 Knowledge of skip counting and explain “why” the pattern works.
 Fluently add and subtract within 100.
 Using arrays up to 5 x 5 to model repeated addition.
 Represent and solve problems using addition and subtraction.
 Familiar with shapes and their attributes including rectangles, squares, quadrilaterals, pentagons, hexagons, circles, and rectangles.
Websites:
Literature Connection for Unit 3
 Great Estimations by Bruce Goldstone
 Betcha! Estimating (Mathstart, Level 3 by Stuart L. Murphy)
 Take a Guess: A Look at Estimation (Spyglass Books) by Janine Scott
 The, I Hate Mathematics! by Marilyn Burns
 Safari Park (MathStart 3) by Stuart J. Murphy
 7 x 9 = Trouble! By Claudia Mills
 Math Curse by Jon Scieszka
 The Greedy Triangle by Marilyn Burns
 Sigmund Square Finds His Family by Jennifer TaylorCox
 Times Tables the Fun Way: Book for Kids: A Picture Method of Learning the Multiplication Facts by Judy Liautaud
 Multiplying Menace: The Revenge Of Rumpelstiltskin (A Math Adventure) by Pam Calvert
 My Rows and Piles of Coins by Tololwa M. Mollel
 Divide and Ride (MathStart 3) by Stuart J. Murphy
 2 X 2 = Boo: A Set of Spooky Multiplication Stories by Loreen Leedy
 One Grain Of Rice: A Mathematical Folktale by Demi
 Anno's Mysterious Multiplying Jar by Masaichiro Anno
 One Hundred Hungry Ants by Elinor J Pinczes
 Each Orange Had 8 Slices by Paul Giganti
 Big Truck and Car Word Problems Starring Multiplication and Division (Math Word Problems Solved) by Rebecca WingardNelson
 More M&M's Brand Chocolate Candies Math by Barbara Barbieri McGrath
 Great Estimations by Bruce Goldstone
This concludes info for unit 3.

Grade 3, Quarter 1 Unit 2: Problem Solving, Place Value, Measurement, Data
Common Core Standards covered in Unit 2:
Solve problems involving the four operations, and identify and e
xplain patterns in arithmetic.
3.OA.D.8 Solve twostep word problems using the four operations. Represent these problems using equations witha letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies.
3.OA.D.9 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.
Solve problems involving measurement and estimation
3.MD.A.1 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., byrepresenting the problem on a number line diagram.
3.MD.A.2 Measure and estimate liquid volumes
and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add subtract,multiply, or divide to solve onestep 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.
Represent and interpret data.
3.MD.B.3 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.
Use place value understanding and properties of operations to perform multidigit arithmetic.¹
3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship betweenaddition and subtraction.
3.NBT.A.3 Multiply onedigitwhole numbers by multiples of 10 in the range of 1090 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
add 
addend 
algorithm 
AM 
analog clock 
benchmark number 
categories 
data 
decompose 
digit 
difference 
digital clock 
equation 
estimate 
expanded form 
fluently 
gram 
hour 
hour hand 
hundreds 
intervals 
kilograms 
length 
liter 
long hand 
mass 
measure 
minuend 
minute 
minute hand 
multiples 
number line 
ones 
patterns 
place value 
PM 
Property of Operations 
relationship 
represent 
rounding 
scale 
scaled bar graph 
scaled picture graph 
second 
short hand 
standard form 
standard unit 
strategy 
subtract 
subtrahend 
sum 
survey 
tally 
tens 
unknown side 
volume 
Enduring Understandings (Big Ideas):
Enduring understandings go beyond discrete facts or skills. They focus on larger concepts, principles, or processes. They are transferable and apply to new situations within or beyond the subject.
 Rounding is a process for finding the multiple of 10, 100, etc. closest to a given number.
 Place value can be used to name numbers in different ways.
 Using place value builds understanding when regrouping is necessary.
 An equation shows a balance between what is on the right side and what is on the left side of the equal sign.
 Numbers can be decomposed and recomposed into component parts to add and subtract multidigit numbers efficiently.
 Subtraction takes from the original amount.
 Estimation helps us to determine reasonableness of answers.
 Data displays describe and represent data in alternative ways.
 Graphs convey data in a concise way.
 The key for a picture graph determines the number of pictures needed to represent each number in the set.
 In a bar graph, the scale determines how long the bar needs to be to represent each number in a set of data.
 Properties of operations can explain patterns.
Prior knowledge:
What should my child already know before starting Unit 2???
 Standard and expanded forms of numbers
 Adding 3digit numbers with and without regrouping.
 Subtracting 3digit numbers with and without regrouping.
 Fluency of basic addition and subtraction facts.
 Composing and decomposing numbers
 Counting on and counting by 5s, 10s, and 100s
 Understand that addition and subtraction are inverse operations
 Tell time to the nearest five minutes, hour, half hour and quarter hour using analog and digital clocks.
 Distinguish between a.m. and p.m.
 Use the language “quarter to”, “quarter after”, “fifteen minutes after”, and “fifteen minutes before”.
Literature Connection for Unit 2
 How Much, How Many, How Far, How Heavy, How Long, How Tall is 1000? by Helen Nolan
 The Grapes of Math by Greg Tang
 Lucky Beans by Becky Bertha
 Math Potatoes by Greg Tang
 One Hundred Shoes: A Math Reader (StepintoReading, Step 2) by Charles Ghigna
 Pigs on a Blanket: Fun with Math & Time by Amy Axelrod
 Telling Time: How to Tell Time on Digital and Analog Clocks! by Jules Older
 Kids Time With Father TimeLearn How To Tell Time The Time With Father Time by Daisy Wright
 Animal Word Problems Starring Addition and Subtraction (Math Word Problems Solved) by Rebecca WingardNelson
 Addition the Fun Way Book for Kids: A Picture Method of Learning the Addition Facts by Judy Liautaud
 Domino Addition by Lynette Long
 Count On Clifford by Norman Bridwell
 Animals on Board by Stuart J. Murphy
End of Unit 2...

Grade 3, Quarter 1
Unit 1: Understanding Multiplication and Division, Area
Common Core Standards:
Represent and solve problems involving multiplication and division.
• 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 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 x 7.
• 3.OA.A.2 Interpret wholenumber 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.
• 3.OA.A.3 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.
• 3.OA.A.4 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 x ? = 48, 5 = __ ÷ 3, 6 x 6 =?
Understand properties of multiplication and the relationship between multiplication and division.
• 3.OA.B.5Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 x 4= 4 is known, then 4 x 6 = 24 is also known. (Commutativeproperty of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive property.)
• 3.OA.B.6 Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
• 3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
• 3.MD.C.5.a 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.
• 3.MD.C.5.b A plane figure that can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
• 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft., and improvised units).
• 3.MD.C.7 Relate area to the operations of multiplication and addition.
• 3.MD.C.7.a Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
• 3.MD.C.7.b Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning.
• 3.MD.C.7.c Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.
• 3.MD.C.7.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems.
Mathematical Language: VOCABULARY
Additive 
Area 
Area Model 
Arrays 
Column 
Compose 
Decompose 
Divide 
Dividend 
Division 
Divisor 
Equal Groups/Parts 
Equation 
Expression 
Factor 
Gap 
Improvised Unit 
Length 
Inverse operations 
Multiplication 
Multiply 
NonOverlapping 
NonStandard Unit 
Product 
Overlapping 
Properties of Operations 
Quotient 
Rectangle 
Rectangular arrays 
Rectilinear Figure 
Row 
Square Inch 
Square Centimeter 
Square Foot 
Square Meter 
Standard Unit 
Tiling 
Unit 
Unit Square 
Unknown Quantity 
Variable 

Enduring Understandings (Big Ideas):
Enduring understandings go beyond discrete facts or skills. They focus on larger concepts, principles, or processes. They are transferable and apply to new situations within or beyond the subject.
• Multiplication and division are inverses; they undo each other.
• With whole numbers, as the divisor increases, the quotient decreases.
• An equal sign represents balance or equivalence.
• When multiplying two numbers, the order in which the two numbers are multiplied does not change product (Commutative Property).
• You can add or multiply numbers regardless of how they are grouped (Associative Property).
• Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products (Distributive Property).
• Properties of operations can be used to develop efficient strategies to multiply.
• The region inside a shape is its area and can be measured using square units.
• Area can be found by counting the square units or by multiplying.
• Area is additive when rectilinear figures are broken into parts.
• Area is an attribute used to describe and measure twodimensional figures.
• The area of rectangular regions is a multiplicative relationship of the number of square units in a row and the number of rows.
Websites:
Literature Connection:
• Amanda Bean's Amazing Dream by Cindy Neuschwander
• The Best of Times by Gregory Tang
• Cheetah Math by Ann Whitehead Nagda
• A Remainder of One by Elinor J. Pinczes
• Times Tables the Fun Way: Book for Kids: A Picture Method of Learning the Multiplication Facts by Judy Liautaud
• Multiplying Menace: The Revenge Of Rumpelstiltskin (A Math Adventure) by Pam Calvert
• My Rows and Piles of Coins by Tololwa M. Mollel
• Divide and Ride (MathStart 3) by Stuart J. Murphy
• 2 X 2 = Boo: A Set of Spooky Multiplication Stories by Loreen Leedy
• One Grain Of Rice: A Mathematical Folktale by Demi
• Anno's Mysterious Multiplying Jar by Masaichiro Anno
• One Hundred Hungry Ants by Elinor J Pinczes
• Each Orange Had 8 Slices by Paul Giganti
• Big Truck and Car Word Problems Starring Multiplication and Division
(Math Word Problems Solved) by Rebecca WingardNelson
• More M&M's Brand Chocolate Candies Math by Barbara Barbieri McGrath
• Great Estimations by Bruce Goldstone
• Betcha! Estimating (Mathstart, Level 3) by Stuart L. Murphy
• 7 x 9 = Trouble! By Claudia Mills
• The Greedy Triangle by Marilyn Burns
• The Doorbell Rang by Pat Hutchins
• Spunky Monkeys on Parade by Stuart J. Murphy
• Perimeter, Area, and Volume by David A. Adler
















Website updated on: Wednesday, January 17, 2018







