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Grade 3, Quarter 2 Unit 3: Problem Solving, Properties of Operations, and Area
Common Core Standards:
heartRepresent 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 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.
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 =?

 
heartUnderstand 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 unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

 
heartMultiply 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 one-digit numbers.
 
heartSolve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.D.8 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.
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.

 
heartGeometric 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 two-dimensional 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 Taylor-Cox
  • 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 Wingard-Nelson
  • 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:
heartSolve problems involving the four operations, and identify and e
xplain patterns in arithmetic.
3.OA.D.8 Solve two-step 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.

heartSolve 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 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.


heartRepresent and interpret data.
3.MD.B.3 Draw a scaled picture gra
ph and a scaled bar graph to represent a data set with several categories. Solve one and two-step “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.



 
heartUse place value understanding and properties of operations to perform multi-digit 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 one-digitwhole numbers by multiples of 10 in the range of 10-90 (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 multi-digit 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 3-digit numbers with and without regrouping.
  • Subtracting 3-digit 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”. 
 
Websites:
 
 
 
Common Core State Standards
http://www.corestandards.org/
 
Rounding Numbers
http://www.wartgames.com/themes/math/rounding.html
 
Place Value and Rounding
http://www.funbrain.com/tens/index.html

 Math Games for Rounding and Place Value
http://www.ehow.com/way_5182955_math-games-rounding.html
 http://www.wartgames.com/themes/math/rounding.html
 
National Library of Virtual Manipulatives - Interactive Glossary
http://nlvm.usu.edu/en/nav/vlibrary.html
 
Interactive Lessons (register for FREE)
http://learnzillion.com/resources/73932

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 (Step-into-Reading, 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 Time-Learn 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 Wingard-Nelson
  • 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


heartCommon Core Standards:


heartRepresent 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 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 obj
ects 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 
=?

heartUnderstand 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 unknown-factor problem. For example, find 32 ÷ 8 by finding the numb
er that makes 32 when multiplied by 8.

heartGeometric 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 whole-number side l
engths 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 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.

• 3.MD.C.7.c 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 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 non-overlapping rectangles and adding the areas of the non-overlapping 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
Non-Overlapping Non-Standard 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 two-dimensional 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:
Base Ten Blocks and Algorithms
http://mason.gmu.edu/~mmankus/whole/base10/asmdb10.htm#div
 
Math Glossary
http://math.about.com/library/ble.htm
 
Interactive Activities
http://www.pbs.org/teachers/math/

National Library of Virtual Manipulatives - Interactive Glossary
http://nlvm.usu.edu/en/nav/vlibrary.html
 
Word Problem Strategies
http://www.mathstories.com/strategies.htm
 
Multiplication facts
http://www.studyzone.org/testprep/math4/e/multiplicationstrategies3l.cfm

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 Wingard-Nelson

• 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


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  Website updated on: Wednesday, January 17, 2018  
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