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Unit 4:
Place Value integrated with

Measurement and Data

 
Common Core Standards: 
heartUse place value understanding and properties of operations to add and subtract.
? 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and / or the relationship between addition and subtraction.
? 2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
? 2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and /or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtract hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
? 2.NBT.B.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.
? 2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations 1.

 
heart? Measure and Estimate Length
? 2.MD.A.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
? 2.MD.A.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
? 2.MD.A.3 Estimate lengths using units of inches, feet, centimeters, and meters.
? 2.MD.A.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

 
heart? Relate Addition and Subtraction to Length
? 2.MD.B.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
? 2.MD.B.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

 
heart? Represent and Interpret Data
? 2.MD.D.9 Generate measurement data by measuring several objects to the nearest whole unit, by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked-off in whole-number units.
? 2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart and compare problems using information presented in a bar graph. 

 
Addition Bar Graph Centimeter Data Differences
Drawing Equations Equally Spaced Estimate Foot
Inch Length Line Plot Longer Measure
Measuring tape Measurement Tools Meter Meter Stick Number Line Diagram
Picture Graph Ruler Size Standard Length Unit Strategy
Subtraction Sums Tools Twice Units
Whole Number Whole Unit Word Problems Yard Stick  
 

Enduring Understanding (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.
  • ? There are place value patterns that can be observed and explained when adding or subtracting 10 or 100 to or from a given number. The patterns support mental computations.
  • ? Patterns and strategies provide generalization for computations. These generalized rules are formalized as the Properties of Operations.
  • ? Understanding the meaning of the equal sign (=) lays the foundation for equality and equivalence in concepts.
  • ? Place value is based on groups or bundles of ten (10 ones = 10 and 10 tens = 100).
  • ? Zeroes in a numbers have meaning.
  • ? Decomposing and composing multi-digit numbers in flexible ways is a necessary foundation for computational estimation and exact computation.
  • ? Developing number sense of how numbers relate to each other supports the understanding of reasonableness of solutions.
  • ? Before anything can be measured meaningfully, it is necessary to understand the attribute to be measured.
  • ? Measurement involves a comparison of an attribute of an item with a unit that has the same attribute. Lengths are compared to units of length (inches, feet, yards, centimeters, or meters. )
  • ? Standard length units are a consistent distance: inch, centimeter, foot, yard or meter.
  • ? The length of objects can be measured using customary units (inch, foot, yard).
  • ? The length of objects can be measured using metric units (centimeter, meter).
  • ? The relationship between one unit to another unit may be compared by measuring an object with each unit. For example, something that measures 12 inches could also be expressed as 1 foot.
  • ? Estimation of measures and the development of benchmarks for frequently used units of measure help children increase their familiarity with units to prevent unreasonable measurements.
  • ? A reasonable estimate is one that is close to the actual measurement.
  • ? Smaller units such as inches or centimeters would be an appropriate unit to measure shorter items such as the length of a paper clip.
  • ? A yard or meter would be an appropriate unit to use when measuring the length of a longer item, such as the length of a classroom.
  • ? A ruler, yardstick, and a meter stick are special types of number lines that are used for measurement.
  • ? A ruler, yardstick, and a meter stick are tools with standard units used for linear measurement.
  • ? A number line has evenly spaced points corresponding to the numbers.
  • ? An open number line does not always have to start at ?0? or count by ?1‘s?.
  • ? Data are gathered and organized in order to answer questions.
  • ? Different types of graphs provide different information about the data.
  • ? Graphs can provide a sense of the shape of the data to show the big picture of the data. 

Prior knowledge: 

 
What should my child already know before starting Unit 4???
Students in Grade 1:
Literature Connection for Unit 4
 
  • ? Elevator Magic by Stuart J. Murphy
  • ? Safari Park by Stuart J. Murphy
  • ? Ready, Set, Hop by Stuart J. Murphy
  • ? Double the Ducks by Stuart J. Murphy
  • ? Two of Everything by Lily Toy Hong
  • ? Ten Red Apples by Pat Hutchins
  • ? Quack and Count by Keith Baker
  • ? How Many Snails by Paul Giganti
  • ? One Hundred Angry Ants by Elinor J. Pinczes
  • ? Remainder of One by Elinor J. Pinczes
  • ? Each Orange Had 8 Slices by Paul Giganti
  • ? How Tall, How Short, How Far Away by David Adler
  • ? Length by Henry Pluckrose
  • ? How Big Is a Foot by Rolf Myller
  • ? Inchworm and a Half by Elinor J. Pinczes
  • ? Measuring Penny by Loreen Leedy
  • ? Actual Size by Steve Jenkins
  • ? Life-Size Zoo by Toyofumi Fukuda
  • ? The Great Graph Contest by Loreen Leed
 

 
---------------------------------------------------------------------------
Grade 2, Quarter 2, Unit 3: Add and Subtract Using Strategies; Telling Time; Counting Money 
Common Core Standards:
heartRepresent and solve problems involving addition and subtraction
2.OA.A. 1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 
 
heartAdd and subtract within 20
2.OA.B.2 Add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.
 
heartWork with equal groups to gain a foundation for multiplication.
2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as the sum of two equal addends.
2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

 
heartUnderstand place value
2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
2.NBT.A.1a 100 can be thought of as a bundle of ten tens — called a ?hundred.?
2.NBT.A.1b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

 
heartUse place value understanding and properties of operations to add and subtract.
2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and / or the relationship between addition and subtraction.
2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.B.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.
2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. 
addends adding to addends A.M. analog clock array
base ten numerals bills bundle of ten cent sign (¢) cents columns
compare comparing comparison compose concrete models count
decompose difference digit digital clock dimes dollar
dollar bill dollar sign $ empty or open number line equal to (=) equations even
expanded form explain flats hundreds less than (<) mental strategies
minute hand minutes nickels number line number names odd
one-step word problems ones pairs pennies place place value
property of operations memory P.M. putting together quarters repeated addition
rods rows skip count solve strategies subtraction
sum symbols two-step word problems take from taking apart tens
tell time units        
 

Enduring Understanding (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.
  • Real world situations can be represented symbolically and visually with models.
  • Operations create relationships between quantities. These can be represented with numbers and symbols.
  • There can be different strategies to solve a problem, but some are more effective and efficient than others.
  • The context of a problem determines the reasonableness of a solution.
  • Computation involves combining, taking apart and comparing numbers using a variety of strategies.
  • Addition can be thought of as physically or conceptually placing two or more quantities together.
  • Subtraction can be thought of as taking an amount away from a given quantity, comparing two quantities or finding a missing part given the whole and the other part.
  • The operations are related to each other. Addition and Subtraction are inverse operations. Each undoes the other.
  • Addition names the whole in terms of the parts, and subtractions names a missing part.
  • Number relationships provide the foundation for strategies to remember basic facts or figure out unknown facts from those already known.
  • There are place value patterns that can be observed and explained when adding or subtracting 10 or 100 to or from a given number. The patterns support mental computations.
  • Patterns and strategies provide generalization for computations. These generalized rules are formalized as the Properties of Operations.
  • Understanding the meaning of the equal sign (=) lays the foundation for equality and equivalence in concepts.
  • Place value is based on groups of ten (10 ones = 10 and 10 tens = 100).
  • The digits in each place represent amounts of hundreds, tens, or ones (e.g. 853 is 8 hundreds + 5 tens + 3 ones).
  • Zeroes in a numbers have meaning.
  • The number system has structure in which patterns can be recognized and explained.
  • Using visual models and drawings support the development of reasoning and number sense. Visual models and drawings can be converted into written equations.
  • Decomposing and composing multi-digit numbers in flexible ways is a necessary foundation for computational estimation and exact computation.
  • Time and money have distinct attributes that can be measured.
  • Being able to tell time and count money are critical life skills. 

Prior knowledge: 

 
What should my child already know before starting Unit 3???
Students in Grade 1:
  • Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • Apply properties of operations as strategies to add and subtract 1 Examples: If 8+3 = 11 is known, then 3+8=11 is also known. (Commutative property of addition.) To add 2+6+4 the second two numbers can be added to make a ten, so 2+6+4 = 2+10 = 12 (Associative property of addition.)
  • Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
  • Relate counting to addition and subtraction (e.g. by counting on 2 to add 2).
  • Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten (e.g., 8+6 = 8+2+4 =10+4 =14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 – 3 – 1 =10 -1=9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or know sums (e.g., adding 6 +7 by creating the known equivalent 6 + 6 + 1 = 12+1= 13).
  • Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7=8-1, 5 +2 = 2+5, 4+1=5+2
  • Understand that the two digits of a two-digit number represent amounts of tens and ones.
  • Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8+? = 11, 5 = ? - 3, 6+6= ?
  • Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
  • Understand that the two digits of a two-digit number represent amounts of tens and ones.
  • Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
  • Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
  • Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
  • Subtract multiples of 10 in the range of 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • Tell and write time in hours and half-hours using analog and digital clocks.
  • There is no prior formal experience with money in Kindergarten or Grade 1 
 
 
Websites to support instruction:
Literature Connection for Unit 3
  • Elevator Magic by Stuart J. Murphy
  • Safari Park by Stuart J. Murphy
  • Ready, Set, Hop by Stuart J. Murphy
  • Double the Ducks by Stuart J. Murphy
  • Two of Everything by Lily Toy Hong
  • Ten Red Apples by Pat Hutchins
  • Quack and Count by Keith Baker
  • How Many Snails by Paul Giganti
  • One Hundred Angry Ants by Elinor J. Pinczes
  • Remainder of One by Elinor J. Pinczes
  • Each Orange Had 8 Slices by Paul Giganti
  • Twelve Ways to Get to 11 by Eve Merriam
  • Animal on Board by Stuart J. Murphy
  • Moira‘s Birthday by Robert Munsch
  • 100th Day Worries by Margery Cuyler
  • 100 Days of School by Trudy Harris
  • The King‘s Commissioners by Aileen Friedman
     ·  Clocks and More Clocks by Pat Hutchins
  • It‘s About Time by Stuart J. Murphy
  • Bats Around the Clock by Kathi Appelt
  • Clockwise by Sara Pinto
  • I.Q. It‘s Time by Mary Ann Fraser
  • 10 Minutes Till Bedtime by Peggy Rathman
  • Frog and Toad Together: The Garden by Arnold Lobel
  • Every Minute on Earth: Fun Facts That Happen Every 60 Seconds by Steve and Matthew Murrie
  • The Purse by Kathy Caple
  • Alexander, Who Used to Be Rich Last Sunday by Judith Viorst
  • The Penny Pot by Stuart J. Murphy
  • Bunny Money by Rosemary Wells
  • On Market Street by Arnold Lobel 
---------------------------------------------------------------------------------------------
Grade 2, Quarter 2
Unit 2: Measurement and Data
Common Core Standards: 
heartMeasure and Estimate Length
2.MD.A.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.A.3 Estimate lengths using units of inches, feet, centimeters, and meters.
2.MD.A.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

heartRelate Addition and Subtraction to Length
2.MD.B.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
 heartRepresent and Interpret Data
2.MD.D.10 Draw a picture graph and bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart and compare problems using information presented in a bar graph. 


 

 
addition bar graph centimeter
data drawing differences
equations equally spaced estimate
foot inch length
longer measure measuring tape
measurement tool meter meter stick
number line diagram ruler size
standard length unit subtraction sums
tools twice units
whole number whole unit word problems
yard stick    

Enduring Understanding (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.
  • Before anything can be measured meaningfully, it is necessary to understand the attribute to be measured.
  • Measurement involves a comparison of an attribute of an item with a unit that has the same attribute. Lengths are compared to units of length (inches, feet, yards, centimeters, or meters.)
  • Standard length units are a consistent distance: inch, centimeter, foot, yard or meter.
  • The relationship between one unit to another unit may be compared by measuring an object with each unit. For example: something that measures 12 inches could also be expressed as 1 foot.
  • Estimation of measures and the development of benchmarks for frequently used units of measure help children increase their familiarity with units to prevent unreasonable measurements.
  • Smaller units such as inches or centimeters would be a good unit to measure shorter items such as the length of a paper clip.
  • A yard or meter would be an appropriate unit to use when measuring the length of a longer item, such as the classroom.
  • A ruler, yardstick, and a meter stick are special types of number lines that are used for linear measurement.
  • A number line has evenly spaced points corresponding to the numbers.
  • An open number line can be used to show your reasoning. It does not always have to start at ?0? or count by ?1‘s?.
  • Data are gathered and organized in order to answer questions.
  • Different types of graphs provide different visual information about the data.
  • Graphs can provide a sense of the shape of the data to show the big picture of the data. 

Prior knowledge: 

 
What should my child already know before starting Unit 2???
Students in Grade 1:
  • Order three objects by length; compare the lengths of two objects indirectly by using a third object.
  • Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
  • Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 
Websites to support instruction:
National Library of Virtual Manipulatives:
http://nlvm.usu.edu/en/nav/category_g_1_t_1.html
 
NCTM Illuminations K-2 Measurement Activities
http://illuminations.nctm.org/Search.aspx?view=search&type=ls_ac&st=m&gr=Pre-K-2
 
Quantiles: Measurement Activities and Resources
www.quantiles.com/tools/quantile-skill-concept/649/?state=MD
 
Math Booster
http://www.fuelthebrain.com/Game/play.php?ID=27
 
K-5 Math Teaching Resource Measurement and Data
http://www.k-5mathteachingresources.com/2nd-grade-measurement-and-data.html
 
Funbrain Linear Measurement Activities: Centimeters or Inches
http://www.funbrain.com/measure/index.html
Literature Connection for Unit 2
 
 
  • How Tall, How Short, How Far Away by David Adler
  • Length by Henry Pluckrose
  • How Big Is a Foot by Rolf Myller
  • Inchworm and a Half by Elinor J. Pinczes
  • Measuring Penny by Loreen Leedy
  • Actual Size by Steve Jenkins
  • Life-Size Zoo by Toyofumi Fukuda
  • The Great Graph Contest by Loreen Leedy 
End of Unit 2
---------------------------------------------------------------------------

Grade 2, Quarter 1 
Unit 1: Solve Addition & Subtraction; Place Value; Time and Money

Common Core Standards:
heartRepresent and solve problems involving addition and subtraction
2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
Add and subtract within 20
2.OA.A.2 Add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.

heartUnderstand place value
2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
2.NBT.A 1a 100 can be thought of as a bundle of ten tens — called a hundred.
2.NBT.A 1b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
2.NBT.A 2 Count within 1000; skip-count by 5s, 10s, and 100s.
2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and ex
panded form.

heartWork with time and money
2.MD.C.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
2.MD.C.8 S
olve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: if you have 2 dimes and 3 pennies, how many cents do you have?


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  Website updated on: Wednesday, September 26, 2018  
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