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Grade 5, Quarter 2, Unit 3:
Number and Operations with Base Ten and Fractions; Measurement and Data


Maryland College and Career-Ready Standards (MDCCR Standards):
 
heartUse equivalent fractions as a strategy to add and subtract fractions
5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd).
 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result: 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.

 
heartPerform operations with multi-digit whole numbers and with decimals to hundredths
5.NBT.B.7 - Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.*
 
heartRepresent and interpret data
5.MD.B.2 - Make a line plot to display a data set of measurements in fractions of a unit (1/2,1/4, 1/8). Use operations on fractions for this grade to solve problems involving different information presented in the line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
 
*Bold components are the focus of instruction within the standard. 
Mathematical Language:Vocabulary
 
alignment benchmark fraction common denominator
common multiple data decimal
difference denominator equation
equivalent fraction improper fraction Least Common Denominator LCD
Least Common Multiple LCM line plot mixed number
numerator sample scale
simplest form sum survey
unit fraction visual fraction model whole number
 
 












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.
  • Rounding can be used to estimate the sum or difference of fractions.
  • ? Fractions are relative to the size of the whole.
  • ? Fractions and decimals are interchangeable.
  • ? Equivalent fractions represent the same value even if the numerators and denominators are different.
  • ? Fraction amounts greater than 1 can be represented in different ways.
  • ? Fractions are the division of the numerator by the denominator.
  • ? Computation with rational numbers (decimals and fractions) is an extension of computation with whole numbers but introduces some new ideas and processes.
  • ? A fraction is in simplest form when 1 is the only common factor of the numerator and denominator.
  • ? The same fractional part can have different names that are equivalent.
  • ? Use of a variety of strategies including visual models to add and subtract fractions.
  • ? A line plot organizes data on a number line and is useful for showing visually how a data set is distributed.
  • ? Fractional data can be organized and represented on a line plot. The data can be applied to solve real world problems involving addition, subtraction, multiplication, or division. 
  • Understand that proper fractions are numbers that represent quantities less than a whole.
  • In grade 3, students began to represent a fraction by decomposing the fraction as the sum of unit fractions. For example, 3/4 = 1/4 + 1/4 + 1/4. That led to addition of unit fractions with the same denominator. That understanding, combined with knowledge of whole number multiplication, was used to begin multiplication of fractions in the 4th grade.
  • Students should apply their understanding of equivalent fractions developed in fourth grade and their ability to rewrite fractions in an equivalent form to find common denominators.
  • Students should extend their work of partitioning a number line from third and fourth grade. Students need ample experiences to explore the concept that a fraction is a way to represent the division of two quantities.
  • Represent a whole number as a fraction. Example: 12 = . 1 12
  • In grade 4, students made line plots using fractional data and solved problems involving addition and subtraction using the information from the line plot. 
Literature Connection:
  • ? Fraction Action by Loreen Leedy
  • ? Working With Fractions by David A. Adler
  • ? The Wishing Club by Donna Jo Napoli
  • ? Clean Sweep Campers by Lucille Recht Penner
 
Websites:
National Library of Virtual Manipulatives- interactive glossary of manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
 
? Share My Lesson – Number and Operations: Fractions
http://www.sharemylesson.com/article.aspx?storyCode=50005620
 
? K-5 Teaching Resources: Number Activities with Fractions
 http://www.k-5mathteachingresources.com/5th-grade-number-activities.html

 

-------------------------------------------------------------------------End of Unit 3------------------------------------------------------

Grade 5, Quarter 2, Unit 2: Place Value, Operations with Decimals, and Volume 
Maryland College and Career-Ready Standards (MDCCR Standards):
heartUnderstanding Place Value System

5.NBT.A.3 - Read, write, and compare decimals to thousandths.
5.NBT.A.3a - Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).
5.NBT.A.3b - Compare two decimals to thousandths based on meanings of the digits in each place, using >,=, and < symbols to rec
ord the results of comparisons.
5.NBT.A.4 - Use place value understanding t
o round decimals to any place.
 

heartPerform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.B.5 - Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.B.6 -Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and /or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays and/or area models
5.NBT.B.7 - Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.*
 
heartGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
5.MD.C.3 - Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
5.MD.C.3a - A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
5.MD.C.3b - A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.C.4 - Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
5.MD.C.5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
5.MD.C.5a - Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
5.MD.C.5b - Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
5.MD.C.5c - Recognize volume as additive. Find volumes of solid figures composed of two non- overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
 
heartConvert like measurement units within a given measurement system
5.MD.A.1 - Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05m), and use these conversions in solving multi-step real world problems. 
*Bold components are the focus of instruction within the standard.
Mathematical Language:Vocabulary
Area Model Base Ten base ten numeral centimeter compare
concrete model conversions cube cubic units decimal point
difference digits dividend division divisor
edge equal to equation expanded form exponent
exponential notation face formula fraction greater than
hundreds hundredths hundred thousands inch length
less than  meter millimeter millions multiplication
net patterns perimeter place value powers of 10
prism product property of operations Quotient rectangle
rectangular array rectangular prism sum solid figure tenths
ten thousand thousands thousandths verticies volume
whole number        
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.
  • Multiplying and dividing multi-digit decimal numbers is similar to multiplying and dividing whole numbers.
  • Rounding decimals should be “reasonable” for the context of the problem.
  • Decimal numbers can be represented with models.
  • Since place-value is based on the Base 10 system, dividing or multiplying by 10, 100, or 1000 gives the same result as moving the decimal point 1, 2, or 3 places.
  • We measure volume by counting “unit cubes” using cubic cm, cubic in, cubic ft. and improvised cubic units.
  • We can solve real world and mathematical problems involving volume by relating volume to the operations of addition and multiplication. 
  • In fourth grade students fluently add and subtract multi-digit whole numbers using standard algorithm.
  • Students developed understanding of multiplication through using various strategies. While the standard algorithm is mentioned, alternative strategies are also appropriate to help students develop conceptual understanding. The size of the numbers should NOT exceed a three-digit factor by a two-digit factor. Use place value understanding and properties of operations to perform multi-digit arithmetic (Grade 4 NBT 5 and 6).
  • The standards related to volume represent the first time that students begin exploring the concept of volume. Prior student experiences with volume were restricted to liquid volume. In third grade, students begin working with area and covering spaces.
  • In previous grades, students’ experiences with division were limited to dividing by one-digit divisors.
  • Understand the relative sizes of measurement units within one system of units including kilometer, meter, centimeter; kilogram, gram, pound, ounce; liter, milliliter; hour, minute, second. Expressed measurements within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.
  • Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
  • Apply the area and perimeter formulas for rectangles in real world situations.
  • Analyzed and compared properties of two-dimensional shapes.
  • Compared and classified shapes by their sides and angles, and connected these with definitions of shapes.
  • Built, drew and analyzed two-dimensional shapes to deepen their understanding of the properties of two-dimensional shapes. ?
 
Literature Connection:
  • Counting on Frank by Rod Clement
  • Anno’s Mysterious Multiplying Jar by Mitsumasa Anno
  • Can You Count to a Googol? by Robert Wells
  • The Hundred Penny Box (making ten) by Sharon Bell Mathis
  • How Strong Is It? by Ben Hillman
  • Super Bowl Super Touchdowns by James Preller
  • Skyscraper by Lynn Curlee 
Websites:

NCTM Illuminations – Lesson for Conversion of Units
http://illuminations.nctm.org/LessonDetail.aspx?ID=L512
 
National Library of Virtual Manipulatives - interactive glossary of manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html
 
A Maths Dictionary for Kids– interactive, animated, online dictionary
http://www.amathsdictionaryforkids.com/dictionary.html
 
Learn Zillion - Interactive lesson videos, lesson plans and clarifying standards
https://learnzillion.com/resources/17037-5th-grade-math-video-lessons
 
Inside Mathematics- Tasks, videos, and assessment tools
http://insidemathematics.org/index.php/5th-grade
 
Share My Lesson – Number and Operations in Base Ten
 https://sharemylesson.com/grades/grade-5
 
Share My Lesson – Geometry
https://sharemylesson.com/grades/grade-5
 
MSDE Blackboard – unit and lesson plans (number and operations in base ten)
https://msde.blackboard.com/webapps/portal/frameset.jsp?tab_tab_group_id=_216_1
 
MSDE Blackboard – Measurement and Data: Geometry
https://msde.blackboard.com/webapps/portal/frameset.jsp?tab_tab_group_id=_216_1
 
K-5 Teaching Resources: Geometry Activities
http://www.k-5mathteachingresources.com/5th-grade-geometry.html
 
Math-Aids.com – Geometry Resources
http://www.math-aids.com/Geometry/
 
The Teaching Channel – Conversion Lesson Ideas and Videos
https://www.teachingchannel.org/videos?q=grade+5+math+unit+conversions
 
Volume Shape Shoot – interactive game to determine volume in cubic units
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/VolumeShapesShoot.htm)
 
Mom and Me – Finding volume by packing cubes
http://momandmemath.blogspot.com/2013/05/5mdc5-find-volume-by-packing-cubes.html



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Grade 5 Quarter 1
Unit 1: Understanding Place Value and Volume
Maryland College and Career-Ready Standards (MDCCR Standards):


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  Website updated on: Wednesday, January 17, 2018  
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