



Grade 5, Quarter 2, Unit 3:
Number and Operations with Base Ten and Fractions; Measurement and Data
Maryland College and CareerReady Standards (MDCCR Standards):
Use 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.
Perform operations with multidigit 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.*
Represent 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
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
? K5 Teaching Resources: Number Activities with Fractions
http://www.k5mathteachingresources.com/5thgradenumberactivities.html
End of Unit 3
Grade 5, Quarter 2, Unit 2: Place Value, Operations with Decimals, and Volume
Maryland College and CareerReady Standards (MDCCR Standards):
Understanding 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 baseten 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 record the results of comparisons.
5.NBT.A.4  Use place value understanding to round decimals to any place.
Perform operations with multidigit whole numbers and with decimals to hundredths.
5.NBT.B.5  Fluently multiply multidigit whole numbers using the standard algorithm.
5.NBT.B.6 Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit 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.*
Geometric 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 wholenumber 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 wholenumber 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 wholenumber 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 nonoverlapping parts, applying this technique to solve real world problems.
Convert like measurement units within a given measurement system
5.MD.A.1  Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05m), and use these conversions in solving multistep 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 multidigit 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 placevalue 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 multidigit 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 threedigit factor by a twodigit factor. Use place value understanding and properties of operations to perform multidigit 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 onedigit 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 twodimensional shapes.
 Compared and classified shapes by their sides and angles, and connected these with definitions of shapes.
 Built, drew and analyzed twodimensional shapes to deepen their understanding of the properties of twodimensional 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














Website updated on: Wednesday, January 17, 2018








