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Grade 4, Quarter 2  Unit 4: Numbers and Operations – Fractions, Measurement and Data
 Common Core Standards
heartExtend understanding of fraction equivalence and ordering
4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

heartBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
4.NF.B.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
4.NF.B.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
4.NF.B.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
4.NF.B.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

heartUnderstand decimal notation for fractions and compare decimal fractions.
4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
heartSolve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
 4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given 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.
heartRepresent and interpret data
4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. 

 
Benchmark Fraction Common Denominator Compare Decimal
Decompose Denominator Distance Equal
Equation Equivalent Factor Fraction
Fraction Model Greater Than Hour Hundredths
Intervals of Time Kilometer Less than Line Plot
Liquid Volume Mass Measure Measurement
Meter Mile Millimeter Minute
Mixed Number Multiple Multiplication Numerator
Part Products Seconds Unit
Unit Fraction Tenths Visual Model Whole
Whole Number Improper Fraction    
 
 
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.
  • Fractions and decimals are numbers.
  • Fractions can be used to represent numbers equal to, less than or greater than 1.
  • A decimal is another name for a fraction.
  • A fraction describes the division of a whole (region, set, segment) into equal parts.
  • Fractional parts are relative to the size of the whole or the size of the set.
  • The more fractional parts used to make a whole, the smaller the parts.
  • Fractions and decimals can be placed on a number line that is infinite.
  • Fractions and decimals express a relationship between two numbers.
  • Fractions and decimals can be represented visually and in written form.
  • The same fractional amount can be represented by an infinite set of equivalent fractions.
  • Comparisons of fractions or decimals are valid when they refer to the same whole.
  • Fractional amounts can be added or subtracted.
  • Fractions can be composed and decomposed.
  • When adding and subtracting fractions, fractions must refer to the same whole.
  • Benchmark fractions can be used to estimate fractional amounts.
  • Information in a problem can be often shown using a diagram and can be used to solve the problem.
  • A line plot is used to organize and display data.
  • Fractional amounts can be multiplied.
  • Multiplication by a fraction is similar to division of whole numbers.
  • Length and capacity can be estimated and measured in different systems (customary, metric) using different units in each system that is related to each other.
  • The weight of an object is a measure of how heavy an object is.
  • The mass of an object is the quantity of matter in an object.
  • Time can be expressed using different units that are related to each other. 
     
Prior Knowledge:

What does my child need to already know?
  • Knowledge of unit fractions
  • Knowledge of place value
  • Knowledge of basic addition and subtraction facts
  • Knowledge of basic multiplication facts 
     
Literature Connection:
  •  Fraction Action by Loreen Leedy
  •  Fraction Fun by David Adler
  •  Funny and Fabulous Fraction Stories by Dan Greenburg
  •  Painless Fractions, by Alyece Cummings
  •  Give Me Half by Stuart Murphy
  •  Funny and Fabulous Fraction Stories, by Dan Greenburg 

Websites

National Library of Virtual Manipulatives-interactive glossary of manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
 
Maryland Common Core State Curriculum Frameworks
http://www.mdk12.org/instruction/curriculum/mathematics/index.html
 
Fraction Number Line
http://www.mathsisfun.com/numbers/fraction-number-line.html
 
Recognize Equivalent Fractions Using Number lines
http://learnzillion.com/lessons/617-recognize-equivalent-fractions-using-number-lines
 
Fraction Pac-Man
http://www.sheppardsoftware.com/mathgames/fractions/mathman_add_subtract_fractions.htm
 
Adding and Subtracting Fractions
http://www.sheppardsoftware.com/mathgames/fractions/FruitShootFractionsAddition.htm
 
Visual Fractions
http://www.visualfractions.com/
 
Subtracting Fractions With Like Denominators
http://ntnmath.kemsmath.com/D%20Pages/Lesson17.html

 
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Grade 4, Quarter 2, Unit 3:
Operations and Algebraic Thinking, Numbers and

Operations in Base Ten, Measurement and Data

Common Core Standards in Unit 3

 
heartUse the four operations with whole numbers to solve problems
4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.


heartUse place value understanding and properties of operations to perform multi-digit arithmetic
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.



4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-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.


heartGain familiarity with factors and multiples
4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

heartGenerate and analyze patterns
4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
 
heartSolve problems involving measurement and conversion of measurements from a larger unit to a smaller unit
 4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft. is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given 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.
4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 
           Mathematical Language:  Vocabulary
area composite conversion
conversion table dividend division
divisor equation equivalence
estimate factor gram
hour kilogram liter
mass minute multiple
multiplication ounce unit
pattern perimeter place value 
prime pound product
quotient rectangular array remainder
rounding seconds variable
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.
  •  Place value is based on groups of ten.
  • Mathematical expressions represent relationships.
  • Rounding is a strategy for solving problems and estimating.
  • In certain situations, an estimate is as useful as an exact answer.
  • Mental computations are the basis for making reasonable estimates and sensible predictions.
  • Addition and subtraction are inverse operations.
  • Multiplication and division are inverse operations.
  • The context of a problem determines the reasonableness of a solution.
  • A multiplication equation can be interpreted as a comparison.
  • Some real world problems involving joining or separating equal groups or comparison can be solved using multiplication or division.
  • There are two common situations where division may be used: fair sharing and measurement. 
 
Prior Knowledge:
What does my child need to know in order to be

successful in unit 3?
Knowledge of basic addition, subtraction, multiplication and division facts
Knowledge of units of length, volume, mass and time
Knowledge of the attributes of rectangles 

 
Literature Connection:
  • Spaghetti and Meatballs For All! by Marilyn Burns
  • How Big is a Foot by Rolf Myller
  • Inchworm and a Half by Elinor J. Pinczes
  • Jim and the Beanstalk by Raymond Briggs
  • Room For Ripley by Stuart J. Murphy
  • 200 Super Fun, Super Fast Math Story Problems by Dan Greenberg 

Websites
National Library of Virtual Manipulatives-interactive glossary of manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
 
Maryland Common Core State Curriculum Frameworks
http://www.mdk12.org/instruction/curriculum/mathematics/index.html
 
Learn Zillion- Interactive lesson videos for clarifying and teaching standards
http://learnzillion.com/common_core/math/k-8

-------------------------------------------------------------------------------------------------End of Unit 3----------------------------------
__________________________________________________________________________________________
Grade 4, Quarter 2 Unit 2: Numbers and Operations – Fractions 

laughCommon Core Standards:

heartExtend understanding of fraction equivalence and ordering
4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

 
 heartUnderstand decimal notation for fractions and compare decimal fractions.
4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. 
           Mathematical Language:  Vocabulary
bechmark fraction common denominator
compare decimal
denominator equal
equivalent fraction
fraction model greater than
hundredths less than
numerator part
tenths visual model
whole  
 
                                       

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  Website updated on: Wednesday, September 26, 2018  
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