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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  
 
                                       
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. 
Prior Knowledge:

What does my child need to know in order to be successful in unit 2?
  • Knowledge of unit fractions
  • Knowledge of place value 
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 

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
 
Visual Fractions
http://www.visualfractions.com/
 
Subtracting Fractions With Like Denominators
http://ntnmath.kemsmath.com/D%20Pages/Lesson17.html
 
Teaching Channel
https://www.teachingchannel.org/videos/understanding-modeling-and-creating-equivalent-fractions-core-challenge
---------------------------------------------------------------------------
Grade 4, Quarter 1

Unit 1: Operations and Algebraic Thinking, Numbers and Operations in Base Ten

Common Core Standards:


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 p
roblems 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.

heartGeneralize
 place value understanding for multi-digit numbers
• 4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten tim
es what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
• 4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of compariso
ns.
• 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place.

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.
Watch this video to help explain the model:
https://www.youtube.com/watch?v=N7boECP9BAE



 
           Mathematical Language:  Vocabulary
Addend Addition Area model
 Array Base ten  Difference
Digit Dividend Division
Divisor Estimate Equal
Equation Expanded form Factor
Greater than  Inverse Less than
 Multi-digit Multiplication  Minuend
 Place value Product Quotient
Rectangular array Remainder    Rounding
 Standard form Subtraction Subtrahend
Sum  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.
• Number patterns and relationships can be represented using variables.
• Rounding numbers is approximate not exact.
• 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.
• A multiplication equation can be interpreted as a comparison.
• Multiplication and division can be represented by rectangular arrays and area models.
• Multiplication and division are related.
• Fair sharing and measurement are two common situations where division is used.
• Remainders must be less than the divisor.
• How the remainder is interpreted depends on the problem situation.
• Number relationships and patterns can be represented using variables.
• Some real world problems involving joining or separating equal groups or comparison can be solved using multiplication or division.
• The properties of addition, subtraction, multiplication and division help us solve computation problems easily and provide reasoning for choices we make for problem solving.
Prior Knowledge:
What does my child need to know in order to be successful in this unit?
• Knowledge of place value to 1,000
• Round whole numbers to the nearest 10 or 100
• Knowledge of basic addition and subtraction facts
• Add and subtract within 1,000
• Multiplica

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  Website updated on: Wednesday, January 17, 2018  
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