GTPS Curriculum 4Th Grade Math

GTPS Curriculum – 4th Grade Math Suggested Blocks of Instruction: Topic: 1 - Multiplication and Division: Meanings and Facts 12 days /September

Objectives/CPI’s/Standards Essential Questions/Enduring Understandings Materials/Assessment

Essential Questions Use the four operations with whole numbers to solve Materials: enVision Math problems. 4.OA.1. Interpret a multiplication equation as a comparison,  How can patterns and properties be used to 1.1 Meanings of multiplication e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as find some multiplication facts? 1.2 Patterns for facts many as 7 and 7 times as many as 5. Represent verbal  How can unknown multiplication facts be 1.3 Multiplication properties statements of multiplicative comparisons as multiplication found by breaking them apart into known 1.4 3,4,6,7, and 8 as factors equations. facts? 1.5 Look for a pattern 4.OA.2. Multiply or divide to solve word problems involving  How can unknown division facts be found by 1.6 Meanings of division multiplicative comparison, e.g., by using drawings and thinking about a related multiplication fact? equations with a symbol for the unknown number to 1.7 Relating multiplication & represent the problem, distinguishing multiplicative Enduring Understandings division comparison from additive comparison 1.8 Special quotients 4.OA.3. Solve multistep word problems posed with whole  Some real-world problems involving joining or 1.9 Using Multiplication facts to numbers and having whole-number answers using the four separating equal groups or comparison can be find division facts operations, including problems in which remainders must be solved using multiplication. Repeated addition and interpreted. Represent these problems using equations with a arrays are two ways to think about multiplication. Web Site Resources: letter standing for the unknown quantity. Assess the  Some real-world problems involving joining or www.pearsonsuccessnet.com reasonableness of answers using mental computation and separating equal groups or comparison can be estimation strategies including rounding. solved using division. Sharing and repeated Gain familiarity with factors and multiples. subtraction are two ways to think about division. Assessments: 4.OA.4. Find all factor pairs for a whole number in the range  Multiplication and division have an inverse Formative 1–100. Recognize that a whole number is a multiple of each of relationship. The inverse relationship between  Topic Readiness Test its factors. Determine whether a given whole number in the multiplication and division can be used to find  Teacher observation division facts; every division fact has a related range 1–100 is a multiple of a given one-digit number.  Daily Quick Check Masters Determine whether a given whole number in the range 1–100 multiplication fact. Summative is prime or composite.  There are patterns in the products for multiplication End of module performance facts with factors of 2,5, and 9.  Generate and analyze patterns. assessment 4.OA.5. Generate a number or shape pattern that follows a  Two numbers can be multiplied in any order  Portfolio assessment given rule. Identify apparent features of the pattern that were  Any number (except 0) divided by itself equals 1. not explicit in the rule itself.  Basic multiplication facts with 3, 4, 6, 7, and 8 as a factor can be found by breaking apart the unknown fact into know facts.  Information in a problem can often be shown using a picture or diagram and used to understand and solve problems. GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 2 - Generate and Analyze Patterns Instruction: 8 days / September / October Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Generate and analyze patterns. Essential Questions Materials: enVision Math 4.OA.5. Generate a number or shape  How can patterns be used to describe how two 2.1 Repeating patterns pattern that follows a given rule. quantities are related? 2.2 number sequences Identify apparent features of the  How can a relationship between two quantities be 2.3 Extending tables pattern that were not explicit in the shown using a table? 2.4 Writing rules for situations rule itself. 2.5 Geometric patterns Enduring Understandings 2.6 Act it out and use reasoning Web Site Resources:  Some patterns consist of shapes or numbers arranged www.pearsonsuccessnet.com in a unit that repeats.  Some numerical sequences have rules that tell how to generate more numbers in the sequence. Assessments:  Some real-world quantities have a mathematical Formative relationship; the value of one quantity can be found if  Topic Readiness Test you know the value of the other quantity.  Teacher observation  Some real-world quantities have a mathematical  Daily Quick Check Masters relationship; the value of one quantity can be found if Summative the value of the other quantity is known.  End of module performance  Some sequences of geometric objects change in assessment predictable ways that can be described using mathematical rules.  Portfolio assessment GTPS Curriculum – 4th Grade Math Suggested Blocks of Instruction: Topic: 3 -Place Value 8 days /October

Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings

Generalize place value Essential Questions Materials: enVision Math understanding for multi-digit whole numbers.  How are greater numbers read and 3.1 Representing numbers written? 3.2 Place value relationships 4.NBT.1. Recognize that in a multi-digit  How can whole numbers be compared 3.3 Comparing numbers whole number, a digit in one place and ordered? 3.4 Ordering numbers represents ten times what it represents in 3.5 Rounding whole numbers the place to its right. Enduring Understandings 3.6 make an organized list 4.NBT.2. Read and write multi-digit whole Web Site Resources: numbers using base-ten numerals, number  Our number system is based on www.pearsonsuccessnet.com names, and expanded form. Compare two groups of ten. Whenever we get 10 in one multi-digit numbers based on meanings of place value, we move to the next greater the digits in each place, using >, =, and < place value. symbols to record the results of Assessments:  In a multi-digit whole number, a digit comparisons. Formative in one place represents ten times what if  Topic Readiness Test 4.NBT.3. Use place value understanding to would represent in the place immediately round multi-digit whole numbers to any to its right.  Teacher observation place.  Place value can be used to compare  Daily Quick Check Masters and order numbers. Summative  Rounding whole numbers is a process  End of module performance assessment for finding the multiple of 10, 100, and so  Portfolio assessment on closest to a given number. GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 4 - Addition and Subtraction of Whole Numbers Instruction: 8 days /October / November Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Generalize place value Essential Questions Materials: enVision Math understanding for multi-digit whole numbers.  How can sums and differences of whole 4.1 Using mental math to add & subtract 4.2 Estimating sums & differences of whole #’s 4.NBT.3. Use place value numbers be estimated? 4.3 Adding whole numbers understanding to round multi-digit  What are standard procedures for adding and 4.4 Subtracting whole numbers whole numbers to any place. subtracting whole numbers? 4.5 Subtracting across zeros Use place value understanding Enduring Understandings 4.6 Draw a picture and write an equation and properties of operations to perform multi-digit  Representing numbers and numerical arithmetic. Web Site Resources: expressions in equivalent forms can make www.pearsonsuccessnet.com 4.NBT.4. Fluently add and subtract some calculations easy to do mentally. multi-digit whole numbers using  There is more than one way to do a mental the standard algorithm. calculation. Assessments:  The standard addition and subtraction Formative algorithms for multi-digit numbers break the  Topic Readiness Test calculation into simpler calculations using  Teacher observation place value starting with the ones, then the tens, and so on.  Daily Quick Check Masters Summative  There is more than one way to estimate a sum or difference. Each estimation technique haves  End of module performance assessment a way to replace numbers with other numbers  Portfolio assessment that are close and easy to compute with mentally. GTPS Curriculum – 4th Grade Math Suggested Blocks of Instruction: Topic: 5 - Number Sense: Multiplying by 1-Digit Numbers 8 days / November Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Use the four operations with whole Essential Questions Materials: enVision Math numbers to solve problems.  How can some products be found 5.1 Arrays and multiplying by 10 and 100 4.OA.3. Solve multistep word problems posed mentally? 5.2 Multiplying by multiples of 10 and 100 with whole numbers and having whole-number  How can products be estimated? 5.3 Breaking apart to multiply answers using the four operations, including 5.4 Using mental math to multiply problems in which remainders must be Enduring Understandings 5.5 Using rounding to estimate interpreted. Represent these problems using 5.6 Reasonableness equations with a letter standing for the  Making an array with place-value blocks Web Site Resources: unknown quantity. Assess the reasonableness provides a way to visualize and find products. of answers using mental computation and www.pearsonsuccessnet.com  Making an array with place-value blocks estimation strategies including rounding. provides a way to visualize and find products. Assessments: Use place value understanding and A 2-digit by 1-digit multiplication calculation Formative properties of operations to perform can be broken into simpler problems: a basic  Topic Readiness Test multi-digit arithmetic. fact and a 1-digit number times a multiple of  Teacher observation 44.NBT.5. Multiply a whole number of up to 10. Answers to simpler problems can be Daily Quick Check Masters four digits by a one-digit whole number, and added to give the product.  multiply two two-digit numbers, using  There is more than one way to do a mental Summative strategies based on place value and the calculation. Techniques for doing  End of module performance properties of operations. Illustrate and explain multiplication calculations mentally involve assessment the calculation by using equations, rectangular changing the numbers or the expression so  Portfolio assessment arrays, and/or area models. the calculation is easy to do mentally.  Basic facts and place value patterns can be used to find products when one factor is 10 or 100.  Rounding is one way to estimate products. GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 6 - Developing Fluency: Multiplying by 1-Digit Numbers Instruction: 8 days / November / December Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Use place value understanding Essential Questions Materials: enVision Math and properties of operations to perform multi-digit arithmetic.  How can arrays be used to find products? 6.1 Arrays and using an expanded algorithm 6.2 Connecting the expanded and standard 4.NBT.5. Multiply a whole number  What is a standard procedure for multiplying algorithms of up to four digits by a one-digit multi-digit numbers? 6.3 Multiplying 2 digit by 1 digit numbers whole number, and multiply two 6.4 Multiplying 3 and 4 digit by 1 digit #’s two-digit numbers, using strategies Enduring Understandings 6.5 Multiplying by 1 digit numbers based on place value and the 6.6 Missing or extra information properties of operations. Illustrate  There is an expanded algorithm for multiplying and explain the calculation by using where numbers are broken apart using place value Web Site Resources: equations, rectangular arrays, and the parts are used to find partial products. The www.pearsonsuccessnet.com and/or area models. partial products are than added together to find the product.  The standard multiplication algorithm is just a Assessments: shortened way of recording the information in the Formative expanded multiplication algorithm.  Topic Readiness Test  The standard multiplication algorithm is a shortcut  Teacher observation for the expanded algorithm. Regrouping is used rather than showing all partial products.  Daily Quick Check Masters Summative  The standard algorithm for multiplying three-digit by one-digit numbers is just an extension to the  End of module performance hundreds place of the algorithm for multiplying two- assessment digit by one-digit numbers.  Portfolio assessment  The standard algorithm for multiplication involves breaking apart numbers using place value, finding partial products, and then adding partial products to get the final product. The process is the same regardless of the size of the factors. GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 7 - Number Sense: Multiplying by 2-Digit Numbers Instruction: 7 days / December Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings

Generalize place value Essential Questions Materials: enVision Math understanding for multi-digit whole numbers.  How can greater products be found 7.1 Arrays and multiplying 2 digit numbers by multiples of 10 4.NBT.3. Use place value understanding mentally? 7.2 Using mental math to multiply 2 digit to round multi-digit whole numbers to  How can greater products be estimated? numbers any place. Enduring Understandings 7.3 Using rounding to estimate Use place value understanding and 7.4 Using compatible numbers to estimate properties of operations to 7.5 Multiple step problems perform multi-digit arithmetic.  Making an array with place-value blocks provides a way to visualize and find Web Site Resources: 4.NBT.5. Multiply a whole number of up products. www.pearsonsuccessnet.com to four digits by a one-digit whole  Basic facts and place-value patterns can number, and multiply two two-digit be used to mentally multiply a two-digit numbers, using strategies based on place number by a multiple of 10 or 100. value and the properties of operations. Assessments:  Products can be estimated by replacing Illustrate and explain the calculation by Formative numbers with the closest multiple 10 or 100. using equations, rectangular arrays,  Topic Readiness Test and/or area models.  Products can be estimated by replacing  Teacher observation numbers with other numbers that are close  Daily Quick Check Masters and easy to multiply mentally. Summative  End of module performance assessment  Portfolio assessment GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 8 - Multiplying by 2-Digit Numbers Instruction: 7 days / January Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Use place value Essential Questions Materials: enVision Math understanding and properties of operations to perform  How can arrays be used to find greater 8.1 Arrays and multiplying 2 digit numbers multi-digit arithmetic. products? 8.2 Arrays and an expanded algorithm 8.3 Multiplying 2 digit numbers by multiples of 10 4.NBT.5. Multiply a whole number  What is a standard procedure for 8.4 Multiplying 2 digit by 2 digit numbers of up to four digits by a one-digit multiplying multi-digit numbers? 8.5 Two question problems whole number, and multiply two two-digit numbers, using strategies Enduring Understandings based on place value and the Web Site Resources: properties of operations. Illustrate  The expanded algorithm for multiplying by www.pearsonsuccessnet.com and explain the calculation by using two-digit numbers is just an extension of the equations, rectangular arrays, expanded algorithm for multiplying with one- and/or area models. digit numbers. Assessments:  Making an array with place-value blocks Formative provides a way to visualize and find products  Topic Readiness Test using an expanded algorithm.  Teacher observation  The standard algorithm for multiplying a two- digit number by a multiple of 10 is just an  Daily Quick Check Masters extension of the algorithm for multiplying Summative multi-digit numbers by a one-digit number.  End of module performance assessment  The standard multiplication algorithm is a  Portfolio assessment shortcut for the expanded algorithm. Regrouping is used rather than showing all partial products. GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 9 - Number Sense: Dividing by 1-Digit Divisors Instruction: 8 days /January Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Generalize place value Essential Questions Materials: enVision Math understanding for multi-digit whole numbers.  What are different meanings of division? 9.1 Using mental math to divide  How can mental math and estimation be used 9.2 Estimating quotients 4.NBT.6. Find whole-number quotients to divide? 9.3 Estimating quotients for greater dividends and remainders with up to four-digit 9.4 Dividing with remainders dividends and one-digit divisors, using Enduring Understandings 9.5 Multiplication & division stories strategies based on place value, the 9.6 draw a picture and write an equation properties of operations, and/or the  Basic facts and place-value patterns can be relationship between multiplication used to divide multiples of 10 and 100 by one- Web Site Resources: digit numbers. and division. Illustrate and explain the www.pearsonsuccessnet.com calculation by using equations,  Substituting compatible numbers is an rectangular arrays, and/or area efficient technique for estimating quotients. models.  Mentally multiplying by different powers of Assessments: ten will help you arrive at an estimate for a Formative quotient of a multi-digit division problem.  Topic Readiness Test  The remainder when dividing must be less  Teacher observation than the divisor. The nature of the question  Daily Quick Check Masters asked determines how to interpret and use the Summative remainder.  End of module performance  Some real-world problems involving joining assessment equal groups, separating equal groups, or comparison can be solved using multiplication;  Portfolio assessment others can be solved using division. GTPS Curriculum – 4th Grade Math Suggested Blocks of Instruction: . 10 days / January / February Topic: 10 - Developing Fluency: Dividing by 1-Digit Divisors

Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings

Use the four operations with whole Essential Questions Materials: enVision Math numbers to solve problems.  How can repeated subtraction be 10.1 Using objects to divide: division as 4.OA.3. Solve multistep word problems posed with used to model division? repeated subtraction whole numbers and having whole-number  What is the standard procedure for 10.2 Division as repeated subtraction answers using the four operations, including dividing multi-digit numbers? 10.3 Division as sharing problems in which remainders must be 10.4 Dividing 2 digit by 1 digit #’s interpreted. Represent these problems using Enduring Understandings 10.5 Dividing 3 digit by 1 digit numbers equations with a letter standing for the unknown 10.6 Deciding where to start dividing quantity. Assess the reasonableness of answers 10.7 Dividing 4 digit numbers by 1 digit #’s  Repeated subtraction situations can be using mental computation and estimation 10.8 Multistep problems strategies including rounding. modeled and solved using division.  Repeated subtraction situations can be Generalize place value understanding for Web Site Resources: solved using a division algorithm different multi-digit whole numbers. www.pearsonsuccessnet.com form the standard algorithm. 4.NBT.6. Find whole-number quotients and  The sharing interpretation of division can remainders with up to four-digit dividends and be used to model the standard division Assessments: one-digit divisors, using strategies based on place algorithm. Formative value, the properties of operations, and/or the  The standard division algorithm breaks  Topic Readiness Test relationship between multiplication and division. the calculation into simpler calculations  Teacher observation using basic facts, place value the Illustrate and explain the calculation by using  Daily Quick Check Masters equations, rectangular arrays, and/or area models. relationship between multiplication and division, and estimation. Summative  The relationship between multiplication,  End of module performance division, and estimation can help assessment determine the place value of the largest digit in a quotient.  Portfolio assessment

Suggested Blocks of Instruction: Topic: 11 - Fraction Equivalence and Ordering 10 days / February GTPS Curriculum – 4th Grade Math Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Gain familiarity with factors and multiples. Essential Questions Materials: enVision Math

4.OA.4. Find all factor pairs for a whole number in  How can the same fractional amount be 11.1 Factors the range 1–100. Recognize that a whole number named using symbols in different ways? 11.2 Prime & composite numbers is a multiple of each of its factors. Determine  How can fractions be compared and 11.3 Multiples whether a given whole number in the range 1–100 ordered? 11.4 Equivalent fractions is a multiple of a given one-digit number. 11.5 # lines and equivalent fractions Determine whether a given whole number in the Enduring Understandings 11.6 Comparing fractions range 1–100 is prime or composite. 11.7 Ordering fractions 11.8 Writing to explain  Every counting number is divisible by 1 Extend understanding of fraction and itself, and some counting numbers are equivalence and ordering. Web Site Resources: also divisible by other numbers. www.pearsonsuccessnet.com 4.NF.1. Explain why a fraction a/b is equivalent to  Some counting numbers have exactly a fraction (n × a)/(n × b) by using visual fraction two factors; others have more than two. models, with attention to how the number and size  The product of any nonzero number and Assessments: of the parts differ even though the two fractions any other nonzero number is divisible by Formative themselves are the same size. Use this principle to each number and is called a multiple of each  Topic Readiness Test number. recognize and generate equivalent fractions.  Teacher observation 4.NF.2. Compare two fractions with different  The same fractional amount can be  Daily Quick Check Masters numerators and different denominators, e.g., by represented by an infinite set of different creating common denominators , or by comparing but equivalent fractions. Equivalent to a benchmark fraction. Recognize that fractions are found by multiplying or Summative comparisons are valid only when the two fractions dividing the numerator and denominator by refer to the same whole. Record the results of the same nonzero number.  End of module performance assessment comparisons with symbols >, =, or <, and justify  If two fractions have the same the conclusions, e.g., by using a visual fraction denominator, the fraction with the greater  Portfolio assessment model. Build fractions from unit fractions by numerator is the greater fraction. If two applying and extending previous understandings fractions have the same numerator, the of operations on whole numbers. fraction with lesser denominator is the greater fraction.  Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to the other numbers. GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 12 - Adding & Subtracting Fractions and Mixed Numbers with Like Denominators Instruction: 13 days / February / March Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Extend understanding of fraction Essential Questions Materials: enVision Math equivalence and ordering.  What does it mean to add and subtract 12.1 Modeling addition of fractions 4.NF.3. Understand a fraction a/b with a fractions and numbers with like denominators? 12.2 Adding fractions with like denominators > 1 as a sum of fractions 1/b.  What is a standard procedure for adding and 12.3 Modeling subtraction of fractions 3a. Understand addition and subtraction subtracting fractions and mixed numbers with 12.4 Subtracting fractions with like denominators of fractions as joining and separating like denominators? 12.5 Adding & subtracting on the #line parts referring to the same whole.  How can fractions and mixed numbers be 12.6 Improper fractions & mixed #’s 3b. Decompose a fraction into a sum of added and subtracted on a number line? 12.7 Modeling addition & subtraction of mixed #’s fractions with the same denominator in 12.8 Adding Mixed #’s more than one way, recording each Enduring Understandings 12.9 Subtracting mixed #’s decomposition by an equation. Justify 12.10 Decomposing & composing fractions decompositions, e.g., by using a visual  A model can be used to add or subtract two or more 12.11 Draw a picture & write an equation fraction model. Examples: 3/8 = 1/8 + fractions. 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1  When adding or subtracting fractions with like Web Site Resources: + 1/8 = 8/8 + 8/8 + 1/8. denominators, you are adding or subtracting www.pearsonsuccessnet.com 3c. Add and subtract mixed numbers portions of the same size. So, you can add or with like denominators, e.g., by replacing subtract the numerators without changing the Assessments: each mixed number with an equivalent denominators. Formative fraction, and/or by using properties of  One way to add or subtract mixed numbers is to add  Topic Readiness Test the fractional parts and then add or subtract the operations and the relationship between  Teacher observation addition and subtraction. whole number parts. Sometimes whole numbers or fractions need to be renamed.  Daily Quick Check Masters 3d. Solve word problems involving Summative addition and subtraction of fractions  Models can be used to show different ways of adding referring to the same whole and having and subtracting mixed numbers.  End of module performance assessment like denominators, e.g., by using visual  Positive fractions can be added or subtracted by  Portfolio assessment fraction models and equations to locating a fraction on the number line and then represent the problem. moving to the right to add or to the left to subtract.  Fractional amounts greater than 1 can be represented using a whole number and a fraction. Whole number amounts can be represented as fractions. When the numerator and denominator are equal, the fraction equals 1. GTPS Curriculum – 4th Grade Math Suggested Blocks of Instruction: Topic: 13 - Extending Fractions Concepts 12 days / March / April

Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings 4.NF.4. Apply and extend previous understandings of Essential Questions Materials: enVision Math multiplication to multiply a fraction by a whole number.  How is decimal numeration related to 4a. Understand a fraction a/b as a multiple of 1/b. Use a visual whole number numeration? 13.1 Fractions as multiples of unit fraction model to represent 5/4 as the product 5 × 1/4  How can decimals be compared and fractions 4b. Understand a multiple of a/b as a multiple of 1/b, and use this 13.2 Multiplying a fraction by a whole # understanding to multiply a fraction by a whole number. Use a ordered? visual fraction model to express 3 × (2/5) as 6 × (1/5) – 6/5  How are fractions and decimals related? 13.3 Multiplying a fraction by a whole # 4c. Solve word problems involving multiplication of a fraction by using symbols a whole number, e.g., by using models and equations to represent Enduring Understandings 13.4 Fractions & decimals the problem. If each person at a party will eat 3/8 lb of roast beef, 13.5 Fractions & decimals on the # line and there will be 5 people at the party, how many pounds of beef  Physical representations and symbols can be 13.6 Equivalent fractions & decimals will be needed? Between what 2 whole # ‘s does your answer lie? used to develop the understanding that a/b = 13.7 Decimal place value Understand decimal notation for fractions, and compare a x 1/b. 13.8 Comparing & ordering decimals decimal fractions.  Models can be used to find the product of a 13.9 Using money to understand 4.NF.5. Express a fraction with denominator 10 as an equivalent whole number and a fraction. decimals fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example,  To multiply a fraction by a whole number, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. one must multiply the whole number by the 4.NF.6. Use decimal notation for fractions with denominators 10 numerator of the fraction and then divide the Web Site Resources: or 100. For example, rewrite 0.62 as 62/100; describe a length as product by the denominator of the fraction. www.pearsonsuccessnet.com 0.62 meters; locate 0.62 on a number line diagram.  Place value can be used to compare and order 4.NF.7. Compare two decimals to hundredths by reasoning about numbers. Assessments: their size. Recognize that comparisons are valid only when the  A decimal is another name for a fraction. Formative two decimals refer to the same whole. Record the results of  Topic Readiness Test comparisons with the symbols >, =, or <, and justify conclusions.  Each fraction, mixed number, and decimal 4.MD.2. Use the four operations to solve word problems involving can be associated with a unique point on the  Teacher observation distances, intervals of time, liquid volumes, masses of objects, and number line.  Daily Quick Check Masters money, including problems involving fractions or decimals, and  Every fraction can be represented by an problems that require expressing measurements given in a larger infinite number of equivalent fractions, but Summative each fraction is represented by the same unit in terms of a smaller unit. Represent quantities using  End of module performance number line diagrams that use a measurement scale. decimal or an equivalent form. assessment  Decimal numeration is just an extension of whole number numeration.  Portfolio assessment  Relationships among dollars, dimes, and pennies are a good model for decimal numeration. GTPS Curriculum – 4th Grade Math Suggested Blocks of Topic: 14 - Measurement Units and Conversions Instruction: 13 days / April Objectives/CPI’s/Standards Essential Questions/Enduring Understandings Materials/Assessment

Solve problems involving Essential Questions Materials: enVision Math measurement and conversion of measurements from a larger unit  What are the customary and metric units for measuring 14.1 Using customary units of length to a smaller unit. length, capacity, and weight/mass, and how are they 14.2 Customary units of capacity related? 14.3 Units of weight 4.MD.1. Know relative sizes of 14.4 Changing customary units measurement units within one system Enduring Understandings 14.5 Writing to explain of units including km, m, cm; kg, g; lb, 14.6 Using metric units of length oz.; l, ml; hr, min, sec. Within a single  Length can be estimated and measured in different 14.7 Metric units of capacity system of measurement, express systems (customary, metric) and using different units in 14.8 Units of mass measurements in a larger unit in terms each system that are related to each other. 14.9 Changing metric units 14.10 Units of time of a smaller unit. Record measurement  Capacity is a measure of the amount of liquid a container 14.11 Work backward equivalents in a two-column table. For can hold. Capacity can be measured in different systems example, know that 1 ft is 12 times as (customary, metric) and using different units in each Web Site Resources: long as 1 in. Express the length of a 4 ft system that are related to each other. snake as 48 in. Generate a conversion www.pearsonsuccessnet.com  The weight of an object is a measure of how heavy an table for feet and inches listing the object is. number pairs (1, 12), (2, 24), (3, 36), ... Assessments: 4.MD.2. Use the four operations to  Mass is a measure of the quantity of matter in an object. Formative solve word problems involving Weight and mass are different measures.  Topic Readiness Test distances, intervals of time, liquid  Time can be expressed using different units that are  Teacher observation related to each other. volumes, masses of objects, and money,  Daily Quick Check Master including problems involving simple  Length can be estimated in different measurement fractions or decimals, and problems systems. Summative that require expressing measurements  Relationships between customary measurement units can  End of module performance given in a larger unit in terms of a be expressed as a function (e.g., 12 inches to 1 ft or 12 in. = assessment smaller unit. Represent measurement 1 ft). Relationships exist that enable you to convert  Portfolio assessment quantities using diagrams such as between metric units of the same attribute by multiplying number line diagrams that feature a or dividing. measurement scale.  Relationships between metric units can be expressed as a function (e.g., 10 mm to 1 cm or 10 mm = 1 cm). Relationships exist that enable you to convert between metric units of the same attribute by multiplying or dividing. GTPS Curriculum – 4th Grade Math Suggested Blocks of Instruction: Topic: 15 - Solving Measurement Problems 7 days / April / May Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Solve problems involving measurement and Essential Questions Materials: enVision Math conversion of measurements from a larger unit to a smaller unit.  What do area and perimeter mean 15.1 Solving perimeter & area problems and how can each be found? 15.2 Solving measurement problems 4.MD.2. Use the four operations to solve word  How can line plots and other tools 15.3 Solving problems involving money problems involving distances, intervals of time, help to solve measurement problems? 15.4 Solving problems involving line plots liquid volumes, masses of objects, and money, 15.5 Solve a simpler problem and make a including problems involving simple fractions or Enduring Understandings table decimals, and problems that require expressing measurements given in a larger unit in terms of a  Some problems can be solved by applying Web Site Resources: smaller unit. Represent measurement quantities the formula for the perimeter of a www.pearsonsuccessnet.com using diagrams such as number line diagrams that rectangle or the formula for the area of a feature a measurement scale. rectangle. 4.MD.3. Apply the area and perimeter formulas for  Some measurement problems can be rectangles in real world and mathematical problems. Assessments: represented and solved using models. For example, find the width of a rectangular room Formative given the area of the flooring and the length, by  Making change is often easiest by  Topic Readiness Test counting from the smaller amount to the viewing the area formula as a multiplication  Teacher observation larger amount. equation with an unknown factor.  Daily Quick Check Master  Some data can be represented using a line plot and the line plot can be sued to Represent and interpret data. Summative 4.MD.4. Make a line plot to display a data set of answer certain questions about the data.  End of module performance measurements in fractions of a unit (1/2, 1/4, 1/8). assessment Solve problems involving addition and subtraction of fractions by using information presented in line  Portfolio assessment plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. GTPS Curriculum – 4th Grade Math Suggested Blocks of Instruction: Topic: 16 - Lines, Angles and Shapes 13 days / May / June Objectives/CPI’s/Standards Essential Questions/Enduring Materials/Assessment Understandings Draw and identify lines and angles, and classify Essential Questions Materials: enVision Math shapes by properties of their lines and angles.  How can line, angles, and shapes be 16.1 Points, lines and planes 4.G.1 Draw points, lines, line segments, rays, angles (right, described, analyzed, and classified? 16.2 Line segments, rays and angles acute obtuse), and perpendicular and parallel lines.  How are angles measured, added, 16.3 Understanding angles and unit Identify these in two-dimensional figures. and subtracted? angles 4.G.2 Classify two-dimensional figures based on the 16.4 Measuring with unit angles presence or absence of parallel or perpendicular lines, or Enduring Understandings 16.5 Measuring angles the presence or absence of angles of a specified size. 16.6 Adding & subtracting angle measures Recognize right triangles as a category, and identify right 16.7 Polygons triangles.  Point, line, and plane are the core 16.8 Triangles 4.G.3 Recognize a line of symmetry for a two-dimensional attributes of space objects, and real- 16.9 Quadrilaterals figure as a line across the figure such that the figure can be world situations can be sued to think 16.10 Line symmetry folded along the line into matching parts. Identify line- about these attributes. symmetric figures and draw lines of symmetry. 16.11 Make & test generalizations  Line segments and rays are sets of points Geometric measurement: understand concepts of that describe parts of lines, shapes and angle and measure angles. solids. Angles are formed by two Web Site Resources: 4.MD.5. Recognize angles as geometric shapes that are intersecting lines or by rays with a www.pearsonsuccessnet.com formed wherever two rays share a common endpoint common endpoint and are classified by 5a. An angle is measured with reference to a circle with its size. center at the common endpoint of the rays, using the  Two-dimensional or plane shapes have Assessments: fraction of the circular arc between the points where the many properties that make them Formative two rays intersect the circle. An angle that turns through different from one another. Polygons can  Topic Readiness Test 1/360 of a circle is called a “one-degree angle.” be described and classified by their sides  Teacher observation 5b. An angle that turns through n one-degree angles is said and angles. to have an angle measure of n degrees.  Daily Quick Check Master 4.MD.6. Measure angles in whole-number degrees using a  The measure of an angle depends upon the fraction of the circle cut off by its protractor. Sketch angles of specified measure. Summative 4.MD.7. Recognize angle measure as additive. When an rays.  End of module performance angle is decomposed into non-overlapping parts, the angle  The unit for measuring the size of the assessment measure of the whole is the sum of the angle measures of opening of an angle is 1 degree. the parts. Solve addition and subtraction problems to find  Portfolio assessment unknown angles using equations and real world  Angle measures can be added or applications. subtracted.