Allamuchy Township School



Course Name: Mathematics Grade 3

In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

. 1. Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.

. 2. Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.

. 3. Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.

4. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.

Grade 3: Overview

. Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.

Understand properties of multiplication and the relationship between multiplication and division.

Multiply and divide within 100.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

|Domain: Represent and solve problems involving multiplication and division. |Assessment |Resources |Instructional Methods |

|Standards: | | | |

|3. OA.1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the | | |Each standard is supported in the McGraw-Hill|

|total number of objects in 5 groups of 7 objects each. For example, describe| | |My Math series by the following lesson |

|a context in which a total number of objects can be expressed as 5 × 7. | | |extensions. |

|3. OA.2. Interpret whole-number quotients of whole numbers, e.g., interpret |Bake Sale Project TE 60 A | |Digital Dashboard |

|56 ÷ 8 as the number of objects in each share when 56 objects are | |4.1-6 |eGlossary |

|partitioned equally into 8 shares, or as a number of shares when 56 objects |The Fruit Store Project TE 192A |6.2,4,7,8 |Visual Vocabulary Cards |

|are partitioned into equal shares of 8 objects each. For example, describe a| |7.1,3,4,6,7 8.1,2,4,5,8 |Lesson Animation |

|context in which a number of shares or a number of groups can be expressed |Clothing Drive Project TE 294A |NLVM Number Line Arithmetic |Problem of the Day |

|as 56 ÷ 8. | | |Games |

|3. OA.3. Use multiplication and division within 100 to solve word problems |Plant an Array Project TE 364A | |Personal Tutor |

|in situations involving equal groups, arrays, and measurement quantities, | |5.1-3 |Virtual Manipulatives |

|e.g., by using drawings and equations with a symbol for the unknown number |Stocking the Store Project TE 428A |6.3,5,9 |Base Ten Blocks |

|to represent the problem.1 | |7.2,5,8 |Bucket Balance |

|3. OA.4. Determine the unknown whole number in a multiplication or division |Make a Game Project TE 500A |8.3,6,9 |Calendar |

|equation relating three whole numbers. For example, determine the unknown | | |Centimeter Cubes |

|number that makes the equation true in each of the equations 8 × ? = 48, 5 =|As well as: Formative Assessments | |Clock |

|_ ÷ 3, 6 × 6 = ? | | |Connecting Cubes |

| |Homework | |Currency |

| |Am I Ready? | | |

| |Diagnostic Test | | |

| |Pre-test |4.1-6 | |

| |Check My Progress |6.2-5,7-9 | |

| |Common Core Quick Check Quizzes |7.1-8; 8.1-7 | |

| |Vocabulary Test |11.2,7; 12.7 | |

| |Online Self-Check Quizzes | | |

| | | | |

| | | | |

| | |5.1-6 | |

| | |6.2-9 | |

| | |7.1,2,4,5,7 | |

| | |8.1-6,9 | |

|Domain: Understand properties of multiplication and the relationship between|Summative Assessments | |Fraction Circles |

|multiplication and division. |Chapter Tests | |Fraction Tiles |

|Standards: |Standardized Test Practice | |Geoboard/Bands |

|3. OA.5. Apply properties of operations as strategies to multiply and |Extended Response Tests |4.3,4 |Geometric Solids |

|divide.2Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. |Oral Assessment |6.1,2,4,7,8 |Hundred Chart |

|(Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = |eAssessment |7.1,7,8 |Number Cubes |

|15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative | |8.1,2,4,5 |Number Line |

|property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can| |9.1-5 |Pattern Blocks |

|find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive | | |Spinner |

|property.) | | |Tangrams |

|3. OA.6. Understand division as an unknown-factor problem. For example, find| | |Thermometer |

|32 ÷ 8 by finding the number that makes 32 when multiplied by 8. | | |Two-Color Counter |

| | | |Strategic Intervention Guide |

| | | |Math Songs |

| | | |Manipulative Masters |

| | |5.4,5 | |

| | |6.3,5,9 | |

| | |7.2,5 | |

| | |8.3,6,9 | |

| | |NLVM Rectangle Division | |

|Domain: Multiply and divide within 100. | | |My Foldables |

|Standards: | | |Real-World Problem Solving Library |

|3. OA.7. Fluently multiply and divide within 100, using strategies such as | | |Animals Habitats |

|the relationship between multiplication and division (e.g., knowing that 8 ×| |5.3-6 |Appalachian Journey |

|5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of | |6.2-9 |Craft Store Supplies |

|Grade 3, know from memory all products of two one-digit numbers. | |7.1-8 |Ecosystems All Around |

| | |8.1-5 |Food, Energy and You |

| | |9.1-4 | |

| | |NLVM Function Machines | |

|Domain: Solve problems involving the four operations, and identify and | | |Light, Sight and Colors So Bright |

|explain patterns in arithmetic. | | |Moon Gazing |

|Standards: | | |Populations on the Rise |

|3. OA.8. Solve two-step word problems using the four operations. Represent | | |Students at Work |

|these problems using equations with a letter standing for the unknown | |3.1-4,6,7 |Understanding the Government |

|quantity. Assess the reasonableness of answers using mental computation and | |4.2,4,6 |My Learning Stations |

|estimation strategies including rounding.3 | |9.6-9 |Activity Cards |

|3. OA.9. Identify arithmetic patterns (including patterns in the addition | | |Problem-Solving Cards |

|table or multiplication table), and explain them using properties of | | |Literature |

|operations. For example, observe that 4 times a number is always even, and | | | |

|explain why 4 times a number can be decomposed into two equal addends. | | | |

| | | | |

| | |2.2,3 | |

| | |6.1-4,6-8 | |

| | |7.1-4,7 | |

| | |8.1,2,4,5 | |

| | |NLVM 100s Chart | |

| | |NLVM Sieve of Eratosthenes | |

Number and Operations in Base Ten

Use place value understanding and propertiesof operations to perform multi-digit arithmetic.

|Domain: Use place value understanding and properties of operations to perform | | |Games |

|multi-digit arithmetic. | | |Graphic Novels |

| | | |A Leader for All |

|Standards: | | |Birthday Dilemma |

| | | |Carnival Cash |

|3. NBT.1 Use place value understanding to round whole numbers to the nearest 10| | |Extreme Park Makeover! |

|or 100. | | |Field Day Decisions |

| | | |Hard Work Pays Off |

|3. NBT.2 Fluently add and subtract within 1000 using strategies and algorithms | | |High Flying Adventures |

|based on place value, properties of operations, and/or the relationship between|Book Count Project TE 8A |1.4-6 |Recycling “Can” Make a Difference |

|addition and subtraction. | |NLVM Base Block |Time Flies |

| |Bake Sale Project TE 60A |NLVM Place Value Number Line |Weather Talks |

| | | |Printable Assets |

| |As well as: Formative Assessments |2.1,4-9 |Editable Enrich Masters |

| | |3.1-7 |Editable Reteach Masters |

| |Homework |NLVM Base Blocks Addition | |

| |Am I Ready? |NLVM Base Blocks Subtraction | |

| |Diagnostic Test |NLVM Chip Abacus | |

| |Pre-test |NLVM Circle 99 | |

| |Check My Progress |NLVM Number Puzzles | |

| |Common Core Quick Check Quizzes | | |

|3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 |Vocabulary Test | | |

|(e.g., 9 × 80, 5 × 60) using strategies based on place value and |Online Self-Check Quizzes | | |

|properties of operations. |Summative Assessments | | |

| |Chapter Tests |6.8 | |

| |Standardized Test Practice | | |

| |Extended Response Tests | | |

| |Oral Assessment | | |

| |eAssessment | | |

Number and Operations—Fractions

Develop understanding of fractions as numbers.

|Domain: Develop understanding of fractions as numbers. | | |Family Letters and Activities |

| | | |Manipulative Masters |

|Standards: | | |Homework Help |

| | | |My Vocabulary Cards |

|3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is| | |Differentiated Instructional Practice |

|partitioned into b equal parts; understand a fraction a/b as | | |Reteach |

|the quantity formed by a parts of size 1/b. |A Class Carnival Project TE 568A |10.1-8 |Enrich |

| | |NLVM Fraction Bars |Reading and Language Arts Cross |

| |As well as: Formative Assessments |NLVM Fraction Naming |Curricular Lesson |

| | |NLVM Fractions Part of a Whole |Extensions |

| |Homework |NLVM Visualizing Fractions |21st Century Skills |

| |Am I Ready? | | |

| |Diagnostic Test | | |

| |Pre-test | | |

| |Check My Progress | | |

| |Common Core Quick Check Quizzes | | |

|3. NF.2 Understand a fraction as a number on the number line; represent fractions |Vocabulary Test | | |

|on a number line diagram. |Online Self-Check Quizzes | | |

| | |10.5-8 | |

| |Summative Assessments |NLVM Number Line Bars | |

|Represent a fraction 1/b on a number linediagram by defining the interval from 0 |Chapter Tests | | |

|to 1 as the whole and partitioning it into b equal parts. Recognize that each part|Standardized Test Practice | | |

|has size 1/b and that the endpoint of the part based at 0 locates the number 1/b |Extended Response Tests |10.5,6,8 | |

|on the number line. |Oral Assessment | | |

| |eAssessment | | |

|Represent a fraction a/b on a number line diagram by marking off a lengths 1/b | | | |

|from 0. Recognize that the resulting interval has size a/b and that its endpoint | | | |

|locates the number a/b on the number line. | | | |

| | | | |

|3. NF.3 Explain equivalence of fractions in special cases, and compare fractions | |10.5-8 | |

|by reasoning about their size. | | | |

| | | | |

|a. Understand two fractions as equivalent | | | |

|(equal) if they are the same size, or the | | | |

|same point on a number line. | | | |

| | |10.6-8 | |

|Recognize and generate simple equivalent | |NLVM Fraction Pieces | |

|fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, | |NLVM Fraction Equivalent | |

|e.g., by using a visual fraction model. | |10.6,7 | |

| | | | |

|Express whole numbers as fractions, and | | | |

|recognize fractions thatare equivalent to whole numbers. Examples: Express 3 in | | | |

|the form3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same pointof a | | | |

|number line diagram. | |10.6,7 | |

| | | | |

|Compare two fractions with the same | | | |

|numerator or the samedenominator by reasoning about their size. Recognize that | | | |

|comparisons are valid only when the two | | | |

|fractions refer to the same whole. Record | |10.7 | |

|the results of comparisons with the | | | |

|symbols>, =, or , =, and ,| |8.6-8.9 |Math and Social Studies: Life in the United|

|=, or 1 as a sum of fractions 1/b. | | |Math and Social Studies: The Olympic Games |

|Understand addition and subtraction of fractions as joining and separating parts |As well as: Formative Assessments | | |

|referring to the same whole. | | | |

|Decompose a fraction into a sum of fractions with the same denominator in more than |Homework | | |

|one way, recording each decomposition by an equation. Justify decompositions, e.g., |Am I Ready? | | |

|by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 |Diagnostic Test | | |

|; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. |Pre-test | | |

|Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed|Check My Progress | | |

|number with an equivalent fraction, and/or by using properties of operations and the|Common Core Quick Check Quizzes | | |

|relationship between addition and subtraction. |Vocabulary Test | | |

|Solve word problems involving addition and subtraction of fractions referring to the|Online Self-Check Quizzes | | |

|same whole and having like denominators, e.g., by using visual fraction models and |Summative Assessments | | |

|equations to represent the problem. |Chapter Tests |8.9,10 | |

| |Standardized Test Practice |9.1-7 | |

|4. NF.4. Apply and extend previous understandings of multiplication to multiply a | | | |

|fraction by a whole number. | | | |

|Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction |As well as: Formative Assessments |NLVM Fraction Pieces | |

|model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the | | | |

|equation 5/4 = 5 × (1/4). |Homework | | |

|Understand a multiple of a/b as a multiple of 1/b, and use this understanding to |Am I Ready? | | |

|multiply a fraction by a whole number. For example, use a visual fraction model to |Diagnostic Test | | |

|express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × |Pre-test | | |

|(a/b) = (n × a)/b.) |Check My Progress | | |

|Solve word problems involving multiplication of a fraction by a whole number, e.g., |Quizzes | | |

|by using visual fraction models and equations to represent the problem. For example,|Vocabulary Test | | |

|if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5|Online Self-Check Quizzes | | |

|people at the party, how many pounds of roast beef will be needed? Between what two |Summative Assessments | | |

|whole numbers does your answer lie? |Chapter Tests | | |

|Domain: Understand decimal notation for fractions, and compare decimal fractions. |Standardized Test Practice | | |

|Standards: |Extended Response Tests | | |

|4. NF.5. Express a fraction with denominator 10 as an equivalent fraction with |Oral Assessment | | |

|denominator 100, and use this technique to add two fractions with respective |eAssessment | | |

|denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 | | | |

|= 34/100. | | | |

| | | | |

|4. NF.6. Use decimal notation for fractions with denominators 10 or 100. For | |9.8-9 | |

|example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a | | | |

|number line diagram. | | | |

| | | | |

|4. NF.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 < symbols to record the results of comparisons. |Check My Progress | |Real-World Problem Solving Library |

|5. NBT.4. Use place value understanding to round decimals to any place. |Common Core Quick Check Quizzes |5.1-3 |City Planning |

|Domain: Perform operations with multi-digit whole numbers and with decimals |Vocabulary Test |6.1 |A Growing Nation |

|to hundredths. |Online Self-Check Quizzes |NLVM Place Value Number Line |Into Uncharted Territory |

|Standards: |Summative Assessments | |Math and Science: How Big is a Solar System?|

|5. NBT.5. Fluently multiply multi-digit whole numbers using the standard |Chapter Tests | |Math and Science: Matter All Around |

|algorithm. |Standardized Test Practice | |Math and Science: Inside a Science Museum |

|5. NBT.6. Find whole-number quotients of whole numbers with up to four-digit |Extended Response Tests |2.6-10 |Math and Science: The Shifting Nature of |

|dividends and two-digit divisors, using strategies based on place value, the |Oral Assessment |6.1,8,9 |Weather |

|properties of operations, and/or the relationship between multiplication and |eAssessment |8.4 |Math and Science: Water Works |

|division. Illustrate and explain the calculation by using equations, | | | |

|rectangular arrays, and/or area models. | |3.1-13 | |

|5. NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using | |4.1-6 | |

|concrete models or drawings and strategies based on place value, properties | |NLVM Rectangle Multiplication | |

|of operations, and/or the relationship between addition and subtraction; | | | |

|relate the strategy to a written method and explain the reasoning used. | | | |

| | |5.2-10 | |

| | |6.2-14 | |

| | |NLVM Circle 3 | |

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Number and Operations-Fractions

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

|Domain: Use equivalent fractions as a strategy to add and subtract fractions. | | |Math and Social Studies: Early American |

|Standards: | | |Settlements |

|5. NF.1. Add and subtract fractions with unlike denominators (including mixed |Fraction Party Project TE 550A |9.4-13 |Math and Social Studies: Life in Colonial |

|numbers) by replacing given fractions with equivalent fractions in such a way |I’m Game Project TE 706A | |America |

|as to produce an equivalent sum or difference of fractions with like |As well as: Formative Assessments | |Math and Social Studies: Our Nation’s 50 |

|denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b +| | |States |

|c/d = (ad + bc)/bd.) |Homework |9.2-13 |My Learning Stations |

|5. NF.2. Solve word problems involving addition and subtraction of fractions |Am I Ready? |NLVM Fractions Adding |Activity Cards |

|referring to the same whole, including cases of unlike denominators, e.g., by |Diagnostic Test | |Problem-Solving Cards |

|using visual fraction models or equations to represent the problem. Use |Pre-test | |Literature |

|benchmark fractions and number sense of fractions to estimate mentally and |Check My Progress | |Games |

|assess the reasonableness of answers. For example, recognize an incorrect |Common Core Quick Check Quizzes | |Graphic Novels |

|result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. |Vocabulary Test | |A Big Book |

|Domain: Apply and extend previous understandings of multiplication and division|Online Self-Check Quizzes |8.1 |A Carrier For Kitty |

|to multiply and divide fractions. |Summative Assessments | |Filling a Phone |

|Standards: |Chapter Tests |NLVM Number Line Bar Fractions |Greenhouse Shopping Spree |

|5. NF.3. Interpret a fraction as division of the numerator by the denominator |Standardized Test Practice | |Happy Trails |

|(a/b = a ÷ b). Solve word problems involving division of whole numbers leading |Extended Response Tests | |Man, Oh Manatee |

|to answers in the form of fractions or mixed numbers, e.g., by using visual |Oral Assessment | |Mowing Money |

|fraction models or equations to represent the problem. For example, interpret |eAssessment | |Popular Pet |

|3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3,| |10.1-6, 12 |Ride Riddle |

|and that when 3 wholes are shared equally among 4 people each person has a | | |Sandwich Slice Sizes |

|share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by| |NLVM Fractions Rectangle |Printable Assets |

|weight, how many pounds of rice should each person get? Between what two whole | |Multiplication |Editable Enrich Masters |

|numbers does your answer lie? | | |Editable Reteach Masters |

|5. NF.4. Apply and extend previous understandings of multiplication to multiply| | |Family Letters and Activities |

|a fraction or whole number by a fraction. | | |Manipulative Masters |

|Interpret the product (a/b) × q as a parts of a partition of q into b equal | | |Homework Help |

|parts; equivalently, as the result of a sequence of operations a × q ÷ b. For | | | |

|example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a | | | |

|story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In | | | |

|general, (a/b) × (c/d) = ac/bd.) | | | |

|Find the area of a rectangle with fractional side lengths by tiling it with | | | |

|unit squares of the appropriate unit fraction side lengths, and show that the | | | |

|area is the same as would be found by multiplying the side lengths. Multiply | | | |

|fractional side lengths to find areas of rectangles, and represent fraction | | | |

|products as rectangular areas. | |8.3,6,7,8 | |

|5. NF.5. Interpret multiplication as scaling (resizing), by: | |10.6,8 | |

|Comparing the size of a product to the size of one factor on the basis of the | | | |

|size of the other factor, without performing the indicated multiplication. | | | |

|Explaining why multiplying a given number by a fraction greater than 1 results | | | |

|in a product greater than the given number (recognizing multiplication by whole| | | |

|numbers greater than 1 as a familiar case); explaining why multiplying a given | | | |

|number by a fraction less than 1 results in a product smaller than the given | | | |

|number; and relating the principle of fraction equivalence a/b = (n × a)/(n × | | | |

|b) to the effect of multiplying a/b by 1. | | | |

|5. NF.6. Solve real world problems involving multiplication of fractions and | | | |

|mixed numbers, e.g., by using visual fraction models or equations to represent | | | |

|the problem. | | | |

|5. NF.7. Apply and extend previous understandings of division to divide unit | | | |

|fractions by whole numbers and whole numbers by unit fractions.1 | | | |

|Interpret division of a unit fraction by a non-zero whole number, and compute | | | |

|such quotients. For example, create a story | | | |

|Context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. | | | |

|Use the relationship between multiplication and division to explain that (1/3) | | | |

|÷ 4 = 1/12 because (1/12) × 4 = 1/3. | |10.1-4, 6-8,12 | |

|Interpret division of a whole number by a unit fraction, and compute such | | | |

|quotients. For example, create a story context for 4 ÷ (1/5), and use a visual | | | |

|fraction model to show the quotient. Use the relationship between | | | |

|multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) =| |10.9-12 | |

|4. | | | |

|Solve real world problems involving division of unit fractions by non-zero | | | |

|whole numbers and division of whole numbers by unit fractions, e.g., by using | | | |

|visual fraction models and equations to represent the problem. For example, how| | | |

|much chocolate will each person get if 3 people share 1/2 lb of chocolate | | | |

|equally? How many 1/3-cup servings are in 2 cups of raisins? | | | |

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Measurement and Data

Convert like measurement units within a given measurement system.

Represent and interpret data.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

|Domain: Convert like measurement units within a given measurement system. | | | |

|Standards: | | | |

|5. MD.1. Convert among different-sized standard measurement units within a given | | | |

|measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in |Stepping It Up Project TE 800A |11.1-7, 9-13 | |

|solving multi-step, real world problems. |As well as: Formative Assessments |NLVM Converting Units | |

|Domain: Represent and interpret data. | | | |

|Standards: |Homework | | |

|5. MD.2. Make a line plot to display a data set of measurements in fractions of a|Am I Ready? |11.8 | |

|unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve |Diagnostic Test | | |

|problems involving information presented in line plots. For example, given |Pre-test | | |

|different measurements of liquid in identical beakers, find the amount of liquid |Check My Progress | | |

|each beaker would contain if the total amount in all the beakers were |Common Core Quick Check Quizzes | | |

|redistributed equally |Vocabulary Test | | |

|Domain: Geometric measurement: understand concepts of volume and relate volume |Online Self-Check Quizzes |12.8,12 | |

|to multiplication and to addition. |Summative Assessments |NLVM Space Blocks | |

|Standards: |Chapter Tests |NLVM How High? | |

|5. MD.3. Recognize volume as an attribute of solid figures and understand |Standardized Test Practice | | |

|concepts of volume measurement. |Extended Response Tests | | |

|A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic |Oral Assessment | | |

|unit” of volume, and can be used to measure volume. |eAssessment |12.8,12 | |

|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. | |12.9-12 | |

|5. MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic | | | |

|ft, and improvised units. | | | |

|5. MD.5 Relate volume to the operations of multiplication and addition and solve | | | |

|real world and mathematical problems involving volume. | | | |

|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. | | | |

|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. | | | |

|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. | | | |

Geometry

Graph points on the coordinate plane to solve real-world and mathematical problems.

Classify two-dimensional figures into categories based on their properties.

|Domain: Graph points on the coordinate plane to solve real-world and | | | |

|mathematical problems. | | | |

|Standards: | | | |

|5. G .1. Use a pair of perpendicular number lines, called axes, to define a | | | |

|coordinate system, with the intersection of the lines (the origin) arranged to | | | |

|coincide with the 0 on each line and a given point in the plane located by using| | | |

|an ordered pair of numbers, called its coordinates. Understand that the first | | | |

|number indicates how far to travel from the origin in the direction of one axis,|Geo-ville Project TE 902A |7.8,9 | |

|and the second number indicates how far to travel in the direction of the second| | | |

|axis, with the convention that the names of the two axes and the coordinates |As well as: Formative Assessments |NLVM Block Patterns | |

|correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | |NLVM Line Plotter | |

|5. G.2. Represent real world and mathematical problems by graphing points in the|Homework |NLVM Point Plotter | |

|first quadrant of the coordinate plane, and interpret coordinate values of |Am I Ready? | | |

|points in the context of the situation. |Diagnostic Test | | |

| |Pre-test | | |

|Domain: Classify two-dimensional figures into categories based on their |Check My Progress | | |

|properties. |Common Core Quick Check Quizzes | | |

|5. G.3. Understand that attributes belonging to a category of two-dimensional |Vocabulary Test | | |

|figures also belong to all subcategories of that category. For example, all | |7.7-9 | |

|rectangles have four right angles and squares are rectangles, so all squares |Online Self-Check Quizzes | | |

|have four right angles. | | | |

|5. G.4. Classify two-dimensional figures in a hierarchy based on properties. |Summative Assessments | | |

| |Chapter Tests | | |

| |Standardized Test Practice | | |

| |Extended Response Tests | | |

| |Oral Assessment | | |

| |eAssessment | | |

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| | | | |

| | |12.1-5 | |

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| | |NLVM Attribute Blocks | |

| | |NLVM Attribute Trains | |

| | |NLVM Pattern Blocks | |

| | |NLVM Geoboard | |

| | |NLVM Geoboard Circular | |

| | |NLVM Geoboard Isometric | |

| | |NLVM Geoboard Coordinate | |

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