North Adams Public Schools 5 th Grade Math Curriculum Map Unit: 1  Addition and Subtraction with Fractions


 Augusta Powell
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1 Unit: 1  Addition and Subtraction with Fractions Pacing: 20 Days (Sept.) From the previous year, students should have mastered: Representing fractions as sums of unit fractions Composed and decomposed fractions and mixed numbers Use bar models to represent equivalent fractions and find sums and differences. Enduring Understandings Essential Questions Knowing how to use fractions will help me solve complex mathematical problems. What is an equivalent fraction? How do you add and subtract fractions with unlike denominators? How do you add and subtract mixed numbers with unlike denominators? By the end of this unit, students should be able to: Use number lines to represent equivalent fractions; Express fractions with unlike denominators in terms of the same unit fraction so they can be added or subtracted; Use bar models to visualize a sum or difference; Use equations and models to solve real world problems; Use estimation to determine whether answers are reasonable MA Learning Standards 2017 Revisions 5.NF.A.1,2: edited to clarify the concept of whole as being a single unit or a set of objects Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, = = (In general, a b + c d = (ad + bc) bd) Solve word problems involving addition and subtraction of fractions referring to the same whole (the whole can be a set of objects), including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result = 3 7, by observing that 3 7 < 1 2.
2 5.MD.2: Measurement and Data Represent and interpret data. Make a line plot (dot plot) to display a data set of measurements in fractions of a unit. Use operations on fractions for this grade to solve problems involving information presented in line plot (dot plot). For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Vocabulary Resources Assessment Denominator Fraction Math Expressions, Common Core Math Expressions Unit 1 Assessment Numerator Unit Fraction Grade 5 Openresponse, Multiple choice, or Equivalent Fractions Multiplier Differentiated Instruction Cards Performance based Nsplit Simplify Math Writing Prompts NAPS Unit Test 1 Unsimplify Benchmark Fast Bridge online assessments Common Denominator Regroup Common Factor Greater Than > Less than, < Mixed Number Add on Ungroup Line plot Estimate Round Situation equation Solution equation
3 Unit: 2  Addition and Subtraction with Decimals Pacing: 20 Days (Oct) From the previous year, students should have mastered: Using placevalue drawings to help conceptualize numbers and understand the relative sizes of place values. Using different methods to add and subtract whole numbers. Enduring Understandings Essential Questions If I can use decimals, I can compute money problems and understand more complex math in middle school. How can I read and write, compare, and round decimals? How will knowing how to compute with decimals connect to my life? By the end of this unit, students should be able to: Understand decimals as equal divisions of a whole; read, write, and model whole and decimal numbers; Model and identify equivalent decimals; Model adding and subtracting decimals; Add and subtract whole numbers and decimals to hundredths; Use the Commutative Associative, and Distributive properties to compute mentally; Estimate decimal sums and differences; Read and construct graphs with decimal scales and decimal numbers; Use content standards and practices in a variety of real world problems solving situations. MA Learning Standards 2017 Revisions 5.NB.1,7: Edited to include the term decimal and to retain focus in grade 5 on developing fluency in multidigit multiplication and division. Understand the place value system. Recognize that in a multidigit number, including decimals, a digit in any place represents 10 times as much as it represents in the place to its right and 1 10 of what it represents in the place to its left. Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., = ( 1 10) + 9 ( 1 100) + 2 ( ). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
4 Use place value understanding to round decimals to any place. Perform operations with multidigit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and between multiplication and division; relate the strategy to a written method and explain the reasoning used. 5.MD: Measurement and Data Convert like measurement units within a given measurement system. Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems Vocabulary Resources Assessment Decimal Tenth Math Expressions, Common Core Math Expressions Unit 2 Assessment Hundredth Thousandth Grade 5 Openresponse, Multiple choice, or Notation Standard form Differentiated Instruction Cards Performance based Word form Expanded form Math Writing Prompts Quick Quizzes Power of ten Equivalent decimal Fast Bridge online assessments NAPS Unit Test 1 Meter Decimeter Centimeter Millimeter Grouping Ungrouping Break apart drawing Round Estimate Commutative Property of Addition Associative Property of Addition Distributive Property of Multiplication over Addition
5 Unit 3  Multiplication and Division with Fractions Pacing: 23 days (Nov./Dec.) From the previous year, students should have mastered: Represented fractions as sums of unit fractions; Composed and decomposed fractions and mixed numbers; Used bar models to represent equivalent fractions and to find sums and differences Enduring Understandings Essential Questions The knowledge of fractions will provide the opportunity for students to be able to solve the many real world applications of fractions and mixed numbers and complex mathematical problems. How do I multiply a whole number by a fraction? A mixed number by a fraction? A fraction by a fraction? How are fractions used in solving realworld problems? How do I know if a word problem requires multiplication or division? By the end of this unit, students should be able to: Use comparison bars to solve multiplicative comparison problems involving fractions; Use number lines to solve problems involving nonunit fractions; Use area models to solve problems involving fractions; Use bar models to multiply, compare, and divide fractions. MA Learning Standards 2017 Revisions 5.NF.2, 4a, 5a: edited to clarify the concept of whole as being a single unit or a set of objects, to maintain mathematical rigor by providing options for ways of showing conceptual understanding when multiplying fractions by whole numbers, and to provide an example to clarify the standard and to maintain the focus of the standard. Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, = = (In general, a b + c d = (ad + bc) bd) Solve word problems involving addition and subtraction of fractions referring to the same whole (the whole can be a set of objects), including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the
6 problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result = 3 7, by observing that 3 7 < 1 2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 3. Interpret a fraction as division of the numerator by the denominator ( a b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret ¾ as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when three wholes are shared equally among four people each person has a share of size ¾. If nine people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. o Interpret the product ( a b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model and/or area model to show ( 2 3) 4 = 8 3, and create a story context for this equation. Do the same with ( 2 3) ( 4 5) = (In general, ( a b) ( c d) = ac bd.) o 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. Interpret multiplication as scaling (resizing), by: o 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. For example, without multiplying tell which number is greater: 225 or ¾ x 225; or 3 2 x 11 50? o 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. Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1 o Interpret division of a unit fraction by a nonzero 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. o Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story
7 o 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) = 4. Solve realworld problems involving division of unit fractions by nonzero 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 three people share ½ lb. of chocolate equally? How many 1 3 cup servings are in two cups of raisins. 5.MD: Measurement and Data Represent and interpret data. Make a line plot (dot plot) to display a data set of measurements in fractions of a unit. Use operations on fractions for this grade to solve problems involving information presented in line plot (dot plot). For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Vocabulary Resources Assessment Comparison Bars Factor Multiplicative comparison Product Area model for multiplication Fractionbar model for multiplication Multiply & Simplify Method and viceversa Unit Fraction Method Dividend Associative Property Divisor Commutative Property Quotient Distributive Property Decimal fraction Math Expressions, Common Core Grade 5 Differentiated Instruction Cards Math Writing Prompts Fast Bridge online assessments Math Expressions Unit 3 Assessment Openresponse, Multiple choice, or Performance based Quick Quizzes NAPS Unit Test 3
8 Unit 4  Multiplication with Whole Numbers and Decimals Pacing: 20 days (Dec./Jan.) From the previous year, students should have mastered: Used strategies based on place value and properties to multiply whole numbers; represented multiplying multidigit numbers with arrays and area models; wrote equations to represent multiplication situations. Enduring Understandings Essential Questions If I can use decimals, I can compute money problems and understand more complex math in middle school. How will knowing how to compute with decimals connect to my life? What methods can I use to solve multidigit multiplication problems? By the end of this unit, students should be able to: Represent multiplying decimals with money and drawings; use strategies based on place value and properties to multiply decimal numbers; write equations to represent multiplication situations. MA Learning Standards 2017 Revisions 5.NBT.1, 5, 7: edited to include the term decimal, to provide parameters that clarify the student learning expectation of the standard, to retain focus in grade 5 on developing fluency in multidigit multiplication and division. 5.NF.5a: edited to provide an example to clarify the standard and to maintain the focus of the standard. Understand the place value system. Recognize that in a multidigit number, including decimals, a digit in any place represents 10 times as much as it represents in the place to its right and 1 10 of what it represents in the place to its left. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. Read, write, and compare decimals to thousandths. o b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
9 Use place value understanding to round decimals to any place. Perform operations with multidigit whole numbers and with decimals to hundredths. Fluently multiply multidigit whole numbers. (Include twodigit x fourdigit numbers and, threedigit x threedigit numbers) using the standard algorithm. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and between multiplication and division; relate the strategy to a written method and explain the reasoning used. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing), by: o 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. For example, without multiplying tell which number is greater: 225 or ¾ x 225; or 3 2 x 11 50? o 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. Vocabulary Resources Assessment Shift Base Exponent Exponential Form Power of ten Even Odd Partial Products Place Value Sections Expanded Notation New Groups Below Place Value Rows Short Cut Commutative Property of Multiplication Associative Property of Multiplication Distributive Property of Multiplication over Addition Math Expressions, Common Core Grade 5 Differentiated Instruction Cards Math Writing Prompts Fast Bridge online assessments Math Expressions Unit 4 Assessment Openresponse, Multiple choice, or Performance based Quick Quizzes NAPS Unit Test 4
10 Unit 5  Division with Whole Numbers and Decimals Pacing: 20 days (Feb./March) From the previous year, students should have mastered: Drawing visual arrays and rectangle diagrams to represent multiplication; Reason about the connection between math drawings and written numerical work; Division algorithms are summaries of the reasoning about quantities. Enduring Understandings Essential Questions Understanding decimals enables me to perform the mathematics I need for higher level problems. What are the different ways to do long division with and without remainders? How can you estimate answers? By the end of this unit, students should be able to: Understand the place value system; perform operations with multidigit whole numbers and with decimals to hundredths; Apply and extend previous understandings of multiplication and division to multiply and divide fractions; Solve realworld problems. MA Learning Standards 2017 Revisions 5.NBT.5, 7: edited to include the term decimal, to provide parameters that clarify the student learning expectation of the standard, to retain focus in grade 5 on developing fluency in multidigit multiplication and division. 5.NF.5.a: edited to provide an example to clarify the standard and to maintain the focus of the standard Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. Read, write, and compare decimals to thousandths. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Perform operations with multidigit whole numbers and with decimals to hundredths. Fluently multiply multidigit whole numbers. (Include twodigit x fourdigit numbers and, threedigit x threedigit numbers)
11 using the standard algorithm. Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and between multiplication and division; relate the strategy to a written method and explain the reasoning used. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing), by: 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. Vocabulary Resources Assessment Digitbydigit method dividend Divisor quotient Expanded notation method remainder Place value sections method Overestimate Underestimate Math Expressions, Common Core Grade 5 Differentiated Instruction Cards Math Writing Prompts Fast Bridge online assessments Math Expressions Unit 5 Assessment Openresponse, Multiple choice, or Performance based Quick Quizzes NAPS Unit Test 5
12 Unit 6 Operations and Word Problems Pacing: 18 days (Feb./March) From the previous year, students should have mastered: Using drawings and equations with a symbol for the unknown number to represent the problem; Representing verbal statements of multiplicative comparisons as multiplication equations; Writing equations to represent problems with more than one step. Enduring Understandings Essential Questions Students need to understand the basic algebraic operations in order to perform the everyday math they need to accomplish to solve everyday problems that require algebraic thinking. What is an equation? How do you write an equation? Why do I need to learn to solve word problems? By the end of this unit, students should be able to: Write situation and solution equations to solve addition, subtraction, multiplication, division, problems along with problems involving fractions and decimals; Solve twostep and multistep problems. MA Learning Standards 2017 Revisions 5.OA.1: edited to include an example to clarify the expectation in the standard for grade 5 NBT.5, 7: edited to provide parameters that clarify the student learning expectation of the standard, to retain focus in grade 5 on developing fluency in multidigit multiplication and division. 5.NF.2, 4a,5a: edited to clarify the concept of whole as being a single unit or a set of objects, Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, e.g.,(6 x 30) + (6 x 1 2). Understand the place value system. Use place value understanding to round decimals to any place.
13 Perform operations with multidigit whole numbers and with decimals to hundredths. Fluently multiply multidigit whole numbers. (Include twodigit x fourdigit numbers and, threedigit x threedigit numbers) using the standard algorithm. Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and between multiplication and division; relate the strategy to a written method and explain the reasoning used. Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, = = (In general, a b + c d = (ad + bc) bd.) Solve word problems involving addition and subtraction of fractions referring to the same whole (the whole can be a set of objects), including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result = 3 7, by observing that 3 7 < 1 2. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator ( a b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret ¾ as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when three wholes are shared equally among four people each person has a share of size ¾. If nine people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product ( a b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model and/or area model to show ( 2 3) 4 = 8 3, and create a story context for this equation. Do the same with ( 2 3) ( 4 5) = (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. Interpret multiplication as scaling (resizing), by: 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. For example, without multiplying tell which number is greater: 225 or ¾ x 225; or 3 2 x 11 50?
14 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. Solve realworld problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 2 Interpret division of a unit fraction by a nonzero 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. 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) = 4. Solve realworld problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Vocabulary Resources Assessment Situation equation Solution equation Break apart drawing Rectangle model Benchmark Comparison Leading Language Misleading Language Scaling Additive Multiplicative Parentheses Equation Math Expressions, Common Core Grade 5 Differentiated Instruction Cards Math Writing Prompts Fast Bridge online assessments Math Expressions Unit 6 Assessment Openresponse, Multiple choice, or Performance based Quick Quizzes NAPS Unit Test 6
15 Unit 7  Algebra, Patterns, and Coordinate Graphs Pacing: 20 days (March/Apr.) From the previous year, students should have mastered: Represent multiplicative comparison problems using drawings and equations with a symbol for the unknown number; Represent problems using equations with a letter standing for the unknown quantity; Identify apparent features of a pattern that are not explicit in the rule itself. Enduring Understandings Essential Questions Students need to understand the basic algebraic operations in order to perform the everyday math they need to accomplish to solve everyday problems that require algebraic thinking. By the end of this unit, students should be able to: Why do I need to learn Algebra? What is the Order of Operations? Why do I need to use the Order of Operations when solving mathematical problems? What is a coordinate plane? How do you graph in a coordinate plane? Simplify an expressing using the Order of Operations; Interpret expressions without simplifying them; identify relationships between corresponding terms in two patterns, represent points in a coordinate plane. MA Learning Standards 2017 Revisions 5.OA.1: edited to include an example to clarify the expectation in the standard for grade 5 Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, e.g.,(6 x 30) + (6 x 1 2). Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation Add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product. Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
16 For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Graph points on the coordinate plane to solve realworld and mathematical problems. 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 zero 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, 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 correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). Represent realworld and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Vocabulary Resources Assessment Expression Simplify Variable Term Ordered Pair yaxis xaxis Order of Operations Evaluate Numerical expression Coordinate Plane Origin ycoordinate xcoordinate Math Expressions, Common Core Grade 5 Differentiated Instruction Cards Math Writing Prompts Fast Bridge online assessments Math Expressions Unit 7 Assessment Openresponse, Multiple choice, or Performance based Quick Quizzes NAPS Unit Test 7
17 Unit 8  Measurement and Geometry Pacing: 25 days (April/May) From the previous year, students should have mastered: Represent multiplicative comparison problems using drawings and equations with a symbol for the unknown number; Represent problems using equations with a letter standing for the unknown quantity; Identify apparent features of a pattern that are not explicit in the rule itself. Enduring Understandings Essential Questions. Measurement and data analysis are the basis of understanding geometric shapes, composition and problem solving. Most applied math involves measurement. How can I convert customary units? Do I need to use more than one operation when I use line plots? What is volume? How can I find the volume of a rectangular prism? By the end of this unit, students should be able to: Convert like measurement units within a given measurement system; Represent and interpret data; understand concepts of volume and relate volume to multiplication and to addition; Classify twodimensional figures into categories based on their properties. MA Learning Standards 2017 Revisions 5.MD.2, 4: edited to include the words dot plot because it is a more commonly used term and to help clarify the standard about the expectation for using this method for representing data and to maintain the mathematical rigor. Dot plot added to glossary. Convert like measurement units within a given measurement system. Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, realworld problems. Represent and interpret data. Make a line plot (dot plot) to display a data set of measurements in fractions of a unit. Use operations on fractions for this grade to solve problems involving information presented in line plot (dot plot). For example, given different measurements
18 of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and nonstandard units. Relate volume to the operations of multiplication and addition and solve realworld and mathematical problems involving volume. Find the volume of a right rectangular prism with wholenumber edge lengths by packing it 5.G: Geometry Classify twodimensional figures into categories based on their properties. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify twodimensional figures in a hierarchy based on properties. For example, all rectangles are parallelograms because they are all quadrilaterals with two pairs of opposite sides parallel. Vocabulary Resources Assessment Meter Centimeter Dekameter Kilometer Milliliter Deciliter Hectoliter Mass Milligram Decigram Hectogram Mile Frequency table Perimeter Square Centimeter Face Rectangular prism Millimeter Decimeter Hectometer Liter centimeter dekaliter kiloliter gram centigram dekagram kilogram ton Line plot Area Square Unit Edge Cube Math Expressions, Common Core Grade 5 Differentiated Instruction Cards Math Writing Prompts Fast Bridge online assessments Math Expressions Unit 8 Assessment Openresponse, Multiple choice, or Performance based Quick Quizzes NAPS Unit Test 8
19 Unit cube Cubic Unit Rectangular prism Onedimensional Threedimensional Acute angle Adjacent sides Counterexample Line of Symmetry Opposite Sides Perpendicular Acute Triangle Congruent Sides Isosceles Triangle Obtuse Triangle Right Angle Scalene Triangle Concave Open Reflex Angle Volume Volume Cubic Unit twodimensional Composite Adjacent angles Congruent Parallel Opposite Angles Parallelogram Quadrilateral Congruent angles Equilateral triangle Obtuse angle Perpendicular sides Right Triangle Closed Convex Polygon Regular Polygon
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