Student Targets NBT.1.1 Recognize that in a multi-digit number, a digit in one 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. NBT.2.5 NBT.1.2 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. Perform operations with multi-digit whole numbers and with decimals to hundredths. Fluently multiply multi-digit whole numbers using the standard algorithm. understand the 10 to 1 relationship among placevalue positions. • write and evaluate powers of 10 in exponent form. • multiply by powers of 10 and explain patterns in the number of zeros. Vocabulary area model Place Value of Whole Numbers base Powers of Ten and Exponents digit estimate Multiplication Patterns with Zeros expanded form exponent 13 days: August 20 – September 8 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Unit 1: Whole Number Multiplication and Expressions OA.1.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Lessons The student will: • Understand the place value system. Number and Operations in Base Ten (NBT) Unit Write and interpret numerical expressions. OA.1.2 Operations and Algebraic Thinking (OA) Cluster/ Standards (MAFS) Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 1st Trimester • multiply by 1-digit numbers. • explain the multiplication process using strategies based on place value. • multiply by 2-digit numbers. • use the order of operations to evaluate expressions with grouping symbols. • use grouping symbols in expressions and explain their effect. • write numerical expressions to represent word phrases. • describe the relationship between expressions without evaluating them. Multiply by 1-Digit Numbers Multiplication Strategies Based on Place Value factor multiply pattern period Multiply by 2-Digit Numbers Evaluate Numerical Expressions with Grouping Symbols Use Grouping Symbols in Expressions place value power (partial) product standard form word form Write Numerical Expressions Interpret Numerical Expressions evaluate grouping symbols numerical expression order of operations parentheses (also braces and brackets) *Strikethrough within a standard denotes that the content is addressed in a different unit. Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 1st Trimester Student Targets The student will: 14 days: September 9 – September 30 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Unit 2: Whole Number Division NBT.1.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its 1 right and of what it represents in the 10 place to its left. Perform operations with multi-digit numbers and with decimals to hundredths. NBT.2.6 Number and Operations in Base Ten (NBT) Understand the place value system. 1 • understand that of a number is 10 the same as dividing the number by 10. • use multiplication to solve division problems. Lessons Place Value and Patterns area model Relate Multiplication to Division compatible numbers Divide by 1-Digit Divisors use the Distributive Property to solve division problems. • use place value and estimation to divide by 1-digit divisors. • model division with 2-digit divisors using area models. Estimate with 2-Digit Divisors • estimate quotients using compatible numbers. Partial Quotients • use partial quotients to divide by 2-digit divisors. Divide by 2-Digit Divisors • divide by 2-digit divisors using models and strategies. Connect Division Models and Strategies Based on Place Value • interpret remainders to solve division problems. Interpret the Remainder solve word problems involving equal groups. digit Use the Distributive Property • • Vocabulary Distributive Property (for × and ÷) Model Division with 2-Digit Divisors divide dividend Multiplication and Division Word Problems divisor estimate inverse operations 1 10 of (one-tenth) partial quotients pattern place value quotient regroup remainder Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 1st Trimester Perform operations with multi-digit 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; relate the strategy to a written method and explain the reasoning used. • understand the 10 to 1 relationship among decimals to thousandths. • read and write decimals to thousandths using numbers, words, and expanded form. • 14 days: October 1 – October 20 Use place value understanding to round decimals to any place. Unit 3: Decimal Addition and Subtraction NBT.1.1 NBT.1.4 NBT.1.3 NBT.1.3a NBT.1.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. NBT.2.7 Number and Operations in Base Ten (NBT) Recognize that in a multi-digit number, a digit in one 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 and write decimals to thousandths using base-ten numerals, number names, and expanded form. Lessons • rename decimals using different place values. compare decimals to thousandths using place value. • round decimals to any place. • model decimal addition using base-ten blocks. • model decimal subtraction using base-ten blocks. • make reasonable estimates of decimal sums and differences. • add and subtract decimals using place value. • solve addition and subtraction word problems involving decimal amounts. Vocabulary benchmark The student will: Understand the place value system. Read, write, and compare decimals to thousandths. Student Targets Decimals to Thousandths compare Place Value of Decimals decimal Rename Decimals decimal point Compare Decimals digit Round Decimals estimate Decimal Addition expanded form Decimal Subtraction hundredth Estimate Decimal Sums and Differences place value Add and Subtract Decimals round Decimal Addition and Subtraction Word Problems standard form Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education regroup tenth thousandth whole number word form Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 1st Trimester Student Targets The student will: 10 days: October 21 – November 4 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; relate the strategy to a written method and explain the reasoning used. • find patterns in products when multiplying by powers of 10. • model multiplication of whole numbers and decimals. • Unit 4: Decimal Multiplication NBT.1.2 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 whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to hundredths. NBT.2.7 Number and Operations in Base Ten (NBT) Understand the place value system. • • Lessons Multiplication Patterns with Decimals Multiply Decimals and Whole Numbers area model decimal decimal point digit multiply a decimal and a whole number using drawings and place value. Multiplication with Decimals and Whole Numbers use expanded form and place value to multiply a decimal and a whole number. Multiply Using Expanded Form Multiplying Money Word Problems solve word problems involving equal amounts of money. Decimal Multiplication model multiplication of two decimals. Multiply Decimals • place the decimal point in decimal multiplication. Zeros in the Product • multiply decimals with zeros in the product. • Vocabulary estimate expanded form exponent factors hundredths multiplication ones patterns place value power of ten product tenths thousandths whole number Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 1st/2nd Trimester Student Targets The student will: 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 whole-number exponents to denote powers of 10. 10 days: November 5 – November 20 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; relate the strategy to a written method and explain the reasoning used. • Unit 5: Decimal Division NBT.1.2 • Perform operations with multi-digit whole numbers and with decimals to hundredths. NBT.2.7 Number and Operations in Base Ten (NBT) Understand the place value system. • find patterns in quotients when dividing by powers of 10. model division of decimals by whole numbers. Lessons Vocabulary Division Patterns with Decimals area model Divide Decimals by Whole Numbers compatible numbers decimal Estimate Quotients decimal point estimate decimal quotients. Division of Decimals by Whole Numbers • divide decimals by whole numbers. • model division by decimals. Decimal Division • place the decimal point in decimal division. Divide Decimals • explain the reasoning used in a division problem. Reason about Division • solve multistep decimal problems. Multistep Decimal Problems digit division dividend divisor estimate exponent hundredths patterns power of ten quotient regroup tenths thousandths End of Trimester: November 13, 2015 Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education Unit Suggested Pacing Cluster/ Standards (MAFS) Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. 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. 14 days: November 23 – December 15 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. • Unit 6: Fraction Addition and Subtraction NF.1.1 NF.1.2 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. Student Targets The student will: Use equivalent fractions as a strategy to add and subtract fractions. MD.2.2 Measurement and Data (MD) Number and Operations – Fractions (NF) Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 2nd Trimester use models and multiplication to generate equivalent fractions. • use models to add fractions with unlike denominators. • use models to subtract fractions with unlike denominators. • make reasonable estimates of fraction sums and differences. • use equivalent fractions to add and subtract fractions. • add and subtract mixed numbers with unlike denominators. • rename to find the difference of two mixed numbers. Lessons Rename Fractions with Equivalent Fractions Addition with Unlike Denominators Subtraction with Unlike Denominators Estimate Fraction Sums and Differences Vocabulary Associative Property (+) benchmark common denominator Commutative Property (+) data denominator Add and Subtract Fractions Add and Subtract Mixed Numbers Subtraction with Renaming Use Properties of Addition • add fractions and mixed numbers with unlike denominators using the properties. • use equivalent fractions to find missing numerators or denominators in equations. Fraction Addition and Subtraction Word Problems solve word problems by using models or equations to represent the problem. Line Plots - Addition and Subtraction Problems Missing Numbers in Fraction Equations difference equivalent fractions estimate fraction fraction greater than 1 (improper) graph • • line plot measurement solve addition and subtraction problems involving data from line plots. mixed number multiples numerator regroup/ rename sum whole number Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 2nd Trimester The student will: 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; 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. • 14 days: December 16 – January 20 NF.2.5a Interpret multiplication as scaling (resizing), by: • Unit 7: Fraction Multiplication NF.2.4 NF.2.4a 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. NF.2.5b NF.2.5 NF.2.4b 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. NF.2.6 Number and Operations – Fractions (NF) Apply and extend previous understandings of multiplication and division to fractions. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Student Targets model to find the fractional part of a group. model the product of a fraction and a whole number. Lessons Find Part of a Group Multiply Fractions and Whole Numbers compare Multiply Fractions Distributive Property (×) • multiply fractions using models. • relate the size of the product compared to the size of one factor when multiplying fractions. Compare Fraction Factors and Products • multiply fractions. Fraction Multiplication • use an area model to multiply two mixed numbers. Multiply Mixed Numbers • find the area of a rectangle with fractional side lengths. Area and Mixed Numbers • area model denominator multiply fractions and whole numbers. relate the size of the product to the factors when multiplying fractions greater than one. area Fraction and Whole Number Multiplication • • Vocabulary dimension equal groups equivalent fraction factor fraction Compare Mixed Number Factors and Products fraction greater than 1 (improper) Multiply Mixed Numbers mixed number solve real world problems involving mixed number multiplication. Solve real world problems involving multiplication of fractions and mixed numbers. Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education numerator product scale/resize square unit unit fraction whole number Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 2nd Trimester The student will: 7 days: January 21 – February 2 Interpret division of a whole number by a unit fraction, and compute such quotients. Unit 8: Fraction Division NF.2.3 NF.2.7a NF.2.7b NF.2.7 • Interpret a fraction as division of the 𝑎𝑎 numerator by the denominator ( = a ÷ 𝑏𝑏 b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. interpret a fraction as division and solve whole-number division problems that result in a fraction or mixed number. • divide a unit fraction by a whole number. • divide a whole number by a unit fraction. • use multiplication to divide whole numbers by fractions and fractions by whole numbers. • Lessons Connect Fractions to Division Vocabulary area model Divide Fractions by Whole Numbers dividend Divide Whole Numbers by Fractions division divisor equal groups Fraction and Whole Number Division Interpret Division with Fractions use diagrams and equations to solve real world unit fraction division problems. equation expression fraction fraction greater than 1 (improper) fraction number line inverse operations mixed numbers NF.2.7c Number and Operations – Fractions (NF) Apply and extend previous understandings of multiplication and division to fractions. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Student Targets 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. multiplication quotient unit fraction whole number Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 2nd/3rd Trimester The student will: OA.1.2 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. OA.2.3 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. Measurement & Data (MD) Represent and interpret data. MD.2.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. 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. Geometry (G) Graph points on the coordinate plane to solve real-world and mathematical problems. G.1.1 G.1.2 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, 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. 11 days: February 3 – February 18 Analyze patterns and relationships. Unit 9: Patterns and Graphing Operations & Algebraic Thinking (OA) Write and interpret numerical expressions. OA.1.1 Student Targets • write and evaluate expressions with fractions. • solve problems involving data from line plots. • graph and name points on a coordinate grid using ordered pairs. • graph and interpret data on a coordinate grid. • use two rules to generate a numerical pattern and identify the relationship between the corresponding terms in the patterns. • • Lessons Expressions with Fractions Line Plots – Multiplication and Division Problems Ordered Pairs Vocabulary data equally redistribute expression fraction line plot Graph Data Numerical Patterns Graph and Analyze Relationships Graph and Analyze 2-Step Patterns graph and analyze the relationship between two numerical patterns on a coordinate grid. graph and analyze the relationship between two numerical 2-step patterns on a coordinate grid. Represent real world 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. End of Trimester: February 12, 2016 Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education order of operations coordinate grid graph/plot ordered pair origin pattern point relationship rule term x-axis x-coordinate y-axis y-coordinate Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 3rd Trimester Student Targets The student will: 11 days: February 18 – March 7 • Unit 10: Measurement Conversions Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb., oz.; l, ml; hr., min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. MD.1.1 Measurement and Data (MD) Convert like measurement units within a given measurement system. Lessons Metric Measures compare, contrast, and convert metric units. Customary Length • compare, contrast, and convert customary units of length. Customary Capacity • compare, contrast, and convert customary units of capacity. • compare, contrast, and convert customary units of weight. • convert customary measurement units to solve multi-step real world problems. Multi-step Metric Measurement Problems • convert metric measurement units to solve multi-step real world problems. Customary and Metric Conversions • solve conversion problems with fractional parts of a unit. • convert units of time to solve problems. Weight Multi-step Customary Measurement Problems Vocabulary metric gram kilogram mass milligram kilometer liter milliliter centimeter decimeter kilometer meter millimeter conversion unit fractions decimals Time Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education customary foot inch length mile yard capacity cup fluid ounce gallon pint quart ounce pound ton weight time Cluster/ Standards (MAFS) Unit Suggested Pacing Domain The School District of Palm Beach County 5th Grade Mathematics Scope 2015-2016 3rd Trimester Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. MD.3.3b MD.3.4 MD.3.5 MD.3.5a MD.3.5b Geometry (G) MD.3.5c Classify two-dimensional figures into categories based on their properties. G.2.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. G.2.4 Classify and organize two-dimensional figures into Venn diagrams based on attributes of the figures. • identify and classify polygons. • classify and compare triangles using their properties. • • 13 days: March 8 – April 1 Measurement and Data (MD) MD.3.3a Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. 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. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft., and improvised units. 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. 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. The student will: Unit 11: Geometry and Volume MD.3.3 Student Targets • classify and compare quadrilaterals using their properties. reason about the properties (of sides, angles, and symmetry) of quadrilaterals. understand unit cubes and how they can be used to build a solid figure. Lessons Vocabulary Polygons congruent decagon Triangles heptagon hexagon Quadrilaterals Reason about Quadrilaterals Unit Cubes and Solid Figures Understand Volume Estimate Volume Volume of Rectangular Prisms nonagon octagon parallel lines parallelogram pentagon perpendicular lines polygon quadrilateral rectangle regular polygon rhombus • count unit cubes that fill a solid figure to find volume. Apply Volume Formulas and Compare Dimensions trapezoid equilateral triangle • estimate the volume of a rectangular prism. Find Volume of Combined Figures isosceles triangle scalene triangle • find the volume of rectangular prisms. • use a formula to find the volume of rectangular prisms and compare dimensions. • find the volume of combined rectangular prisms. Spring Break: March 18 – 25, 2016 Review 5th Grade Mathematics Florida Standards (MAFS): April 4 – 8, 2016 Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education acute triangle obtuse triangle right triangle cubic unit estimate formula rectangular prism solid figure unit cube volume The School District of Palm Beach County 5th Grade Mathematics Scope 2014-2015 3rd Trimester Florida Standards Assessment (FSA) Testing Window: April 11 – May 6, 2016 Finalizing Mastery of 5th Grade Mathematics Standards (MAFS): May 9 – June 2, 2016 Last Day of School: June 2, 2016 Copyright © 2015 by School Board of Palm Beach County, Department of Secondary Education
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