# The School District of Palm Beach County 5 th Grade Mathematics Scope st Trimester. 13 days: August 18 September 6

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1 1 st Trimester Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) OA.1.1 OA.1.2 NBT.1.1 Write and interpret numerical expressions. 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. Understand the place value system. 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. 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. NBT.1.2 NBT.2.5 Fluently multiply multi-digit whole numbers using the standard algorithm. *Strikethrough within a standard denotes that the content is addressed in a different unit. 1: Whole Number Multiplication and Expressions 13 days: August 18 September 6 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. 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. Place Value of Whole Numbers Powers of Ten and Exponents Multiplication Patterns with Zeros Multiply by 1-Digit Numbers Multiplication Strategies Based on Place Value Multiply by 2-Digit Numbers Evaluate Numerical Expressions with Grouping Symbols Use Grouping Symbols in Expressions Write Numerical Expressions Interpret Numerical Expressions area model base digit expanded form exponent factor multiply pattern period place value power (partial) product standard form word form evaluate grouping symbols numerical expression order of operations parentheses (also braces and brackets)

2 1 st Trimester Number and Operations in Base Ten (NBT) NBT.1.1 Understand the place value system. 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 of what it represents in the place to its left. Perform operations with multi-digit numbers and with decimals to hundredths. NBT.2.6 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. 2: Whole Number Division 14 days: September 7 September 26 understand that of a number is the same as dividing the number by 10. divide using the Distributive Property. divide by 1-digit divisors using place value and estimation. model division with 2-digit divisors using area models. quotients using compatible numbers. use partial quotients to divide by 2-digit divisors. divide by 2-digit divisors using models and strategies. interpret remainders to solve division problems. solve word problems involving equal groups. Place Value and Patterns Use the Distributive Property Divide by 1-Digit Divisors Model Division with 2-Digit Divisors Estimate with 2-Digit Divisors Partial Quotients Divide by 2-Digit Divisors Connect Division Models and Strategies Based on Place Value Interpret the Remainder Multiplication and Division Word Problems area model compatible numbers digit Distributive Property (for and ) divide dividend divisor inverse operations partial quotients pattern place value quotient regroup remainder unknown factor

4 1 st Trimester Number and Operations in Base Ten (NBT) NBT.1.2 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 whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to hundredths. NBT.2.7 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. 4: Decimal Multiplication 11 days: October 17 November 1 find patterns in products when multiplying by powers of 10. model multiplication of whole numbers and decimals. multiply a decimal and a whole number using place value and estimation. model multiplication of two decimals. model multiplication of two decimals. place the decimal point in decimal multiplication. explain the reasoning used in a multiplication problem. solve decimal word problems involving equal groups. Multiplication Patterns with Decimals Model Multiplication of Decimals and Whole Numbers Use Patterns and Estimation to Multiply Decimals and Whole Numbers Model Decimal Multiplication Multiply Using the Area Model Multiply Decimals: Place the Decimal Point Reason About Multiplication Multiplying Decimals Word Problems area model decimal decimal point digit expanded form exponent factors hundredths multiplication ones patterns place value power of ten product tenths thousandths whole number

5 1 st /2 nd Trimester Number and Operations in Base Ten (NBT) NBT.1.2 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 whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to hundredths. NBT.2.7 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. 5: Decimal Division 11 days: November 2 November 20 find patterns in quotients when dividing by powers of 10. model division of decimals by whole numbers. divide decimals by whole numbers using place value and estimation. model division by decimals. place the decimal point in decimal division. explain the reasoning used in a division problem. solve multistep decimal problems. Division Patterns with Decimals Model Division of Decimals by Whole Numbers Use Patterns and Estimation to Divide Decimals by Whole Numbers Decimal Division Divide Decimals: Place the Decimal Point Reason about Division Multistep Decimal Problems area model compatible numbers decimal decimal point digit division dividend divisor exponent hundredths patterns power of ten quotient regroup tenths thousandths

7 2 nd Trimester Number and Operations Fractions (NF) NF.2.4 NF.2.4a NF.2.4b NF.2.5 NF.2.5a NF.2.5b 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. 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. 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. 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. 7: Fraction Multiplication 14 days: December 19 January 23 find multiples of fractions using models. find part of a whole using models. multiply fractions and whole numbers. multiply two fractions using area models. relate the size of the product compared to the size of one factor when multiplying fractions. multiply two fractions. use an area model to multiply two mixed numbers. find the area of a rectangle with fractional side lengths. relate the size of the product to the factors when multiplying fractions greater than one. solve real world problems involving mixed number multiplication. Multiply Fractions by Whole Numbers: Multiples of Fractions Multiply Fractions by a Whole Number: Find Part of a Whole Fraction and Whole Number Multiplication Multiply Fractions Compare Fraction Factors and Products Fraction Multiplication Area and Mixed Numbers Tiling and Mixed Numbers Compare Mixed Number Factors and Products Multiply Mixed Numbers area area model compare denominator dimension Distributive Property ( ) equal groups equivalent fraction factor fraction fraction greater than 1 (improper) mixed number numerator product scale/resize square unit NF.2.6 Solve real world problems involving multiplication of fractions and mixed numbers. unit fraction whole number

8 - 2 nd Trimester Operations and Algebraic Thinking (OA) Measurement and Data (MD) OA.1.1 OA.1.2 NF.2.3 NF.2.7 NF.2.7a NF.2.7b NF.2.7c MD.2.2 Write and interpret numerical expressions. 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. Apply and extend previous understandings of multiplication and division to fractions. Interpret a fraction as division of the numerator by the denominator ( = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Interpret division of a whole number by a unit fraction, and compute such quotients. 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. 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. 8: Fraction Division 11 days: January 25 February 7 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. use diagrams and equations to solve real world unit fraction division problems. write and evaluate expressions with fractions. solve problems involving data from line plots. Connect Fractions to Division Divide Fractions by Whole Numbers Divide Whole Numbers by Fractions Fraction and Whole Number Division Interpret Division with Fractions Expressions with Fractions Line Plots Multiplication and Division Problems area model dividend divisor division equal groups equation expression fraction fraction greater than 1 (improper) fraction number line inverse operations mixed numbers multiplication quotient unit fraction whole number data equally redistribute expression fraction line plot order of operations

9 2 nd Trimester Operations & Algebraic Thinking (OA) Geometry (G) OA.2.3 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. Graph points on the coordinate plane to solve real-world and mathematical problems. G.1.1 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, 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. 9: Patterns and Graphing 7 days: February 8 February 16 graph and name points on a coordinate grid using ordered pairs. graph and interpret data on a coordinate grid. generate two numerical patterns and identify the relationship between the corresponding terms in the 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. Ordered Pairs Graph Data Numerical Patterns Graph and Analyze Relationships Graph and Analyze 2-Step Patterns coordinate grid graph/plot ordered pair origin pattern point relationship rule term x-axis x-coordinate y-axis y-coordinate G.1.2 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.

10 2 nd /3 rd Trimester Measurement and Data (MD) Convert like measurement units within a given measurement system. MD.1.1 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. 10: Measurement Conversions 11 days: February 17 March 7 compare, contrast, and convert metric units. compare, contrast, and convert customary units of length. 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. convert metric measurement units to solve multi-step real world problems. solve conversion problems with fractional parts of a unit. convert units of time to solve problems. Metric Measures Customary Length Customary Capacity Weight Multi-step Customary Measurement Problems Multi-step Metric Measurement Problems Customary and Metric Conversions Time metric gram kilogram mass milligram kilometer liter milliliter centimeter decimeter kilometer meter millimeter conversion unit fractions decimals customary foot inch length mile yard capacity cup fluid ounce gallon pint quart ounce pound ton weight time

12 Scope rd Trimester Florida Standards Assessment (FSA) Testing Window: April 10 May 5, 2017 Finalizing Mastery of Standards (MAFS): May 8 June 2, 2017 Last Day of School: June 2, 2017

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