# Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence First Quarter

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1 Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence First Quarter Common Core Operations and Algebraic Thinking (5.OA) Common Core Number and Operations in Base Ten (5.NBT) Common Core Number and Operations - Fractions (5.NF) Common Core Measurement and Data (5.MD) Common Core Geometry (5.G) State Standard Objectives Action Plan Resources Identify the value of envision Math CC: Number and Operation in Base Ten each place of a given number Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. 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. (5.NBT.1) Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. (5.NBT.2) Read, write, and compare decimals to thousandths. (5.NBT.3) o o Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). (5.NBT.3a) Compare two decimals to thousandths based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons. (5.NBT.3b) Represent parts of a whole interchanging fractions and decimals up to thousandths Write whole numbers and decimals in standard, word, and expanded form to the thousandths Compare and order whole numbers and decimals up to thousandths Topic 1-Place Value Topic 2- Adding and Subtracting Decimals Topic 3 Multiplying whole numbers Topic 4 Dividing by 1- digit Divisors Recording Sheet: TT4 Fraction Model Strips: TT5 10X10X10 Cube Use place value understanding to round decimals to any Identify patterns in place. (5.NBT.4) whole numbers and decimals solve problems Place Value Chart: TT6 Fluently multiply multi-digit whole numbers using the standard algorithm. (5.NBT.5) Demonstrate an Comparing and Find whole-number quotients of whole numbers with up understanding of Ordering Decimals: TT7 to four-digit dividends and two-digit divisors, using Commutative and strategies based on place value, the properties of Associative Properties of Place Value Materials: operations, and/or the relationship between whole numbers to TT9

2 multiplication and division. (5.NBT.6) 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.NBT.7) decimals using mental math strategies Use a number line to round whole numbers through millions Use a number line to round decimals through thousandths Round to estimate sums and differences of whole numbers and decimals Use concrete objects, such as base-ten blocks, to add and subtract decimals in tenths and hundredths Use pictures and write equations to help solve problems Compute sums and differences of decimals involving tenths, hundredths, and thousandths Find the solution to a multi-step problem involving the use of addition and subtraction of whole/decimal numbers Identify and apply the properties of multiplication (Commutative, Associative, Identity, and Zero) Teaching Tool 10 Teaching Tool 11 Teaching Tool 12 Teaching Tool 31 Teaching Tool 24 Colored Pencils, Crayons, Markers, Scissors Problem Solving Recording Sheet: TT1 Two-Color Counters: TT13 Exponents: TT14 Distributive Property: TT15 Teaching Tool 18 Straightedges, Colored Pencils Small Grid Paper: TT16 Multiplication Table: TT17 Bill and Coins: TT18 Four Number Cubes ENO Board Visual Bridge Interactive component

3 Compute products/quotients of whole numbers using place value patterns and the properties of multiplication with mental math strategies envision AIMSweb M-CAP AIMSweb M-COMP Round to estimate products/quotients of whole numbers (over and under estimates) Pair repeated multiplication with exponent counterpart Simplify expressions and solve equations using the Distributive Property Multiply multi-digit numbers by a one and two digit number Use pictures to show repeated addition as multiplication and division with remainders Check for reasonableness of an answer Use money to understand division Divide three-digit divisors Divide with zeros in the quotient

4 Common Core Operations and Algebraic Thinking (5.OA) Common Core Number and Operations in Base Ten (5.NBT) Common Core Number and Operations - Fractions (5.NF) Common Core Measurement and Data (5.MD) Common Core Geometry (5.G) Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence Second Quarter State Standard Objectives Action Plan Resources CC: Number and Operations in Base envision Math Ten² Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic 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. (5.NBT.1) Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. (5.NBT.2) 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. (5.NBT.6) 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.NBT.7) Compute quotients with dividends and divisors that are multiples of 10 Estimate to find solutions to division problems with two-digit divisors Use arrays and area models to model division Divide by multi-digit dividends and divisors Estimate or use calculator to solve division problems Evaluate problems for missing and/or extraneous information Topic 5 Dividing by 2- Digit Divisors Topic 6 Multiplying Decimals Topic 7 Dividing Decimals Grid Paper Calculator Problem Solving Recording Sheet: TT1 Estimating the Product of a Decimal and a Whole Number: TT20 Mentally multiply/divide decimals by 10;100;1,000 Decimal Grids: TT21 Colored Pencils Use rounding and estimation to multiply Multiplying a Whole Number and a Decimal:

5 and divide decimals (over estimate and under estimates) Use number sense and place value to multiply decimals to the ten thousandths Multiply/divide whole numbers and decimals by decimals TT41 Multiplying Two Decimals: TT22 Decimal Models: TT23 Scissors Decimal Grids: TT21 Solve multiple-step problems by finding the hidden question Determine correct decimal placement in a quotient Use multiple steps to solve a variety of problems Translate verbal expressions to written expressions using variables and vice versa Apply values to given variables to evaluate expressions Use order of operations to simplify and solve expressions with whole numbers and decimals Determine the rule for a table and write the rule as an expression (addition, subtraction, multiplication, division)

6 Determine the pattern to extend the sequence on a table CC: Operations and Algebraic Thinking Write and interpret numerical expressions. Analyze patterns and relationships. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (5.OA.1) Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. (5.OA.2) Generate two numerical patterns using two given rules. (5.OA.3) Use color tiles to solve problems and draw conclusions Demonstrate calculations by solving within parentheses first Explain the process and steps for using, parentheses, brackets, and braces effectively Topic 8 Numerical Expressions, Patterns and Relationships Place Value Blocks: TT24 Counters Color Tiles; 10 Red, 10 Green, 10 Yellow ENO Board Visual Bridge Interactive component envision AIMSweb M-CAP AIMSweb M-COMP

7 Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence Third Quarter Common Core Operations and Algebraic Thinking (5.OA) Common Core Number and Operations in Base Ten (5.NBT) Common Core Number and Operations - Fractions (5.NF) Common Core Measurement and Data (5.MD) Common Core Geometry (5.G) State Standard Objectives Action Plan Resources Write equivalent envision Math CC: Number and Operations Add and subtract fractions with unlike denominators fractions (including mixed numbers) by replacing given fractions Use equivalent fractions as a with equivalent fractions in such a way as to produce an Identify and find strategy to add and subtract equivalent sum or difference of fractions with like simplest form of fractions. denominators. (5.NF.1) fractions Solve word problems involving addition and subtractions Apply and extend previous Estimate the fractional of fractions referring to the same whole, including cases understandings of multiplication and part of objects of unlike denominators, e.g., by using visual fraction division to multiply and divide models or equations to represent the problem. (5.NF.2) fractions. Write a mathematical Interpret a fraction as division of the numerator by the equation and draw a denominator (a/b = a b). (5.NF.3) picture Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. (5.NF.4) 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. (5.NF4a) 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. (5.NF.4b) Interpret multiplication as scaling (resizing), by: (5.NF.5) 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 Use a number line to estimate sums/differences of fractions Determine common multiples and least common multiple Find common denominators Add/subtract fractions with unlike denominators Topic 9 Adding and Subtracting Fractions Topic 10 Adding and Subtracting Mixed Numbers Topic 11 Multiplying and Dividing Fractions and Mixed Numbers Fraction Model Strips: TT5 Fraction in Simplest Form: TT25 Number Lines: TT26 Fraction Models: TT5 Scissors Hundred Chart: TT27 Fraction Models: TT28

8 multiplication. (5.NF.5a) 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. (5.NF.5b) 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.6) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (5.NF.7) o Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. (5.NF.7a) o Interpret division of a whole number by a unit fraction, and compute such quotients. (5.NF.7b) o 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. (5.NF.7c) Pair improper fraction and mixed numbers on a number line Estimate sums/differences of fractions and mixed numbers by rounding to the nearest whole number Use models and computational procedures to add and subtract mixed numbers Use fractions strips to model the adding/subtracting of fractions Locate and place fractions on a number line Display equivalent fractional parts to make connections of equal representation Multiply a fraction by a whole number Use compatible numbers and rounding to estimate with fractions Give the product of two fractions Find area of rectangles Multiply mixed numbers Problem Solving Recording Sheet: TT1 Circle Patterns: TT29 3 Same-Size Circles per Group Centimeter Grid Paper: TT31 Paper Multiplying Mixed Numbers: TT30 Four 8 ½ X 11 Sheets of Paper Scissors

9 Use multiplication to scale or resize something Divide whole numbers by fractions Discover the inverse relationship between multiplication and division Use diagrams and write equations to solve problems CC: 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. 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 solving multistep, real world problems. (5.MD.1) Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4., 1/8). (5.MD.2) Recognize volume as an attribute of solid figures and understand concepts of volume measurement. (5.MD.3) o 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. (5.MD.3a) o 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. (5.MD.3b) Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (5.MD.4) Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. (5.MD.5) o 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 it would be found by multiplying the edge lengths. (5.MD.5a) o Apply the formulas V = 1 w h and V = b Describe, classify and analyze three dimensional shapes according to faces, edges and vertices Identify different views of a solid Determine the volume of rectangular solids Use formulas to find the volume of rectangular prisms Find volume of irregular solids envision Math Topic 12 volume of Solids Centimeter Cubes Centimeter Grid Paper: TT31 Unit Cubes Manila Folder Combining Volume: TT32 Markers in Two Colors Problem Solving Recording Sheet: TT1 ENO Board Visual Bridge Interactive component envision

10 o 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. (5.MD.5b) Recognize volume as additive. (5.MD.5c) AIMSweb M-CAP AIMSweb M-COMP

11 Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence Fourth Quarter Common Core Operations and Algebraic Thinking (5.OA) Common Core Number and Operations in Base Ten (5.NBT) Common Core Number and Operations - Fractions (5.NF) Common Core Measurement and Data (5.MD) Common Core Geometry (5.G) State Standard Objectives Action Plan Resources CC: Measurement and Data Convert like measurement units within a given measurement system. Represent and interpret data. 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 solving multistep, real world problems. (5.MD.1) Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4., 1/8). (5.MD.2) Convert between customary units of length (in, ft, yd, mi) Convert between customary units of capacity (gal, qt, pt, c, fl oz) Convert between customary units of weight (oz, lb, T) Convert between metric units of length (km, cm, mm) Convert between metric units of capacity (L, ml) Convert between metric units of mass (mg, g, kg) Solve multiple-step problems by searching for hidden questions Draw line plots, interpret points and recognize outliers envision Math Topic 13 Units of Measure Topic 14 - Data Inch and Yardstick Rulers: TT33 Two Different Colored Markers Strips of Paper One Yard Long Teaching Tool 34 Liquid Measuring Cup Empty Containers (Pint, Quart, ½ Gallon, and Gallon) Water Centimeter Ruler Marked in Millimeters: TT35 Empty Liter Container

12 CC: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two-dimensional figures into categories based on their properties. CC: Operations and Algebraic Thinking Analyze patterns and relationships. 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. (5.G.1) 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. (5.G.2) Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. (5.G.3) Classify two-dimensional figures in a hierarchy based on properties. (5.G.4) Generate two numerical patterns using two given rules. (5.OA.3) Collect, record and interpret data in frequency tables to construct line plots and solve problems involving the data Use words, pictures, numbers and symbols to demonstrate changes in data on a graph Identify and classify polygons, triangles and quadrilaterals by sides and angles Classify and sort two dimensional shapes into categories based on their properties Find and use commonalities and attributes of objects to make generalizations about patterns Identify and graph points on a coordinate grid Find the distance between two points by using ordered pairs Problem-Solving Recording Sheet: TT1 Problem- Solving, Look for a Pattern: TT8 Reading Time: TT36 Topic 15 Classifying Plane Figures Topic 16: Coordinate Geometry Wooden Sticks or Straws TT37 TT38 Scissors Paper Coordinate Grids: TT39 10X10 Grids: TT40 Grid Paper Create, interpret and use coordinate graphs to explain the relationship between two rules ENO Board Visual Bridge Interactive component envision AIMSweb M-CAP AIMSweb M-COMP

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