# GTPS Curriculum 5 th Grade Math. Topic: Topic 1 - Understand Place Value

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1 Topic: Topic 1 - Understand Place Value Understand the place value system. 5.NBT.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. 5.NBT.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 NBT.3. Read, write, and compare decimals to thousandths. 5.NBT.4. Use place value understanding to round decimals to any place. How are whole numbers and decimals written, compared, and ordered? 1-1 Patterns with Exponents and Powers of Understand Whole-Number Place Value 1-3 Decimals to Thousandths 1-4 Understand Decimal Place Value 1-5 Compare Decimals 1-6 Round Decimals 1-7 Math Practices and Problem Solving: Look For and Use Structure

2 Topic: Topic 2 - Add and Subtract Decimals to Hundredths Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.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. How can sums and differences of decimals be estimated? What are the standard procedures for adding and subtracting whole numbers and decimals? How can sums and differences be found mentally? 2-1 Mental Math 2-2 Estimate Sums and Differences 2-3 Use Decimals to Add and Subtract Decimals 2-4 Add Decimals 2-5 Subtract Decimals 2-6 Add and Subtract Decimals 2-7 Math Practices and Problem Solving: Model with Math

3 Topic: Topic 3 - Fluently Multiply Multi-Digit Whole Numbers Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.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 NBT.5. Fluently multiply multi-digit whole numbers using the standard algorithm. What are the standard procedures for estimating and finding products of multi-digit numbers? 3-1 Multiply Greater Numbers by Powers of Estimate Products 3-3 Multiply 3-Digit by 2-Digit Numbers 3-4 Multiply Whole Numbers with Zeros 3-5 Multiply Multi-Digit Numbers 3-6 Solve Word Problems Using Multiplication 3-7 Math Practices and Problem Solving: Critique Reasoning

4 Topic: Topic 4 - Use Models and Strategies to Multiply Decimals Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.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 NBT.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. What are the standard procedures for estimating and finding products involving decimals? 4-1 Multiply Decimals by Powers of Estimate the Product of a Decimal and a Whole Number 4-3 Use Models to Multiply a Decimal and a Whole Number 4-4 Multiply a Decimal by a Whole Number 4-5 Use Models to Multiply a Decimal and a Decimal 4-6 Multiply Decimals Using Partial Products 4-7 Use Properties to Multiply Decimals 4-8 Use Number Sense to Multiply Decimals 4-9 Multiply Decimals 4-10 Math Practices and Problem Solving: Model with Math

5 Topic: Topic 5 - Use Models and Strategies to Divide Whole Numbers Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.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. What is the standard procedure for division and why does it work? 5-1 Use Patterns and Mental Math to Divide 5-2 Estimate Quotients with 2-Digit Divisors 5-3 Use Models to Divide with 2-Digit Divisors 5-4 Use Partial Quotients to Divide 5-5 Divide by Multiples of Use Estimation to Place the First Digit of the Quotient 5-7 Divide by 2-Digit Divisors 5-8 Math Practices and Problem Solving: Make Sense and Persevere

6 Topic: Topic 6 - Use Models and Strategies to Divide Decimals Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.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 NBT.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. What are the standard procedures for estimating and finding quotients involving decimals? 6-1 Patterns for Dividing with Decimals 6-2 Estimate Decimal Quotients 6-3 Use Models to Divide by a 1-Digit Whole Number 6-4 Divide by a 1-Digit Whole Number 6-5 Divide by a 2-Dgit Whole Number 6-6 Use Number Sense to Divide Decimals 6-7 Divide by a Decimal 6-8 Continue to Divide by Decimals 6-9 Math Practices and Problem Solving: Reasoning

7 Topic: Topic 7 - Use Equivalent Fractions to Add and Subtract Fractions Use equivalent fractions as a strategy to add and subtract fractions. 5.NBT.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. 5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. How can sums and differences of fractions and mixed numbers be estimated? What are standard procedures for adding and subtracting fractions and mixed numbers? 7-1Estimate Sums and Differences of Fractions 7-2 Find Common Denominators 7-3 Add Fractions with Unlike Denominators 7-4 Subtract Fractions with Unlike Denominators 7-5 Add and Subtract Fractions 7-6 Estimate Sums and Differences of Mixed Numbers 7-7 Use Models to Add Mixed Numbers 7-8 Add Mixed Numbers 7-9 Use Models to Subtract Mixed Numbers 7-10 Subtract Mixed Numbers 7-11 Add and Subtract Mixed Numbers 7-12 Math Practices and Problem Solving: Model with Math

8 Topic: Topic 8 - Apply Understanding of Multiplication to Multiply Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.5. Interpret multiplication as scaling (resizing), by: 5.NF.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. What does it mean to multiply whole numbers and fractions? How can multiplication with whole numbers and fractions be shown using models and symbols? 8-1 Use Models to Multiply a Whole Number by a Fraction 8-2 Use Models to Multiply a Fraction by a Whole Number 8-3 Multiply Fractions and Whole Numbers 8-4 Use Models to Multiply Two Fractions 8-5 Multiply Two Fractions 8-6 Area of a Rectangle 8-7 Multiply Mixed Numbers 8-8 Multiplication as Scaling 8-9 Math Practices and Problem Solving: Make Sense and Persevere

9 Topic: Topic 9 - Apply Understanding of Division to Divide Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.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 5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 How are fractions related to division? How can you divide with whole numbers and unit fractions? 9-1 Fractions and Division 9-2 Fractions and Mixed Numbers as Quotients 9-3 Use Multiplication to Divide 9-4 Divide Whole Numbers by Unit Fractions 9-5 Divide Unit Fractions by Non-Zero Whole Numbers 9-6 Divide Whole Numbers and Unit Fractions 9-7 Solve Problems Using Division 9-8 Math Practices and Problem Solving: Repeated Reasoning

10 Topic: Topic 10 - Understand Volume Concepts Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.C.3A 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.C.3.B 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. 5MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5.MD.C.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. What is the meaning of volume of a solid? How can the volume of a rectangular prism be found? 10-1 Model Volume 10-2 Develop a Volume Formula 10-3 Volume of Prisms 10-4 Combine Volumes of Prisms 10-5 Solve Word Problems Using Volume 10-6 Math Practices and Problem Solving: Use Appropriate Tools

11 Topic: Topic 11 - Convert Measurements Convert like measurement units within a given measurement system. 5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. 5.NBT.5. Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit 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. What are customary measurement unites and how are they related? What are metric measurement units and how are they related? 11-1 Convert Customary Units of Length 11-2 Convert Customary Units of Capacity 11-3 Convert Customary Units of Weight 11-4 Convert Metric Units of Length 11-5 Convert Metric Units of Capacity 11-6 Convert Metric Units of Mass 11-7 Solve Word Problems Using Measurement Conversions 11-8 Math Practices and Problem Solving: Precision

12 Topic: Topic 12 - Represent and Interpret Data Convert like measurement units within a given measurement system. 5.MD.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. 5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. 5.NF.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. How can line plots be used to represent data and answer questions? 12-1 Analyze Line Plots 12-2 Make Line Plots 12-3 Solve Word Problems Using Measurement Data 12-4 Math Practices and Problem Solving: Critique Reasoning

13 Topic: Topic 13 - Algebra: Write and Interpret Numerical Expressions Write and interpret numerical expressions. 5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. How is the value of a numerical expression found? 13-1 Order of Operations 13-2 Evaluate Expressions 13-3 Write Numerical Expressions 13-4 Interpret Numerical Expressions 13-5 Math Practices and Problem Solving: Reasoning

14 Topic: Topic 14 - Graph Points on the Coordinate Plane Graph points on the coordinate plane to solve real-world mathematical problems. 5.G.A.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 (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 5.G.A.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. How are points plotted? How are relationships shown on a graph? 14-1 The Coordinate System 14-2 Graph Data Using Ordered Pairs 14-3 Solve Problems Using Ordered Pairs 14-4 Math Practices and Problem Solving: Reasoning

15 Topic: Topic 15 - Algebra: Analyze Patterns and Relationships Analyze patterns and Relationships. 5.OA.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. 5.G.A.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. How can number patterns be analyzed and graphed? How can number patterns and graphs be used to solve problems? 15-1 Numerical Patterns 15-2 More Numerical Patterns 15-3 Analyze and Graph Relationships 15-4 Math Practices and Problem Solving: Make Sense and Persevere

16 Topic: Topic 16 - Geometric Measurement: Classify Two-Dimensional Figures Classify two-dimensional figures into categories based on their properties. 5.G.B.3 Understand that attributes belonging to a category of two-dimensional 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. 5.G.B.4 Classify two-dimensional figures in a hierarchy based on properties. How can triangles and quadrilaterals be described, classified, and named? 16-1 Classify Triangles 16-2 Classify Quadrilaterals 16-3 Continue to Classify Quadrilaterals 16-4 Math Practices and Problem Solving: Construct Arguments

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