# Grade 5 Mathematics Standards (Georgia) > Georgia Standards of Excellence: Mathematics, Grade 5. 9 standards. > Source: https://georgiahomeroom.org/standards/math/grade-5 > Interactive explorer: https://georgiahomeroom.org/explorer?subject=math&grade=05 ## Numerical Reasoning (NR) Numerical Reasoning. Place value, fractions, decimals, integers — the spine of K-8 number sense. ### 5.NR.1: Place Value Problem Solving Use place value understanding to solve real-life, mathematical problems. - **5.NR.1.1**: Explain 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 $\frac{1}{10}$ of what it represents in the place to its left. - **5.NR.1.2**: Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to $10^3$. ### 5.NR.2: Multi-Digit Multiplication and Division Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems. - **5.NR.2.1**: Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems. - **5.NR.2.2**: Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems. ### 5.NR.3: Fraction Operations Overview Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. - **5.NR.3.1**: Explain the meaning of a fraction as division of the numerator by the denominator ($\frac{a}{b}$ = a ÷ b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. - **5.NR.3.2**: Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies. - **5.NR.3.3**: Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators. - **5.NR.3.4**: Model and solve problems involving multiplication of a fraction and a whole number. - **5.NR.3.5**: Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number. - **5.NR.3.6**: Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction. ### 5.NR.4: Decimals to Thousandths Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers to the hundredths place to solve relevant, mathematical problems. - **5.NR.4.1**: Read and write decimal numbers to the thousandths place using base-ten numerals written in standard form and expanded form. - **5.NR.4.2**: Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. - **5.NR.4.3**: Use place value understanding to round decimal numbers to the hundredths place. - **5.NR.4.4**: Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies. ### 5.NR.5: Numerical Expressions Write, interpret, and evaluate numerical expressions within authentic problems. - **5.NR.5.1**: Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations. ## Patterning & Algebraic Reasoning (PAR) Patterning & Algebraic Reasoning. Patterns build into expressions and equations across K-8. ### 5.PAR.6: Numerical Pattern Rules Solve relevant problems by creating and analyzing numerical patterns using the given rule(s). - **5.PAR.6.1**: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table. - **5.PAR.6.2**: Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane. ## Measurement & Data Reasoning (MDR) Measurement & Data Reasoning. Length, time, money, and graphical data displays in K-5. ### 5.MDR.7: Measurement & Data Analysis Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions. - **5.MDR.7.1**: Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time. - **5.MDR.7.2**: Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life - **5.MDR.7.3**: Convert among units within the metric system and then apply these conversions to solve multistep, practical problems. - **5.MDR.7.4**: Convert among units within relative sizes of measurement units within the customary measurement system. ## Geometric & Spatial Reasoning (GSR) Geometric & Spatial Reasoning. Shapes, area, volume, and transformations from K through high school. ### 5.GSR.8: Polygons & Rectangular Prisms Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms. - **5.GSR.8.1**: Classify, compare, and contrast polygons based on properties. - **5.GSR.8.2**: Determine, through exploration and investigation, that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. - **5.GSR.8.3**: Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems. - **5.GSR.8.4**: Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems. ## Mathematical Practices (MP) Mathematical Practices. Cross-grade habits of mind: perseverance, precision, argument. ### 5.MP: Mathematical Practices Overview Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals. - **5.MP.1**: Make sense of problems and persevere in solving them. - **5.MP.2**: Reason abstractly and quantitatively. - **5.MP.3**: Construct viable arguments and critique the reasoning of others. - **5.MP.4**: Model with mathematics. - **5.MP.5**: Use appropriate tools strategically. - **5.MP.6**: Attend to precision. - **5.MP.7**: Look for and make use of structure. - **5.MP.8**: Look for and express regularity in repeated reasoning.