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.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
| Standard | Definition | Code |
|---|---|---|
| Display perseverance and patience in problem-solving | 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 |
| Make sense of problems and persevere in solving them | Make sense of problems and persevere in solving them. | 5.MP.1 |
| Reason abstractly and quantitatively | Reason abstractly and quantitatively. | 5.MP.2 |
| Construct viable arguments and critique the reasoning of others | Construct viable arguments and critique the reasoning of others. | 5.MP.3 |
| Model with mathematics | Model with mathematics. | 5.MP.4 |
| Use appropriate tools strategically | Use appropriate tools strategically. | 5.MP.5 |
| Attend to precision | Attend to precision. | 5.MP.6 |
| Look for and make use of structure | Look for and make use of structure. | 5.MP.7 |
| Look for and express regularity in repeated reasoning | Look for and express regularity in repeated reasoning. | 5.MP.8 |
Use place value understanding to solve real-life, mathematical problems.
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 1/10 of what it represents in the place to its left.
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 1 0 3 10^3.
Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.
Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems.
Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems.
Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models.
Explain the meaning of a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies.
Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.
Model and solve problems involving multiplication of a fraction and a whole number.
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.
Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
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.
Read and write decimal numbers to the thousandths place using base-ten numerals written in standard form and expanded form.
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.
Use place value understanding to round decimal numbers to the hundredths place.
Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.
Write, interpret, and evaluate numerical expressions within authentic problems.
Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.
| Standard | Definition | Code |
|---|---|---|
| Use place value understanding to solve real-life, mathematical problems | Use place value understanding to solve real-life, mathematical problems. | 5.NR.1 |
| Explain that in a multi-digit number, a digit in one place represents 10 times… | 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 1/10 of what it represents in the place to its left. | 5.NR.1.1 |
| Explain patterns in the placement of digits when multiplied or divided by a… | 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 1 0 3 10^3. | 5.NR.1.2 |
| Multiply and divide multi-digit whole numbers to solve relevant, mathematical… | Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems. | 5.NR.2 |
| Fluently multiply multi-digit | Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems. | 5.NR.2.1 |
| Fluently divide multi-digit whole numbers | 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.2.2 |
| Describe fractions and perform operations with fractions to solve relevant… | Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models. | 5.NR.3 |
| Explain the meaning of a fraction as division of the numerator by the… | Explain the meaning of a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. | 5.NR.3.1 |
| Compare and order up to three fractions with different numerators and/or… | 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.3.2 |
| Model and solve problems involving addition and subtraction of fractions and… | Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators. | 5.NR.3.3 |
| Model and solve problems involving multiplication of a fraction and a whole… | Model and solve problems involving multiplication of a fraction and a whole number. | 5.NR.3.4 |
| Explain why multiplying a whole number by a fraction greater than one results… | 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.3.5 |
| Model and solve problems involving division of a unit fraction by a whole… | Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction. | 5.NR.3.6 |
| Read, write, and compare decimal numbers to the thousandths place | 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 |
| Read and write decimal numbers to the thousandths place using base-ten numerals… | Read and write decimal numbers to the thousandths place using base-ten numerals written in standard form and expanded form. | 5.NR.4.1 |
| Represent, compare, and order decimal numbers to the thousandths place based on… | 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.4.2 |
| Use place value understanding to round decimal numbers to the hundredths place | Use place value understanding to round decimal numbers to the hundredths place. | 5.NR.4.3 |
| Solve problems involving addition and subtraction of decimal numbers to the… | Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies. | 5.NR.4.4 |
| Write, interpret, and evaluate numerical expressions within authentic problems | Write, interpret, and evaluate numerical expressions within authentic problems. | 5.NR.5 |
| Write, interpret, and evaluate simple numerical expressions involving whole… | Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations. | 5.NR.5.1 |
Multi-digit whole numbers
Fractions with unlike denominators
Fractions greater than 1
Decimal fractions to thousandths
Counting decimal numbers
Magnitude of place value extended to decimal numbers
Powers of 10 to 10<sup>3</sup>
Read & write decimal numbers to thousandths place
Round decimal numbers to hundredths place
Decimal fractions to thousandths place
Fractions greater than 1
Fluency with multiplication and division with multi-digit whole numbers
Fractions with unlike denominators
Decimal fractions to the hundredths place
Multiply multi-digit whole numbers
Multiply fractions and whole numbers
Divide unit fractions and whole numbers
Reason about multiplying by a fraction >, <, or = 1
Simple numerical expressions involving whole numbers with or without grouping symbols
Express fractions as division problems
Generate two numerical patterns using a given rule
Identify relationships using a table
Plot order pairs in first quadrant
Classify polygons based on geometric properties
Relationships between categories and subcategories of shapes
Volume of right rectangular prisms
Measure length and weight in metric units
Convert between units of measurement
Create and analyze dot plots (line plots) with fraction measurements
Using money as a tool to solve problems involving decimals
Solving problems involving time
| Standard | Definition | Code |
|---|---|---|
| Multi-digit whole numbers | Multi-digit whole numbers | 5.LP1.1.1 |
| Fractions with unlike denominators | Fractions with unlike denominators | 5.LP1.1.2 |
| Fractions greater than 1 | Fractions greater than 1 | 5.LP1.1.3 |
| Decimal fractions to thousandths | Decimal fractions to thousandths | 5.LP1.1.4 |
| Counting decimal numbers | Counting decimal numbers | 5.LP1.2.1 |
| Magnitude of place value extended to decimal numbers | Magnitude of place value extended to decimal numbers | 5.LP1.3.1 |
| Powers of 10 to 10<sup>3</sup> | Powers of 10 to 10<sup>3</sup> | 5.LP1.3.2 |
| Read & write decimal numbers to thousandths place | Read & write decimal numbers to thousandths place | 5.LP1.3.3 |
| Round decimal numbers to hundredths place | Round decimal numbers to hundredths place | 5.LP1.3.4 |
| Decimal fractions to thousandths place | Decimal fractions to thousandths place | 5.LP1.4.1 |
| Fractions greater than 1 | Fractions greater than 1 | 5.LP1.4.2 |
| Fluency with multiplication and division with multi-digit whole numbers | Fluency with multiplication and division with multi-digit whole numbers | 5.LP1.5.1 |
| Fractions with unlike denominators | Fractions with unlike denominators | 5.LP1.6.1 |
| Decimal fractions to the hundredths place | Decimal fractions to the hundredths place | 5.LP1.6.2 |
| Multiply multi-digit whole numbers | Multiply multi-digit whole numbers | 5.LP1.7.1 |
| Multiply fractions and whole numbers | Multiply fractions and whole numbers | 5.LP1.7.2 |
| Divide unit fractions and whole numbers | Divide unit fractions and whole numbers | 5.LP1.7.3 |
| Reason about multiplying by a fraction >, < | Reason about multiplying by a fraction >, <, or = 1 | 5.LP1.7.4 |
| Simple numerical expressions involving whole numbers with or without grouping… | Simple numerical expressions involving whole numbers with or without grouping symbols | 5.LP1.8.1 |
| Express fractions as division problems | Express fractions as division problems | 5.LP1.8.2 |
| Generate two numerical patterns using a given rule | Generate two numerical patterns using a given rule | 5.LP2.1.1 |
| Identify relationships using a table | Identify relationships using a table | 5.LP2.1.2 |
| Plot order pairs in first quadrant | Plot order pairs in first quadrant | 5.LP2.2.1 |
| Classify polygons based on geometric properties | Classify polygons based on geometric properties | 5.LP3.1.1 |
| Relationships between categories and subcategories of shapes | Relationships between categories and subcategories of shapes | 5.LP3.1.2 |
| Volume of right rectangular prisms | Volume of right rectangular prisms | 5.LP3.2.1 |
| Measure length and weight in metric units | Measure length and weight in metric units | 5.LP4.1.1 |
| Convert between units of measurement | Convert between units of measurement | 5.LP4.1.2 |
| Create and analyze dot plots | Create and analyze dot plots (line plots) with fraction measurements | 5.LP4.1.3 |
| Using money as a tool to solve problems involving decimals | Using money as a tool to solve problems involving decimals | 5.LP4.2.1 |
| Solving problems involving time | Solving problems involving time | 5.LP4.3.1 |
Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.
Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane.
| Standard | Definition | Code |
|---|---|---|
| Solve relevant problems by creating and analyzing numerical patterns using the… | Solve relevant problems by creating and analyzing numerical patterns using the given rule(s). | 5.PAR.6 |
| Generate two numerical patterns using two given rules | Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table. | 5.PAR.6.1 |
| Represent problems by plotting ordered pairs and explain coordinate values of… | Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane. | 5.PAR.6.2 |
Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions.
Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.
Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
Convert among units within the metric system and then apply these conversions to solve multistep, practical problems.
Convert among units within relative sizes of measurement units within the customary measurement system.
| Standard | Definition | Code |
|---|---|---|
| Solve problems involving customary measurements, metric measurements | Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions. | 5.MDR.7 |
| Explore realistic problems involving different units of measurement, including… | Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time. | 5.MDR.7.1 |
| Ask questions and answer them based on gathered information, observations | Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life. | 5.MDR.7.2 |
| Convert among units within the metric system and then apply these conversions… | Convert among units within the metric system and then apply these conversions to solve multistep, practical problems. | 5.MDR.7.3 |
| Convert among units within relative sizes of measurement units within the… | Convert among units within relative sizes of measurement units within the customary measurement system. | 5.MDR.7.4 |
Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.
Classify, compare, and contrast polygons based on properties.
Determine, through exploration and investigation, that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.
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.
| Standard | Definition | Code |
|---|---|---|
| Examine properties of polygons and rectangular prisms, classify polygons by… | Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms. | 5.GSR.8 |
| Classify, compare, and contrast polygons based on properties | Classify, compare, and contrast polygons based on properties. | 5.GSR.8.1 |
| Determine, through exploration and investigation, that attributes belonging to… | 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.8.2 |
| Investigate volume of right rectangular prisms by packing them with unit cubes… | 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.8.3 |
| Discover and explain how the volume of a right rectangular prism can be found… | 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. | 5.GSR.8.4 |
Multi-digit whole numbers
Fractions with unlike denominators
Fractions greater than 1
Decimal numbers to thousandths
Powers of 10 to 10<sup>3</sup>
Add & subtract fractions with unlike denominators
Add and subtract decimal numbers to the hundredths place
Multiply & divide multi-digit whole numbers
Multiply fractions and whole numbers
Divide unit fractions and whole numbers
Reason about multiplying by a fraction >, <, or = 1
Decimal fractions to thousandths place
Fractions greater than 1
Generate two numerical patterns from a given rule
Identify relationships using a table
Simple numerical expressions involving whole numbers with or without grouping symbols (Numerical Reasoning)
Express fractions as division problems (Numerical Reasoning)
Plot order pairs in first quadrant
Classify polygons based on geometric properties
Volume of right rectangular prisms
| Standard | Definition | Code |
|---|---|---|
| Multi-digit whole numbers | Multi-digit whole numbers | 5.LP5.1.1 |
| Fractions with unlike denominators | Fractions with unlike denominators | 5.LP5.1.2 |
| Fractions greater than 1 | Fractions greater than 1 | 5.LP5.1.3 |
| Decimal numbers to thousandths | Decimal numbers to thousandths | 5.LP5.1.4 |
| Powers of 10 to 10<sup>3</sup> | Powers of 10 to 10<sup>3</sup> | 5.LP5.1.5 |
| Add & subtract fractions with unlike denominators | Add & subtract fractions with unlike denominators | 5.LP5.2.1 |
| Add and subtract decimal numbers to the hundredths place | Add and subtract decimal numbers to the hundredths place | 5.LP5.2.2 |
| Multiply & divide multi-digit whole numbers | Multiply & divide multi-digit whole numbers | 5.LP5.2.3 |
| Multiply fractions and whole numbers | Multiply fractions and whole numbers | 5.LP5.2.4 |
| Divide unit fractions and whole numbers | Divide unit fractions and whole numbers | 5.LP5.2.5 |
| Reason about multiplying by a fraction >, < | Reason about multiplying by a fraction >, <, or = 1 | 5.LP5.2.6 |
| Decimal fractions to thousandths place | Decimal fractions to thousandths place | 5.LP5.3.1 |
| Fractions greater than 1 | Fractions greater than 1 | 5.LP5.3.2 |
| Generate two numerical patterns from a given rule | Generate two numerical patterns from a given rule | 5.LP6.1.1 |
| Identify relationships using a table | Identify relationships using a table | 5.LP6.1.2 |
| Simple numerical expressions involving whole numbers with or without grouping… | Simple numerical expressions involving whole numbers with or without grouping symbols (Numerical Reasoning) | 5.LP6.2.1 |
| Express fractions as division problems | Express fractions as division problems (Numerical Reasoning) | 5.LP6.2.2 |
| Plot order pairs in first quadrant | Plot order pairs in first quadrant | 5.LP6.6.1 |
| Classify polygons based on geometric properties | Classify polygons based on geometric properties | 5.LP8.1.1 |
| Volume of right rectangular prisms | Volume of right rectangular prisms | 5.LP8.2.1 |