# Grade 5: Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 27 concepts ready. In the app: https://ai.page/roadmap/ne-grade-5

Part of: [Nebraska: Mathematics](https://ai.page/roadmap/ne.md)

Goal: Nebraska academic standards: Mathematics, Grade 5

## 1. Grade 5 · Analyze Data and Interpret Results: Students will analyze the data and interpret the results.

- [Line graphs (age 10+)](https://ai.page/c/line-graphs-age-10/index.md): Interpret and construct pie charts and line graphs; use these to solve problems

## 2. Grade 5 · Area and Volume: Students will extend area problems for rectangles to include fractions and build meaning for measuring volume.

- [Estimating answers (age 10+)](https://ai.page/c/estimating-answers-age-10/index.md): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)
- [Volume as additive](https://ai.page/c/volume-as-additive/index.md): Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
- [Angles in triangles (age 11+)](https://ai.page/c/angles-in-triangles-age-11/index.md): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
- [Area with Fractions](https://ai.page/c/area-with-fractions/index.md): Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths

## 3. Grade 5 · Measurement: Generate conversions within the customary and metric systems of measurement to solve authentic problems.

- [Measurement Conversions](https://ai.page/c/measurement-conversions/index.md): Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts

## 4. Grade 5 · Coordinate Geometry: Graph points on the coordinate plane to solve authentic problems.

- [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-2/index.md): Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin
- [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context

## 5. Grade 5 · Shapes and Their Attributes: Students will classify two-dimensional figures into categories based on their properties.

- [Classifying shapes by properties](https://ai.page/c/classifying-shapes-by-properties/index.md): Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties
- [Measuring length (age 10+)](https://ai.page/c/measuring-length-age-10/index.md): Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units

## 6. Grade 5 · Operations and Algebraic Thinking: Students will extend understanding of division and apply operational properties to solve problems involving order of operations.

- [Order of operations (age 10+)](https://ai.page/c/order-of-operations-age-10/index.md): Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structure to solve proportion problems efficiently
- [Division with remainders (age 10+)](https://ai.page/c/division-with-remainders-age-10/index.md): Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate

## 7. Grade 5 · Operations with Fractions and Decimals: Students will apply and extend previous understandings of whole number operations to add, subtract, multiply and divide fractions and decimals.

- [Multiplying fractions](https://ai.page/c/multiplying-fractions/index.md): Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)
- [Fractions of a whole (age 10+)](https://ai.page/c/fractions-of-a-whole-age-10/index.md): 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 fractional or mixed-number answers
- [Dividing fractions (unit fractions)](https://ai.page/c/dividing-fractions-unit-fractions/index.md): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result
- [Mixed & Improper Fractions](https://ai.page/c/mixed-and-improper-fractions/index.md): Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
- [Fraction Addition Concepts](https://ai.page/c/fraction-addition-concepts/index.md): Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
- [Adding and subtracting mixed numbers](https://ai.page/c/adding-and-subtracting-mixed-numbers/index.md): Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
- [Adding fractions (different denominators)](https://ai.page/c/adding-fractions-different-denominators/index.md): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
- [Dividing by Fractions](https://ai.page/c/dividing-by-fractions/index.md): Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend
- [Multiplying fractions (age 11+)](https://ai.page/c/multiplying-fractions-age-11/index.md): Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)

## 8. Grade 5 · Fractions and Decimals: Students will extend understanding of fraction and decimal equivalence and ordering.

- [Decimals and fractions (age 10+)](https://ai.page/c/decimals-and-fractions-age-10/index.md): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
- [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-3/index.md): Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line
- [Fractions on a number line (age 11+)](https://ai.page/c/fractions-on-a-number-line-age-11/index.md): Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations

## 9. Grade 5 · Numeric Relationships: Students will understand the place value system.

- [Place Value × 10 and ÷ 10](https://ai.page/c/place-value-10-and-10/index.md): Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left
- [Patterns with Powers of Ten](https://ai.page/c/patterns-with-powers-of-ten/index.md): Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)
- [Reading Decimal Places](https://ai.page/c/reading-decimal-places/index.md): Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)

## Health: 0 of 100

Of its 27 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version.

Findings (each is a task for anyone's AI):

- Line graphs (age 10+) has no explanation yet
- Estimating answers (age 10+) has no explanation yet
- Volume as additive has no explanation yet
- Angles in triangles (age 11+) has no explanation yet
- Area with Fractions has no explanation yet
- Measurement Conversions has no explanation yet
- Numbers on a number line has no explanation yet
- Plotting points in the first quadrant has no explanation yet
- Classifying shapes by properties has no explanation yet
- Measuring length (age 10+) has no explanation yet
- Order of operations (age 10+) has no explanation yet
- Division with remainders (age 10+) has no explanation yet
- Multiplying fractions has no explanation yet
- Fractions of a whole (age 10+) has no explanation yet
- Dividing fractions (unit fractions) has no explanation yet
- Mixed & Improper Fractions has no explanation yet
- Fraction Addition Concepts has no explanation yet
- Adding and subtracting mixed numbers has no explanation yet
- Adding fractions (different denominators) has no explanation yet
- Dividing by Fractions has no explanation yet
- Multiplying fractions (age 11+) has no explanation yet
- Decimals and fractions (age 10+) has no explanation yet
- Fractions on a number line has no explanation yet
- Fractions on a number line (age 11+) has no explanation yet
- Place Value × 10 and ÷ 10 has no explanation yet
- Patterns with Powers of Ten has no explanation yet
- Reading Decimal Places has no explanation yet

Credit: The structure of Nebraska academic standards: Mathematics (https://www.education.ne.gov/wp-content/uploads/2022/10/Nebraskas-College-and-Career-Ready-Standards-for-Mathematics-Final-10.20.22.pdf); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.