# Grade 5: Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 29 concepts ready. In the app: https://ai.page/roadmap/ar-grade-5

Part of: [Arkansas: Mathematics](https://ai.page/roadmap/ar.md)

Goal: Arkansas academic standards: Mathematics, Grade 5

## 1. Grade 5 · Organize and analyze data.

- [Measurement Line Plots](https://ai.page/c/measurement-line-plots/index.md): Make a line plot to display measurement data in fractions of a unit (1/2, 1/4, 1/8); solve problems involving addition and subtraction of fractions using line plot data
- [Understanding fractions](https://ai.page/c/understanding-fractions/index.md): 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 to solve problems involving data in line plots (e.g. redistribute total equally)
- [Pictograms and tally charts (age 11+)](https://ai.page/c/pictograms-and-tally-charts-age-11/index.md): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type

## 2. Grade 5 · Develop an understanding of the coordinate system.

- [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

## 3. Grade 5 · Apply measurement knowledge to solve real-world 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 · Solve the area of rectangles and volume of rectangular prisms.

- [Counting Unit Cubes](https://ai.page/c/counting-unit-cubes/index.md): Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units
- [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
- [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

## 5. Grade 5 · Expand knowledge of shapes by analyzing sides and angles.

- [Classifying shapes by line properties](https://ai.page/c/classifying-shapes-by-line-properties/index.md): Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category
- [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

## 6. Grade 5 · Develop and apply an understanding of foundational algebraic concepts.

- [Number Pattern Relationships](https://ai.page/c/number-pattern-relationships/index.md): Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane
- [Algebraic Notation](https://ai.page/c/algebraic-notation/index.md): Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently
- [Ratio (age 11+)](https://ai.page/c/ratio-age-11/index.md): Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions

## 7. Grade 5 · Solve real-world problems.

- [Dividing unit fractions and whole numbers](https://ai.page/c/dividing-unit-fractions-and-whole-numbers/index.md): Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations
- [Real-world fraction multiplication](https://ai.page/c/real-world-fraction-multiplication/index.md): Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations

## 8. Grade 5 · Perform operations using place value understanding and properties of operations.

- [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
- [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)
- [Adding Fractions (Unlike Denominators)](https://ai.page/c/adding-fractions-unlike-denominators/index.md): Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
- [Fluent addition and subtraction (age 9+)](https://ai.page/c/fluent-addition-and-subtraction-age-9/index.md): Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm
- [Addition and subtraction strategies (age 10+)](https://ai.page/c/addition-and-subtraction-strategies-age-10/index.md): Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning
- [Decimal place value](https://ai.page/c/decimal-place-value-2/index.md): Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)

## 9. Grade 5 · Build a conceptual understanding of fractions.

- [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

## 10. Grade 5 · Use place value understanding to compare numbers.

- [Comparing Decimals](https://ai.page/c/comparing-decimals/index.md): Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
- [Reading and writing numbers (age 10+)](https://ai.page/c/reading-and-writing-numbers-age-10/index.md): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning

## 11. Grade 5 · Understand the base ten place value system.

- [Decimal place value](https://ai.page/c/decimal-place-value-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
- [Place Value × 10 Pattern](https://ai.page/c/place-value-10-pattern/index.md): Recognise that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g. 700 ÷ 70 = 10)
- [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)

## Health: 0 of 100

Of its 29 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):

- Measurement Line Plots has no explanation yet
- Understanding fractions comes before Adding Fractions (Unlike Denominators), which it needs
- Understanding fractions has no explanation yet
- Pictograms and tally charts (age 11+) has no explanation yet
- Plotting points in the first quadrant has no explanation yet
- Measurement Conversions has no explanation yet
- Counting Unit Cubes has no explanation yet
- Estimating answers (age 10+) has no explanation yet
- Volume as additive has no explanation yet
- Area with Fractions has no explanation yet
- Classifying shapes by line properties has no explanation yet
- Classifying shapes by properties has no explanation yet
- Number Pattern Relationships has no explanation yet
- Algebraic Notation has no explanation yet
- Ratio (age 11+) has no explanation yet
- Dividing unit fractions and whole numbers comes before Dividing fractions (unit fractions), which it needs
- Dividing unit fractions and whole numbers has no explanation yet
- Real-world fraction multiplication has no explanation yet
- Fractions on a number line has no explanation yet
- Multiplying fractions has no explanation yet
- Adding Fractions (Unlike Denominators) has no explanation yet
- Fluent addition and subtraction (age 9+) has no explanation yet
- Addition and subtraction strategies (age 10+) comes before Reading and writing numbers (age 10+), which it needs
- Addition and subtraction strategies (age 10+) has no explanation yet
- Decimal place value has no explanation yet
- Dividing fractions (unit fractions) has no explanation yet
- Comparing Decimals has no explanation yet
- Reading and writing numbers (age 10+) has no explanation yet
- Decimal place value has no explanation yet
- Place Value × 10 Pattern has no explanation yet
- Place Value × 10 and ÷ 10 has no explanation yet
- Patterns with Powers of Ten has no explanation yet

Credit: The structure of Arkansas academic standards: Mathematics (https://dese.ade.arkansas.gov/admin/Files/AR_2023_K-8,_Alg,_Geo_Math_Standards_LS_6.21.23_LS.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.