# Grade 5: Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 20 concepts ready. In the app: https://ai.page/roadmap/al-grade-5

Part of: [Alabama: Mathematics](https://ai.page/roadmap/al.md)

Goal: Alabama academic standards: Mathematics, Grade 5

## 1. Measurement · Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving 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

## 2. Measurement · Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units.

- [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
- [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

## 3. Data Analysis · Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, 1/8).

- [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)

## 4. Operations with Numbers: Fractions · Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit 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
- [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

## 5. Operations with Numbers: Fractions · Interpret multiplication as scaling (resizing).

- [Multiplication as scaling](https://ai.page/c/multiplication-as-scaling/index.md): Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1

## 6. Operations with Numbers: Fractions · Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.

- [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
- [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
- [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)

## 7. Operations with Numbers: Fractions · Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

- [Dividing fractions](https://ai.page/c/dividing-fractions/index.md): Divide a fraction by a fraction using the 'keep-change-flip' method and visual models; interpret and solve word problems involving division of fractions by fractions
- [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

## 8. Operations with Numbers: Base Ten · Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or the relationships between additio

- [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

## 9. Operations with Numbers: Base Ten · Read, write, and compare decimals to thousandths.

- [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

## 10. Operations with Numbers: Base Ten · Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in t

- [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)

## 11. Operations and Algebraic Thinking · Generate two numerical patterns using two given rules and complete an input/output table for the data.

- [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

## Health: 0 of 100

Of its 20 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):

- Estimating answers (age 10+) comes before Counting Unit Cubes, which it needs
- Estimating answers (age 10+) has no explanation yet
- Volume as additive has no explanation yet
- Measuring length (age 10+) has no explanation yet
- Counting Unit Cubes has no explanation yet
- Measurement Line Plots has no explanation yet
- Understanding fractions has no explanation yet
- Dividing fractions (unit fractions) comes before Fractions of a whole (age 10+), which it needs
- Dividing fractions (unit fractions) has no explanation yet
- Dividing unit fractions and whole numbers has no explanation yet
- Multiplication as scaling has no explanation yet
- Area with Fractions has no explanation yet
- Real-world fraction multiplication has no explanation yet
- Multiplying fractions has no explanation yet
- Dividing fractions has no explanation yet
- Fractions of a whole (age 10+) 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
- Reading and writing numbers (age 10+) 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
- Number Pattern Relationships has no explanation yet

Credit: The structure of Alabama academic standards: Mathematics (https://www.alsde.edu/sec/sct/COS/2019%20Alabama%20Course%20of%20Study%20Mathematics.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.