# Grade 5: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 17 concepts ready. In the app: https://ai.page/roadmap/sd-grade-5 Part of: [South Dakota: Mathematics](https://ai.page/roadmap/sd.md) Goal: South Dakota academic standards: Mathematics, Grade 5 ## 1. Number and Operations — Fractions · Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. - [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 - [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 ## 2. Number and Operations — Fractions · Interpret multiplication as scaling (resizing), by: - [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 ## 3. Number and Operations — Fractions · Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. - [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) - [Multiplying fractions (age 10+)](https://ai.page/c/multiplying-fractions-age-10/index.md): Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form - [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 ## 4. Number and Operations — Fractions · Solve word problems involving addition and subtraction of fractions. - [Fraction Word Problems](https://ai.page/c/fraction-word-problems/index.md): Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness - [Addition and subtraction word problems](https://ai.page/c/addition-and-subtraction-word-problems-maths/index.md): Solve word problems involving addition and subtraction of fractions with like denominators, 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 ## 5. Number and Operation in Base Ten · Use the four operations with decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the rela - [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 ## 6. Number and Operation in 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 ## 7. Measurement and Data · Make a line plot to display a data set. - [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) ## 8. Measurement and Data · 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 ## 9. Measurement and Data · Recognize volume as an attribute of solid figures and understand concepts of volume measurement. - [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 ## Health: 0 of 100 Of its 17 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): - Dividing by Fractions comes before Multiplying fractions (age 10+), which it needs - Dividing by Fractions has no explanation yet - Dividing fractions (unit fractions) comes before Multiplying fractions (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 comes before Multiplying fractions (age 10+), which it needs - Multiplication as scaling has no explanation yet - Multiplying fractions has no explanation yet - Multiplying fractions (age 10+) has no explanation yet - Area with Fractions has no explanation yet - Fraction Word Problems has no explanation yet - Addition and subtraction word problems has no explanation yet - Real-world fraction multiplication 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 - Measurement Line Plots has no explanation yet - Understanding fractions has no explanation yet - Estimating answers (age 10+) has no explanation yet - Volume as additive has no explanation yet - Measuring length (age 10+) has no explanation yet Credit: The structure of South Dakota academic standards: Mathematics (http://doe.sd.gov/contentstandards/documents/SD-Math-Standard.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.