# Grade 5: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 22 concepts ready. In the app: https://ai.page/roadmap/in-grade-5 Part of: [Indiana: Mathematics](https://ai.page/roadmap/in.md) Goal: Indiana academic standards: Mathematics, Grade 5 ## 1. Data Analysis · Calculate measures of central tendency (mean, median, and mode) to describe a data set. Analyze data sets to determine which measure of central tendency appropriately describes the dis - [Comparing measurements](https://ai.page/c/comparing-measurements/index.md): Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers ## 2. Data Analysis · Formulate questions that can be addressed with categorical and numerical data and make predictions about the data. Collect, organize, and graph data from observations, surveys, and exp - [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 ## 3. Measurement · Apply the formulas V = l × w × h and V = B × h for right rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths to solve real-world problems and ot - [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) ## 4. Measurement · Develop and use formulas for the area of triangles, parallelograms, and trapezoids. Solve real-world and other mathematical problems that involve perimeter and area of triangles, paralle - [Area of Triangles & Parallelograms](https://ai.page/c/area-of-triangles-and-parallelograms/index.md): Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles) ## 5. Measurement · Find the area of a rectangle with fractional side lengths by modeling with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be foun - [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 ## 6. Measurement · Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, 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 ## 7. Geometry · Identify, describe, and draw triangles (right, acute, obtuse) and circles using appropriate tools (e.g., ruler or straightedge, compass, and technology). Define and model the relationship b - [Lines, Rays & Angles](https://ai.page/c/lines-rays-and-angles/index.md): Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures - [Parts of a circle](https://ai.page/c/parts-of-a-circle/index.md): Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius ## 8. Computation and Algebraic Thinking · Represent real-world problems and equations by graphing ordered pairs in the first quadrant of the coordinate plane, and interpret coordinate values of points in t - [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 ## 9. Computation and Algebraic Thinking · Solve real-world problems involving addition, subtraction, multiplication, and division with decimals to hundredths including problems that involve money in decima - [Rounding Answers](https://ai.page/c/rounding-answers/index.md): Solve problems which require answers to be rounded to specified degrees of accuracy ## 10. Computation and Algebraic Thinking · Add, subtract, multiply, and divide decimals to hundredths, using models or drawings and strategies based on place value or the properties of operations. Describe - [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 ## 11. Computation and Algebraic Thinking · Solve real-world problems involving division of fractions and mixed numbers (e.g., by using visual fraction models and equations to represent the problem). (E) - [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 ## 12. Computation and Algebraic Thinking · Use visual fraction models and numbers to divide a fraction by a fraction or a whole number. (E) - [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 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 ## 13. Computation and Algebraic Thinking · Use visual fraction models to multiply a fraction by a fraction or a whole number. (E) - [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) ## 14. Computation and Algebraic Thinking · Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators (e.g., by using visua - [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 ## 15. Computation and Algebraic Thinking · Add and subtract fractions and mixed numbers with unlike denominators using strategies or the standard algorithm. - [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 ## 16. Computation and Algebraic Thinking · Find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors using strategies based on place value, the properties of operatio - [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 ## 17. Number Sense · Model percents as parts of 100 using pictures or diagrams and identify the equivalent fraction. - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% ## 18. Number Sense · Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied - [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) ## 19. Number Sense · Explain different interpretations of fractions, including as parts of a whole, parts of a set, and division of whole numbers by whole numbers. - [Fractions of a whole](https://ai.page/c/fractions-of-a-whole/index.md): Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b ## 20. Number Sense · Use a number line to compare and order fractions, mixed numbers, and decimals to thousandths. Write the results using > , = , and < symbols. (E) - [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 ## Health: 0 of 100 Of its 22 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): - Comparing measurements has no explanation yet - Line graphs (age 10+) has no explanation yet - Estimating answers (age 10+) has no explanation yet - Area of Triangles & Parallelograms has no explanation yet - Area with Fractions has no explanation yet - Measurement Conversions has no explanation yet - Lines, Rays & Angles has no explanation yet - Parts of a circle has no explanation yet - Plotting points in the first quadrant has no explanation yet - Rounding Answers has no explanation yet - Addition and subtraction strategies (age 10+) has no explanation yet - Real-world fraction multiplication has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Dividing fractions has no explanation yet - Multiplying fractions has no explanation yet - Adding Fractions (Unlike Denominators) has no explanation yet - Adding and subtracting mixed numbers has no explanation yet - Division with remainders (age 10+) has no explanation yet - Percentages as Fractions has no explanation yet - Patterns with Powers of Ten has no explanation yet - Fractions of a whole has no explanation yet - Fractions on a number line (age 11+) has no explanation yet Credit: The structure of Indiana academic standards: Mathematics (https://www.in.gov/doe/files/AlgebraI-Math-Content-Connectors.docx.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.