# Grade 5: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 26 concepts ready. In the app: https://ai.page/roadmap/pa-grade-5 Part of: [Pennsylvania: Mathematics](https://ai.page/roadmap/pa.md) Goal: Pennsylvania academic standards: Mathematics, Grade 5 ## 1. Use, describe, and develop procedures to solve 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. Organize, display, and answer questions based on data. - [Pictograms and tally charts (age 6+)](https://ai.page/c/pictograms-and-tally-charts-age-6/index.md): Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting 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) ## 3. Solve problems using simple conversions (may include multistep, 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. Use basic properties to classify two-dimensional figures. - [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 ## 5. Identify parts of a coordinate grid and describe or interpret points given an ordered pair. - [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 ## 6. Create, extend, and analyze patterns. - [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 ## 7. Analyze and complete calculations by applying the order of operations. - [Substituting into Formulae](https://ai.page/c/substituting-into-formulae/index.md): Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations - [Brackets in Expressions](https://ai.page/c/brackets-in-expressions/index.md): Use parentheses, brackets, or braces in numerical expressions and evaluate expressions containing these grouping symbols ## 8. Solve multiplication and division problems involving fractions and whole numbers (straight computation or word problems). - [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 - [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 - [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 - [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) ## 9. Solve addition and subtraction problems involving fractions (straight computation or word problems) - [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 - [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 ## 10. Use whole numbers and decimals to compute accurately (straight computation or word problems). - [Division with Decimals](https://ai.page/c/division-with-decimals/index.md): Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers ## 11. Demonstrate understanding of place-value of whole numbers and decimals, and compare quantities or magnitudes of 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 - [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 - [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) - [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 26 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+) has no explanation yet - Volume as additive has no explanation yet - Pictograms and tally charts (age 6+) has no explanation yet - Understanding fractions comes before Adding Fractions (Unlike Denominators), which it needs - Understanding fractions has no explanation yet - Measurement Conversions has no explanation yet - Classifying shapes by properties has no explanation yet - Numbers on a number line has no explanation yet - Plotting points in the first quadrant has no explanation yet - Number Pattern Relationships has no explanation yet - Substituting into Formulae has no explanation yet - Brackets in Expressions has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Dividing unit fractions and whole numbers has no explanation yet - Real-world fraction multiplication has no explanation yet - Multiplication as scaling has no explanation yet - Multiplying fractions has no explanation yet - Adding and subtracting mixed numbers has no explanation yet - Adding fractions (different denominators) has no explanation yet - Adding Fractions (Unlike Denominators) has no explanation yet - Division with Decimals 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 - Reading Decimal Places 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 Pennsylvania academic standards: Mathematics (https://www.pdesas.org/Page/Viewer/ViewPage/12/); 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.