ai.page · roadmaps

How to learn Grade 4: Mathematics

Washington academic standards: Mathematics, Grade 4

0 of 35 concepts ready to learn · Markdown, for your AI

1. Data Science

  1. Bar graphs: Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

2. Geometry

  1. 2-D shapes (age 8+): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry
  2. Lines, Rays & Angles: Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures
  3. Classifying shapes by line properties: 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

3. Measurement and Data

  1. Measuring angles: Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure
  2. Measuring angles (age 9+): Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown
  3. What Is an Angle?: Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes
  4. Measurement Line Plots: 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
  5. Using Simple Formulae: Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))
  6. Fractions on a number line: Solve word problems involving distances, time intervals, liquid volumes, masses, and money using the four operations with fractions or decimals; represent with diagrams including number lines
  7. Measuring with different units: Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen

4. Numbers and Operations—Fractions

  1. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  2. Equivalent fractions (age 9+): Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths
  3. Converting tenths to hundredths: Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100)
  4. Decimals for Tenths & Hundredths: Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)
  5. Fraction Addition Concepts: Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
  6. Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
  7. Real-world fraction multiplication: Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations
  8. Multiplying fractions: 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. Fraction Notation: Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a whole
  10. Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
  11. Comparing fractions (age 9+): Compare and order fractions with different numerators and denominators by creating common denominators/numerators or comparing to a benchmark such as 1/2; justify conclusions with visual models
  12. Dividing fractions (unit fractions): 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

5. Numbers and Operations in Base Ten

  1. Multiplying by Tens: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations
  2. Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations
  3. Reading and writing numbers (age 10+): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning
  4. Place Value × 10 Pattern: 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)
  5. Place Value × 10 and ÷ 10: 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

6. Operations and Algebraic Thinking

  1. Shape patterns: Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur
  2. Factors, multiples, and primes: Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems
  3. Advanced Multi-Step Problems: Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations
  4. Multi-step problems: choosing operations: Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts
  5. Two-Step Equations: Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity
  6. Multiplication and Division Word Problems: Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities
  7. Multiplicative Comparison: Interpret a multiplication equation as a comparison (e.g. 35 = 5 × 7 means 35 is 5 times as many as 7); represent verbal statements of multiplicative comparisons as equations