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How to learn Grade 4: Mathematics

Florida academic standards: Mathematics, Grade 4

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1. Data Analysis and Probability

  1. Real-World Mathematical Modelling: Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations
  2. Statistical Analysis Vocabulary: Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes
  3. Understanding fractions: 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)

2. Geometric Reasoning

  1. Perimeters of polygons: Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa)
  2. Measuring angles: Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure
  3. 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
  4. Types of angles: Identify acute and obtuse angles; compare and order angles up to two right angles by size

3. Fractions

  1. 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
  2. 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
  3. 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
  4. Fractions of a whole: 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
  5. 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)
  6. Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
  7. Adding and subtracting mixed numbers: Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
  8. 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)

4. Measurement

  1. Adding and subtracting (age 10+): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why, with numbers up to 10,000,000 and decimals
  2. 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
  3. Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
  4. Converting measurement units: Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day)
  5. Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
  6. Measuring length (age 7+): Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, metre sticks, and measuring tapes

5. Algebraic Reasoning

  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. Prime numbers: Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19
  4. Unknown in Multiplication & Division: Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g. 8 × ? = 48, ? × 6 = 42)
  5. Real-world fraction multiplication: Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations
  6. Dividing unit fractions and whole numbers: Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations
  7. Rounding Answers: Solve problems which require answers to be rounded to specified degrees of accuracy

6. Number Sense and Operations

  1. Tenths (age 8+): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10
  2. Decimal place value: Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)
  3. Dividing by two-digit numbers: Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context
  4. Division with remainders (age 10+): 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
  5. Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations
  6. Multiplying and dividing: Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000
  7. All times tables to 12×12: Recall multiplication and division facts for multiplication tables up to 12 × 12
  8. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  9. Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
  10. Rounding Large Numbers: Round any whole number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000, or 100,000 using place-value understanding
  11. Comparing Large Numbers: Order and compare numbers beyond 1000
  12. Reading and writing numbers to 1000: Read and write numbers to 1000 in numerals, number names, and expanded form
  13. Reading and writing numbers (age 9+): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
  14. 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