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How to learn Grade 4: Mathematics

Texas Essential Knowledge and Skills: Mathematics, Grade 4

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1. Data analysis

  1. Multi-Step Problem Solving: Make sense of multi-step problems involving four operations, fractions, and area/volume by identifying sub-steps, choosing a strategy, and monitoring progress
  2. 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. Geometry and measurement

  1. Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
  2. 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
  3. Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
  4. Degrees and turns: Know that angles are measured in degrees, where one degree is 1/360 of a full turn; understand that an angle turning through n one-degree angles has a measure of n degrees
  5. Measuring angles: Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure
  6. 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
  7. Types of angles: Identify acute and obtuse angles; compare and order angles up to two right angles by size
  8. 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
  9. 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
  10. 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

3. Algebraic reasoning

  1. Using Simple Formulae: Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))
  2. Number Pattern Relationships: Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane
  3. Two-Step Equations: Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity

4. Number and operations

  1. 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
  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. Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
  4. Estimating by rounding: Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning
  5. Dividing by Fractions: 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
  6. Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations
  7. Long multiplication: Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models
  8. 10 or 100 More or Less: Find 10 or 100 more or less than a given number up to 1000
  9. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  10. 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
  11. Addition and subtraction strategies (age 10+): 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
  12. Decimal equivalents of tenths and hundredths: Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27)
  13. 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)
  14. 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
  15. Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
  16. 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
  17. Fractions on a number line: Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows
  18. Equivalent fractions on a number line: Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams
  19. 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
  20. 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
  21. Comparing Large Numbers: Order and compare numbers beyond 1000
  22. Multiplying and dividing: Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000
  23. 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
  24. Reading Decimal Places: Identify the value of each digit in numbers given to three decimal places (e.g. in 4.378, the 7 represents 7 hundredths)

5. Mathematical process standards

  1. Precise Maths Communication: Communicate with mathematical precision: use correct vocabulary, specify units, and use symbols accurately
  2. Real-World Mathematical Modelling: Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations
  3. Choosing mathematical tools: Select and use appropriate tools and representations strategically: choose between mental, written, and diagrammatic methods; use calculators for checking; select fraction models suited to the task