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How to learn Grade 4: Mathematics

Nebraska academic standards: Mathematics, Grade 4

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1. Grade 4 · Analyze Data and Interpret Results: Students will analyze the data and interpret the results.

  1. 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. Grade 4 · Data Collection: Students will formulate questions to collect, organize, and represent data.

  1. Halves and quarters (age 8+): Generate measurement data by measuring lengths to the nearest half and quarter inch; display the data on a line plot with a scale marked in whole numbers, halves, and quarters

3. Grade 4 · Area and Perimeter: Students will apply perimeter and area formulas for rectangles.

  1. Perimeter (age 10+): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically

4. Grade 4 · Measurement: Students will generate simple conversions from a larger unit to a smaller unit to solve authentic problems and measure angles.

  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. Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts

5. Grade 4 · Shapes and Their Attributes: Students will draw and identify lines and angles and classify shapes by properties of their lines and angles.

  1. Types of angles: Identify acute and obtuse angles; compare and order angles up to two right angles by size
  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

6. Grade 4 · Operations and Algebraic Thinking: Students will extend understanding of multiplication and division and apply operational properties to solve problems involving variables.

  1. Division with remainders: Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation
  2. Writing Algebraic Equations: Express missing number problems algebraically using letters for unknowns; translate word problems into equations
  3. Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
  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

7. Grade 4 · Factors and Multiples: Students will find factors and multiples and classify numbers as prime or composite.

  1. 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

8. Grade 4 · Operations with Fractions: Students will understand and demonstrate fractional computation.

  1. 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)
  2. Fractions of a whole (age 10+): Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
  3. 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
  4. 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

9. Grade 4 · Fractions and Decimals: Students will extend understanding of fractions by equivalence and ordering and will develop an understanding of decimals.

  1. Comparing fractions (age 10+): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
  2. 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
  3. Decimals and fractions (age 10+): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
  4. 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

10. Grade 4 · Numeric Relationships: Students will demonstrate and represent multi-digit numbers using relationships with the base-ten number system.

  1. 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)
  2. 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
  3. Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations