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How to learn Grade 4: Mathematics

South Carolina academic standards: Mathematics, Grade 4

0 of 33 concepts ready to learn · Markdown, for your AI

1. Patterns, Algebra, and Functional Reasoning · Use reasoning to represent and solve algebraic and numerical situations.

  1. Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients
  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. Algebraic Transformations: Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
  4. 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

2. Patterns, Algebra, and Functional Reasoning · Use multiple representations to reason and solve problems involving operational properties of fractions.

  1. 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
  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. Real-world fraction multiplication: Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations
  4. Fractions, Decimals & Percentages: Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically
  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

3. Patterns, Algebra, and Functional Reasoning · Use multiple representations to reason and solve problems involving operational properties of whole numbers and decimals.

  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. 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
  3. 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
  4. Reasoning with Equivalences: Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms

4. Numerical Reasoning · Represent and compare fractions in multiple ways using part-whole relationships.

  1. Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
  2. Comparing fractions (age 10+): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
  3. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  4. Decimal & Percent Notation: Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value

5. Numerical Reasoning · Represent and compare numbers using relationships within the base ten number system.

  1. Comparing Large Numbers: Order and compare numbers beyond 1000
  2. 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
  3. 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

6. Measurement, Geometry, and Spatial Reasoning · Extend geometric reasoning to attributes of polygons and/or polyhedrons.

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

7. Measurement, Geometry, and Spatial Reasoning · Estimate and measure using units of length, liquid volume, weight, currency, and intervals of time.

  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 Liquids & Masses: Measure and estimate liquid volumes and masses of objects using grams, kilograms, and litres; solve one-step word problems involving mass or volume
  3. Estimating Lengths: Estimate lengths using units of inches, feet, centimetres, and metres
  4. 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

8. Measurement, Geometry, and Spatial Reasoning · Solve area and perimeter problems in real-world and mathematical situations.

  1. Modelling with multiplication and fractions: Model real-world problems involving multiplication, area, fractions, and unit conversion by choosing appropriate representations and interpreting mathematical results in context
  2. Real-World Maths Modelling: Model real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and interpreting results in context
  3. 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)

9. Data, Probability, and Statistical Reasoning · Represent the probability of simple events and determine possible outcomes.

  1. Calculating Simple Probability: Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations

10. Data, Probability, and Statistical Reasoning · Create questions, collect and analyze data, and communicate interpretations through multiple representations.

  1. Pictograms and tally charts (age 6+): 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
  2. Representing numbers with objects (age 8+): Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables