M1MT1

• Mathematics


  The study of numbers and arithmetic operations
• Mathematics


  A set of tools or a collection of skills that can be applied to questions of "how many" or "how much"
• Mathematics


  A science which involves logical reasoning, drawing conclusions from assumed premises, and strategic reasoning based on accepted rules, laws, or probabilities
• Mathematics


  An art which studies patterns for predictive purposes
• Mathematics


  A specialized language which deals with form, size, and quantity
• Mathematics is universal
• People from around the world use math to get things done
• Mathematics helps people perform daily tasks and make important decisions
• Pattern


  An arrangement which helps observers anticipate what they might see or what happens next
• Pattern


  Shows what may have come before
• Pattern


  Organizes information so that it becomes more useful
• Pattern


  Seeks to discover relationships and connections between seemingly unrelated bits of information
• Pattern-seeking behaviour of humans

  • A toddler separating blue blocks from red blocks
  • A kindergarten student learning to count
  • A first grader doing skip counting
  • A third grader noticing that multiples of two are even numbers
  • A sixth grader creating patterns that cover a plane
  • A junior high school student learning that a function is essentially a pattern of how one number is transformed to one another
  • A college biology undergraduate studying the sequence of DNA and proteins
  • A stock trader studying trends in the stock market
  • A weatherman making weather forecasts based on atmospheric patterns
  • A doctor deciding who is healthy and who is not by recognizing certain health patterns
• Patterns are studied because they are everywhere; people just need to learn to notice them
• Mathematics


  The study of patterns
• Those who recognize, generalize, and use patterns around them are better at solving problems, have deeper appreciation of the use of mathematics, and are better equipped to work with mathematics than those who do not
• Studying patterns


  Allows one to observe, hypothesize, discover, and create
• Today's mathematics is much more than algebra and geometry
• Mathematics has become a diverse discipline that deals with data, measurements, and observations from science and works with models of natural phenomena, human behaviour, and social systems
• Mathematics reveals patterns that help individuals better understand the world and predict what comes next, imagine what came before, and estimate if the same pattern will occur when variables are changed
• Types of patterns


  • Logic patterns
  • Number patterns
  • Geometric patterns
  • Word patterns
• Logic patterns


  Classifying things, being able to tell which things are blocks and which are not, precede learning to count blocks
• Number patterns


  Patterns such as 2, 4, 6, 8, 10 are familiar to students since they are among the first patterns encountered in school
• Geometric patterns


  Motifs or designs that depict abstract shapes like lines, polygons, and circles, and typically repeat like a wall paper
• Word patterns


  Patterns found in language like the morphological rules on pluralizing nouns or conjugating verbs for tense, as well as the metrical rules or poetry
• Patterns indicate a sense of structure and organization that it seems only humans are capable of producing these intricate, creative, and amazing formations
• Snowflakes


  • Symmetric about an axis, with left and right portions being exactly the same (line or bilateral symmetry)
• Honeycombs


  • Symmetric about an axis, with left and right portions being exactly the same (line or bilateral symmetry)
• Rotational symmetry


  When a figure can be rotated by several degrees and still achieve the same appearance as the original position
• Angle of rotation


  The smallest angle that a figure can be rotated while still preserving the original formation
• Symmetry


  Indicates that you can draw an imaginary line across an object and the resulting parts are mirror images of each other
• Symmetric objects


  • Snowflakes
  • Honeycombs
• Line or bilateral symmetry


  • Evident in most animals, including humans
• Rotational symmetry


  A figure can be rotated by several degrees and the same appearance as the original position will be achieved
• Figures with rotational symmetry

  • Spiderwort (120°)
  • Baby starfish (72°)
  • Recycle logo (3-fold)
  • Paper windmill (4-fold)
  • Triangle (3-fold)
  • Swastika symbol (4-fold)
• Order of rotation


  A figure has a rotational symmetry of order n (n – fold rotational symmetry) if 1 of a complete 𝑛 turn leaves the figure unchanged
• Calculating angle of rotation

  Angle of rotation = 360°/n
• Snowflakes


  • Patterns repeat six times, indicating six-fold symmetry
  • Angle of rotation is 60°
  • Not perfectly symmetric due to effects of humidity and temperature
• Honeycomb


  • Hexagonal formation enables the bee colony to maximize their storage using the smallest amount of wax
• Arranging coins in a hexagonal formation

  Covers more area compared to a square formation