# Math Primers

How each episode of The Prime Radicals television series fits into the math curriculum.

## Episode 1: “Rule of Thumb”

**THIS EPISODE IS ABOUT...** the concept of a measurement unit; non-standard measurement units; non-standard measure; and, indirect measure (such as "a head taller") and estimates using referents. The notion of proportion is introduced using visual non-standard relationships within the human body that have been used for centuries by artists and designers (e.g., the human figure is approximately 7 of its own ‘feet’ tall, the height of the human figure is approximately equal to its arm span). Indirect measure is used as a tool for establishing reasonable estimates for body part dimensions, illustrating the practical application and utility of long-established and widely-used non-standard measures.”

## Episode 2: “No Accounting for Taste!”

**THIS EPISODE IS ABOUT...** the base 10 number system and place value, and addresses the fundamental issue of computational fluency, which includes the appropriate application of efficient math strategies. Of note is the fact that all illuminative and illustrative examples emphasize and concretize the importance and utility of place value and provide alternate, mathematically-rich strategies and algorithms for regrouping and multi-digit addition and subtraction: key teaching points in elementary mathematics. This episode is also about simple counting and counting devices.

## Episode 3: “ACE THE LACE!”

**THIS EPISODE IS ABOUT...** patterning (over/under, left/right, in/out red/black) and following instructions. Perhaps most importantly, it concomitantly underscores the significance of critical affective goals while demonstrating how different people, not just mathematicians, enjoy and appreciate mathematics. This episode is aimed at developing a sense of wonder: planting the seeds that can sustain a lifelong curiosity about mathematics by using examples that illustrate the ubiquity, utility and beauty of mathematics. It all helps to instill a sense of wonder, curiosity and a positive attitude in our viewers when it comes to Math.

## Episode 4: “RAD AND ROLL”

**THIS EPISODE IS ABOUT...** patterns in rhythms and musical notes (and the ‘sounds’ of fractions, i.e., instruments vibrate in wholes, halves, thirds, fourths—fractions called the harmonic series.) The application of these concepts comes from the fact that students can build their own simple instruments by measuring fractions of length and liquid volume, then use standard and non-standard units to measure and make homemade versions of traditional instruments. All (good) music is math based!

## Episode 5: “Numberlicious!”

**THIS EPISODE IS ABOUT...** fractions, measurement (volume, weight, temperature), and simple ratios. The tools and procedures for measuring liquids, solids, and dry ingredients are presented. Following a recipe involves understanding and enacting a step-by-step process: applications of mathematical processes such as logic, sequential thinking and following directions. Recipes involve portions and measurements, often needing doubling for a large crowd or dividing for a smaller group, necessitating the application of arithmetic skills with fractions and whole numbers involving all the computational operations: adding, subtracting, multiplying, and dividing.

## Episode 6: “Anything With Anything”

**THIS EPISODE IS ABOUT... **non-standard measurement units and estimates. It reinforces the notion that reliable measurement units can be derived from representational objects in the everyday world (apart from the human body, which is covered in *Rule of Thumb*). Visual proportionality is introduced, and children learn they can calculate measurement even without rulers, tape measures etc. E.g. How many yogurt containers of sand does it take to fill a bucket? How many shovels full of snow does it take to clear a driveway? How many wheelbarrows full of leaves on a tree? Etc. Builders, contractors and others have been making these sorts of measurements so for centuries, right up to this very day.

## Episode 7: “Code Name: Rad”

**THIS EPISODE IS ABOUT...** patterning and algebra; specifically the notions of colour and geometric codes and patterning. Pictorial and graphical modes are employed to create, describe and represent a variety of patterns and introduce an early sense of variables.

## Episode 8: “Tessellational!”

**THIS EPISODE IS ABOUT...** tessellations and transformational geometry (e.g. slides, flips and turns). The suite of examples and activities in this show provide visual opportunities to experience arithmetic beyond numeric calculations. Tessellations provide visually rich opportunities to explore geometry, patterning, spatial sense/relationships and the exciting synthesis between mathematics and the visual arts.

## Episode 9: Let’s Face It”

**THIS EPISODE IS ABOUT...** bilateral symmetry (reflection symmetry) and geometric mirror images (reflections). We see how objects both in the natural and manufactured world are symmetrical and how planes, space and shapes of the human face interconnect. We are introduced to the bilateral category of animals (including humans) that are more or less left/right symmetric and the sagittal (or median) plane, which divides the body into two halves of equal proportions. We also discover that while the human face has approximate symmetry along a vertical axis, digital photography can provide powerful evidence of just how approximate bilateral symmetry is where human features are concerned.

## Episode 10: “True Grid”

**THIS EPISODE IS ABOUT...**the most common type of grid, i.e., the square grid and its application to early map skills. The focus is on using a square grid as a map; reading the symbols (e.g., house, treasure) and labels (letters for horizontal axis and numbers for vertical axis) on the map for information; and using directional (right, left) and transformational geometry (turn, slide, flip) language to describe paths of motion on the map. The episode demonstrates how to read a grid map, and how to create a grid map. Learning to read a grid is a very important early mathematics skill, because it is a first step towards reading coordinates (in later grades) as well with finding places on a map through the use of latitude and longitude.

## Episode 11: Radical Reflections

**THIS EPISODE IS ABOUT…** rotational symmetry. The ways in which rotational symmetry occurs in nature, art and everyday shapes (e.g., hubcaps, Ferris wheels) is featured. These concrete examples are used to illustrate the ways in which lines of symmetry and positional relationships are determined. Principles of reflection using triangular prismswill be used to illuminate why kaleidoscopes are constructed as they are, i.e., using 3 mirrors configured as an equilateral triangular prism to create an image that repeats one triangular pattern continuously, producing a faceted pattern that fills the entire field of view.

## EPISODE 12: “Thinking Inside the Box!”

**THIS EPISODE IS ABOUT…** the common mathematical solids: a family comprised of the cube, prism, pyramid, sphere and cone. A common theme highlighted throughout each illuminative example is not only what these polyhedra look like, but their properties and deconstruction, i.e., isolating faces and the way in which those faces fit together. Nets are featured as tools for representing 3D shapes in two dimensions, and a focal point is the practical implications of designing and constructing nets efficiently and creatively, e.g., the activity in which a tetrahedron is made from an envelope is included to explore the relationship between three-dimensional and two-dimensional objects.

## Episode 13: “To Infinity and Beyond”

**THIS EPISODE IS ABOUT…** understanding large numbers: their names and the enormity of their magnitudes. The concept of doubling is introduced using paper-folding to illuminate that once a very small quantity (like the thickness of a piece of paper) starts growing, it grows faster and faster, reaching magnitudes that are fantastical. Real-world referents are used to make sense of the impact of doubling of paper and visual representations are used to authenticate the referents.

## Episode 14: LEADER OF THE PACK

**THIS EPISODE IS ABOUT… **discovering all of the possible combinations for outfits consisting of shirts and shorts. The notion of using drawings, tree diagrams and cross diagrams is introduced as is the general rule or pattern for determining the total number of combinations, i.e., that it is possible to get the answer by multiplying the number of shirts possible (4) by the total number of shorts possible (4) to get a correct total number of 16 combinations.

## Episode 15: KNOW WHEN TO FOLD ‘EM

**THIS EPISODE IS ABOUT…** the connections among geometry of paperfolding. Every origami fold has associated geometric patterns. We see this by unfolding origami models. When we unfold even simple origami models, we find “paper trails” of many interesting geometric patterns in the folds: different types of triangles, angles, polygons, lines and symmetry. Unfolded models also provide a real context for fractions, ratios (of area) and geometric vocabulary such as *parallel*, *congruent*, and *right angle*.

## Episode 16: “TOTALLY A MAZE THING!”

**THIS EPISODE IS ABOUT… **directionality, relative positions, turns and grids. The importance of distinguishing *left* from *right *(steps and quarter- or half-turns), *in front of, behind, beside* is made concrete through the task of travelling through or creating a maze. The value of trial, revise, re-trial problem-solving is promoted through the authentic task of planning and following a route described in steps and turns. The concept of equivalence is introduced through travelling the maze: one right quarter turn is the same as three left quarter turns or one left half turn followed by one left quarter turn.

## Episode 17: “SO YOU THINK UNCLE NORM CAN DANCE”

**THIS EPISODE IS ABOUT… **patterning (rhythm, number), transformational geometry (slides, flips and turns) and symmetry through movement. Dance steps and rhythms are repeated, numbered patterns and the patterns of footsteps help to build an understanding of the geometric relationship between positions and moves. The communication of sequential steps using precise mathematical language is also emphasized.

## Episode 18: “IT’S ABOUT TIME”

**THIS EPISODE IS ABOUT… **the measurement of time (to half-hours) and the units (hours and minutes) that we use to count elapsed time. Instruments for measuring time are introduced as is the concept of “reading” a clock. Telling time and counting minutes or hours helps to give meaning to the number system and represents an important life skill.

## Episode 19: “MEETING THE STANDARD”

**THIS EPISODE IS ABOUT… **the standard metric linear measurement referents: the centimetre and the metre. The episode introduces two of the most important frame of references used for linear measurement, the standard tools used for measuring them and shows when and how they are used in real-world applications. A principle focus is on how to recognize the size of the centimetre and metre and estimate lengths of familiar objects.

## Episode 20: GOING THE DISTANCE

**THIS EPISODE IS ABOUT…** the metre and its relationship to the kilometre. By using real-world examples of how the metre and kilometre are used to measure linear distances as well as the tools used to measure standard and extremely long lengths, the episode demonstrates application of math beyond the classroom. By using patterning (skip counting by 10s, 100s and 1000s) we show how numbers are built. By connecting units to authentic referents, the episode demonstrates that prefixes such as *kilo* communicate precise numeric information.

## Episode 21: ”THE CUBIC RUBE”

**THIS EPISODE IS ABOUT.... **volume, specifically it provides a visual demonstration ofthe cubic metre: a fundamental benchmark for measurement. Examples of the cubic metre in everyday life are provided to provide referents and visual models that can aid in estimation of 3D measures (volume and capacity).** **

## Episode 22: Thinking About Linking

**THIS EPISODE IS ABOUT..... **congruent shapes, patterning and symmetry and simple transformational geometry. In a paper doll chain every other doll is a flipped copy of the one next to it - a reflection. If you start with the right “generator” you can alternate arm up, arm down and so on. Symmetry is an essential component of many traditionally handicrafts: lacework, embroidery, weaving, hair braiding to name a few. The folding and cutting of paper dolls does not have the practical value of these crafts, but still may be used to illustrate some of the important tools of transformation geometry.

## Episode 23: A Cute Look At Angles

**THIS EPISODE IS ABOUT… **types of angles: acute, obtuse and right. The emphasis is on the right angle, right triangle and equilateral triangle and how they have been used in architecture and design through the ages.

## Episode 24: How Things Stack Up...and Down

**THIS EPISODE IS ABOUT…** growing or shrinking patterns, i.e., patterns in which every element in the pattern is related to the preceding element in the pattern in the same way (illustrated with numbers and shapes). An example of a growing pattern is 0, 2, 4, 6, 8, 10, 12,…; a shrinking pattern is 100, 90, 80, 70, 60,…. It is growing and shrinking patterns that lead to generalizations and to representations of the generalizations using variables; thus, this episode introduces fundamental concepts related to algebra.

## Episode 25: A Balancing Act or A Question of Balance

**THIS EPISODE IS ABOUT…** the fact that in addition to length, height or colour, objects have other measurable properties such as weight, and that you can measure and compare this property using specific tools and units. Scales (at home or at the grocery store) are introduced to demonstrate one of the real-world tools for measuring weight, and the concepts of greater than, less than or equal to are used to demonstrate how balance can be used to determine weight.

## Episode 26: Show Me The Money

**THIS EPISODE IS ABOUT… **distinguishing between quantity and value with respect to coins; and, about combinations of coins—such as 25 pennies, 2 dimes and 5 pennies, 5 nickels, or 1 quarter (an important concept in decomposing numbers).