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The short version A perfect square is a whole number you get by multiplying a whole number by itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 and so on. The full list of perfect squares from 1² to 50² is in the table below, ending at 50² = 2,500. Quick test: a…
The short version A rational number can be written as a fraction of two integers, like 3/4, -5 or 0.333… (which is 1/3). An irrational number can’t be written as a fraction at all, like π or √2. The decimal test: if the decimal stops or repeats a block forever, the number is rational. If…
The short version The radius of a circle is the distance from the center to any point on the edge. Every radius of the same circle is the same length. The radius is half the diameter: r = d ÷ 2. The diameter is twice the radius: d = 2r. If you know the circumference,…
The short version Perimeter is the total distance around the outside of a flat shape. To find it, add up the lengths of all the sides. Rectangle: P = 2 × (length + width). Square: P = 4 × side. For a circle, the perimeter is called the circumference: C = 2πr. Perimeter measures the…
The short version Vertices are the corner points of a shape, where two or more sides or edges meet. One corner is a vertex, and two or more are vertices. A polygon has the same number of vertices as sides: a triangle has 3, a hexagon has 6. A circle has none. In 3D, a…
The short version A factor is a whole number that divides another whole number evenly, with nothing left over. The factors of 12 are 1, 2, 3, 4, 6 and 12. Factors come in pairs that multiply to the number. For 12, the pairs are 1 × 12, 2 × 6 and 3 × 4….
The short version The main parts of a circle are the center, radius, diameter and circumference. Kids in upper elementary and middle school also learn chord, arc, sector, segment, tangent and secant. The radius runs from the center to the edge. The diameter goes all the way across through the center, so it’s always twice…
The short version An obtuse triangle has one angle bigger than 90° and smaller than 180°. The other two angles are always acute. A triangle can only ever have one obtuse angle, because the three angles add to exactly 180°. If you only know the side lengths, square them. When the longest side squared is…
The short version A cube has 6 sides, which mathematicians call faces. Each face is a square, and all six are the same size. A cube also has 12 edges (where two faces meet) and 8 vertices (corners). “Sides” is ambiguous. On a flat shape, a side is a line segment. On a 3D shape,…
The short version An irregular polygon is a polygon whose sides aren’t all the same length, or whose angles aren’t all the same size, or both. A regular polygon has to pass two tests: every side equal and every angle equal. Fail either one and it’s irregular. Rectangles, rhombuses, kites, trapezoids, right triangles and scalene…