The short version 3D shapes are solid shapes with three measurements: length, width and height (or depth). They take up space, so you can measure their volume. Flat-sided 3D shapes (cubes, prisms, pyramids) are called polyhedra and are described by their faces, edges and vertices. For every one of them, vertices – edges + faces…
The short version Math enrichment is extra math that goes deeper and wider than the grade-level curriculum: puzzles, multi-step problems, patterns and reasoning. The focus is depth. Moving ahead early is a separate thing. It fits kids who finish classwork fast, ask “why,” or seem bored. It can also help an average student who likes…
The short version To add fractions with different denominators, rewrite them so they share a denominator, add the numerators, keep the denominator, then simplify. The best shared denominator is the least common multiple of the two denominators. For 1/4 + 1/6 that’s 12, so 3/12 + 2/12 = 5/12. Never add the bottoms. 1/2 +…
The short version A scale factor is the number you multiply every length by to make a bigger or smaller copy of a shape. Scale factor = new length ÷ original length. A scale factor greater than 1 enlarges, a scale factor between 0 and 1 shrinks, and a scale factor of exactly 1 gives…
The short version A quotient in math is the answer to a division problem. In 20 ÷ 4 = 5, the quotient is 5. The number being divided is the dividend, the number you divide by is the divisor, and anything left over is the remainder. Order matters. “The quotient of 20 and 4” means…
The short version Slope is rise over run: how much a line goes up or down for every one step to the right. From two points, use m = (y2 – y1) ÷ (x2 – x1). Subtract the y-values on top and the x-values on the bottom, in the same order. From an equation in…
The short version A bar model is a drawing that shows the numbers in a word problem as rectangles, so a child can see how the parts relate before doing any arithmetic. Most problems use one of two shapes: a part-whole model (pieces that make a total) or a comparison model (two bars side by…
The short version A monomial is an algebraic expression with exactly one term: a number, a variable, or numbers and variables multiplied together. Examples: 7, x, -5×2, 3xy and ½a3b. Non-examples: x + 2 (two terms), 4/x (variable in a denominator) and x-2 (negative exponent). The exponents on the variables have to be whole numbers:…
The short version A solution in math is a value that makes an equation or inequality true when you plug it in. For x + 6 = 11, the solution is 5, because 5 + 6 = 11. You can always test a possible solution by substituting it back in and checking that both sides…
The short version You only need five symbols for Roman numerals 1 to 100: I = 1, V = 5, X = 10, L = 50 and C = 100. Write a smaller symbol after a bigger one to add (VI = 6). Write it before a bigger one to subtract (IV = 4). Only…