MTTC Mathematics (Elementary) (089) key terms

The value a digit has because of its position in a numeral; in 4,725 the 7 means 700 because it sits in the hundreds place. Regrouping and expanded form both depend on this idea.

A numeral rewritten as the sum of each digit's place value, such as 4,725 = 4,000 + 700 + 20 + 5. It makes the meaning of each digit visible and supports mental computation.

Trading ten units in one place for one unit in the next place to the left, or the reverse, so an operation can be completed. Borrowing in subtraction and carrying in addition are both examples.

Manipulatives in which a small cube is one, a rod is ten, a flat is one hundred, and a large cube is one thousand. They model place value and regrouping concretely before symbols are introduced.

A fixed, digit-by-digit procedure for computing with multi-digit numbers, such as lining up place values and regrouping. Efficiency comes at the cost of transparency, so it is usually taught after meaning is built.

The separate products formed when a multi-digit multiplication is broken apart by place value, as in 23 x 14 = 230 + 92. Adding them gives the total and shows why the standard algorithm works.

A rectangle diagram whose side lengths are the factors of a product, so the area equals the product. Splitting the rectangle by place value turns multiplication and division into visible, additive steps.

An arrangement of objects in equal rows and columns. It models multiplication as repeated groups and division as sharing, and it connects directly to the area model and to factors.

A whole number that divides a given number with no remainder; the factors of 12 are 1, 2, 3, 4, 6, and 12. In a multiplication expression, factors are the numbers being multiplied.

The result of multiplying a whole number by any counting number; multiples of 4 are 4, 8, 12, 16, and so on. Every number is a multiple of each of its factors.

A whole number greater than 1 with exactly two factors, 1 and itself, such as 2, 3, 5, 7, and 11. One is not prime because it has only a single factor.

A whole number greater than 1 that has more than two factors, such as 9, whose factors are 1, 3, and 9. Every composite number can be written as a product of primes.

Writing a composite number as a product of primes, for example 36 = 2 x 2 x 3 x 3. The result is unique apart from order, which makes it useful for finding common factors and multiples.

The largest whole number that divides two or more given numbers evenly; the greatest common factor of 18 and 24 is 6. It is used to simplify fractions and factor expressions.

The smallest nonzero number that is a multiple of two or more given numbers; the least common multiple of 6 and 8 is 24. It gives a common denominator when adding fractions.

A quick test that predicts whether one number divides another without doing the division; a number is divisible by 3 when its digit sum is divisible by 3. Rules exist for 2, 3, 4, 5, 6, 9, and 10.

Fractions that name the same amount even though the numerals differ, such as 1/2 and 3/6. Multiplying or dividing numerator and denominator by the same nonzero number produces an equivalent fraction.

A fraction written with the smallest possible whole-number numerator and denominator, found by dividing both by their greatest common factor; 8/12 becomes 2/3. The value of the fraction does not change.

A shared denominator that lets two or more fractions be compared or added; for 1/4 and 1/6, 12 works. The least common multiple of the denominators is the most efficient choice.

A familiar fraction such as 1/4, 1/2, 3/4, or 1 used as a reference point for estimating and comparing other fractions. Comparing to 1/2 quickly shows whether a fraction is more or less than half.

The interpretation that a/b means a divided by b, so 3/4 is three wholes shared among four. This meaning explains improper fractions, decimals, and why dividing by a fraction can increase a quantity.

A fraction whose numerator is greater than or equal to its denominator, such as 7/4. It can be rewritten as a mixed number and often arises as an intermediate result in computation.

A number written as a whole number plus a fraction, such as 2 3/4. Converting to an improper fraction makes multiplication and division of such numbers straightforward.

The number formed by swapping a fraction's numerator and denominator; the reciprocal of 3/5 is 5/3. A number times its reciprocal equals 1, which is why dividing by a fraction means multiplying by its reciprocal.

A base-ten numeral using a decimal point to mark the ones place, with each place to the right worth one-tenth of the place before it. Decimals and fractions are two notations for the same rational values.

A ratio out of one hundred, so 45% equals 45/100 or 0.45. Percent problems are solved by identifying the whole, the part, and the rate and setting up part = rate x whole.

A comparison of two quantities by division, written as 3:5, 3 to 5, or 3/5. Ratios can compare part to part or part to whole, and that distinction changes the meaning.

An equation stating that two ratios are equal, such as 3/4 = 9/12. Cross multiplication solves proportions because it equates the products of the means and the extremes.

A rate expressed per one unit of the second quantity, found by dividing; 150 miles in 3 hours is 50 miles per hour. Unit rates make comparisons between different offers or speeds direct.

The fixed multiplier k linking two proportional quantities in the equation y = kx. It equals the unit rate and appears as the slope of the graph of a proportional relationship.

The multiplier that relates a figure or drawing to its image under a dilation or to the original object. Lengths scale by this factor while areas scale by its square.

Figures with equal corresponding angles and proportional corresponding side lengths. Congruent figures are a special case with a scale factor of exactly 1.

Figures that have exactly the same size and shape, related by a sequence of translations, rotations, and reflections. Corresponding sides and angles are equal, so the scale factor is 1.

A rule that moves or changes a figure on the coordinate plane: translation (slide), rotation (turn), reflection (flip), or dilation (resize). The first three preserve size and shape; a dilation does not.

A property of a figure that maps onto itself under a reflection or rotation. A line of symmetry divides a figure into two mirror-image halves.

The amount of space a solid occupies, measured in cubic units. For a rectangular prism it equals length x width x height, which is the same as base area times height.

The total area of all faces of a three-dimensional figure, measured in square units. A net makes each face visible so the areas can be summed without omission.

A flat pattern that folds into a three-dimensional solid, showing every face. Nets help students connect two-dimensional area to the surface area of prisms, pyramids, and cylinders.

A grid formed by a horizontal x-axis and a vertical y-axis intersecting at the origin, with points named by ordered pairs (x, y). It links geometry to algebra through graphs of relationships.