Mathematics 5

More decimal places means more PRECISION — 12.403 pins the time down more exactly than 12.4.

Line up place values and work right to left, regrouping (carrying or borrowing) between columns as needed.

Divisible means dividing leaves NO remainder. Test for 2: the last digit is even. Test for 5: the last digit is 0 or 5.

The algorithm multiplies one place value at a time and adds the partial products — 24 × 145 is 4 × 145 plus 20 × 145.

An improper fraction's numerator is bigger than its denominator — 5/4 means five quarter-pieces, which is more than one whole.

Parentheses group numbers and operations — whatever is inside gets done FIRST.

(2 + 3) × 4 = 20 but 2 + (3 × 4) = 14: the parentheses decide the story of the calculation.

A variable is a letter standing for an unknown value. In 3n, the 3 is a coefficient and the multiplication sign is invisible (3n means 3 × n); n/4 writes division as a fraction.

To evaluate, replace the variable with its number and compute: if n = 5, then 3n + 2 = 17.

Inverse operations undo each other: addition ↔ subtraction, multiplication ↔ division.

A 2-D shape has reflection symmetry if a straight line splits it into two halves that match exactly when folded.

A 3-D shape has reflection symmetry too — but over a PLANE (an invisible flat slice) instead of a line.

A shape has rotation symmetry if it lands exactly on itself before completing a full 360° turn; the ORDER counts how many times it matches in one full turn.

A regular polygon with n sides has n reflection symmetries AND rotation symmetry of order n — and a circle has infinitely many of both.

An ordered pair gives two distances: FIRST from the vertical axis (how far over), THEN from the horizontal axis (how far up).

Order matters — (3, 4) and (4, 3) are different places.

Movements combine directions: from (2, 1), going right 3 and up 2 lands at (5, 3) — the first number changes with left/right, the second with up/down.

Clear grid directions use the words left, right, up and down with counts.

Area counts unit squares: a cm² is a 1 cm by 1 cm square, an m² is a 1 m square, a km² is a 1 km square — pick the unit that fits the object.

A rectangle's area is length × width — that's just counting the rows of unit squares quickly.

Different rectangles can hold the SAME area: 1×16, 2×8 and 4×4 all cover 16 squares — but their perimeters differ.

Among all rectangles with the same area, the SQUARE has the least perimeter — the most compact shape.

An arithmetic sequence grows by the same amount each step; a table of values pairs each POSITION (1st, 2nd, 3rd…) with its TERM (5, 10, 15…).

The table makes the pattern visible: every step down the table adds the same amount.

Plot each row of the table as a point (position, term) — arithmetic sequence points always line up on a STRAIGHT line.

An expression captures the rule: saving $5 a week means the term at position n is 5 × n.

Frequency is the count for each category; comparing frequencies answers statistical questions ('which topping is most popular?').

The MODE is the category with the highest frequency — the most common answer.

Closed-list questions give choices to pick from (easy to tally); open-ended questions allow ANY answer (richer, but need categorizing afterwards).

Frequency can be pictured as bar graphs, dot plots, or stem-and-leaf plots — each tells the same story a different way.