Mathematics 4

In a number like 4,672, each digit's place tells its value: 4 thousands, 6 hundreds, 7 tens, 2 ones.

The first place after the decimal point is tenths; the second place is hundredths — just like tens and ones, but for parts smaller than one whole.

The bigger the denominator, the smaller each piece is — eighths are smaller pieces than quarters, even though 8 is a bigger number than 4.

To compare two numbers, start from the leftmost (biggest) place value and compare digit by digit.

A hundredths grid has 100 tiny squares; shading 45 of them shows 0.45, or 45 hundredths.

Line up numbers by place value (thousands under thousands, ones under ones) before adding or subtracting.

Break a bigger number into place-value parts (235 = 200 + 30 + 5) and multiply each part by the one-digit number, then add the results.

Line up the decimal points (and therefore the place values) before adding or subtracting decimals.

Known facts (like doubles: 8+8=16) can help you figure out nearby facts (like 8+9, one more than the double).

Skip-counting (like 5, 10, 15, 20…) helps find multiplication facts for that number.

A pattern rule describes how each term changes from the one before it (like 'add 2 each time' or 'subtract 3 each time').

When one quantity changes, a related quantity often changes in a predictable, connected way (more bikes means more wheels, always doubling).

An equation like 8 + ? = 15 asks: what number, added to 8, makes 15? You can use the opposite (inverse) operation to find it.

Checking the rule against at least three pairs of numbers in the table confirms it really works every time, not just once.

A table, a diagram, or words can all show the same relationship between two quantities.

On an analog clock, the short hand shows the hour and the long hand shows the minutes, counting by 5s around the face.

Perimeter is the total distance all the way around the outside edge of a shape — add up the length of every side.

12-hour time repeats 1 to 12 twice a day (am and pm); 24-hour time counts the hours straight through from 0 to 23 without repeating.

For a regular shape, you can multiply one side's length by the number of sides instead of adding each one separately.

To convert an afternoon/evening 12-hour time to 24-hour time, add 12 to the hour (3:45 pm becomes 15:45).

A regular polygon has ALL sides the same length AND all angles the same size (like a square or a stop sign's octagon).

A shape has line symmetry if you can fold it along a line so that both halves match up exactly, edge to edge and point to point.

An irregular polygon has sides and/or angles that are not all equal (like a rectangle or a scalene triangle).

Some shapes have more than one line of symmetry (a square has 4), some have exactly one (like most hearts), and some have none at all.

You must check both sides AND angles before deciding a polygon is regular — one alone isn't enough.

In a one-to-one graph, each bar unit or picture symbol equals exactly 1 item.

A probability experiment (like flipping a coin or spinning a spinner) has an outcome you can record every time you try it.

Making change means figuring out the difference between what was paid and what something costs — you can subtract, or count UP from the price to the amount paid.

In a many-to-one graph, each picture symbol stands for more than 1 item (like 1 picture = 5 votes) — the key (legend) always tells you the value.

What we EXPECT (like 5 heads out of 10 flips) is likely but not guaranteed — real results often come out a little different from the expectation.