A figure has line symmetry when you can fold it along a line so the two halves match exactly. That fold line is called a line of symmetry. A square has 4 lines of symmetry, a rectangle that is not a square has 2, and a slanted parallelogram has none. Many letters and animals are symmetric too.
A point is an exact spot. A line goes on forever in both directions, a ray has one endpoint and goes on forever one way, and a line segment has two endpoints. Lines can be parallel or perpendicular. Shapes are sorted by their parallel sides and by right, acute, or obtuse angles.
An angle is formed by two rays that share an endpoint, and it is measured in degrees. A full turn is 360 degrees, a half turn is 180 degrees, and a quarter turn is 90 degrees. One degree is 1/360 of a full circle. Use a protractor to measure angles, and add parts to find a whole angle.
A line plot is a number line with a dot or an X above each measurement in a data set. In Grade 4, the number line shows fractions such as 1/2, 1/4, and 1/8. Taller stacks mean more measurements at that length. You can add and subtract the fractions shown on the plot to answer questions.
Area is the number of unit squares that cover a flat shape, and perimeter is the distance around it. For a rectangle, area = length × width and perimeter = 2 × length + 2 × width. A rectangle 8 feet long and 3 feet wide has an area of 24 square feet and a perimeter of 22 feet.
Measurement units tell how long, how heavy, or how much liquid something is. To change a larger unit into a smaller unit, multiply by the number of small units in one large unit. For example, 1 kilometer is 1,000 meters, so 3 km is 3,000 m. Smaller units give bigger numbers.
Tenths and hundredths are decimal places. One tenth is 1/10, or 0.1, and one hundredth is 1/100, or 0.01. Ten hundredths make one tenth, so 3/10 = 30/100 = 0.30. To compare decimals, write them to the same place, then compare the digits from left to right.
To multiply a whole number by a fraction, multiply the whole number by the numerator and keep the denominator: 3 x 2/5 = 6/5. A fraction such as 5/6 is a multiple of the unit fraction 1/6, because it is 5 x 1/6. Change an improper fraction to a mixed number to read the answer more easily.
To add or subtract fractions with the same denominator, add or subtract the numerators and keep the denominator: 2/8 + 3/8 = 5/8. A fraction can be decomposed into a sum of fractions with the same denominator. Mixed numbers can be changed to improper fractions to add or subtract them.
To compare fractions, make the pieces easy to match. With the same denominator, the greater numerator is greater. With the same numerator, the smaller denominator is greater. Otherwise use a common denominator or compare to 1/2, then write the answer with the symbols >, < or =.
Equivalent fractions are different fractions that name the same amount, such as 1/2 and 2/4. To make one, multiply the numerator and the denominator by the same number. For example, 3/4 becomes 6/8 when both parts are multiplied by 2. You can also divide both parts by the same number.
A number pattern follows a rule, such as start at 1 and add 3. Use the rule to make each term: 1, 4, 7, 10, 13. Then look for features the rule does not state, such as terms that alternate odd and even. An input-output table shows the same rule as pairs of numbers.
A factor is a whole number that divides another whole number with no remainder. A multiple is the product of a number and 1, 2, 3, and so on. A prime number has exactly two factors, 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite.
A multistep word problem takes two or more operations to solve. Draw a bar model and use a letter for the unknown. Solve one step at a time, such as 6 × 24 = 144 and then 144 − 37 = 107. Decide what to do with any remainder, and use estimation to check that your answer is reasonable.
To divide by a 1-digit number, break the dividend into easy parts, find partial quotients, and add them. Anything left that is smaller than the divisor is the remainder. Check by multiplying the quotient by the divisor and adding the remainder. For example, 47 ÷ 5 = 9 R 2 because 9 × 5 + 2 = 47.
To multiply multi-digit numbers, break a factor into place-value parts, multiply each part, and add the partial products. An area model draws this as a rectangle: 36 × 24 is 600 + 120 + 120 + 24 = 864. The distributive property allows the split. For multiples of 10, multiply the basic facts and attach the zeros.
A multiplicative comparison tells how many times as many or times as much one amount is than another. It uses multiplication, such as 28 = 4 × 7, which means 28 is 4 times as many as 7. An additive comparison tells how many more or fewer. Draw a bar model, then multiply or divide.
To add or subtract multi-digit numbers, line up the digits by place value and work from the ones place to the left. Carry when a column adds to 10 or more. Regroup when a top digit is too small to subtract from. Check by using the opposite operation.
Rounding replaces a number with the closest multiple of a place, such as ten, hundred, or thousand. Look at the digit to the right of that place. If it is 5 or more, round up. If it is 4 or less, keep the digit. Then change the digits to its right to zeros. Rounding also helps estimate sums and differences.
Place value tells how much a digit is worth based on where it sits in a number. Each digit is worth ten times the digit to its right. In 305,718, the 5 is in the thousands place, so it means 5,000. You can write numbers up to 1,000,000 three ways and compare them with <, >, or =.