NYS Math Grade 4 flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Place value relationship

In a multi-digit number, each place value is 10 times the value of the place to its right, so one digit in the thousands place equals ten of the same digit in the hundreds place.

Expanded form

A number written as the sum of the values of each of its digits, such as 4,206 written as 4,000 + 200 + 6, showing the value of every place.

Word form of numbers

A number written using words with commas and hyphens, such as 32,045 written as thirty-two thousand, forty-five; the word "and" is not used for whole numbers.

Rounding to a place

To round, locate the digit in the rounding place and check the digit to its right; 0 through 4 keeps the digit, 5 through 9 increases it by one, and digits to the right become zero.

Comparing whole numbers

Compare digits starting from the leftmost place value; the number with the greater digit at the first place where they differ is the greater number.

Standard algorithm for addition

Line up numbers by place value, add digits in each column starting from the ones place, and regroup ten ones as one ten, ten tens as one hundred, and so on.

Subtraction with regrouping

Line up by place value and subtract from the ones place; when the top digit is too small, borrow one from the next place to the left, which is worth ten of the current place.

Multiplicative comparison

A statement such as "12 is 3 times as many as 4" compares quantities by multiplication; the equation 3 × 4 = 12 or 12 ÷ 3 = 4 models it.

Factors and multiples

Factors are whole numbers multiplied to give a product; multiples are the products of a number and whole numbers, such as 4, 8, 12, 16 for the number 4.

Prime and composite numbers

A prime number greater than 1 has exactly two factors, 1 and itself (2, 3, 5, 7); a composite number has more than two factors (4, 6, 8, 9).

Division with remainders

Dividing a whole number may leave a remainder smaller than the divisor; check with quotient × divisor + remainder = dividend, as in 17 ÷ 5 = 3 remainder 2.

Area formula for rectangles

Area equals length times width for a rectangle, reported in square units; a 6-by-4 rectangle has area 24 square units.

Perimeter of a rectangle

Perimeter is the distance around a figure, found for a rectangle by adding all four sides or computing 2 × (length + width), reported in linear units.

Area of composite figures

A figure made of rectangles can be decomposed into non-overlapping rectangles; add the areas of the parts, or subtract a missing rectangle from a larger one.

Equivalent fractions

Fractions that name the same amount, such as 1/2, 2/4, and 4/8; multiplying or dividing numerator and denominator by the same nonzero number creates them.

Comparing fractions unlike denominators

Compare fractions by reasoning about size: same denominator, compare numerators; same numerator, the larger denominator gives the smaller fraction, so 1/8 is less than 1/3.

Adding like-denominator fractions

Add or subtract fractions with the same denominator by combining only the numerators and keeping that denominator, as in 3/8 + 2/8 = 5/8.

Decomposing a fraction

Any fraction can be written as a sum of unit fractions or other fractions with the same denominator, such as 3/5 = 1/5 + 1/5 + 1/5.

Mixed number

A number made of a whole number and a fraction, such as 2 1/3, which equals 7/3; it can be rewritten as a fraction greater than one.

Multiplying fraction by whole number

Multiplying a fraction by a whole number means repeated addition of that fraction, so 3 × 2/5 = 2/5 + 2/5 + 2/5 = 6/5.

Tenths and hundredths

Fractions with denominators 10 and 100 can be written as decimals: 7/10 = 0.7 and 35/100 = 0.35; 7/10 equals 70/100, so 0.7 = 0.70.

Comparing decimals

Compare decimals place by place from the left, aligning the decimal points; 0.5 is greater than 0.45 because five tenths exceeds four tenths.

Measurement unit conversions

Within one measurement system, larger units convert to smaller ones by multiplying: 1 foot = 12 inches, 1 yard = 3 feet, 1 meter = 100 centimeters, 1 kilogram = 1,000 grams.

Elapsed time

Elapsed time is the difference between a start time and an end time; count forward in hours and minutes, regrouping 60 minutes as one hour when needed.

Line plot with fractions

A line plot shows data marks above a number line; for fractional data, the scale is divided into equal parts such as fourths or eighths, and each mark represents one data value.

Angle measurement

Angles are measured in degrees with a protractor; a right angle is 90 degrees, a straight angle is 180 degrees, and an angle's size is the amount of turn between its rays.

Lines of symmetry

A line of symmetry divides a figure into two matching halves that fold onto each other; a square has four lines of symmetry and a rectangle has two.

Classifying triangles

Triangles are classified by angles as right, acute, or obtuse, and by sides as equilateral (three equal sides), isosceles (two equal sides), or scalene (no equal sides).

Perimeter and area relationship

Figures can have the same perimeter but different areas, or the same area but different perimeters; a 1-by-12 rectangle and a 3-by-4 rectangle both have area 12 but differ in perimeter.

Pattern rules

A numerical pattern follows a rule such as "add 6" or "multiply by 2"; identify the rule from consecutive terms, then extend the pattern forward or backward.

Multi-step word problems

Solve problems with more than one operation by identifying what is asked, choosing operations, and checking whether the answer is reasonable in the context of the problem.

Rounding to estimate

Estimate a sum, difference, product, or quotient by rounding numbers to nearby friendly values before computing, then compare the estimate with the exact answer to judge reasonableness.