STAAR Grade 4 Math

Place value is the foundation of our number system. Every digit in a number has a specific position, and that position determines the digit's value. In fourth grade, students work with whole numbers through the hundred thousands place and decimals through the hundredths place.

The place value chart for whole numbers extends from ones on the right to hundred thousands on the left. Each place is exactly ten times greater than the place to its right. This relationship is called the base-ten system.

Consider the number 547,382. The 5 is in the hundred thousands place, so its value is 500,000. The 4 is in the ten thousands place, so its value is 40,000. The 7 is in the thousands place, so its value is 7,000. The 3 is in the hundreds place, so its value is 300. The 8 is in the tens place, so its value is 80. The 2 is in the ones place, so its value is 2.

When we add all these values together (500,000 + 40,000 + 7,000 + 300 + 80 + 2), we get 547,382. This is called expanded form. Standard form is simply writing the number as 547,382. Word form is writing the number using words: five hundred forty-seven thousand, three hundred eighty-two.

When reading numbers with four or more digits, we group digits into periods. The first period (from the right) is the ones period, containing ones, tens, and hundreds. The second period is the thousands period, containing thousands, ten thousands, and hundred thousands.

A comma separates the periods. When reading, we say the number in each period followed by the period name. For 85,412, we read "eighty-five thousand, four hundred twelve." Notice we do not say "and" between the thousands and hundreds in whole numbers.

For the number 304,056, we read "three hundred four thousand, fifty-six." The zeros act as placeholders. The zero in the ten thousands place means there are no ten thousands. The zero in the hundreds place means there are no hundreds.

To compare two whole numbers, first check if they have the same number of digits. If one number has more digits, it is greater. If both numbers have the same number of digits, compare digit by digit from left to right until you find digits that differ.

Compare 45,892 and 45,978. Both have five digits. The ten thousands digits are both 4. The thousands digits are both 5. The hundreds digits differ: 8 and 9. Since 8 is less than 9, we know 45,892 is less than 45,978. We write 45,892 < 45,978.

When ordering multiple numbers from least to greatest or greatest to least, compare pairs of numbers systematically. Line up the numbers by place value to make comparison easier.

Rounding means replacing a number with a nearby number that is easier to work with. We round to a specific place value: tens, hundreds, thousands, ten thousands, or hundred thousands.

The rounding rule states: Look at the digit to the right of the rounding place. If that digit is 5 or greater, round up (increase the rounding digit by 1). If that digit is less than 5, round down (keep the rounding digit the same). All digits to the right of the rounding place become zeros.

Round 47,853 to the nearest thousand. The thousands digit is 7. Look at the hundreds digit: 8. Since 8 is greater than 5, round up. The 7 becomes 8. The answer is 48,000.

Round 47,853 to the nearest ten thousand. The ten thousands digit is 4. Look at the thousands digit: 7. Since 7 is greater than 5, round up. The 4 becomes 5. The answer is 50,000.

Round 47,853 to the nearest hundred. The hundreds digit is 8. Look at the tens digit: 5. Since the digit is exactly 5, we round up. The 8 becomes 9. The answer is 47,900.

Decimals extend place value to the right of the ones place. The decimal point separates whole numbers from fractional parts. The first place to the right of the decimal point is the tenths place. The second place is the hundredths place.

In the number 3.47, the 3 is in the ones place, the 4 is in the tenths place, and the 7 is in the hundredths place. We read this as "three and forty-seven hundredths."

The tenths place represents one-tenth (1/10) of a whole. The hundredths place represents one-hundredth (1/100) of a whole. Just as moving left in whole numbers multiplies by 10, moving right in decimals divides by 10.

Decimals and fractions both represent parts of a whole. Tenths as fractions have a denominator of 10. Hundredths as fractions have a denominator of 100.

The decimal 0.3 equals the fraction 3/10. The decimal 0.07 equals the fraction 7/100. The decimal 0.35 equals the fraction 35/100.

To convert a fraction with a denominator of 10 to a decimal, write the numerator in the tenths place. The fraction 9/10 equals 0.9.

To convert a fraction with a denominator of 100 to a decimal, write the numerator so it fills the tenths and hundredths places. The fraction 42/100 equals 0.42. The fraction 6/100 equals 0.06 (we need the zero placeholder in the tenths place).

To compare decimals, align the decimal points and compare digit by digit from left to right. Adding zeros after the last decimal digit does not change the value: 0.5 equals 0.50.

Compare 0.47 and 0.5. Rewrite 0.5 as 0.50. Compare tenths: 4 and 5. Since 4 is less than 5, we know 0.47 < 0.5.

Compare 3.8 and 3.72. Rewrite 3.8 as 3.80. Compare ones: both are 3. Compare tenths: 8 and 7. Since 8 is greater than 7, we know 3.8 > 3.72.

When ordering decimals, use the same comparison process. Arrange from least to greatest or greatest to least as directed.

Number lines provide a visual representation of number relationships. Whole numbers and decimals can both be placed on number lines.

For whole numbers, the intervals might represent ones, tens, hundreds, or larger values depending on the scale. To place a number, identify the interval and count the subdivisions.

For decimals, a number line from 0 to 1 might be divided into ten equal parts (tenths) or one hundred equal parts (hundredths). The point 0.7 would be located at the seventh mark when the line is divided into tenths.

The STAAR exam tests place value through multiple question types. Students must identify the value of a specific digit within a number. Students must write numbers in standard, expanded, and word form. Comparison questions ask which symbol (<, >, =) makes a statement true. Ordering questions require arranging three or four numbers. Rounding questions specify the place to round to. Decimal questions often connect to fractions and visual models like grids or number lines.