Represent and compare numbers through one thousand

Learning goal: Read, write, represent and compare numbers to 1,000 using hundreds, tens and ones. A digit's place determines the value it represents. In 346, the 3 means three hundreds, the 4 means four tens and the 6 means six ones; they do not represent three, four and six loose objects.

A hundred can be composed from ten tens, and each ten can be composed from ten ones. A bundle of ten tens is called a hundred. The model shows one hundred as a ten-by-ten square of one hundred unit cells, one ten as a strip of ten cells and one as a single cell. These models must use the same unit-cell size so their relative values are meaningful.

In 706, seven hundreds contribute 700, the zero records no tens in the usual hundreds-tens-ones representation and six ones contribute 6. Write 700 + 0 + 6 = 706, or 700 + 6 when the zero term is omitted from the sum. Do not write 76; removing a zero digit from the numeral changes the places and therefore the number.

The round hundreds 100, 200, 300, 400, 500, 600, 700, 800 and 900 name one through nine hundreds with no additional tens or ones in the usual representation. Ohio lists the hundred and these round hundreds as special cases of place value. For example, 600 is six hundreds, 0 tens and 0 ones: six bundles of ten tens with nothing left over. One thousand is ten hundreds. Read 346 as three hundred forty-six and 1,000 as one thousand. Write number names alongside numerals to connect spoken language with place value.

Expanded form shows the values added: 716 = 700 + 10 + 6. The order of those addends may change without changing the sum, so 6 + 700 + 10 is equivalent. Other groupings work too: 71 tens and 6 ones also represent 716 because 71 tens equal 710. An equivalent representation need not use fewer than ten units of every place.

Compare three-digit numbers from the greatest place first. For 346 and 364, the hundreds match. Compare tens: four tens is less than six tens, so 346 < 364. There is no need to let the larger ones digit in 346 override the tens comparison. For 506 and 496, five hundreds exceed four hundreds, so 506 > 496 even though 496 has more tens and ones.

The symbols > and < name greater-than and less-than relationships. Read the entire statement aloud: “346 is less than 364.” The symbol's open side faces the greater quantity. Use = when quantities are equivalent, including 700 + 16 = 716. Equality compares values, not whether the two sides use identical-looking notation.

Worked example 1: Explain a zero. In 706, the zero holds the tens place. Seven hundred six contains seven hundreds and six ones in the usual model. Its zero does not mean the number has no value, and it cannot be deleted from the numeral.

Worked example 2: Regroup a representation. Start with seven hundreds, one ten and six ones. Exchange seven hundreds for seventy tens, then include the additional ten. That gives seventy-one tens and six ones: still 716.

Worked example 3: Compare in order. Compare 438 and 431. Hundreds match and tens match, so compare ones: eight is greater than one. Thus 438 > 431. State which place first decides the comparison.

Guided practice: Build numbers containing a zero, read their names and write expanded forms. Exchange tens for hundreds while preserving the unit amount. Compare number pairs that differ first in hundreds, then tens, then ones. Include equality examples written in different forms.

Independent tasks: Represent a three-digit number with a labeled model, write its numeral and name, provide an equivalent grouping and compare it with another number using a symbol and explanation. Include 1,000 as the boundary of the reading/writing range.

Feedback: If a learner reads each digit as a loose count, label the place and corresponding value. If an expanded form is concatenated incorrectly, recombine the place-value amounts. Credit equivalent representations when the total value is preserved.