Use tens and ones to compare two-digit numbers

Learning goal: Explain two-digit numbers as tens and ones and compare them using >, < and =. Use bundles of exactly ten sticks or base-ten drawings with their units clearly labeled. The digits represent quantities because of their positions, not because the physical digit on one side is drawn larger.

Count ten separate counters and group them as one ten. The phrase one ten names a grouped unit containing ten ones. It does not mean that nine objects disappeared. Build 34 with three groups of ten and four additional ones. Thirty-four can be described as three tens and four ones, or thirty plus four.

Review the special cases. Eleven through nineteen contain one ten and additional ones. Exact tens such as 20, 50 and 90 contain two, five and nine tens respectively, with zero ungrouped ones. In 50, zero is meaningful: it records that there are no additional ones beyond the five full tens. A blank ones area is not an unfinished representation when the zero is explicitly labeled.

The diagram contrasts 34 and 43. The first has three tens and four ones; the second has four tens and three ones. Even though they use the same digits, forty-three has more because four tens already exceed three tens, and the remaining ones cannot reverse this comparison. Count the actual grouped objects to verify.

Compare tens first. If the tens counts differ, the number with more tens is greater. If tens counts match, compare the ones. For 46 and 42, both have four tens, but six ones are more than two ones, so 46 is greater. For 38 and 38, both the tens and ones counts match, so the numbers are equal.

Connect words to comparison symbols. Write 34 < 43 to say thirty-four is less than forty-three, and 43 > 34 for the reverse comparison. The open side of < or > faces the greater amount; the point faces the lesser. The equal sign means both sides name the same amount. Read each complete statement aloud so the symbol does not become a shape guessed without a quantity relationship.

Worked example 1: Different tens. Compare 28 and 35. Two tens and eight ones make twenty-eight; three tens and five ones make thirty-five. Three tens exceed the two-ten amount even with eight extra ones, so 28 < 35.

Worked example 2: Same tens. Compare 67 and 64. Both have six tens. Compare seven ones with four ones; seven is more, so 67 > 64. The ones decide only because the tens matched.

Worked example 3: Zero ones. Model 40 as four groups of ten and no extras. Compare with 37. Four tens make forty, which is more than three tens and seven ones. A missing loose-counter area is intentional and should be labeled zero ones.

Guided practice: Build teen numbers, exact tens and other two-digit amounts. Name tens and ones, then record the numeral. Compare pairs with different tens, matching tens and equal values. Ask partners to write both forward and reverse comparison statements when the values differ.

Independent tasks: Explain 17, 80 and 65 using grouped units; compare 57/75, 86/82 and 24/24; and draw one pair of models supporting a comparison symbol. Identify zero ones in an exact-ten number rather than leaving its meaning implicit.

Assessment and feedback: Credit accurate grouping, digit meaning, comparison and symbol interpretation separately. If the child compares only the ones, build the tens physically and revisit the complete amount. If the symbol is reversed, read the sentence aloud while pointing from left to right. Extend by asking for a two-digit number with the same tens as 52 but a greater amount, and justify the choice.