Comparing and ordering numbers to 100
Which is more, greater than and less than, and putting numbers in order using tens and ones
About three lessons of 40 to 50 minutes
Who has more? You already know how to find out
Two friends tip out their sticker collections. Mia counts 45 stickers. Leo counts 54. Before anyone finishes counting again, hands shoot up: who has more? That one word, more, is the whole lesson. You compare numbers every day, when you check who scored the most goals, who is taller, or which jar has more sweets.
Today we turn that everyday sense of more and less into something you can write down. You will learn to read a two-digit number as tens and ones, decide which of two numbers is greater, write it with the > and < symbols, and put a whole set of numbers in order from smallest to largest.
- Mia has 45 stickers, Leo has 54same digits, but 54 is more, because 5 tens beats 4 tens
- 23 and 32swap the digits and the number changes, so read the tens first
- Line numbers up on a number linethe further right a number sits, the bigger it is
- Which jar has more sweets, 60 or 6?60 is ten times as many, even though the digit 6 looks the same
What students will be able to do
Students will read a two-digit number as a count of tens and ones, compare two numbers to at least 100 by looking at the tens first and then the ones, record the comparison with the symbols >, = and <, and order a small set of numbers from smallest to largest.
- I can read a two-digit number as tens and ones.
- I can compare two numbers by looking at the tens digit first, then the ones.
- I can write a comparison using >, < or =.
- I can put three or more numbers in order from smallest to largest.
- I can place numbers on a number line and use it to compare them.
Standards this unit teaches
- 1.NBT.B.3Common Core (US)Compare two-digit numbers
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, = and <.
- 1.NBT.B.2Common Core (US)Understand tens and ones
Understand that the two digits of a two-digit number represent amounts of tens and ones. The place-value reading in this unit is what makes comparing possible.
- AC9M1N01Australian Curriculum v9 (ACARA)Recognise, represent and order whole numbers
Recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts.
- AC9M1N02Australian Curriculum v9 (ACARA)Partition and rename with place value
Partition one- and two-digit numbers in different ways using part-part-whole relationships and physical and virtual materials. Comparing rests on reading a number as tens and ones.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Compare
- to decide which of two numbers is greater, which is less, or if they are equal
- Greater than (>)
- the first number is more, the open side of the symbol faces the bigger number
- Less than (<)
- the first number is smaller, the point faces the smaller number
- Equal (=)
- the two numbers are exactly the same amount
- Tens and ones
- the two digits of a number: how many groups of ten, and how many single ones
- Order
- to arrange numbers from smallest to largest, or largest to smallest
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Read a number as tens and ones
ConcreteBefore you can compare two numbers you have to read each one properly. Build 45 with base-ten blocks: 4 ten-rods and 5 single ones. Say it out loud, four tens and five ones. The tens digit tells you how many bundles of ten, and it counts for far more than the ones digit, because each ten is worth ten single cubes.
Do the same with 54: 5 ten-rods and 4 ones. Put the two builds next to each other. Even though 45 and 54 use the very same two digits, the piles are clearly different sizes, because 54 has an extra whole bundle of ten and 45 does not.
The big idea to hold onto: the tens digit is in charge. One extra ten is worth more than any number of extra ones you could have (the most ones you can hold is 9, and ten ones just become another ten).
- How many tens and how many ones are in 63?
- Which digit in 45 is worth more, the 4 or the 5? Why?
2. Compare two numbers: tens first
PictorialNow the main routine of the unit, and it is short: to compare two numbers, look at the tens digit first. The number with more tens is greater. Only if the tens are the same do you go on to compare the ones. Draw two bars, one for Mia's 45 and one for Leo's 54, on the same scale, and the taller bar shows the bigger number at a glance.
Mia has 45 (4 tens) and Leo has 54 (5 tens). Five tens is more than four tens, so 54 is greater, no matter what the ones digits are. We write 54 > 45, or the same fact the other way round, 45 < 54.
When the tens match, move to the ones. Compare 63 and 61: both have 6 tens, so look at the ones, 3 against 1. Three ones is more than one one, so 63 > 61.
Compare 45 and 54, then compare 63 and 61. Use > or <.
- 45 has 4 tens, 54 has 5 tens. 5 tens is more than 4 tens, so 54 is greater.
- Write it: 54 > 45 (which is the same as 45 < 54).
- 63 and 61 both have 6 tens, so the tens are equal. Compare the ones: 3 is more than 1.
- So 63 > 61.
Answer: 54 > 45 and 63 > 61.
- Which is greater, 72 or 27, and how do the tens tell you?
- How do you know the > symbol is pointing the right way?
3. Writing it with >, < and =
AbstractThe three symbols are just a quick way to record what you found. The wide open end always faces the bigger number, and the point always faces the smaller one. Read the whole thing left to right as a sentence: 54 > 45 says 'fifty-four is greater than forty-five'.
If the two numbers are exactly the same, they are equal and we use the = sign: 30 = 30. Equal is not a leftover, it is a real answer, and it matters later when the two tens digits and the two ones digits both match.
A useful self-check: whichever way you write it, the open mouth of the symbol should be next to the number you would rather have more of.
Fill in >, < or =: 38 __ 41, 70 __ 70, 26 __ 24.
- 38 and 41: 3 tens against 4 tens, so 38 is less. Write 38 < 41.
- 70 and 70: same tens, same ones, they match. Write 70 = 70.
- 26 and 24: both 2 tens, compare ones, 6 is more than 4. Write 26 > 24.
Answer: 38 < 41, 70 = 70, 26 > 24.
- Say 29 < 31 out loud as a full sentence.
- When do we use the = sign instead of > or <?
4. Putting numbers in order
PictorialOrdering is just comparing more than two numbers. Take 27, 54 and 45 and place each on a number line from 0 to 100. The line does the sorting for you: read left to right and you get smallest to largest. The further right a number sits, the bigger it is.
You can also order by reading tens first, exactly as when comparing a pair. Line the numbers up and find the one with the fewest tens (27 has 2 tens), then the next (45 has 4 tens), then the most (54 has 5 tens).
When two numbers share the same tens, break the tie with the ones, then keep going until every number has a place.
Order 54, 27 and 45 from smallest to largest.
- Compare the tens: 27 has 2 tens, 45 has 4 tens, 54 has 5 tens.
- Fewest tens first: 27, then 45, then 54.
- Check on the number line: the marks go 27, 45, 54 from left to right.
Answer: 27, 45, 54.
- Order 60, 16 and 61 from smallest to largest.
- How does the number line show which number is smallest?
Common misconceptions and how to address them
MisconceptionA number with a bigger ones digit is always bigger, so 45 is more than 54 because 5 is more than 4.
Why it happens: Students compare the digits they see first, or the last digit, without noticing that the tens digit outranks the ones.
How to address it: Build both numbers with ten-rods and single cubes. 54 has an extra whole rod of ten. Say the rule aloud every time: compare the tens first.
MisconceptionThe number with more digits, or the one you say later when counting, must be bigger, so 9 is bigger than 12 because 9 comes 'higher' in your head.
Why it happens: Single-digit numbers still feel large to a Grade 1 student, and 12 has a small-looking 1 at the front.
How to address it: Put 9 and 12 on the number line: 12 sits further right, so it is greater. A two-digit number has a tens digit and so is at least ten, which beats any single digit.
MisconceptionThe > and < symbols are the same, or their direction does not matter.
Why it happens: The two symbols are mirror images and easy to muddle before the meaning is secure.
How to address it: Anchor one image and keep it: the wide open end faces the bigger number, the point faces the smaller. Trace the open mouth toward the number you would rather have more of.
MisconceptionEqual numbers cannot be compared, so 30 and 30 is not a real answer.
Why it happens: Students expect a winner, so a tie feels like the question is unfinished.
How to address it: Show 30 = 30 with two identical bars. Equal is a proper result: the tens match and the ones match, so neither is greater.
MisconceptionTo order numbers you just line them up in the order they were written or spoken.
Why it happens: Ordering gets confused with simply listing, and the sorting step is skipped.
How to address it: Place each number on the number line before writing the order. The line forces smallest to largest and shows any number that is out of place.
Guided practice (with answers)
1. Which is greater, 38 or 41?
Answer: 41. It has 4 tens against 3 tens, so 41 > 38.
2. Fill in the blank: 26 __ 24.
Answer: 26 > 24. Same tens, and 6 ones is more than 4 ones.
3. Compare 70 and 70.
Answer: 70 = 70. The tens match and the ones match, so they are equal.
4. Which is greater, 19 or 91?
Answer: 91. It has 9 tens against 1 ten, so 91 > 19, even though the digits are the same.
5. Order 33, 13 and 31 from smallest to largest.
Answer: 13, 31, 33. Compare tens first (1 ten, then two numbers with 3 tens), then break the tie with the ones (31 before 33).
6. True or false: because 8 is bigger than 5, the number 8 is bigger than 15.
Answer: False. 15 has a ten in it, so 15 > 8. A two-digit number is always at least ten.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with comparing pairs, then move to ordering sets.
Differentiation
- Keep base-ten blocks on the desk so every comparison can be built and seen, not just read.
- Start with numbers that have different tens (45 and 54) before any that share a tens digit.
- Give a number line with the numbers already marked so the student only reads off the order.
- Use the mouth-eats-the-bigger-number image to lock in symbol direction, then move to saying 'greater than' and 'less than'.
- Compare and order numbers all the way to 120, past the friendly 100.
- Order four or five numbers at once, including a tie that needs the ones digit to break.
- Give a comparison such as 4_ > 47 and ask which digits could fill the blank.
- Ask students to write their own tricky pair (same digits, swapped) and explain which is greater.
Assessment: exit ticket
A three-question exit ticket for the last five minutes. It samples reading tens and ones, comparing with a symbol, and ordering.
1. Write >, < or =: 52 __ 49.
Answer: 52 > 49 (5 tens beats 4 tens).
2. Which is greater, 7 or 17, and why?
Answer: 17, because it has a ten in it and 7 does not.
3. Order 40, 14 and 41 from smallest to largest.
Answer: 14, 40, 41.
Teacher notes and timings
- Rough timing across three lessons: Lesson 1 reading tens and ones and comparing a pair (sections 1 to 2), Lesson 2 the symbols (section 3), Lesson 3 ordering plus the exit ticket (section 4 and assessment).
- Language to keep saying: compare the tens first, then the ones. This one sentence pre-empts the most common error.
- Keep base-ten blocks out through the pictorial sections. When a student is unsure, have them build both numbers and compare the piles.
- The number line runs 0 to 100 in tens. If a class is still shaky counting by tens, count the ticks aloud together before marking any numbers.
- Watch for the same-digits pair (45 and 54, 19 and 91): it is the single best diagnostic for whether a student is truly reading the tens first.
- US and AU alignment: the US Grade 1 standard (1.NBT.B.3) compares two-digit numbers to 100. ACARA Year 1 (AC9M1N01) orders whole numbers to at least 120, a slightly wider range, and both rest on reading a number as tens and ones. Numbers here stay within 100 so the unit fits either framework.
- Present mode and print both work: use the Print button for a clean teacher copy or a student handout, and project the page to teach straight from the diagrams.