Comparing and ordering numbers
In this topic you will
- Use place value to compare and order numbers.
- Generate and continue number sequences.
- Read, say, and use ordinal numbers (for example, $1^\text{st}$, $2^\text{nd}$, $3^\text{rd}$).
Key Words
- close, closer
- end, stop, finish
- extend
- ordering
- ordinal numbers
- sequence
- start, beginning
Show Definitions
- close, closer: Words used to compare distance or difference, meaning “near” and “nearer” (for example, which number is closer to $50$).
- end, stop, finish: To reach the last part of something, such as the last number in a count or the last term in a pattern.
- extend: To continue something further, such as adding more terms to a number pattern or sequence.
- ordering: Arranging numbers in the correct sequence, usually from smallest to largest (or largest to smallest).
- ordinal numbers: Numbers that tell position in an order, such as $1^\text{st}$, $2^\text{nd}$, $3^\text{rd}$.
- sequence: A list of numbers that follows a rule or pattern, such as adding $2$ each time.
- start, beginning: The first point of a process or list, such as the first number in a count or the first term of a sequence.
Now that you know about numbers to $100$, you can use them to compare quantities.
$36$ is more than $24$, so there are more marbles in the box of $36$ marbles than in the bag of $24$ marbles.
❓ EXERCISES
1. Show $29$, $65$ and $82$ on this number line.
👀 Show answer
- $29$ is between $20$ and $30$, just before $30$.
- $65$ is between $60$ and $70$, halfway between them.
- $82$ is between $80$ and $90$, just after $80$.
2. Use what you know about ordinal numbers to find each monster.
Start at the bus stop. Draw a ring around the $2$nd monster.
Draw a line under the $6$th monster.
Tick the $3$rd monster.
👀 Show answer
- The $2$nd monster is the second one after the bus stop (the grey monster with green arms).
- The $6$th monster is the sixth one after the bus stop (the grey spiky monster).
- The $3$rd monster is the third one after the bus stop (the blue monster).
❓ EXERCISES
$3$. A number sequence starts at $37$. It counts on in tens and stops at $77$. What are the numbers in the sequence?
👀 Show answer
$4$. What can you say about all the numbers in the sequence you wrote for question $3$?
👀 Show answer
$5$. Sofia’s number sequence is $74$, $64$, $54$, $44$, $34$. Complete the description of Sofia’s number sequence.
__________ at $74$. Count __________ in tens. Stop at __________.
👀 Show answer
❓ EXERCISES
$6$. Compare $75$ and $57$. Which is the greater number?
Use a number line or place value grid to help you.
👀 Show answer
Greater number:$75$.
$75$ has $7$ tens and $57$ has $5$ tens, so $75$ is greater.
$7$. Order these numbers from smallest to greatest.
$67$,$42$,$86$,$34$,$21$
You could use a place value grid or a number line to help you.
👀 Show answer
Smallest to greatest:$21$, $34$, $42$, $67$, $86$.
Compare tens first: $2$ tens, then $3$ tens, then $4$ tens, then $6$ tens, then $8$ tens.
🧠 Think like a Mathematician
Question: Zara says, ‘You only need to look at the tens number to order numbers’. Is this always true, sometimes true or never true?
Method:
- Pick two different $2$-digit numbers that have different tens digits (for example, $57$ and $75$).
- Decide which number is greater by comparing the tens digits first.
- Now pick two different $2$-digit numbers that have the same tens digit (for example, $34$ and $39$).
- Decide which number is greater and write down what you needed to look at this time.
- Write a clear rule: when is looking only at the tens digit enough, and when is it not enough?
Follow-up Questions:
Show Answers
- 1: It is sometimes true. If the tens digits are different, the number with the larger tens digit is greater. If the tens digits are the same, you must compare the ones digits too.
- 2: Example: $75$ is greater than $57$ because $7$ tens is more than $5$ tens.
- 3: Example: $34$ and $39$ both have $3$ tens, so you must look at the ones: $9 > 4$, so $39$ is greater.
- 4: A good method is: compare tens first; if the tens are equal, compare ones. Someone else might use a number line or a place value grid, but it should lead to the same conclusion.