🌱 Starter Village · Number Sense

Counting & Comparing

Read, order and compare whole numbers, and place them on a number line. This is the foundation every later skill stands on.

In short

On the number line, further right always means greater.
Compare digits from the left; the first place where they differ decides the comparison.
The point of $<$ and $>$ aims at the smaller number.
On a number line, always check what one mark is worth before you count.

Numbers live on a line

Every whole number has a fixed home on the number line. Numbers get larger as you move right and smaller as you move left. That single picture answers almost every question about comparing and ordering.

When you count $1, 2, 3, 4$ you are walking right along the line one step at a time. When you count backwards you are walking left.

Further right means greater.
Further left means less.
The same spot means equal.

Comparing by place value

You do not have to draw a line to compare two numbers. Line them up by place value instead — ones under ones, tens under tens — and read from the left.

The first place where the digits differ decides everything. Nothing after it can change the result, because a difference in the hundreds place is worth more than every digit to its right put together.

4,281 and 4,219 both start 4,2. The next place is 8 against 1, so 4,281 is greater.
If one number has more digits than the other, it is automatically greater (as long as neither starts with $a 0)$ .

Writing the comparison

Three symbols say everything:

$<$ means "is less than": $12 < 30$
$>$ means "is greater than": $30 > 12$
$=$ means "is equal to": $30 = 30$

The pointed end of $<$ and $>$ always aims at the smaller number, and the open end faces the larger one. Some people picture a hungry crocodile that turns to eat the bigger meal. That is a memory trick, not a rule — the real rule is the number line.

Ordering a whole set

To put several numbers in order, sort them in passes rather than all at once.

1. Group them by how many digits they have. Fewer digits go first. 2. Within a group, compare the leftmost digits. 3. Where those tie, move one place right and compare again.

Writing the finished list with $<$ between the numbers, like $118 < 181 < 811$ , proves you meant "least to greatest" and makes a mistake easy to spot.

Reading a number line

A number line does not always count by ones. Look at the labels first and work out what one mark is worth.

If the line runs $0, 50, 100, 150$ , then each mark is worth $50. A$ point three marks past 100 is at $100 + 3 x 50 = 250$ , not 103.

Find two labelled marks.
Subtract to get the gap, then divide by the number of spaces between them.
That gives the value of one step.

Worked examples

Example 1

Which symbol makes this true? 6,304 __ 6,340

Both numbers have 4 digits, so compare from the left.
Thousands: 6 and 6 — the same, keep going.
Hundreds: 3 and 3 — the same, keep going.
Tens: 0 and 4. This is the first place where they differ, and 0 is less than 4.
So $6,304 < 6,340$ . The point of the symbol aims at the smaller number.

Example 2

A number line runs from 200 to 400 with a mark every 25. What number is 3 marks to the right of 250?

Each mark is worth 25, so a mark is not a single step of 1.
3 marks are worth $3 x 25 = 75$ .
Start at 250 and add: $250 + 75 = 325$ .
Check it lies between 200 and 400 — it does.

Practice problems, with solutions

Three problems of increasing difficulty, each with the full working. In the game these are generated fresh every time; these three are fixed so this page always shows the same ones.

Problem 1

Difficulty 1 of 5

Which symbol makes this true? 14 __ 5

Answer: $B. >$

14 has 2 digits, 5 has 1 digit.
Reading from the left, the first place where they differ makes 14 the larger number.
So $14 > 5$ .

Problem 2

Difficulty 3 of 5

Which of these numbers is the least? $789, 138, 949, 519$ Type the number.

Answer: 138

Compare by place value: $789, 138, 949, 519$
Ordered from least to greatest: $138 < 519 < 789 < 949$
The least is 138.

Problem 3

Difficulty 4 of 5

A number line runs from 75 to 275 with a mark every 25. Point P is 4 marks to the right of 75. What number is at P?

Answer: 175

Each mark is worth 25.
4 marks is $4 x 25 = 100$ .
$75 + 100 = 175$

Common mistakes

Reversing $<$ and $>$ : getting the comparison right but writing the symbol backwards.
Assuming the number that "looks longer" is bigger without checking for leading zeros or decimals.
Counting marks on a number line as if each one were worth 1.
Comparing from the right-hand digits instead of the left.

What you should be able to do

Compare two whole numbers using $<, >$ and $=$ .
Order a set of whole numbers from least to greatest.
Locate a number on a number line and name the number at a mark.
Find the number that comes just before or just after a given number.

Where this fits in the curriculum

Common Core

1.NBT.B.3
Grade 1 — Compare two two-digit numbers using >, = and <.
4.NBT.A.2
Grade 4 — Read, write and compare multi-digit whole numbers using >, = and <.
2.MD.B.6
Grade 2 — Represent whole numbers as lengths on a number line and find sums and differences on it.
The number-line objective lives in Measurement & Data in the Common Core, not in Number & Operations — an organisational quirk, not a different idea.

Ontario

G1.B1.3
Grade 1 — Compare and order whole numbers up to and including 50.
G2.B1.2
Grade 2 — Compare and order whole numbers up to and including 200.
Ontario re-states comparing in every grade as the range grows, so any one code is a sample of a thread. Placing a number on a number line is not an expectation of its own until integers arrive at Grade 6 (B1.2).