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SSAT Middle Level: Quantitative • Number Properties and Integers

Compare and order integers on a number line.

Visualize negative and positive numbers to see which is bigger, just like points on a road map.

Explore the lesson 4 min read
SSAT Middle Level illustration with a test notebook, quantitative function, and reading book
Inside this lesson 10 sections 5 questions 6 figures

SECTION 1

Historical Context & Motivation

Long ago, people only used positive numbers, like counting apples or steps in a game. Negative numbers came later to show debts or temperatures below zero. The number line helped everyone see and compare them easily, like a straight road.

628 AD

Brahmagupta in India writes rules for negative numbers, like subtracting debts.

1202 • Fibonacci

Brings negative numbers to Europe through his book on math.

1637 • Descartes

Invents coordinate system, linking numbers to a line.

1685 • John Wallis

Draws the first clear number line to show all integers.

Before the number line, comparing negatives confused people, like who owes more money. It solved that by showing order visually. Now you can master it for the SSAT!

SECTION 2

Core Principles & Definitions

Integers are whole numbers like -5, 0, or 7, including negatives (less than zero) and positives (greater than zero). A number line is a straight line with zero in the middle, negatives to the left, and positives to the right. Numbers get bigger as you move right.

1

Zero in the Center

Zero splits positives (right) from negatives (left).
2

Direction Matters

Right = larger, left = smaller, like a race track.
3

Symbols for Comparison

< means left of, > means right of.
4

Ordering from Least to Greatest

Read left to right on the line.
🌡️

Think Like a Thermometer!

The number line is like a thermometer for temperatures. Zero is room temp, left is freezing (smaller), right is hot (bigger). Plot points to compare easily!

SECTION 3

Visual Explanation

Comparing & Ordering Integers on a Number Line Numbers increase in value from left to right -10 -9 -8 -6 -5 -4 -3 -1 1 2 3 4 5 7 8 9 10 −7 −2 0 +6 Increasing Value → Order: −7 < −2 < 0 < +6 Left on the number line = smaller value · Right = larger value ← Negative Positive →
See the points: -7 (leftmost, smallest) < -2 < 0 < 6 (rightmost, largest). Farther right means greater.

Look at the diagram above. The arrow points right for bigger numbers. Plot any integer to compare—you'll see the order right away. Great job visualizing!

SECTION 4

Mathematical Framework

To compare two integers a and b, check their positions. If a is right of b, then a > b. Use symbols: < (less than, opens left), > (greater than, opens right), = (same spot).

COMPARISON RULES

Ifaistotherightofb,thena>bExamples:−5<0,3>−2,−1=−1If a is to the right of b, then a > b Examples: −5 < 0, 3 > −2, −1 = −1

− means negative. Right on line = greater value.

ORDERING STEP

Leasttogreatest:plot→readleft→rightEx:−4,1,−6→−6<−4<1Least to greatest: plot → read left → right Ex: −4, 1, −6 → −6 < −4 < 1

These rules work every time. Practice plotting, and comparing feels like a game. You're building SSAT skills!

SECTION 5

Detailed Breakdown

Break it down by plotting sets of numbers. See how negatives are smaller than positives, and among negatives, closer to zero is bigger. This visual trick makes ordering simple.

Comparing & Ordering Integers on a Number Line Ordering the set { −6, −4, −1, 0, 3 } from least to greatest −7 −5 −3 −2 1 2 4 −6 −4 −1 0 3 −6 −4 −1 0 3 ← Lesser Greater → Ordered from Least to Greatest −6 < −4 < −1 < 0 < 3 💡 Numbers further left on the number line are always lesser in value.
Plot the set and read left to right: −6, −4, −1, 0, 3. Dashed arrow shows increasing order.

In the diagram, notice −1 > −4 because it's right of it, even both negative. Zero beats all negatives. This breakdown builds your confidence!

SECTION 6

Worked Example

Let's order these from least to greatest: 2, −8, 0, −3, 5. You'll see how to do it step by step. You got this!

Order: 2, −8, 0, −3, 5

  1. 1

    Step 1 — Plot on Number Line

    Imagine line: mark −8 far left, then −3, 0, 2, 5 right.
    Positions: −8 < −3 < 0 < 2 < 5
  2. 2

    Step 2 — Read Left to Right

    Least (leftmost) first, greatest last. Check: −8 smallest, 5 biggest.
    −8, −3, 0, 2, 5
  3. 3

    Step 3 — Verify Comparisons

    −3 > −8 (right), 0 > −3, etc. All good!
    Final order correct!

SECTION 7

Strengths & Limitations

MethodStrengthsLimitations
With Number LineVisual—easy for negatives. Quick ordering.Needs drawing or imagining.
Without Number LineFast for positives only.Confusing for negatives, like −5 vs −2.

Number line wins for SSAT integers!

🏆

Key takeaway

Number line is your superpower for integers, like a map in a video game. It turns confusion into wins!

SECTION 8

Connection to Advanced Theory

Integers are the start—next come fractions and decimals on the same line. This builds to algebra inequalities. You're on the path!

LevelWhat You DoExample
Integers (Now)Whole numbers only.−3 < 1 < 4
Advanced (Fractions)Split spots between integers.−1 < −½ < 0

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

Which number is between −2 and 0 on the number line? A. −3 B. −1 C. 1 D. 2 E. −4
Show answer
Correct: B (−1). It's right of −2 and left of 0. A (−3) is left of −2 (smaller). C, D positives right of 0 (bigger). E (−4) farther left (smallest).

Question 2: BASIC CALCULATION

Order −1 and 3 from least to greatest. A. 3, −1 B. −1, 3 C. −1 = 3 D. 3 > −1 E. −1 > 3
Show answer
Correct: B (−1, 3). −1 left of 3, so least first. A reverses order. C wrong, not equal. D true but not order. E false, −1 smaller.

Question 3: INTERMEDIATE

Which is greatest: −5, 0, −2, 4, −1? A. −5 B. 0 C. −2 D. 4 E. −1
Show answer
Correct: D (4). Far right, biggest. A (−5) leftmost smallest. B (0) middle. C (−2), E (−1) negatives smaller than 0 and 4.

Question 4: APPLIED

Temperatures: Miami 3°C, Chicago −6°C, NYC −1°C. Order coldest (least) to warmest. A. 3, −1, −6 B. −6, −1, 3 C. −1, −6, 3 D. 3, −6, −1 E. −6, 3, −1
Show answer
Correct: B (−6, −1, 3). Coldest −6 left, then −1, 3 warmest. A starts warmest. C swaps cold ones. D, E wrong order.

Question 5: CRITICAL THINKING

Order least to greatest: −7, 1, −2, 4, 0, −5. A. −7, −5, −2, 0, 1, 4 B. −2, −5, −7, 0, 1, 4 C. 4, 1, 0, −2, −5, −7 D. −7, −2, −5, 0, 1, 4 E. −5, −7, −2, 0, 4, 1
Show answer
Correct: A (−7, −5, −2, 0, 1, 4). Left to right: −7 < −5 < −2 < 0 < 1 < 4. B wrong negatives. C greatest first. D swaps −5/−2. E swaps −5/−7 and 1/4.

SUMMARY

Lesson Summary

Summary

Master comparing and ordering integers with the number line: zero center, left smaller (negatives), right bigger. Plot, compare > < =, read left to right for order.

Practice visuals build speed for SSAT. You can ace this!

Varsity Tutors • SSAT Middle Level • Compare and order integers on a number line.