A Math Book

Key ConceptsThis chapter covers how to read, write, compare, and compute with whole numbers using place value and number line reasoning. These skills are core exam requirements because most number problems test place value understanding first.

You MUST know:

Place value: the value of a digit depends on its position (ones, tens, hundreds, thousands…).

Reading numbers: identify each digit’s place value and total value.

Writing numbers in expanded form: break a number into sums of place values (e.g., 405 = 4 hundreds + 0 tens + 5 ones).

Comparing whole numbers: use place value first (bigger place value digit usually means bigger number).

Number line reasoning:

Moving right increases; moving left decreases.

The distance between points matches the size of the jump.

Ordering numbers: write from smallest to largest using place value and/or number line positions.

Computation link: addition/subtraction can be checked using number line jumps.

Before you continue: Can you explain why 7 in 72 is worth 70 (not 7)?

Key TermsWhole number - 0, 1, 2, 3, ... (no fractions or negatives)

Place value - the value of a digit based on its position (ones, tens, hundreds…)

Digit - one symbol used to write a number (0-9)

Expanded form - writing a number as a sum of place values (e.g., 602 = 6 hundreds + 0 tens + 2 ones)

Number line - a line with equally spaced points used to show numbers and compare distances

Compare - decide which number is larger or smaller (or if they are equal)

Order - arrange numbers from smallest to largest (or largest to smallest)

Jump - a move on a number line (right/left) showing the size of change

Active RecallWhole number: __________

__________

Place value: __________

__________

Digit: __________

__________

Expanded form: __________

__________

Number line: __________

__________

Compare: __________

__________

Order: __________

__________

Jump: __________

__________

Worked ExamplesExample 1: Read and write using place valueProblem: Write 3 hundreds, 4 tens, and 9 ones as a whole number.

3 hundreds = 300

4 tens = 40

9 ones = 9

Total = 300 + 40 + 9 = 349

Now you try:

Write 5 hundreds, 0 tens, and 7 ones as a whole number.

__________

__________

__________

__________

Example 2: Compare using place valueProblem: Which is larger, 508 or 580?

Compare hundreds digits: 508 has 5 hundreds, 580 has 5 hundreds (tie).

Compare tens digits: 508 has 0 tens, 580 has 8 tens.

8 tens is larger than 0 tens, so 580 > 508.

Now you try:

Which is larger, 392 or 352?

__________

__________

__________

__________

Example 3: Number line reasoning for additionProblem: Starting at 120, you jump +35. What number do you land on?

Jump +30 from 120 to 150

Jump +5 from 150 to 155

Final answer = 155

Now you try:

Starting at 85, you jump +27. What number do you land on?

__________

__________

__________

__________

Practice Questions(Easy) Write the number represented by: 2 hundreds, 6 tens, 1 one.

__________

__________

__________

__________

(Easy) Write 740 in expanded form.

__________

__________

__________

__________

(Medium) Compare: 615 __ 561 (use <, >, or =).

__________

__________

__________

__________

(Medium) Order these numbers from smallest to largest: 309, 319, 299, 300.

__________

...