Grade 4 Mathematics Study Notes

Welcome to Whole Numbers

Whole numbers are the numbers we use for counting: 0, 1, 2, 3, and so on. No fractions, no decimals.

Across the next ten lessons you will learn how to read, write, compare and round whole numbers up to ten thousand. You will also meet special groups — factors, multiples, even and odd — and end with Roman numerals.

This first lesson is about place value and total value.

The place value chart

To understand a big number like 24,579, we put each digit in its own column. The column it sits in tells us its place value.

The five place values, from right to left, are: ones, tens, hundreds, thousands, tens of thousands. The ones column is always on the far right.

Reading the place value of a digit

To find the place value of a digit, write the number into the chart and read the name above the digit.

In the number 24,579:

• The place value of 2 is tens of thousands.
• The place value of 4 is thousands.
• The place value of 5 is hundreds.
• The place value of 7 is tens.
• The place value of 9 is ones.

What total value means

Place value tells us where a digit sits. Total value tells us how much it is worth.

To find the total value of a digit, multiply the digit by its place value:

Total value = digit × place value

Worked example: total value of 5 in 5,732

Below is the number 5,732 set out on an abacus. An abacus is a counting tool with rods and beads. Each rod stands for one place value, and the beads pushed to the middle bar are the ones we are counting.

The place value of the digit 5 is thousands.

Total value = digit × place value
= 5 × thousands
= 5 × 1,000
= 5,000

Total value of every digit in 78,325

Find the place value of each digit using the chart.

Then multiply each digit by its place value:

• Total value of 7 is 7 × tens of thousands = 7 × 10,000 = 70,000
• Total value of 8 is 8 × thousands = 8 × 1,000 = 8,000
• Total value of 3 is 3 × hundreds = 3 × 100 = 300
• Total value of 2 is 2 × tens = 2 × 10 = 20
• Total value of 5 is 5 × ones = 5 × 1 = 5

This is also called the expanded form of the number:

78,325 = 70,000 + 8,000 + 300 + 20 + 5

The parts of an abacus

• A — Wooden frame: holds everything together.
• B — Heaven section (above the bar): each bead = 5.
• C — Middle bar: beads slide to this bar to be counted.
• D — Earth section (below the bar): each bead = 1.
• E — Rod: one rod = one place value.
• F — Bead: slides on the rod.

Key Points

• Place value = the position of a digit. Total value = how much it is worth there.
• Total value = digit × place value.
• From right to left: ones, tens, hundreds, thousands, tens of thousands.
• An abacus has Heaven beads (each = 5) and Earth beads (each = 1).

Reading a number from left to right

A number written in symbols uses the digits 0–9. To read it aloud, name each part from left to right, using its place value name.

Examples:

• 1,572 → one thousand, five hundred and seventy-two
• 4,260 → four thousand, two hundred and sixty
• 24,579 → twenty-four thousand, five hundred and seventy-nine
• 10,000 → ten thousand

When a digit is zero, skip that part

If the tens or hundreds digit is 0, skip that part when reading. The 0 still has to be in the symbols, but you don't say it.

• 9,035 is read "nine thousand and thirty-five." (No hundreds — we don't say "zero hundred.")
• 2,016 is read "two thousand and sixteen."
• 1,010 is read "one thousand and ten."

Number cards as a tool

A number card is a small card with one digit on it. Lay digit cards side by side to build a number.

From the digits 3, 7, 1, 9, 5 you can build many five-digit numbers. The smallest is 13,579; the largest is 97,531.

Writing a spoken number into symbols

Listen for the place value words, then put each digit in the right column.

Worked example: write "two hundred and twenty-two".

1. Hundreds: 2.
2. Tens: 2.
3. Ones: 2.
4. Answer: 222.

Worked example: write "twenty-four thousand, five hundred and seventy-nine".

1. Tens of thousands: 2. Thousands: 4.
2. Hundreds: 5. Tens: 7. Ones: 9.
3. Answer: 24,579.

Worked example: write "ten thousand".

1. Tens of thousands: 1.
2. The other four columns are 0.
3. Answer: 10,000.

Key Points

• Read a number from left to right, using place value names.
• If a digit is 0, write it but don't say it.
• To write a spoken number, put each digit in its column.

Writing a number in words

Writing a number in words means spelling it out. We do this on cheques, school certificates, signs and notices.

Examples:

• 71 → seventy-one
• 201 → two hundred and one
• 444 → four hundred and forty-four
• 625 → six hundred and twenty-five
• 887 → eight hundred and eighty-seven
• 999 → nine hundred and ninety-nine
• 1,000 → one thousand

Three rules to follow

1. Use "and" between the hundreds and the rest. So 887 is "eight hundred and eighty-seven".
2. Use a hyphen for numbers like twenty-one or ninety-nine. So 71 is seventy-one.
3. Skip parts that are zero. So 201 is "two hundred and one" — there is no "zero tens" to say.

Writing words back into symbols

Listen for the place value words, then put each digit in the right column.

Worked example: write "two hundred and two" in symbols.

1. Hundreds: 2.
2. Tens: there are none. Put a 0 here.
3. Ones: 2.
4. Answer: 202.

The 0 is a place-holder. It keeps the 2 in the hundreds. Without it, you would have just 22.

Key Points

• Use "and" between the hundreds and the rest.
• Use a hyphen in numbers like twenty-one or ninety-nine.
• Skip zero parts when saying the number, but keep the 0 in the symbols.
• The 0 is a place-holder — it keeps the other digits in the right places.

Ascending order means smallest to largest

Ascending order means arranging numbers from the smallest to the largest. Like climbing a ladder — each step is bigger than the one below.

Putting numbers in ascending order

To arrange numbers from smallest to largest, compare the digits — starting with the biggest place value (on the left).

Worked example: arrange 168, 158, 118, 138, 128 in ascending order.

1. The hundreds digit of every number is 1 — same.
2. So look at the tens digit: 6, 5, 1, 3, 2.
3. Smallest tens first: 1, 2, 3, 5, 6.
4. Answer: 118, 128, 138, 158, 168.

Descending order means largest to smallest

Descending order is the opposite — from largest to smallest. Like walking down stairs.

Putting numbers in descending order

Same digit-by-digit method — but pick the largest first.

Worked example: arrange 180, 222, 146, 190 in descending order.

1. Hundreds digits: 1, 2, 1, 1.
2. 222 has 2 hundreds — the largest. So 222 comes first.
3. Three numbers left (180, 146, 190) all have 1 hundred. Look at tens: 8, 4, 9.
4. Largest tens first: 9 (190), 8 (180), 4 (146).
5. Answer: 222, 190, 180, 146.

Key Points

• Ascending = smallest to largest. Descending = largest to smallest.
• Compare digit by digit, starting from the left.
• If two left most digits are the same, look at the next digit to the right.

What rounding off means

Rounding off means giving a number that is close to the original, but easier to use and remember. We round off when the exact number doesn't matter — like saying a journey is "about 300 km" instead of "291 km".

Rounding to the nearest ten

To round a number to the nearest ten, ask: which ten is it nearer to? A number line shows this clearly.

Worked example: round 62.

62 is nearer to 60 than 70. 62 rounded off to the nearest ten becomes 60.

Worked example: round 67.

67 is nearer to 70 than 60. 67 rounded off to the nearest ten becomes 70.

More rounding examples

For each number, ask: which ten is it nearer to?

• 21 is nearer to 20 than 30 → rounds to 20.
• 49 is nearer to 50 than 40 → rounds to 50.
• 65 is exactly halfway between 60 and 70. When a number is halfway, we round it up → rounds to 70.
• 172 is nearer to 170 than 180 → rounds to 170.
• 359 is nearer to 360 than 350 → rounds to 360.
• 565 is halfway between 560 and 570 → rounds to 570.
• 995 is halfway between 990 and 1,000 → rounds to 1,000.

Rounding to estimate

Rounding helps us estimate — get a quick answer that is close enough.

Real-life examples:

• Okumu thinks there are 575 trees in a forest. Rounded: about 580 trees.
• The distance from Ukweli to Mamboleo is 373 km. Rounded: about 370 km.

Worked example: a school orders 47 chairs and 32 desks. Estimate the total.

1. 47 is nearer to 50 → rounds to 50.
2. 32 is nearer to 30 → rounds to 30.
3. Estimate: 50 + 30 = 80 items. (The exact answer is 79.)

Key Points

• To round to the nearest ten, ask: which ten is it nearer to?
• If the number is halfway between two tens, round up.
• Rounding is useful for quick estimates.