Place value & number

Reading big numbers, rounding without slips, primes / factors / multiples, divisibility tests.

These questions open the paper and feel like free marks — which is exactly why rushing them is so costly. Losing question 2 to a slip costs the same as losing a monster geometry question at the end.

Value of a digit — the 7 in 472,069

Step 1 · label from the right

units, tens, hundreds, thousands…

Step 2 · find the column

7 is in the ten-thousands

Step 3 · say the value

70,000

⚠ Watch out

The exam wants the VALUE, not the column name. The answer is 70,000 — not "7" and not "ten-thousands". And numbers with a zero in the middle (like 3,048,271) knock your counting off by one: touch each digit as you count.

Divisibility tests

By 2
ends in an even digit
By 3
digit sum divides by 3
By 4
last TWO digits divide by 4
By 5
ends in 0 or 5
By 6
passes the 2-test AND 3-test
By 9
digit sum divides by 9

Remember it like this

“Factors are few, multiples are many.”

Factors divide INTO a number (factors of 12: 1, 2, 3, 4, 6, 12). Multiples are its times table and go on forever.

⚠ Watch out

51, 57 and 91 LOOK prime but are not: 51 = 3 × 17, 57 = 3 × 19, 91 = 7 × 13. The digit-sum test catches the first two (5+1=6 and 5+7=12, both divide by 3). Also: 1 is not prime, and 2 is the only even prime.

Rounding with a carry

Round 148,509 to the nearest 1,000.

  1. Look one place right of the thousands: the hundreds digit is 5
  2. 5 or more rounds up, so 148 thousand becomes 149 thousand

149,000

✏ Your turn

The temperature is −5°C and rises by 11°C. What is it now?

Show the answer
  1. Draw a number line and jump: from −5, going up 5 gets you to 0
  2. That leaves 6 more of the 11 to go: 0 + 6

6°C

For parents — the full topic guide

Place Value, Rounding & Number Facts — 11+ Topic Guide

Part of the GrammarMock topic guides. Drill with the Number & Place Value mini-tests.

Why "easy" number questions still lose marks

Place value questions open most GL maths papers, and children treat them as free marks — which is exactly why careless errors here hurt so much. Losing Q1-Q5 to rushing costs the same as losing five hard geometry questions at the end. Train accuracy first, speed second.

Place value

"What is the value of the digit 7 in 472,069?"

The reliable method: label the columns from the RIGHT — units, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions. The 7 sits in the ten-thousands column, so its value is 70,000 (not "7" and not "ten-thousands" — the exam wants the value).

Trap: numbers with a zero in the middle (like 3,048,271) shift children's counting off by one. The fix is physical: touch each digit from the right while saying the column names.

Writing numbers from words: "eight hundred and seven thousand and twenty-four" = 807,024. The skill is holding the zero placeholders — the answer options will include 87,024 and 807,240 as traps.

Rounding

The rule is one line: look at the digit to the right of the place you're rounding to; 5 or more rounds up.

  • 38,562 to the nearest 1,000 → thousands digit is 8, look right at the 5 → round up → 39,000
  • 24,683 to the nearest 100 → look at the tens digit (8) → 24,700

Trap: "round 148,509 to the nearest 1,000" — children see the 5 in the hundreds place, round up, then mangle the carry: 148 → 149 thousand = 149,000. Practise the carry cases specifically.

Multiples, factors, primes — the vocabulary trio

  • Multiple: in the times table OF the number (multiples of 6: 6, 12, 18...)
  • Factor: divides INTO the number exactly (factors of 12: 1, 2, 3, 4, 6, 12)
  • Prime: exactly two factors (1 and itself). 1 is NOT prime. 2 is the only even prime.

Children muddle multiple/factor constantly. The memory hook: factors are few, multiples are many (a number has finitely many factors but endless multiples).

Primes to 100 worth knowing on sight: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. The exam's favourite trick: 51 (= 3×17), 57 (= 3×19) and 91 (= 7×13) look prime. Digit-sum test catches 51 and 57 (digits sum to a multiple of 3).

LCM and HCF: for LCM, list multiples of the bigger number until one divides by the smaller. For HCF, list factors of the smaller and test them against the bigger, starting from the largest.

Divisibility tests (fast marks on hard papers)

  • By 2: ends in even digit. By 5: ends in 0 or 5. By 10: ends in 0.
  • By 3: digit sum divisible by 3. By 9: digit sum divisible by 9.
  • By 4: last TWO digits divisible by 4. By 6: passes both the 2-test and the 3-test.

Hard papers combine these: "The number A72B is divisible by both 5 and 9 — find A + B." Method: the 5-test fixes B (0 or 5), then the 9-test fixes A via the digit sum. These look intimidating and are actually mechanical.

Negative numbers

Temperature is the standard costume: "−5°C rises by 11°C" → −5 + 11 = 6. The number line is the tool — draw it, jump along it. Range questions with negatives ("range of −8 and 7") need the subtraction 7 − (−8) = 15; subtracting a negative means adding.

One-week drill plan

  • Day 1: place value + writing numbers from words (10 questions)
  • Day 2: rounding, including carry cases
  • Day 3: factor/multiple/prime vocabulary + the fake primes
  • Day 4: divisibility tests
  • Day 5: LCM/HCF pairs
  • Day 6: negative number lines
  • Day 7: Number & Place Value mini-test under 15-minute timing

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