Chapter 1: Number Sense, Rounding, and Integers
Number Sense, Rounding and Integers
Use place value, rounding and number lines to decide what a number means and whether an answer is sensible.
AI maths coach
Step-by-step teaching, practice and checkpoint.
Voice: Browser voice
Voice: Browser voice
Workbook pages
Fun Maths Book 3 pages 3-11
Read large numbers, round and estimate, then reason with directed numbers.
Think first
Good mathematicians decide what the question is asking before they calculate.
- 1What place value are we looking at?
- 2Which digit decides whether to round up or stay?
- 3Where is the number on the number line?
- 4Does the estimate make the final answer sensible?
Visual teaching
See the method
A large number expands into place-value columns, then a thermometer marker moves below zero and a rounding pointer chooses the nearest friendly value.
Millions
Thousands
Hundreds
Ones
Worked examples
Round 48 912 to the nearest thousand.
Step 1: First, what place are we rounding to?
We are rounding to the nearest thousand, so we focus on 48 000 and 49 000.
Why: The answer must be a multiple of one thousand.
Step 2: Now we need to decide: closer to 48 000 or 49 000?
Look at the hundreds digit in 48 912. It is 9.
Why: For thousands, the hundreds digit tells us whether to round up.
Be careful: Do not look at every digit at once. Use the deciding digit.
Step 3: What happens because the deciding digit is 5 or more?
48 912 rounds up to 49 000.
Why: A hundreds digit of 9 means the number is past the halfway point.
Common mistake: Writing 48 000 because the number starts with 48.
Estimate 48 912 + 21 376 to the nearest thousand.
Step 1: What information do we already know?
We are adding two large numbers and only need an estimate.
Why: Rounding first gives a quick answer for checking.
Step 2: Round each number to a useful place value.
48 912 rounds to 49 000. 21 376 rounds to 21 000.
Why: Nearest thousand is accurate enough for a check but still easy to add.
Step 3: Now add the rounded numbers.
49 000 + 21 000 = 70 000.
Why: The estimate tells us the exact answer should be near 70 000.
Common mistake: Rounding only one number, then treating the answer as exact.
A freezer is -14°C and another is -8°C. Which is warmer, and by how much?
Step 1: First, where are the numbers on the number line?
-14 is further left. -8 is closer to zero.
Why: Numbers increase as we move right, even below zero.
Step 2: Which temperature is warmer?
-8°C is warmer than -14°C.
Why: A number closer to zero is greater when both numbers are negative.
Be careful: Do not think 14 is automatically greater because it has bigger digits.
Step 3: How far apart are the temperatures?
From -14 to -8 is 6 steps.
Why: Counting the distance on the number line gives the temperature difference.
Common mistake: Choosing -14 because 14 is larger than 8.
Guided practice
Round 376 842 to the nearest ten thousand.
Independent practice
Your turn
Round 376 842 to the nearest ten thousand.
Which number is smallest?
Which estimate is best for 598 x 31?
Mini checkpoint
Check your thinking
Which estimate is best for 598 x 31?
Which list is ordered from smallest to greatest?
63 741 rounded to the nearest thousand is...
Key idea
Place value tells us what digits mean. Rounding and number lines help us check decisions. Round for the purpose of the question, compare negative numbers on a number line, and use estimates to catch impossible answers.
Parent signal
Listen for place-value language. A Year 6 student should say 70 000, not just digit 7.