45-minute lesson
Year 5 Mathematics: Place value to tens of thousands
Lesson objective
- Read and write numbers up to 99 999 in numerals and words.
- Explain the value of each digit in a five-digit number.
- Order five-digit numbers and round them to the nearest ten, hundred, thousand or ten thousand.
Success criteria:
- I can read and write a five-digit number and say what each digit is worth.
- I can put five-digit numbers in order from smallest to largest.
- I can round a five-digit number to the nearest thousand.
Materials
- Paper and pencil
- Ten small cards or sticky notes with the digits 0 to 9 written on them
- A place value chart drawn on paper with the headings Ten thousands, Thousands, Hundreds, Tens and Ones
Introduction
5 minIntroduce today's words:
- Digit: One of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use to write numbers.
- Place value: The value a digit has because of its place in a number. In 4725, the 7 is worth 700.
- Ten thousand: The number 10 000, which is ten groups of one thousand.
- Expanded form: A number written as the sum of the values of its digits, such as 30 000 + 2000 + 500 + 40 + 6.
- Round: To change a number to a nearby, easier number, such as the nearest thousand.
Ask your child what they already know about place value to tens of thousands.
Explanation
9 minEvery digit in a number has a place, and the place tells us what the digit is worth. Moving one place to the left makes a digit worth ten times as much. Ten ones make a ten, ten tens make a hundred, ten hundreds make a thousand, and ten thousands make ten thousand.
Look at the number 47 352 in a place value chart:
- 4 ten thousands = 40 000
- 7 thousands = 7000
- 3 hundreds = 300
- 5 tens = 50
- 2 ones = 2
We read it as “forty-seven thousand, three hundred and fifty-two”. Notice that we read the first two digits together as “forty-seven thousand”. Large numbers are often written with a small space between the thousands and the hundreds, like 47 352, to make them easier to read.
A zero holds a place when there is nothing in it. In 30 608 there are no thousands and no tens, so zeros keep the other digits in the right places. Without them, 30 608 would become 368, which is a very different number.
To compare and order numbers, line them up and look at the digits from the left. The number with more ten thousands is larger. If those are equal, compare the thousands, then the hundreds, and so on.
To round a number, find the two “friendly” numbers it sits between, then look at the digit just to the right of the place you are rounding to. If that digit is 5 or more, round up. If it is 4 or less, round down. For example, 36 481 is between 36 000 and 37 000. The hundreds digit is 4, so 36 481 rounds down to 36 000 to the nearest thousand.
Worked examples
7 minThe value of each digit
Write 58 064 in expanded form and in words.
Step 1: Put the digits in a place value chart: 5 ten thousands, 8 thousands, 0 hundreds, 6 tens and 4 ones.
Step 2: Write the value of each digit: 50 000 + 8000 + 60 + 4. The zero hundreds adds nothing.
Step 3: Read the first two digits as “fifty-eight thousand”, then read the rest: “sixty-four”.
Answer: 58 064 = 50 000 + 8000 + 60 + 4, which is fifty-eight thousand and sixty-four.
Ordering five-digit numbers
Put these numbers in order from smallest to largest: 23 905, 32 059, 23 590.
Step 1: Compare the ten thousands: 2, 3 and 2. So 32 059 is the largest.
Step 2: Compare 23 905 and 23 590. Their ten thousands and thousands are the same (23 thousand).
Step 3: Compare the hundreds: 9 hundreds is more than 5 hundreds, so 23 905 is larger than 23 590.
Answer: 23 590, 23 905, 32 059
Rounding in different ways
Round 36 481 to the nearest ten, hundred, thousand and ten thousand.
Step 1: Nearest ten: 36 481 is between 36 480 and 36 490. The ones digit is 1, so round down to 36 480.
Step 2: Nearest hundred: it is between 36 400 and 36 500. The tens digit is 8, so round up to 36 500.
Step 3: Nearest thousand: it is between 36 000 and 37 000. The hundreds digit is 4, so round down to 36 000.
Step 4: Nearest ten thousand: it is between 30 000 and 40 000. The thousands digit is 6, so round up to 40 000.
Answer: 36 480, 36 500, 36 000 and 40 000
Guided practice (do together)
9 min1. What is the value of the 6 in 62 145?
(a) 6 (b) 600 (c) 6000 (d) 60 000
2. Which number is twenty-four thousand and fifty-six?
(a) 2456 (b) 24 560 (c) 24 056 (d) 240 056
3. Which of these numbers is the largest?
(a) 48 970 (b) 49 078 (c) 48 999 (d) 49 007
4. What is 53 682 rounded to the nearest thousand?
(a) 53 000 (b) 54 000 (c) 53 700 (d) 50 000
Independent practice
11 min5. Write 30 000 + 5000 + 200 + 7 as a number.
6. Round 71 450 to the nearest ten thousand.
7. What number is 1000 more than 18 950?
8. What is the largest five-digit number you can make using each of the digits 3, 8, 1, 6 and 9 once?
Questions to check understanding
- Can you read and write a five-digit number and say what each digit is worth?
- Can you put five-digit numbers in order from smallest to largest?
- Can you round a five-digit number to the nearest thousand?
- What was the trickiest part today?
Answer guide
1. 60 000 — The 6 is in the ten thousands place, so it is worth 6 × 10 000 = 60 000.
2. 24 056 — Twenty-four thousand is 24 000. There are no hundreds, so we write a zero in the hundreds place, then 56: 24 056.
3. 49 078 — 49 078 and 49 007 both have 49 thousands, which is more than 48 thousands. Comparing the tens, 7 tens is more than 0 tens, so 49 078 is the largest.
4. 54 000 — 53 682 is between 53 000 and 54 000. The hundreds digit is 6, which is 5 or more, so round up to 54 000.
5. 35 207 — 3 ten thousands, 5 thousands, 2 hundreds, 0 tens and 7 ones make 35 207. The zero holds the tens place.
6. 70 000 — 71 450 is between 70 000 and 80 000. The thousands digit is 1, which is 4 or less, so round down to 70 000.
7. 19 950 — Adding 1000 increases the thousands digit by 1: 18 thousand becomes 19 thousand, so the answer is 19 950.
8. 98 631 — Put the largest digit in the place worth the most, then the next largest, and so on: 9, 8, 6, 3, 1 makes 98 631.
Review
4 minRecap the success criteria together. Watch for these common misconceptions:
- Leaving out zeros when writing numbers from words, for example writing “twenty-four thousand and fifty-six” as 2456. Use a place value chart so every place gets a digit.
- Thinking a number with bigger digits at the end is larger, such as believing 23 590 is more than 23 905 because 90 is more than 5. Always compare from the left, starting with the place worth the most.
- Looking at the wrong digit when rounding. Underline the place you are rounding to, then circle the digit just to its right and use only that digit to decide.
Extension activities
- Find the population of a few towns or the heights of several mountains in metres, write the numbers in expanded form and put them in order.
- Use five digit cards to make as many different five-digit numbers as you can that round to 50 000 to the nearest ten thousand.
- Start at 99 990 and count on by ones past 100 000. What happens to each place? Write what you notice.
Suggested follow-up
- Revisit place value to tens of thousands tomorrow with two or three quick questions from memory.
- Try the online practice check for this topic and look at any questions that need another go.
Tips for parents
- Look for big numbers in everyday life, such as car odometers, prices of cars or the number of people at a stadium, and ask the learner to read them aloud.
- Play “Make the biggest number”: each player draws five digit cards and arranges them to make the largest (or smallest) number possible.
- When rounding, ask “Which two numbers is it between, and which one is it closer to?” before using the rule.