B. Number · Number Sense: Numbers to One Million, Integers, Decimals and FractionsReading and Writing Numbers to One Million
B1.1 A1About 40 minutes
Learning goals- I can read whole numbers up to one million out loud.
- I can write numbers to one million in numerals and in words.
- I can name the place and value of each digit in a six-digit number.
- I can count forward and backward by 1000s, 10 000s and 100 000s.
Words to know
hundred thousands place
The sixth place from the right in a whole number. In 386 492 the 3 is worth 300 000.
period
A group of three places in a big number. The ones period is hundreds, tens and ones. The thousands period is hundred thousands, ten thousands and thousands.
one million
1 000 000. It is the same as 1000 thousands.
numeral
A number written with digits, like 506 040.
Remember from Grade 5
In Grade 5 you read, wrote and compared whole numbers up to 100 000. You know the ten thousands, thousands, hundreds, tens and ones places, and that each place is worth 10 times the place to its right. This year we go ten times bigger again, all the way to one million!
A million minutes of reading
A school board in Ontario sets a winter reading challenge. Every student records the minutes they read. At the end of February, the poster in the front hall says:
386 492 minutes read so far! Our goal: 1 000 000 minutes!
How do you read those numbers? The first one has six digits. We need a new place: the hundred thousands place.
| Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |
|---|
| 3 | 8 | 6 | 4 | 9 | 2 |
| 300 000 | 80 000 | 6000 | 400 | 90 | 2 |
Read in groups of three
Big numbers are split into periods, groups of three digits. In Canada we leave a small space between the periods (not a comma).
- The left group, 386, is the thousands period. Read it like a normal three-digit number, then say "thousand".
- The right group, 492, is the ones period. Read it like a normal three-digit number.
So 386 492 is three hundred eighty-six thousand four hundred ninety-two.
We do not say "and" when we read whole numbers. In math, "and" is saved for the decimal point.
| Millions period | Thousands period | Ones period |
|---|
| 1 | 000 | 000 |
| one million | zero thousands | zero ones |
What comes after 999 999?
Add one more and every place fills up and regroups, like a car's odometer rolling over: 999 999 + 1 = 1 000 000. That is one million.
- 1 000 000 = 10 hundred thousands
- 1 000 000 = 100 ten thousands
- 1 000 000 = 1000 thousands
A million is big! One million seconds is about 11 and a half days.
Worked exampleExample 1: Read a six-digit number
- Split it into periods: 704 | 016.
- Read the thousands period: "seven hundred four", then say "thousand".
- Read the ones period: 016 is just sixteen.
seven hundred four thousand sixteen
Worked exampleExample 2: Write the numeral from words
Write five hundred six thousand forty as a numeral.
- The thousands period is "five hundred six": 506.
- The ones period is "forty". Every period needs three digits, so forty is 040.
- Put them together with a space.
506 040. Check: it has 6 digits, because the number is in the hundred thousands.
Worked exampleExample 3: Count by big jumps
Count forward by 10 000s from 960 000. Stop when you reach one million.
- Only the ten thousands digit changes each time: 960 000, 970 000, 980 000, 990 000.
- Ten more thousands after 990 000 regroups everything: 1 000 000.
960 000, 970 000, 980 000, 990 000, 1 000 000
Think like a mathematician
When you say a number, explain how you know. "I know 506 040 has six digits because 'five hundred six thousand' means the thousands period has three digits." Talking through your thinking helps you catch mistakes, and it helps others learn from you too.
Just for funEven at one number per second, with no breaks for snacks or sleep, counting to one million would take about 11 and a half days. And try saying "seven hundred seventy-seven thousand seven hundred seventy-seven" in one second!
Hands-on activityMillion hunt and digit draw
Part 1: Million hunt. With a grown-up, look for big numbers in a flyer, a newspaper, a cereal box or a news website. Look for house prices, kilometres on a car's odometer, or the number of people at an event.
- Find three numbers bigger than 100 000 (or between 1000 and 1 000 000 if big ones are hard to find).
- Write each one in numerals and in words.
- Read them aloud to your grown-up.
Part 2: Digit draw. Write the digits 0 to 9 on ten small scraps of paper. Fold them and put them in a bowl.
- Draw six scraps, one at a time. Write each digit in a place value chart from left to right.
- Read your number aloud. Your grown-up writes it in words to check.
- Put the scraps back and play again. If you draw a 0 first, put it back and draw again (a number does not start with 0).
Math talk: What is the greatest six-digit number you could make with the six digits you drew? What is the least?
Your turn
1Read 452 300 out loud. Write it in words.
four hundred fifty-two thousand three hundred
2Write six hundred thirty thousand two hundred eight as a numeral.
3What is the value of the 7 in 874 105?
70 000 (7 ten thousands).
4Which digit is in the hundred thousands place in 291 650?
5Count forward by 100 000s from 600 000 to one million.
600 000, 700 000, 800 000, 900 000, 1 000 000
6Count backward by 1000s from 402 000: 402 000, ___, ___, ___
401 000, 400 000, 399 000. After 400 000, the thousands go down to 399.
7Write ninety thousand nine as a numeral.
90 009. The ones period is 009, so there are zeros in the hundreds and tens places.
More practice: warm-up
one hundred twenty-five thousand
2Write three hundred thousand as a numeral.
3How many digits does one million have?
4What number comes just after 599 999?
5What is the value of the 5 in 513 000?
More practice: on your own
eight hundred seven thousand sixty. Thousands period 807, ones period 060.
2Write two hundred thousand fifty-five as a numeral.
200 055. The thousands period is 200 and the ones period is 055.
3Count forward by 10 000s from 945 000: ___, ___, ___
955 000, 965 000, 975 000. Only the ten thousands digit goes up by 1 each time.
4Kai wrote "forty-three thousand six" as 436. What mistake did Kai make? Write the correct numeral.
Kai forgot the zeros that hold empty places. The ones period must have three digits: 006. The correct numeral is 43 006.
5A number has a 4 in the hundred thousands place, a 9 in the hundreds place, and zeros everywhere else. Write it in numerals and words.
400 900, four hundred thousand nine hundred.
Challenge
1Using each of the digits 3, 0, 8, 1, 6, 5 once, make the greatest and the least six-digit numbers. Write both in words.
Greatest: 865 310, eight hundred sixty-five thousand three hundred ten (digits from largest to smallest). Least: 103 568, one hundred three thousand five hundred sixty-eight (smallest non-zero digit first, then 0, then the rest from smallest to largest).
2How many thousands are in one million? How many hundreds? Explain.
1000 thousands and 10 000 hundreds. 1000 × 1000 = 1 000 000, and 10 000 × 100 = 1 000 000.
3About how many days is one million seconds? Use: 1 day = 86 400 seconds.
About 11 or 12 days. 86 400 × 10 = 864 000 (10 days) and 86 400 × 12 = 1 036 800 (12 days). One million is between them, so it is a bit more than 11 days (about 11 and a half).
Quiz
2. Which numeral is seventy thousand five hundred?
3. What is the value of the 6 in 462 917?
4. What comes next? 700 000, 800 000, 900 000, ___
5. One million is the same as...
6. Why does forty thousand six need zeros: 40 006?
Big idea: B1.1 asks Grade 6 students to read and represent whole numbers up to and including one million, and to describe how they are used in everyday life. This first lesson focuses on reading, writing and counting with six-digit numbers and one million.
Common difficulties:
- Missing placeholder zeros. "Two hundred thousand fifty-five" is often written 20055 or 2000055. Have your child write the thousands period and the ones period separately, each with three digits (200 | 055).
- Saying "and". We read 704 016 as "seven hundred four thousand sixteen", with no "and". "And" is used for the decimal point.
- Spaces, not commas. Canadian math books group digits with a space: 386 492. Four-digit numbers are usually written without a space (6000).
- Counting across a big change. Counting backward from 402 000 by 1000s, children may write 400 000, 300 000. Say the numbers aloud slowly.
How to help: Read big numbers you see together (house prices, car odometers, attendance at games). Ask your child to explain how they know how to read or write each one. Explaining their thinking is part of Strand A (mathematical processes) and is woven through this unit.