B. Number · Number Sense: Numbers to One Million, Integers, Decimals and Fractions

Place Value: Building and Breaking Apart Numbers to One Million

B1.1About 40 minutes

Learning goals

I can write a number to one million in standard form, expanded form and words.
I can break apart (decompose) a number in more than one way.
I can build (compose) a number from its parts, even when a place has more than 9.
I can explain how each place is worth 10 times the place to its right.

Words to know

standard form
A number written with digits in the usual way, like 472 305.

expanded form
A number written as the sum of the values of its digits, like 400 000 + 70 000 + 2000 + 300 + 5.

decompose
Break a number into parts, like 472 305 = 472 thousands + 305.

compose
Build a number by putting parts together.

regroup
Trade 10 of one place for 1 of the next place to the left (or the other way).

Remember from Grade 5

In Grade 5 you wrote numbers to 100 000 in expanded form, like 56 207 = 50 000 + 6000 + 200 + 7, and you broke numbers apart in different ways, like 41 700 = 417 hundreds. Now you will do the same with numbers up to one million.

Saving for a new arena

A small town is raising money for a new community arena. So far it has raised $472 305.

There are many ways to think about this number. The mayor might say "about 472 thousand dollars." The banker counts it in $100 bills and other bills and coins. Each way is a different way to decompose the same number.

Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
4	7	2	3	0	5
400 000	70 000	2000	300	0	5

472 305: each digit and its value.

Three ways to write a number

Standard form: 472 305
Expanded form: 400 000 + 70 000 + 2000 + 300 + 5 (we can leave out the 0 tens)
Words: four hundred seventy-two thousand three hundred five

The "times 10" pattern

Each place is worth 10 times the place to its right.

10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand
10 thousands = 1 ten thousand
10 ten thousands = 1 hundred thousand
10 hundred thousands = 1 million

Moving one place to the left multiplies the value by 10. Ten hundred thousands make one million.

Place	Value	Equals
1 million	1 000 000	10 hundred thousands
1 hundred thousand	100 000	10 ten thousands
1 ten thousand	10 000	10 thousands
1 thousand	1000	10 hundreds

Each place is 10 times the place to its right.

Worked example

Example 1: Decompose in different ways

Show 472 305 in three different ways.

Expanded form: 400 000 + 70 000 + 2000 + 300 + 5.
Use the thousands period: 472 thousands + 305 ones (472 000 + 305).
Use hundreds: 472 305 has 4723 hundreds and 5 ones (cover the last two digits to see 4723).

472 305 = 400 000 + 70 000 + 2000 + 300 + 5 = 472 000 + 305 = 4723 hundreds + 5

Worked example

Example 2: Compose a number with regrouping

What number is 3 hundred thousands + 15 ten thousands + 2 thousands + 8 tens?

Find each value: 300 000, 15 × 10 000 = 150 000, 2000 and 80.
Add: 300 000 + 150 000 = 450 000.
450 000 + 2000 + 80 = 452 080.

452 080. The 15 ten thousands regroup into 1 hundred thousand and 5 ten thousands.

Ten of the 15 ten thousands regroup into one hundred thousand. The other 5 stay in the ten thousands place, so the number is 452 080.

Worked example

Example 3: Use money

The arena fund gets a cheque for $250 000. How many $100 bills would that be? How many $1000 amounts?

Count the hundreds: cover the last two digits of 250 000 to see 2500. So it is 2500 hundreds.
Count the thousands: cover the last three digits to see 250.

2500 $100 bills, or 250 thousand-dollar amounts.

Cover-up trick

To find how many hundreds are in a number, cover the tens and ones digits; what's left is the number of hundreds. For thousands, cover the last three digits. In 638 914, there are 6389 hundreds and 638 thousands.

Just for fun

Riddle: What did the 0 in 605 090 say?

"I may be worth nothing, but I'm holding this place together!" Without its zeros, 605 090 would shrink to 659.

Hands-on activity

Sticky note place value

You need: 6 sticky notes or small paper squares, a pencil and a long sheet of paper.

Draw a place value chart with six columns: hundred thousands, ten thousands, thousands, hundreds, tens, ones.
Your grown-up says a number, like "six hundred four thousand two hundred thirty". Write each digit on a sticky note and put it in the right column (604 230).
Under the chart, write the number in expanded form.
Now decompose it another way: how many thousands? How many hundreds?
Switch: you say a number and your grown-up builds it. Check their work!

Bonus: Your grown-up says a "tricky" number like 2 hundred thousands + 14 thousands + 6 ones. Figure out the standard form (214 006).

Your turn

Write 538 402 in expanded form.

Write 700 000 + 4000 + 60 + 1 in standard form.

How many thousands are in 815 600?

How many hundreds are in 815 600?

What number is 9 hundred thousands + 3 ten thousands + 5 hundreds?

Fill in the blank: 362 908 = 362 000 + ___

How many ten thousands make one million?

More practice: warm-up

Write 240 000 in expanded form.

Standard form: 100 000 + 50 000 + 3

10 hundred thousands = ___

10 thousands = ___

What is the value of the 9 in 319 000?

More practice: on your own

Write 605 090 in expanded form and in words.

What number is 4 hundred thousands + 12 ten thousands + 7 thousands?

Write 381 250 as thousands plus ones, and as hundreds plus tens.

A school collected $84 600 for a charity. How many $100 bills is that?

Mira says 207 450 = 20 000 + 7000 + 400 + 50. What did she do wrong?

Challenge

Write one million in three different ways using place value words.

What number is 35 ten thousands + 47 hundreds + 2 ones?

I am a six-digit number. My hundred thousands digit is 3 more than my ones digit. My ones digit is 5. All my other digits are 0 except my thousands digit, which is 4. What number am I? Write me in expanded form.

Check your understanding

Quiz

Which is the expanded form of 603 070?

What is 500 000 + 20 000 + 900 + 4 in standard form?

How many hundreds are in 47 300?

10 hundred thousands is equal to...

What number is 2 hundred thousands + 13 ten thousands?

Which is not equal to 840 000?

For parents and teachers

Big idea: Representing numbers in many ways (standard form, expanded form, words, and decomposed into thousands or hundreds) is part of B1.1. It builds the place value sense your child needs for adding, subtracting, multiplying and dividing big numbers.

Common difficulties:

Mixing up place names. "Ten thousands" vs "hundred thousands" sound alike. A written place value chart helps.
Regrouping. "15 ten thousands" is not a digit. Show that 15 ten thousands = 150 000 = 1 hundred thousand and 5 ten thousands.
How many hundreds? Many children answer "6" for "How many hundreds in 815 600?" because they look only at the hundreds digit. The cover-up trick shows there are 8156 hundreds in all.

How to help: Use money. Ask: "How many $100 bills would it take to make $25 000?" (250) or "How many thousands is a $350 000 house?" (350).