☰ Year plan · Mathematics

Big numbers, groups and arrays

Week 4 · Big numbers, equal groups and arrays · 3 lessons
1

Ordering numbers in the thousands

Discover Mathematics P3: Term 1, Lessons 11–20
GoalWrite 5- and 6-digit numbers in standard and expanded form and put them in order.
New words
standard form · the usual way to write a number with digitsorder · put numbers in a line from the least to the greatest, or the other way roundleast · the smallest
Explanation

Standard form is the usual way to write a number with digits, such as 73,846. We say it: seventy-three thousand, eight hundred forty-six. Expanded form shows the value of each digit: 73,846 = 70,000 + 3,000 + 800 + 40 + 6. To put numbers in order, count the digits first. A number with more digits is greater, so any 6-digit number is greater than any 5-digit number. If two numbers have the same number of digits, compare them from the left, place by place, until the digits are different. A place value mat helps to line up the places.

NumberHundred thousandsTen thousandsThousandsHundredsTensOnes
73,84673846
Worked examples
Standard formExpanded form
48,05240,000 + 8,000 + 50 + 2
48,20540,000 + 8,000 + 200 + 5
480,250400,000 + 80,000 + 200 + 50
Write three numbers in expanded form. 48,052 = 40,000 + 8,000 + 50 + 2. 48,205 = 40,000 + 8,000 + 200 + 5. 480,250 = 400,000 + 80,000 + 200 + 50. A zero in a place means that place adds nothing, so we leave it out.
NumberHundred thousandsTen thousandsThousandsHundredsTensOnes
48,20548205
48,05248052
Compare 48,205 and 48,052. Both have 5 digits. The ten thousands are 4 and 4, the thousands are 8 and 8, and the hundreds are 2 and 0. Since 2 hundreds are more than 0 hundreds, 48,205 > 48,052.
1st (least)2nd3rd4th (greatest)
48,05248,205408,520480,250
Order 480,250; 48,205; 408,520 and 48,052 from the least to the greatest. The two 5-digit numbers come first: 48,052 and 48,205. Of the two 6-digit numbers, 408,520 has 0 ten thousands and 480,250 has 8 ten thousands. The order is 48,052; 48,205; 408,520; 480,250.
Class activity

Number card race. Write six numbers with 5 or 6 digits on cards, such as 91,430 and 190,430, and mix them up. Race to put them in order from the least to the greatest. Then read each number aloud and write it in expanded form.

Practice
1
Write 62,507 in expanded form.
2
Write 600,000 + 5,000 + 90 + 4 in standard form.
3
Which is greater, 91,430 or 190,430? Why?
4
Order from the least to the greatest: 52,716; 52,176; 521,076; 51,999.
5
Mostafa wrote 80,000 + 400 + 7 as 84,007. Is he right?