Number System
Lessons in this chapter
About Number System
Number System is short in 5th grade because it has one new idea to deliver: powers of ten, which turn place value from a pattern kids have noticed into notation they can write.
Read and Write Large Numbers and Identify Place Value of Digits and Write Large Numbers in Expanded Form continue what every grade since 1st has done, now at millions and beyond, where the three-digit grouping and the period names do most of the work.
Express Large Numbers in Powers of Ten is the new lesson. Writing 100 as 10 squared and 1,000 as 10 cubed names the structure explicitly, so expanded form becomes 4 × 10 cubed plus 6 × 10 squared rather than 4,000 plus 600.
This is the notation scientific notation is built from, and it is the reason 6th grade can introduce exponents without fuss. It also explains, at last, why each place is ten times the one to its right: the places are consecutive powers of the same base.
All three lessons open as a 5th grade math worksheet in the page. Read and Write Large Numbers, Identify Place Value of Digits and Write Large Numbers in Expanded Form and Express Large Numbers in Powers of Ten each set their own math questions, scored as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Read and Write Large Numbers and Identify Place Value of Digits and Write Large Numbers in Expanded Form continue what every grade since 1st has done, now at millions and beyond. Express Large Numbers in Powers of Ten is the new lesson, and it names the structure explicitly, so expanded form becomes 4 times 10 cubed plus 6 times 10 squared rather than 4,000 plus 600. The chapter sits in the Common Core domain Number and Operations in Base Ten (5.NBT).
Ten multiplied by itself a number of times. 10 squared is 100, 10 cubed is 1,000. The exponent counts how many tens are multiplied, and also how many zeros follow the 1.
Because it names the structure. 4,600 as 4 × 10 cubed plus 6 × 10 squared shows that the places are consecutive powers of ten, which is the reason place value works.
It is the basis of scientific notation and of the exponents introduced in 6th grade. It also carries straight into decimals, where the powers go negative.
In three-digit groups from the right, naming the period: four million, three hundred eighty-two thousand, nine hundred five.
Because place value has been built every year since 1st grade. All that is left is the notation, which is one lesson, plus the reading and writing at a larger size.