Unit 1: Place Value and Number Sense
What each digit in a big number is actually worth, and how to compare, order, round, and estimate with confidence.
6 topics · 24 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What Place Value Really Means
- How it worksHow does moving a digit one spot to the left make it worth ten times as much?
- Worked exampleFind what the digit 7 is worth in the number 3,752.
- Common mistakeWhy doesn't the 2 in the number 20 stand for the same amount as the 2 in 200?
- Going furtherWhat happens to a number's value if you swap its ones digit with its thousands digit?
Your turn1 of 2
Priya has 7 thousand-dollar prize bonds, 6 hundred-dollar bonds, 8 ten-dollar bonds, and 3 one-dollar bonds in her savings box. What is the value of just the hundred-dollar bonds?Reading and Writing Big Numbers
- How it worksHow do commas split a big number into groups of three so you can read it?
- Going furtherWhat changes about reading a number out loud once it reaches a million?
- Ties togetherHow does the comma-grouping trick connect to what each digit's place is worth?
Your turn1 of 2
A number has 7 thousands and 6 hundreds, 8 tens, 3 ones, written with a comma like 7,683. What does the comma separate?Comparing Multi-Digit Numbers
- How it worksHow do you compare two numbers by lining up their digits and checking the leftmost spot first?
- How it worksHow do you use the less-than and greater-than symbols to show which number wins?
- Worked exampleFind which is bigger: 4,608 marbles or 4,680 marbles.
- Common mistakeWhy isn't 3,459 bigger than 3,461 just because 9 is bigger than 1?
- Going furtherWhat happens when two numbers you are comparing start with the exact same digits up front?
Your turn1 of 2
Tom's high score in a video game is 7267 points and Zoe's high score is 6840 points. What is the higher of the two scores?Ordering Numbers from Least to Greatest
- How it worksHow do you sort a messy list of numbers from smallest to largest one step at a time?
- Worked exampleFind the order from least to greatest for 340, 3,400, 43, and 304.
- Going furtherWhat changes about ordering numbers when two of them are exactly the same?
- Ties togetherHow does comparing two numbers at a time connect to putting a whole list in order?
Your turn1 of 2
Ravi walked 3512 steps on his hike and Nina walked 3280 steps on hers. What is the smaller of the two step counts?Rounding to a Given Place
- How it worksHow do you decide whether to round a number up or down to the nearest ten?
- Common mistakeWhy doesn't rounding 149 to the nearest hundred give you 200?
- Going furtherWhat happens to your rounded answer if you round the same number to the nearest thousand instead of the nearest ten?
Your turn1 of 2
Leo counted 76 marbles in his jar -- that's 7 tens and 6 ones. Round that number of marbles to the nearest ten.Estimating Sums and Differences
- How it worksHow do you round two numbers first so you can add them quickly in your head?
- Worked exampleFind an estimate for 289 plus 412 by rounding each number to the nearest hundred.
- Worked exampleFind an estimate for 803 minus 296 by rounding each number to the nearest hundred.
- Common mistakeWhy isn't an estimate wrong just because it doesn't match the exact answer?
- Going furtherWhat happens to your estimate's accuracy if you round to the nearest ten instead of the nearest hundred?
Your turn1 of 2
A bookstore sold 668 books in spring and 312 books in fall. Estimate the total by rounding each number to the nearest hundred first, then adding.