How to make it
- Choose the question typeValue of a digit underlines one digit to name, Expanded form asks for the parts, and Compare numbers needs <, > or = between two numbers.
- Choose the number sizeFrom 2 to 6 digits. Every number has exactly that many digits, and numbers of four digits or more are printed with commas.
- Print with the keyFifteen problems is the default. Print or save the PDF; the key page shows each value, expansion or sign in pink.
Three ways to practice place value
Value of a digit prints a number with one digit underlined and the prompt Value of the underlined digit, followed by an answer line. Underline the 7 in 4,705 and the answer is 700. The underlined digit is never a zero, so every question has a real answer. Three problems fit across the page.
Expanded form prints a number with an equals sign and a long line, such as 4,305 = , and the child writes the number as a sum of its parts: 4,000 + 300 + 5. Compare numbers prints two numbers with a blank between them, such as 52,618 ___ 52,681, and the child writes <, > or =. Both use two problems per row, and expanded form with five or six digits drops to one per row, so the longest expansions still fit on the line.
Number size runs from 2 to 6 digits and applies to every number on the sheet, so comparing problems always pair numbers of the same length. That is deliberate: children cannot win by counting digits, and they have to look at the places one by one. If six digits overwhelm a child, step back to four with the same question type; the method is identical and only the reading load changes, which makes it easy to tell whether the trouble is the idea or the size of the number.
The digit and its value
Children often mix up two questions: which digit is in the hundreds place, and what is the value of that digit. In 4,705, the hundreds digit is 7, and its value is 700. The value questions on these sheets ask for the second, so a child who writes 7 has found the right place but not finished the thought. Ask what the 7 is worth if this number were money, and most children get there.
Zero matters too. In 4,705 the 0 holds the tens place empty; without it, the number would read 475. Children who understand that zero is a placeholder rather than nothing find long multiplication and decimals much easier later. Base-ten blocks, bundles of ten straws, or play money in ones, tens and hundreds make the same point physically: build 4,705 and there is simply no pile in the tens spot. With three-digit numbers, value questions practice the idea in CCSS 2.NBT.A.1 that the digits of a three-digit number stand for hundreds, tens and ones.
Expanded form and comparing, step by step
To expand 4,305, read each digit with its place: four thousands, three hundreds, no tens, five ones. Write the nonzero parts as numbers and join them with plus signs: 4,000 + 300 + 5. The key leaves out parts that are zero, which is the most common convention. Some teachers prefer 4,000 + 300 + 0 + 5, or the longer expanded notation with multiplication, 4 × 1,000 + 3 × 100 + 5 × 1; mark these as correct if your class uses them.
To compare 52,618 and 52,681, start from the left and move right until the digits differ: 5 and 5, 2 and 2, 6 and 6, then 1 and 8. Since 1 is less than 8, the first number is smaller: 52,618 < 52,681. Some problems compare a number with itself, so = is sometimes the answer. Many teachers remind children that the open side of the sign faces the bigger number; whatever reminder you use, have children read each finished statement aloud as is less than or is greater than.
Place value settings by grade
On US and Canadian sheets (those that open on Letter), two- and three-digit settings show CCSS 2.NBT.A.3 in the footer, the second-grade standard for reading and writing numbers to 1,000, including expanded form. Sheets with four to six digits show CCSS 4.NBT.A.2, which covers reading, writing and comparing multi-digit numbers. In between, third graders often work with four-digit numbers as part of addition and subtraction.
In England, the National Curriculum moves through numbers to 100 in Year 2, to 1,000 in Year 3, to 10,000 in Year 4 and to 1,000,000 in Year 5. In Australia, children typically work to 1,000 in Year 2, to 10,000 in Year 3, and beyond in Years 4 and 5. Those ranges line up neatly with the Number size setting. Place value pays off quickly with coins: the counting money worksheets turn dimes and pennies into tens and ones.
| Number size | Footer code | US grade | England | Australia |
|---|---|---|---|---|
| 2 digits | CCSS 2.NBT.A.3 | Grade 1 to grade 2 | Year 2 | Year 1 to Year 2 |
| 3 digits | CCSS 2.NBT.A.3 | Grade 2 | Year 3 | Year 2 |
| 4 digits | CCSS 4.NBT.A.2 | Grade 3 to grade 4 | Year 4 | Year 3 |
| 5 or 6 digits | CCSS 4.NBT.A.2 | Grade 4 | Year 5 | Year 4 to Year 5 |
A place value chart to go with the sheet
This generator does not print a separate place value chart, but one is easy to make. On a page of one-inch graph paper, label columns from the right as ones, tens, hundreds, thousands, ten thousands and hundred thousands, leaving a thicker line after every three columns where the comma goes. Children write each number from the sheet into the chart, one digit per square, before answering.
For the youngest learners, a hundreds chart shows tens and ones in another way: moving down one row adds a ten, moving right adds a one. Counting by 10s and 100s on number line worksheets is a good warm-up too, and column addition puts the whole idea to work.
Mistakes, the key, and how many to set
Common mistakes: writing the digit instead of its value, miscounting places in long numbers (calling the 2 in 52,618 two thousand), writing expanded form with the wrong number of zeros (4,000 + 30 + 5 for 4,305), and comparing by the last digits instead of the first. The pink key gives the value, the full expansion or the correct sign, so a quick look shows which place went wrong.
Commas help. Numbers of four or more digits print with commas between groups of three, so children can read 352,618 as three hundred fifty-two thousand, six hundred eighteen. For a warm-up, six to eight problems. Fifteen, the default, makes a practice page. For a review, print one sheet of each question type at the same number size.
A sequence that works for many fourth graders meeting six-digit numbers: two days of value questions to get used to the new places, a day of expanded form, and then comparing. Keep the number size the same across the three sheets, so the only new thing each day is the question. When value questions come back mostly right, step up one digit and start the cycle again.
Questions
Can I make rounding worksheets here?
Not at present; the three question types are value of a digit, expanded form and comparing numbers. Rounding builds directly on place value, so these sheets are good preparation: a child who can name the value of each digit can find the place to round to and look at the digit to its right.
How do I make expanded form worksheets?
Choose Expanded form under Question type and set the number size. Each problem prints a number followed by an equals sign and a line, and the key writes it as a sum, such as 6,000 + 400 + 20 + 9. Parts that are zero are left out of the key.
Is there a printable place value chart?
The generator prints question sheets rather than a separate chart. A quick alternative is to draw one on squared paper with columns for ones, tens, hundreds and so on, and have children copy each number into it before answering. The graph paper generator prints squares from 2 mm to one inch.
What grade learns place value to the thousands?
In the US, place value to 1,000 is usually second grade and multi-digit numbers are a fourth-grade standard, CCSS 4.NBT.A.2. In England numbers to 1,000 are a Year 3 topic and to 10,000 a Year 4 topic. In Australia, numbers to 10,000 are typically a Year 3 focus.
Can I make comparing numbers worksheets?
Yes. Choose Compare numbers and every problem shows two numbers of the same length with a blank between them for <, > or =. Some pairs are equal, so children cannot assume one is always larger. Set the number size from 2 to 6 digits.
Do the numbers include zeros?
Yes, zeros can appear in any place except the first, as in 4,305. In value questions the underlined digit is never a zero, and in expanded form the key leaves out zero parts. Numbers with zeros are worth extra discussion, since they show what a placeholder does.
Common Core State Standards: © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.