Grade 4Mathhard
Number Expert
Number Expert — Place Value worksheet for Grade 4.
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What Your Child Will Learn
- Decompose multi-digit numbers (up to 10,000) into expanded form using place values (thousands, hundreds, tens, and ones) to demonstrate understanding of number composition
- Compare and order whole numbers by analyzing the place value of digits in each position, with emphasis on when digits in the same place value differ
- Apply place-value understanding to solve word problems requiring regrouping or composing/decomposing numbers across multiple place values
- Identify the value of individual digits within numbers and explain how moving a digit one place to the left or right changes its value by a factor of 10
How to Use This Worksheet
- Step 1: Read each problem aloud with your student and have them identify what they're being asked to do—are they composing a number from place values, decomposing a number into expanded form, or comparing place values? Highlight or underline the action verb in each problem.
- Step 2: For decomposition or expanded-form problems, have students create a place-value chart with four columns labeled 'Thousands,' 'Hundreds,' 'Tens,' and 'Ones.' Write the number at the top and break it down into each place value, showing the digit in each position and its total value.
- Step 3: For comparison problems, have students write out the place values of each digit being compared in both numbers (for example: '5 in the thousands place = 5,000' vs. '5 in the hundreds place = 500'). This ensures they're comparing the values, not just the digits.
- Step 4: Check each answer by recomposing the number—if they decomposed 3,247, they should add 3,000 + 200 + 40 + 7 to verify they get back to 3,247. This builds self-checking habits and catches errors immediately.
- Step 5: After completing the worksheet, have your student explain one of their answers to you in their own words, using place-value vocabulary. If they struggle to explain, revisit that concept before moving forward.
Tips for Parents & Teachers
Students at this level often struggle with numbers in the thousands place—use physical base-ten blocks or draw grid models to show that one thousand block equals ten hundred blocks. This concrete representation helps them visualize why 1,000 is 10 times 100.
Watch for the common mistake where students confuse digit value with place value (e.g., writing '5' instead of '5,000' when asked for the value of the digit 5 in the thousands place). Explicitly teach that place value includes the digit AND the position, and practice saying aloud: 'The digit is 5, and it is in the thousands place, so its value is 5,000.'
When comparing numbers with the same digits in different positions, require students to circle the digit being compared and write its place-value name before comparing. This slows down their thinking and prevents careless errors where they ignore place value entirely.
Encourage students to use comparison language: 'is equal to,' 'is 10 times as much as,' and 'is 1/10 of' when discussing place-value relationships. This develops deeper conceptual understanding beyond simple greater-than/less-than notation.
Frequently Asked Questions
Why do some of these problems ask about the 'value' of a digit versus just naming the digit itself?
The digit and its value are two different things. For example, in the number 4,582, the digit '5' appears in the hundreds place. The digit itself is simply '5,' but its VALUE is 500 because it's in the hundreds place. Fourth graders need to understand this distinction to build toward multiplication, division, and decimal concepts. Always ask: 'What is the digit?' and 'What is the value of that digit?' as two separate questions.
My student keeps getting confused about thousands. How can I help them understand this bigger place value?
Thousands are abstract for many fourth graders because they can't see or touch 1,000 objects easily. Try these strategies: (1) Use bundles of 100 (like 10 pencil boxes with 100 pencils each) to show that 1,000 is a collection of 10 groups of 100; (2) Count by hundreds up to 1,000 aloud together: '100, 200, 300...' to reinforce the rhythm; (3) Relate it to money—1,000 pennies, 100 dimes, or 10 ten-dollar bills are all the same value, which helps with the '10 times' relationship between place values.
What does it mean when a problem asks students to show how place values 'relate' to each other?
Place values have a multiplicative relationship: each place value is 10 times the place value to its right and 1/10 of the place value to its left. So in 3,200, the thousands place is 10 times the hundreds place (3,000 is 10 times 300). When a problem asks about relationships, it's asking students to explain or show this '10 times as many' or '1/10 of' connection. Students should be able to write or say: 'The 2 in the hundreds place is worth 200, but if that 2 were in the thousands place, it would be worth 2,000, which is 10 times as much.'
How should I correct my student when they write a number in expanded form incorrectly?
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