Getting Started |
| Misconception/Error The student does not have an effective strategy for subtracting multidigit decimal numbers. |
| Examples of Student Work at this Level The student:
- Right- or left-justifies the numbers and subtracts with no regard to place value.
- Writes subtractions in the wrong order when rewriting the subtractions vertically.
- Is unable to attempt two or more problems.
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| Questions Eliciting Thinking Why did you line up the numbers to the right (or to the left)?
How does the decimal point help you identify place values?
Does it matter in which order you subtract these numbers? |
| Instructional Implications Guide the student through the use of the standard algorithm for subtracting multidigit decimal numbers with each of the three problems and provide feedback to the student concerning his or her original approach. Explain why lining up the minuend and subtrahend by place value of the digits is part of an effective strategy for subtracting multidigit decimal numbers. Show how lining up decimal points is an efficient way to line up place values. Encourage the student to use graph paper to better organize his or her work. Be sure the student understands the implied location of the decimal point in whole numbers written without decimal points.
Provide instruction on place value in whole and rational numbers (5.NBT.1.3 and 1.4). Explain the meaning of the decimal point as it relates to place value. Consider implementing CPALMS Lesson Plan Decimal Place Value (ID# 31832) or Decimals Have a Point! (ID# 30766).
Provide focused instruction on the use of the standard algorithm for subtraction of multidigit decimal numbers. Explain and justify each step, so the student can develop a useful understanding of the process. |
Moving Forward |
| Misconception/Error The student has a strategy for subtracting multidigit decimal numbers but makes a systematic error with regard to one aspect of the process. |
| Examples of Student Work at this Level The student sets up the subtraction correctly with decimal points aligned but:
- Makes regrouping errors.
- Subtracts digits in the wrong order.
- Does not know where the decimal point in the whole number 33 is located and makes an alignment error when rewriting the subtraction vertically
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| Questions Eliciting Thinking Why did you borrow? Can you explain the borrowing process?
Can you borrow from a digit of zero? What do you do if you need to borrow and the next digit is zero?
In what order should you subtract the digits? Smaller from larger or bottom from top?
In a subtraction problem, how do you know what to subtract from?
Can you apply the Commutative Property to subtraction? |
| Instructional Implications Provide focused instruction on the use of the standard algorithm for subtraction of multidigit decimal numbers. Make explicit the purpose and process of regrouping. Explain and justify each step, so the student can develop a useful understanding of the process.
Remind the student that whole numbers can be rewritten in an equivalent form with decimal points (e.g., 33 = 33.0 = 33.00). Ask the student to explain what the zero in the tenths (or hundredths) place means. Guide the student to rewrite whole numbers in this way appending as many zeros as needed, so both values in the subtraction have the same number of digits to the right of the decimal point. |
Almost There |
| Misconception/Error The student has an effective strategy for subtracting multidigit numbers but makes a calculation or other minor error. |
| Examples of Student Work at this Level The student sets up the subtraction correctly with decimal points aligned and regroups correctly to complete the subtractions but:
- Makes a calculation error when subtracting a pair of digits.
- Places the decimal point in the wrong location in the answer.
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| Questions Eliciting Thinking You made a small error in the first (second or third) problem. Can you find your error?
What did you do wrong, and how can you correct it?
Can you think of a strategy that will help you avoid that error in the future? |
| Instructional Implications If the student catches his or her own error without prompting, consider the student to be at the Got It level and consider those Instructional Implications. Otherwise, address any minor errors the student may have made. Discuss some strategies the student can use that will help him or her avoid making the same error in the future (e.g., show the student how to use addition to check his or her answers).
Provide additional opportunities to subtract multidigit decimal numbers, so the student can improve his or her fluency with the standard subtraction algorithm. |
Got It |
| Misconception/Error The student provides complete and correct responses to all components of the task. |
| Examples of Student Work at this Level The student completes all three problems accurately within 4-6 minutes getting final answers of:
- 0.9999
- 32.667
- 40.86
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| Questions Eliciting Thinking Can you subtract without rewriting the problem vertically?
How can you check your answer?
What would happen if you lined up the numbers to the right, regardless of the decimal point, and then subtracted the numbers?
How does borrowing work?
What strategies did you use to solve these problems? |
| Instructional Implications Pair the student with an Almost There partner. Have the pair complete a similar set of problems, compare answers, and reconcile any differences.
Consider using MFAS tasks Multiplying Multidigit Decimals (6.NS.2.3) and Dividing Multidigit Decimals (6.NS.2.3) to further assess the student’s ability to perform operations with decimal numbers. |
