Getting Started |
| Misconception/Error The student does not have an effective strategy for adding multidigit decimal numbers. |
| Examples of Student Work at this Level The student right- or left-justifies the addends and adds digits without regard to place value. The student is uncertain where to place the decimal point in the sum. Upon questioning, the student does not indicate an understanding of the role of place value in addition of multidigit decimal numbers.
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| Questions Eliciting Thinking Why did you line up all your numbers to the right before adding them?
How does the decimal point help you identify place values?
Does 30 plus one make 40? Why or why not? Does place value matter when adding numbers? Why or why not?
Does a two in the tens place mean the same thing as a two in the hundreds place? Explain.
What is the name of the place value to the right of the decimal point? |
| Instructional Implications Guide the student through the use of the standard algorithm for adding 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 addends by place value of the digits is an effective strategy for adding 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 5.NBT.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 continued experience with the use of the standard algorithm for addition 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 adding multidigit numbers but makes significant place value errors. |
| Examples of Student Work at this Level The student:Â
- Treats commas embedded in numbers as if they are decimal points.
- Does not know where the decimal point in the whole number 72 is located and makes an alignment error when rewriting the addition vertically.
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| Questions Eliciting Thinking How did you decide how to line up the numbers before adding?
How is the comma used when writing numbers?
What does the decimal point mean? What is its purpose?
Where is the decimal point located in whole numbers? Why?
What happens to the value of a number if you move its decimal point? Explain. |
| Instructional Implications Explain the role and placement of the comma within numbers. Make explicit the difference between a comma and a decimal point. Then show the student how a number written with a comma still has a decimal point (e.g., 12,345 is the same as 12,345.00). Make a reference to money if needed. Help the student understand the location of the implied decimal point in whole numbers. |
Almost There |
| Misconception/Error The student has an efficient strategy for adding multidigit numbers but makes a minor calculation error. |
| Examples of Student Work at this Level The student makes a minor calculation error.
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| Questions Eliciting Thinking You made a small error on your paper. Can you find it and fix it?
What was your error? How did you fix it?
Can you think of strategies that may help you avoid making minor errors? |
| Instructional Implications If the student realizes his or her own mistake without prompting, consider him or her to be at the Got It level. Otherwise, address any minor errors the student may have made. Show the student effective strategies that may help him or her avoid making minor errors (e.g., place the largest number first; put zeros as place holders; double check calculations; or apply properties such as the Commutative Property of Addition). |
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 3-5 minutes getting final answers of:
- 136.974
- 1016.701
- 112.287
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| Questions Eliciting Thinking Why did you line up the decimal points before adding? How did you know where to put the decimal point in your answer?
Why can you line up whole numbers to the right but not decimal numbers (e.g., 23 + 4 + 177 versus 2.3 + 4 + 1.77)?
Does it matter in which order you write your numbers before adding them? Did you use any properties to help you add more quickly?
Could you add without rewriting the addends vertically?
What is the purpose of the comma in some numbers (e.g., in 12,300)? |
| Instructional Implications Pair the student with a student at the Getting Started or Moving Forward level and have the student explain and model his or her strategies for adding multidigit decimal numbers.
Challenge the student to add 10,000 + 3,456 + 0.78 + 0.001 using mental math strategies. Have the student discuss his or her strategies with you.
Consider implementing MFAS task Subtracting Multidigit Decimals (6.NS.2.3) to further assess the student’s ability to perform operations with multidigit decimal numbers. |
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