Getting Started 
Misconception/Error The student does not have an effective strategy for combining the values in the table. 
Examples of Student Work at this Level The student:
 Rewrites numbers to combine in the margin without displaying other work.
 Begins the process of converting fractions to decimals, or decimals to fractions, without evidence of other significant work. The student makes errors in conversion, (e.g., Â = 1.8).
 Attempts to combine a whole number and a decimal but does so incorrectly and without displaying other work.
 Attempts to convert fractions to decimals but does so incorrectly, (e.g., Â = 6.58).
 Demonstrates a lack of mastery of addition and subtraction of fractions.

Questions Eliciting Thinking What was your strategy when working on this problem?
How are fractions added?
How are decimal numbers added?
Do you remember how to convert a fraction to a decimal? A decimal to a fraction? 
Instructional Implications If needed, provide instruction on addition and subtraction of fractions and provide practice problems.
If needed, provide instruction on addition and subtraction of numbers in decimal form and provide practice problems.
If needed, provide instruction on converting decimals to fractions and fractions to decimals. Provide practice problems. 
Moving Forward 
Misconception/Error The student makes sign errors when adding and subtracting rational numbers. 
Examples of Student Work at this Level The student adds all numbers without regard to sign.
The studentâ€™s computational accuracy when dealing with positive and negative numbers is inconsistent. The student sometimes completes additions correctly and sometimes makes errors such as 6 + (2.9) = 3.1 or 3.1. 
Questions Eliciting Thinking What is a negative number? What would it look like on a number line? What does it mean to add 6 to 6? What strategy would you use to evaluate 6 + 4?
What does it mean to add 2.9 to 0.3? What strategy would you use to solve this problem? 
Instructional Implications Review operations on integers. Be sure the student understands how to add, subtract, multiply, and divide integers. Transition the student to working with rational numbers.
Use a number line to illustrate addition of rational numbers.
Guide the student to use a number line representation of an addition problem to determine the sign of the sum and whether the absolute value of the addends should be added or subtracted. Then instruct the student to complete the necessary computation and to be certain the sign of the sum is correct. 
Almost There 
Misconception/Error The student is unable to identify how the properties of operations can be used to simplify a calculation. 
Examples of Student Work at this Level The student converts all numbers to fractions or decimals and accurately adds them in order, generating an answer of â€“3.4 cm.
The student identifies that 3.2 and 3.2 are inverses, but does not identify other useful strategies based on the properties of operations.
The student combines fractions with fractions, and decimals with decimals, but does not identify additive inverses. 
Questions Eliciting Thinking What was your strategy when solving this problem? Is there anything you could have done to simplify the work?
When combining numbers, do you always add numbers in the order they are given? Why or why not? What else might you do?
What strategy would you use to solve the problem Â + 3 + ?Â Explain. 
Instructional Implications Provide practice problems scaffolding the use and usefulness of the properties of operations.
First, challenge the student to identify addends that are opposites in a sum involving several addends. Then demonstrate the use of other properties, (e.g., the Associative and Commutative Properties) to simplify complex computations.
Review the properties of operations. Ask the student to identify where the properties might be used in the problem in order to simplify calculations. 
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 effectively uses the properties of operations to simplify calculations.

Questions Eliciting Thinking What was your strategy when solving this problem? 
Instructional Implications Review the names of the properties of operations. Refer to the problem and ask the student to identify which properties of operations were used where to simplify calculations.
Ask the student to generate a table of values that will result in a sum of , incorporating both fractions and decimals and making use of the properties of operations. 