Getting Started 
Misconception/Error The student is unable to describe quantities represented by positive and negative fractions in context. 
Examples of Student Work at this Level The student:
 Writes the fractions in word form and ignores the context (e.g., “February means one and five eighths; March is zero; April is four and one fourth”).
 Does not differentiate between the descriptions for positive, negative or zero and gives the same statement for each answer (e.g., “the amount of rainfall,” “the amount of change in rainfall,” or “the average rainfall for the month”).

Questions Eliciting Thinking Can you read the title of the second column of the chart? What do you think this means?
What is the difference between describing a number and describing the meaning of a number in context?
Why did you give the same answer to all three questions? Is there a difference between a positive number, a negative number and zero? How could you describe those differences? 
Instructional Implications Expose the student to a variety of realworld situations in which positive and negative numbers are used to represent quantities such as gain/loss, increase/decrease, and above/below (e.g., sea level). Guide the student to represent integer and fraction quantities in the context of a variety of situations. 
Moving Forward 
Misconception/Error The student refers to the values as an amount of rainfall rather than a change from the average amount of rainfall. 
Examples of Student Work at this Level The student uses the given value as the amount of rainfall or as the average amount of rainfall, saying:
 “There are inches of rainfall” or “some rainfall” or “an average of inches” in February.
 “There are 0 inches of rainfall” or “no rainfall” or “there is usually no rain” in March.
 “There is no rainfall” or “very little rainfall” or “they had negative rainfall” in April.
The student tries to explain a reason for the negative amount of rainfall with expressions like: “there was a drought” or “they lost rainfall” in April.

Questions Eliciting Thinking What in the chart tells you it rained inches in February? What other words in the chart describe the meaning of the numbers?
Why did you say it rained inches in April? Is it possible to measure a negative amount of rain?
If your average allowance each month is $10, but this month you get $2 more (or $1 less), how much money are you getting this month? How much will you get next month if there is zero change from your average? 
Instructional Implications Expose the student to a variety of realworld situations in which integers (or positive and negative rational numbers) can be used to describe both quantities and changes in quantities. Help the student understand the distinction between using integers to describe a quantity (such as a temperature) and using integers to describe a change in a quantity (such as a change in temperature). Challenge the student to find additional examples of the use of integers in the real world and to describe the way in which the integers are used.
Consider using tasks Relative Integers (6.NS.3.5), Relative Decimals (6.NS.3.5) and Relative Fractions (6.NS.3.5) for further practice. 
Almost There 
Misconception/Error The student interprets the values as change in rainfall amounts but does so with errors. 
Examples of Student Work at this Level The student:
 Describes the values as changes but is not specific about what has changed.
 Describes the value as a change from the previous month’s amount of rainfall rather than a change from the average.

Questions Eliciting Thinking What has actually changed? Can you be more specific?
What do you mean by increase (or decrease) – an increase (or decrease) from what?
Why did you say the rainfall is a change from the previous month? Where in the chart does it say that? How is the wording in the chart different than your description? 
Instructional Implications Give the student more experience using rational numbers to represent quantities and interpret the meaning of rational numbers, including zero, using a variety of contexts. Guide the student to use a number line to represent positive and negative rational numbers and changes to rational quantities.
Give the student practice reading and interpreting graphs, charts and other forms of data presentation. Have the student describe the meaning of several numbers from each display. 
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 specifies that the amount of rainfall:
 For February was inches more than the monthly average for February.
 For March was the same as the monthly average for March.
 For April was inch less than the monthly average for April.

Questions Eliciting Thinking What if the chart just showed amounts of rainfall for each month? Would a negative value still make sense? What about zero?
Can you think of another example in which a negative value can have meaning when it represents an amount of change but loses its meaning when it represents an amount? 
Instructional Implications Give the student the average rainfall for each month and have him or her use the change values given in the chart to calculate the amount of rainfall for each month.
Introduce the concept of opposites and have the student use a number line to graph pairs of opposite values.
Engage the student in a discussion of the different ways that the minus or negative symbol is used in mathematics. Encourage the student to interpret expressions such as –n as meaning “the opposite of n.” 