Proportional Reasoning - Questions
The Proportional Reasoning Concept Builder is comprised of 14 Question Groups with three questions in each group. Questions in the same group are very similar. If a student misses a question in a Question Group, they will be presented with the other two questions in that Question Group. Questions are selected at random such that two side-by-side students are unlikely to have the same questions or ordering of questions. The 14 Question Groups are organized into three different activities that involve different types of tasks. The activities are described as follows:
- Which Two Rows: Question Groups 1-4 ... Given a Data Table representing generic variables X and Y, students must identify two rows of the table that demonstrated a stated pattern - such as doubling the value of X will double the value of Y.
- Predict the Value: Question Groups 5-8 ... Given information about the relationship between generic variables X and Y and given the values of X and Y, students must predict the value of Y if the value of X is doubled, tripled, or quadrupled.
- Extrapolate: Question Groups 9-14 ... Given a Data Table, students must inspect the values and determine the relationship type (linear, inverse, or quadratic), identify the manner in which Y varies with a given change in X, and extrapolate beyond the domain of the data set to predict the value of Y for a stated value of X.
While we recommend all three activities in the order provided, there is no reason why one activity needs to be done as a pre-cursor to another activity. The questions are shown below. Teachers are encouraged to view the questions in order to judge the appropriateness of each activity for their courses.
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Proportional Reasoning
Activity 1: Which Two Rows?
Question Group 1
Question 1
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A doubling of the value of x results in a doubling of the value of y.
Question 2
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A tripling of the value of x results in a tripling of the value of y.
Question 3
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A quadrupling of the value of x results in a quadrupling of the value of y.
Question Group 2
Question 4
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A doubling of the value of x results in a halving of the value of y.
Question 5
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A tripling of the value of x results in the value of y decreasing by a factor of three.
Question 6
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A quadrupling of the value of x results in the value of y decreasing by a factor of four.
Question Group 3
Question 7
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A doubling of the value of x results in a quadrupling of the value of y.
Question 8
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A tripling of the value of x results in the value of y increasing by a factor of nine.
Question 9
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A quadrupling of the value of x results in the value of y increasing by a factor of 16.
Question Group 4
Question 10
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A doubling of the value of x results in a doubling of the value of y.
Question 11
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A tripling of the value of x results in a tripling of the value of y.
Question 12
Observe the data at the right. Which two rows show the following pattern? Select all that apply.
A quadrupling of the value of x results in a quadrupling of the value of y.
Activity 2: Predict the Value
Question Group 5
Question 13
The variables x and y have a linear relationship. Doubling the value of X causes the value of y to double. When x has a value of 2, y has a value of 6. What will be the value of y when x has a value of 4?
Question 14
The variables x and y have a linear relationship. Tripling the value of X causes the value of y to triple. When x has a value of 2, y has a value of 6. What will be the value of y when x has a value of 6?
Question 15
The variables x and y have a linear relationship. Quadrupling the value of X causes the value of y to quadruple. When x has a value of 2, y has a value of 6. What will be the value of y when x has a value of 8?
Question Group 6
Question 16
The variables x and y have an inverse relationship. Doubling the value of X causes the value of y to halve. When x has a value of 2, y has a value of 24. What will be the value of y when x has a value of 4?
Question 17
The variables x and y have an inverse relationship. Tripling the value of X causes the value of y to decrease by a factor of one-third. When x has a value of 2, y has a value of 24. What will be the value of y when x has a value of 6?
Question 18
The variables x and y have an inverse relationship. Quadrupling the value of X causes the value of y to decrease by a factor of one-fourth. When x has a value of 2, y has a value of 24. What will be the value of y when x has a value of 8?
Question Group 7
Question 19
The variables x and y have a quadratic relationship. Doubling the value of X causes the value of y to quadruple. When x has a value of 3, y has a value of 2. What will be the value of y when x has a value of 6?
Question 20
The variables x and y have a quadratic relationship. Tripling the value of X causes the value of y to increase by a factor of nine. When x has a value of 3, y has a value of 2. What will be the value of y when x has a value of 9?
Question 21
The variables x and y have a quadratic relationship. Quadrupling the value of X causes the value of y to increase by a factor of 16. When x has a value of 3, y has a value of 2. What will be the value of y when x has a value of 12?
Question Group 8
Question 22
The variables x and y have a linear relationship. Doubling the value of X causes the value of y to double. When x has a value of 3, y has a value of 5. What will be the value of y when x has a value of 6?
Question 23
The variables x and y have a linear relationship. Tripling the value of X causes the value of y to triple. When x has a value of 3, y has a value of 5. What will be the value of y when x has a value of 9?
Question 24
The variables x and y have a linear relationship. Quadrupling the value of X causes the value of y to quadruple. When x has a value of 3, y has a value of 5. What will be the value of y when x has a value of 12?
Activity 3: Extrapolate
Question Group 9
Question 25
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Doubling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 16?
Question 26
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Tripling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 18?
Question 27
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Quadrupling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 24?
Question Group 10
Question 28
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Doubling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 12?
Question 29
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Tripling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 18?
Question 30
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Quadrupling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 24?
Question Group 11
Question 31
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Doubling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 12?
Question 32
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Tripling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 24?
Question 33
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Quadrupling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 24?
Question Group 12
Question 34
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Doubling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 24?
Question 35
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Tripling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 36?
Question 36
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Quadrupling the value of X causes the value of Y to …
What would be the value of Y when the value of x is 32?
Question Group 13
Question 37
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Doubling the value of X causes the value of Y to …
What would be the value of Y for a value of X of 32?
Question 38
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Tripling the value of X causes the value of Y to …
What would be the value of Y for a value of X of 12?
Question 39
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Quadrupling the value of X causes the value of Y to …
What would be the value of Y for a value of X of 32?
Question Group 14
Question 40
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Doubling the value of X causes the value of Y to …
What would be the value of Y for a value of X of 12?
Question 41
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Tripling the value of X causes the value of Y to …
What would be the value of Y for a value of X of 18?
Question 42
Observe the data at the right. What type of relationship describes this data?
Complete the following statement so that it is consistent with the data:
Quadrupling the value of X causes the value of Y to …
What would be the value of Y for a value of X of 16?