Getting Started |
Misconception/Error The student has an operational view of the equal sign. |
Examples of Student Work at this Level The student says both equations are false because 29 â€“ 5 does not equal 31 (the number just to the right of the equal sign in the first equation) and 42 â€“ 7 does not equal 39 (the number just to the right of the equal sign in the second equation). |
Questions Eliciting Thinking What does the equal sign mean?
Show the student the equations 23 = 23 and 17 = 21 â€“ 4. Ask the student if the equations are true or false.
I see that you did not consider the number seven to the right of the equal sign. Should we just ignore this number? |
Instructional Implications Consider using the MFAS task True or Not True (1.OA.4.7) which provides insight into the studentâ€™s understanding of the equal sign.
Provide explicit instruction on the meaning of the equal sign. Use base ten blocks to show that quantities on the left and right sides of the equal sign must have the same value. Then provide the student with subtraction equations that contain a missing number, n, such as 23 â€“ 2 = n â€“ 5. Model for the student how to determine the value of one side of the equation and then use that value to determine the unknown quantity on the other side of the equation. Eventually, model comparative relational thinking to solve equations using base ten blocks. |
Moving Forward |
Misconception/Error The student has a relational understanding of the equal sign but is unable to use comparative relational thinking to determine if the equations are true. |
Examples of Student Work at this Level The student understands that the two quantities on each side of the equal sign must have the same value. However, the student needs to calculate 29 â€“ 5 and then 31 â€“ 7 in order to determine if the equation is true or false. |
Questions Eliciting Thinking You have a good understanding of the meaning of the equal sign. Could you determine if the equations are true by comparing the numbers on each side of the equation?
How does 29 compare to 31? How does 5 compare to 7? |
Instructional Implications Model for the student how to use comparative relational thinking to determine if the equations are true. Show the student two numbers on the number line. Demonstrate how the difference (or distance) between them remains the same when both numbers are translated up or down the same distance on the number line. Apply this demonstration to the expression 29 â€“ 5. Make explicit that when 29 is increased by two, then five must also be increased by two in order for the difference between the two numbers to remain the same. Provide the student with additional practice in using comparative relational thinking. Encourage the student to explain his or her thinking to other students.
Provide opportunities for the student to hear the explanations of Got It level students using comparative relational thinking to determine if equations relating two differences are true. |
Almost There |
Misconception/Error The student attempts to use comparative relational thinking but makes errors. |
Examples of Student Work at this Level The student attempts to use comparative relational thinking but makes an error or becomes confused. For example, the student says, â€śSince 29 is two less than 31, five should be two more than seven.â€ť |
Questions Eliciting Thinking If 29 is two less than 31, then what needs to be true of the subtrahends in order for the equation to be true?
If 42 is three more than 39, then what needs to be true of the subtrahends in order for the equation to be true? |
Instructional Implications Assist the student in identifying the error in his or her reasoning. Show the student two numbers on the number line. Demonstrate how the difference (or distance) between them remains the same when both numbers are translated up or down the same distance on the number line. Apply this demonstration to the expression 29 â€“ 5. Make explicit that when 29 is increased by two, then five must also be increased by two in order for the difference between the two numbers to remain the same. Provide the student with additional practice in using comparative relational thinking. Encourage the student to explain his or her thinking to other students. |
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 determines that the first equation is true and explains that since 29 is two less than 31 and five is two less than seven, the equation is true. The student also says that the second equation is false because 42 is three more than 39 but seven is not three more than 14. |
Questions Eliciting Thinking In the second equation, how much larger is the expression on the left than the expression on the right?
What symbol can replace the equal sign to make the second equation true?
What number could be changed in order to make the second equation true? Is there another way to change a single number to make the second equation true? |
Instructional Implications Consider using the MFAS task Comparative Relational Thinking in a Subtraction Equation (4.OA.1.b).
Introduce equations involving multiplication such as 36 x 7 = 12 x 21 or 28 x 6 = 14 x 8. Ask the student to use comparative relational thinking to determine if the equations are true or false. |