Task 4.
Summary of Student Performance Chart
List the categories of evaluative criteria as well as the corresponding characteristics of student work and the percent of students in the class at levels of performance that
increase in quality. This chart is designed to be completed electronically, so the blank space does not represent the space needed. Use as much space and as many rows as you
need.
Questions 1-4
Evaluative Criteria
Write a power of 10 having a positive
exponent in standard form
(question #1)
Write powers of 10 having a negative
exponent in standard form
(question #2)
Write a number greater than or equal
to 10 as a power of 10
(question #3)
Performance Level 1
Actual Student Work
Performance Level 2
Performance Level 3
0 points
½ point
1 point
Student wrote the standard form
incorrectly by placing five zeros after
the 1 rather than four.
Student wrote the product form of the
power of 10 rather than the standard
form.
Students wrote 104 in standard form
correctly, as 10,000. They wrote four
zeros after the 1.
8% of the class
(1 student)
8% of the class
(1 student)
84% of the class
(11 students)
Student wrote the standard form
incorrectly by placing five zeros after
the decimal point rather than six.
Student wrote the product form of the
power of 10 rather than the standard
form.
Students wrote 10-7 in standard form
correctly, as 0.0000001. They wrote six
zeros after the decimal point.
8% of the class
(1 student)
8% of the class
(1 student)
84% of the class
(11 students)
Student wrote the power of 10
incorrectly as 105 rather than 106.
n/a
Students wrote 1,000,000 as a power of
10 correctly, 106. They counted the
correct number of zeros after the 1.
8% of the class
(1 student)
0% of the class
(no students)
Student #1 wrote the power of 10
incorrectly as 10-12 rather than 10-11.
Write a number less than or equal to 1
as a power of 10
Student #2 wrote the power of 10
incorrectly as 1011 rather than 10-11.
(question #4)
15% of the class
(2 students)
n/a
0% of the class
92% of the class
(12 students)
Students wrote 0.00000000001 as a
power of 10 correctly, 10-11. They
counted the correct number of zeros
after the decimal point and added one
to this value to arrive at the correct
exponent.
85% of the class
(11 students)
Questions 5-13
Evaluative Criteria
Write a number greater than or equal
to 10 in scientific notation
(question #5)
Write a number less than or equal to 1
in scientific notation
(question #6)
Performance Level 1
Actual Student Work
Performance Level 2
0 points
1 point
2 points
n/a
Student wrote the number in scientific
notation incorrectly as 31.426 × 10-2
rather than
3.1426 × 103. She didn’t move the
decimal enough places to the left and
wrote the wrong power of 10.
Students wrote 3,142.6 in scientific
notation correctly, as 3.1426 × 103.
They converted a number, 3142.6, from
standard form to scientific notation by
moving the decimal point three places
to the left and multiplying by 103.
8% of the class
(1 student)
92% of the class
(12 students)
Students wrote 10-7 in standard form
correctly, as 0.0000001. They converted
a number, 0.0123456, from standard
form to scientific notation by moving
the decimal point two places to the right
and multiplying by 10-2.
0% of the class
(no students)
n/a
0% of the class
(no students)
Student wrote the number in scientific
notation incorrectly as 1.23456-2 rather
than 1.23456 × 10-2. She forgot the
multiplication sign and the power of 10
altogether.
8% of the class
(1 student)
Student #1 wrote the number in
standard form incorrectly as 425,000
rather than 4,250. She moved the
decimal too many places to the right.
Write a number that is given in
scientific notation in standard form
(question #7)
n/a
Student #2 wrote the number in
standard form incorrectly as 4,070. She
attempted to multiply 4.25 by 1,000 and
made a mistake in calculation.
0% of the class
(no students)
(question #8)
92% of the class
(12 students)
Students wrote 4.25 × 103 correctly, as
4,250. They converted a number,
4.25 × 103, from scientific notation to
standard form by moving the decimal
point to the right three places and
omitting the power 103.
85% of the class
(no students)
15% of the class
(2 students)
Write a number that is given in
scientific notation in standard form
Performance Level 3
n/a
n/a
0% of the class
(no students)
0% of the class
(no students)
Students wrote
5.3 × 10-5 correctly, as 0.000053. They
converted a number, 5.3 × 10-5, from
scientific notation to standard form by
moving the decimal point to the left five
places and omitting the power 10-5.
100% of the class
(13 students)
Evaluate a numerical expression
containing zero exponents
(question #9)
Student evaluated the power of zero as 1 rather than 1.
8% of the class
(1 student)
Students evaluated (-5)0 correctly, as 1.
They applied the zero exponent rule
correctly.
n/a
0% of the class
(no students)
92% of the class
(12 students)
Students evaluated 5-2 correctly, as
Evaluate a numerical expression with
an integer base containing a negative
exponent
(question 10)
Evaluate a numerical expression with a
fractional base containing a negative
exponent
(question 11)
n/a
n/a
0% of the class
(no students)
0% of the class
(no students)
Student evaluated 5-2 incorrectly as 2
rather than 4. He applied the exponent
to the denominator only rather than
applying the exponent to both the
numerator and denominator.
rather than 5 . He
x6
5x
moved the 5 to the denominator rather
than leaving it in the numerator. He
also omitted the negative.
Simplify an algebraic expression with
negative exponents by rewriting it using
only positive exponents
(question 12)
0% of the class
(no students)
92% of the class
(12 students)
Students simplified 5x 6 correctly,
as 5 . They moved only the x term
6
(question 13)
x6
n/a
containing the negative exponent to the
denominator.
0% of the class
(no students)
92% of the class
(12 students)
8% of the class
(1 student)
n/a
0% of the class
(no students)
.
100% of the class
(13 students)
Students evaluated (½)-2 correctly, as 4.
They took the reciprocal of the fraction,
changed the negative exponent to a
positive exponent, and applied that
exponent to both the numerator and the
denominator.
n/a
Student #1 wrote
Simplify an algebraic expression with
negative exponents by rewriting it using
only positive exponents
25
They wrote the power as a denominator
over 1, changed the negative exponent
to a positive exponent, and evaluated
the power.
8% of the class
(1 student)
Student wrote 1
1
x 11
25
rather than
25
.
x 11
She moved the 25 to the denominator
rather than leaving it in the numerator.
She correctly moved the power from the
denominator to the numerator.
Student #’s 2, 3, and 4 made the same
mistake that student #1 made.
31% of the class
(4 students)
Students simplified
25
x 11
correctly, as
25x 11 . They moved only the x term
containing the negative exponent to the
numerator.
69% of the class
(9 students)
Question 14
Evaluative Criteria
Performance Level 1
0 points
Actual Student Work
Performance Level 2
Performance Level 3
1 point
2 points
Performance Level 4
3 points
Student #1 omitted a single
power from the solution. She
correctly simplified all other
portions of the expression.
Simplify an algebraic
expression with negative
exponents by rewriting it using
only positive exponents
(question #14)
Student simplified the expression
incorrectly. He moved everything
from the numerator to the
denominator and vice versa.
8% of the class
(1 student)
Student simplified portions of
the expression incorrectly.
She changed the powers with
negative exponents to powers
with positive exponents and
did not move their positions
across the fraction bar. She
correctly kept the constants
and powers with positive
exponents in their original
positions.
8% of the class
(1 student)
Student #2 made the same
mistake that student #1 made,
but omitted a different power.
Student #3 omitted an
exponent on a single power
and inserted a negative on a
different power in which it did
not belong. He correctly
simplified all other portions of
the expression.
Student #4 wrote all powers
with negative exponents as
fractional powers with positive
exponents in both the
numerator and the
denominator. She applied the
rule correctly, but did not
simplify completely.
31% of the class
(4 students)
4 3 6
Students simplified 5x y z
6a 2b 5c 9
correctly, as
5a 2y
6x 4b 5c 9z 6
.
They moved the powers with
negative exponents in the
numerator to the
denominator, moved the
powers with negative
exponents in the denominator
to the numerator, and wrote
them as powers with positive
exponents.
54% of the class
(7 students)