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Balanced Assessment Test –Eighth Grade 2007
Core Idea
Task
Score
Triangle
Geometry
This task asks students to read and interpret clues about geometric attributes of a
triangle to find the side lengths. Students needed to understand geometric terms, such
as, perimeter, equilateral triangle, and isosceles triangle. Students also needed to
understand number properties, such as prime number, single digit, and ratio.
Successful students could find a solution that met all of the clues and that would make
a closed triangle.
Measurement
Rugs
This task asks students to work with perimeter and circumference of squares,
triangles, and circles. Students were given the formula for circumference to help
them with the calculations. Students needed to make conversions from feet and inches
to feet or inches. Students also needed to find the perimeter of a semi-circle and
explain why it is not the same as half the circumference. Successful students could
use Pythagorean theorem to find the side length of an isosceles triangle and use that
length to find the perimeter.
Number Calculations
Algebra
This task asks students to explore the order of number operations by creating
examples to fit a set of conditions and test those conditions by calculating the answers
to their examples. Successful students could calculate accurately with negative
numbers and understand division with decimal answers. Students were then given a
set of algebraic representations for the relationships that they had investigated and
asked to decide which were true.
Shelves
Functions
This task asks students to work with a pattern of growing shelves, made up of boards
and bricks. Students needed to use spatial thinking to find the number of boards and
bricks needed, determine the height, and find the cost of the bookcase. Successful
students realized that the height would include the bricks and the thickness of the
boards. Students were also asked to look at a graph of the four functions in the
pattern (cost, number of bricks, height, and width) and match the points on the graph
with descriptions and their equations. Successful students could match the verbal
description to the equation.
Take Off
Number
This task asks students to work with speed, time, and distance in the context of an
Indy car race and a rocket launch. Students needed to be able to convert units of
measure and work with rates. Successful students could work with a rate in either
kilometer per second or meters per second to find the distance traveled given an
amount of time or to find the time given the distance.
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The maximum score available for this task is 8 points.
The minimum score needed for a level 3 response, meeting standards, is 4 points.
More than half the students, 56%, could show evidence of using two of the clues; usually
perimeter and a drawing indicating not an equilateral or not an isosceles triangle. Less than half
the students , 40%, could either satisfy all 6 clues but not make a closed figure or satisfy 5 clues
and make a closed figure, with no explicit use of clues or satisfy 5 clues without making a closed
figure or satisfy 4 clues with a closed figure and show evidence of using at least 2 clues. Some
students, about 20 % could either show a correct solution with no work or satisfy all 6 clues but
not make a closed figure or satisfy 5 clues and make a closed figure with evidence of using 3 or
more clues. 44% of the students scored no points on this task. 57% of the students with this score
attempted the task.
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The maximum score available on this task is 8 points.
The minimum score for a level 3 response, meeting standards, is 3 points.
Many students, about 60%, could find the perimeter of a rectangle. Only 18% of the
students could meet standard on this task usually getting the area of the rectangle and
finding the circumference of a circle rounded to the nearest whole number. About 10%
could also explain why the perimeter of a semi-circle is not half the circumference of a
circle. Less than 1% of the students could meet all the demands of the task including
using Pythagorean theorem to find the side length of an isosceles triangle, find the
perimeter of a semicircle, and round the circumference of a circle to the nearest whole
number. Almost 41% of the students scored no points on this task. 91% of the students
with this score attempted the task.
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The maximum score available for this task is 8 points.
The minimum score for a level 3 response, meeting standards, is 4 points.
Most students, about 90%, could use algebraic symbols for commutative property of
addition and multiplication and recognize that the symbols for division were incorrect.
Many students, almost 69%, could give examples for addition and for subtraction
quantifying the answers even when negative and give 3 or 4 solutions on the table.
Almost 50% of the students could meet all the requirements of the task except make the
subtraction generalization and mark the subtraction with parentheses correctly. 9% of the
students scored no points on this task. All of the students in the sample with this score
attempted the task.
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The maximum score available on this task is 8 points.
The minimum score needed for a level 3 response, meeting standards, is 4 points.
Most students, 83%, could either find the cost of the boards or match two or three items
on the table. Less than half the students, 44%, could find the boards, bricks, and cost and
match two or 3 items on the table. About 12% could match all the representations
between graph, equations and descriptors and find boards, bricks, and cost of the
bookshelf. Almost 5% could meet all the demands of the task, including finding the
height of the bookshelves. Almost 17% of the students scored no points on this task. 75%
of the students with this score attempted the task.
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The maximum score available on this task is 8 points.
The minimum score available for a level 3 response, meeting standard, is 3 points.
Some students, about 21% were able to make the conversion from kilometers per second
to kilometers per hour or convert kilometers per hour to kilometers per second. About
12% were able to use this information to find out how many times faster the space rocket
is than the Indy car. About 2% of the students could also reason how long it would take
to hear something from 3.5 kilometers, including converting between kilometers and
meters before making the comparison. Less than 1% of the students could talk about the
difference in speed of light compared to sound. Almost 79% of the students scored no
points on this task. 68% of the students with this score attempted the task.
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Five areas stood out for the Collaborative for 8th grade. These included:
1. Making and Interpreting Diagrams – Students could not interpret the diagrams in
Rugs. They did not distinguish between the height and the side measure in the
triangle. They were unsure of the difference between a diameter and a radius
when looking at the circle diagram. Many did not make diagrams to help them
think about cutting a circular rug in half. In triangles, many students drew
equilateral or isosceles triangles as a generic iconic model for all triangles. These
models may limit the types of thinking students do in trying to find solutions to
problems. In Shelves, many students interpreted the diagram as a picture for a
partially made book shelf. Students did not consider drawing a diagram for the
whole book case as a thinking tool for solving the problem. Students did not
consider the dimensions of all the parts of the diagram when trying to calculate
height.
2. Converting between Measurements – Many students incorrectly converted
between measurement notation and decimal notation in Rugs. Students had
difficulty converting between time measurements or distance measurements in
Take Off.
3. Significant Digits/ Level of Accuracy – In both Rugs and Take Off students did
not round answers. Many students want to use all the digits that appear on their
calculators implying a level of accuracy or precision not justified by the context
or instruments used for original measurements.
4. Relating symbolic notation to context – Students had difficulty matching the
symbolic generalizations in Number Calculations with their investigations and
generalizations in the earlier part of the task. Students could match the graph to
the equations in Shelves, but struggled when trying to match either the graph or
the equation to a description of the context being represented.
5. Comparisons – Students struggled with the idea of making a comparison. They
didn’t understand that the units needed to be the same in order to compare ideas.
Some students tried to make an absolute comparison, how much larger, using
subtractions; rather than making a multiplicative or relative comparison, how
many times larger is a than b.
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