Exemplars
Taco Spread
Mrs. Smith is getting ready for her family to go on
summer vacation. She decided that she needs to use
up any leftovers that are in the refrigerator or throw
them out. She discovered that she has 12 ounces of
cream cheese that she would like to use to make a
taco spread for her family. Mrs. Smith has dug out a
recipe but is stumped as to how much of each
ingredient she must include if she is going to use
up all of the cream cheese that she has in the
refrigerator. Help her determine the amount of each
of the other ingredients she should use.
Taco Spread Recipe
8 ounces cream cheese
8 ounces sour cream
1 jar (12 ounces) taco sauce
1 cup cheddar cheese, shredded
1/2 cup chopped tomato
1/2 cup chopped green pepper
1/2 cup black olives
Exemplars
TM
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Taco Spread
- Page 1 -
Exemplars
Grade Level 3–5
Taco Spread
Mrs. Smith is getting ready for her family to go on summer vacation. She decided that she
needs to use up any leftovers that are in the refrigerator or throw them out. She discovered
that she has 12 ounces of cream cheese that she would like to use to make a taco spread for
her family. Mrs. Smith has dug out a recipe but is stumped as to how much of each
ingredient she must include if she is going to use up all of the cream cheese that she has in
the refrigerator. Help her determine the amount of each of the other ingredients she should
use.
Taco Spread Recipe
8 ounces cream cheese
8 ounces sour cream
1 jar (12 ounces) taco sauce
1 cup cheddar cheese, shredded
1/2 cup chopped tomato
1/2 cup chopped green pepper
1/2 cup black olives
Context
This problem was developed for this particular group of fourth–graders after they had
experience with measurement. We had engaged in several introductory activities that
focused on measurement models and how each measurement was related to ounces, etc. Our
class even got involved into some cooking activities. The students have had a lot of
experience with leaving for vacations and/or the summer as they are at an international
school, so this problem was one to which they could easily relate.
What This Task Accomplishes
This task measures how well the students are able to see relationships between the increasing
of one ingredient in proportion to another.
What the Student Will Do
Many students create a chart to solve the task. Some use purely a computational approach,
while others may need to draw pictures or use diagrams to visualize a solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Taco Spread (cont.)
- Page 2 -
Exemplars
Time Required for Task
One or two 45 minute periods.
Interdisciplinary Links
This task obviously links well to family and consumer sciences. It could also link to a unit on
food. Children’s books that would complement the task well include What’s Cooking Jenny
Archer? by Ellen Clifford, Eating Fractions by Bruce McMillan, and Fiesta! Mexico’s Great
Celebrations by Elizabeth Silverthorne.
Teaching Tips
I did several introductory activities that involved using measuring cups. I recommend
spending some time talking about relationships between numbers (ratios). Most children that
made errors did so because they did not clearly see the ratio of 8 to 12 for the first ingredient,
and therefore did not get the complete recipe correct. Experience with IN/OUT machines
could also be helpful in getting students to practice analyzing the relationships between
numbers.
Suggested Materials
Measuring cups, fraction manipulatives, graph paper, calculators
Possible Solutions
Since Mrs. Smith has 12 ounces of cream cheese, and the recipe calls for 8, she has 4 ounces
more than the recipe calls for. This would allow her to make an additional half of a recipe.
The ingredients would be as follows:
Modified Taco Spread Recipe
12 ounces cream cheese
12 ounces of sour cream
1 /2 jar (18 ounces) taco sauce
1 1/2 cup cheddar cheese, shredded
3/4 cup chopped tomato
3/4 cup chopped green pepper
3/4 cup black olives
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Taco
Spread (cont.)
- Page 3 -
Exemplars
Benchmark Descriptors
Novice
The novice will show that the student had little sense of how to go about solving this task.
The explanation will be weak and will leave a lot of gaps in what was going on inside this
student’s head. The use of math language will not be evident in this work, and no math
representations will be attempted.
Apprentice
The apprentice will show some understanding of the task. The apprentice will be able to
come up with a strategy that works for part of the problem. Some math language will be
used, and representations will be attempted.
Practitioner
The practitioner will show a thorough understanding of the problem and the use of an
approach that works for solving the problem entirely. The student’s explanations will be clear
and won’t leave the reader wondering why the student made the decisions that were made.
Math language will be used throughout, and accurate math representations will be present.
Expert
The expert will use a sophisticated approach to solving the task. Sophisticated math language
will be used, and math representations will be accurate and appropriate. The expert will
make mathematically relevant observations and connections about the solution.
Author
Shawn Parkhurst is currently teaching at the Canadian Academy in Kobe, Japan. He
previously taught at Williston Central School in Williston, Vermont where he also served as
their assessment coordinator, in addition to serving as a math portfolio network leader.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Taco Spread (cont.)
- Page 4 -
Exemplars
Novice
The student explains
an incorrect approach.
Some math language
is attempted.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The student has
a completely
incorrect solution.
The solution lacks
mathematical reasoning.
Taco Spread (cont.)
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Exemplars
Apprentice
A math representation
is attempted.
The apprentice uses
logical reasoning for
some parts of the task.
The student has no
approach for reasoning
proportionally.
Accurate math
language is used.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Taco Spread (cont.)
- Page 6 -
Exemplars
Practitioner
All work
is shown.
Diagrams explain
reasoning.
Accurate math
language is used.
The correct answer
is achieved.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Taco Spread (cont.)
- Page 7 -
Exemplars
Expert
The student explains
the approach used.
The student achieves
a correct solution.
An accurate chart is
created but could be
better organized.
The student makes a
mathematically relevant
observation about
the difference in the
two recipies.
The student makes
another relevant
observation.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Taco Spread (cont.)
- Page 8 -