Hot Dogs for a Picnic
Mrs. Richards is planning a picnic for many of her relatives.
Everyone coming to the picnic wants to eat hot dogs. Mrs.
Richards knows that hot dogs at the local store are sold 10 in a
package. The hot dog rolls are sold 8 in a package.
What is the least number of packages of hot dog and hot dog
rolls Mrs. Richards can buy to have exactly the same amount of
hot dogs and rolls?
Mrs. Richards discovers that 30 relatives are coming to the
picnic and every one wants to eat 2 hot dogs! What is the least
number of packages of hot dogs and hot dog rolls that Mrs.
Richards will have to buy to feed all her relatives?
Hot Dogs for a Picnic
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Hot Dogs for a Picnic
Suggested Grade Span
3–5
Grade(s) in Which Task Was Piloted
4
Task
Mrs. Richards is planning a picnic for many of her relatives. Everyone coming to the picnic
wants to eat hot dogs. Mrs. Richards knows that hot dogs at the local store are sold 10 in a
package. The hot dog rolls are sold 8 in a package.
What is the least number of packages of hot dog and hot dog rolls Mrs. Richards can buy to
have exactly the same amount of hot dogs and rolls?
Mrs. Richards discovers that 30 relatives are coming to the picnic and every one wants to eat 2
hot dogs! What is the least number of packages of hot dogs and hot dog rolls that Mrs.
Richards will have to buy to feed all her relatives?
Alternative Versions of Task
More Accessible Version:
Give the first part of the task only.
More Challenging Version:
Mrs. Richards is planning a picnic for many of her relatives. Everyone coming to the picnic
wants to eat hot dogs. Mrs. Richards knows that hot dogs at the local store are sold 10 in a
package. The hot dog rolls are sold 8 in a package.
What are three ways Mrs. Richards can buy packages of hot dog and hot dog rolls so she has
exactly the same amount of hot dogs and rolls?
Mrs. Richards discovers that 30 relatives are coming to the picnic and every one wants to eat 2
hot dogs! What is the least number of packages of hot dogs and hot dog rolls that Mrs.
Richards will have to buy to feed all her relatives?
Hot Dogs for a Picnic
Copyright 2008, Exemplars, Inc. All rights reserved.
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NCTM Content Standards and Evidence
Number and Operations Standard for Grades 3–5: Instructional programs from prekindergarten through grade 12 should enable students to ...
Understand numbers, ways of representing numbers, relationships among numbers and
number systems.
• NCTM Evidence: Describe classes of numbers according to characteristics of their factors.
• Exemplars Task-Specific Evidence: This task requires students to find the least common
multiple of eight and 10.
Compute fluently and make reasonable estimate.
• NCTM Evidence: Develop fluency in adding, subtracting, multiplying and dividing whole
numbers.
• Exemplars Task-Specific Evidence: This task requires students to add the number of
rolls and hot dogs till they reach a target sum.
Time/Context/Qualifiers/Tip(s) From Piloting Teacher
This is a short- to medium-length task. This is a good task to use as an assessment after
lessons on common multiples.
Links
This task can be used before or after holidays or celebrations at school.
Common Strategies Used to Solve This Task
Many students kept a running total of the number of hot dogs and rolls and checked for their
target sums.
Possible Solutions
The Least Common Multiple of 8 and 10 is 40.
4 packages of hot dogs x 10 = 40 hot dogs
5 packages of rolls x 8 = 40 rolls
6 packages of hot dogs x 10 = 60 hot dogs
8 packages of rolls x 8 = 64 rolls
Hot Dogs for a Picnic
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More Accessible Version Solution:
Same as the first part of original solution.
More Challenging Version Solution:
The Least Common Multiple of 8 and 10 is 40.
4 packages of hot dogs x 10 = 40 hot dogs
5 packages of rolls x 8 = 40 rolls
Other common multiples of 8 and 10 are 80, 120, etc.
8 packages of hot dogs x 10 = 80 hot dogs
10 packages of rolls x 8 = 80 rolls
12 packages of hot dogs x 10 = 120 hot dogs
15 packages of rolls x 8 = 120 rolls
6 packages of hot dogs x 10 = 60 hot dogs
8 packages of rolls x 8 = 64 rolls
Task-Specific Assessment Notes
General Notes
This is a good task to see if students recognize that they are working with multiples and factors.
Novice
The Novice will not be able to successfully engage in a strategy that will give a correct number
of packages of hot dogs and rolls. There will be no mathematical language and if there is a
drawing or representation, it will not represent the mathematics of the task.
Apprentice
The Apprentice will have a strategy that will work but may make an error in computation. They
may be able to solve part of the task but not all of the task. The representation may not be
labeled and there is one mathematical language term. An Apprentice may find a correct solution
to all of the parts of the task but an observation or connection will not be made.
Practitioner
The Practitioner will have the correct number of packages of hot dogs and rolls for each part of
the solution. All the supporting work needed to communicate their strategy and mathematical
reasoning will be present. At least two mathematical terms will be used and a connection or
observation about the task or solution will be made. An accurate and appropriatemathematical
representation will be constructed.
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Expert
The Expert will achieve a correct solution. Evidence will be used to justify and support decisions
made and conclusions reached, for example by solving the task in more than one way to verify
the solution. A sense of audience and purpose is communicated by using precise mathematical
language to consolidate mathematical thinking and to communicate ideas. Mathematical
connections or observations are made and mathematical representation will be used to extend
thinking and clarify or interpret the solution.
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Novice
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Apprentice
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Practitioner
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Practitioner
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Practitioner
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Expert
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Expert
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Expert
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