A Problem on the Prairie

Task

Mary and Laura walk on the prairie to visit Mrs. Peterson. Mrs. Peterson gives Mary a Swedish cookie and Laura a Swedish cookie to eat on their walk home. While walking home, Mary and Laura decide to wait and share their Swedish cookies with baby Carrie. How should Mary and Laura share their Swedish cookies so each girl gets a fair share of the Swedish cookies?

Alternate Versions of Task

More Accessible Version:

Mary and Laura walk on the prairie to visit Mrs. Peterson. Mrs. Peterson gives Mary and Laura one large Swedish cookie to eat on their walk home. While walking home, Mary and Laura decide to wait and share their Swedish cookies with baby Carrie. How should Mary and Laura share their Swedish cookies so each girl gets a fair share of the Swedish cookies?

More Challenging Version:

Mary and Laura walk on the prairie to visit Mrs. Peterson. Mrs. Peterson gives Mary 2 Swedish cookies and Laura 2 Swedish cookies to eat on their walk home. While walking home, Mary and Laura decide to wait and share their Swedish cookies with baby Carrie. How should Mary and Laura share their Swedish cookies so each girl gets a fair share of the Swedish cookies?

Context

This problem was built into a unit that focused on number sense, specifically fractions. The students had been introduced to fractions through the creation of fraction bars and then were engaged in numerous exploratory activities around fractions. This created the background knowledge that the students brought to this task.

What This Task Accomplishes

This task was challenging for most of my third and fourth grade students. It allows students to demonstrate competence with fractional parts of a whole and/or addition of fractions. Many students will solve this task by diagramming the fractional part of the cookies each girl receives.

What the Student Will Do

Many students will first use fraction circles or fraction bars to determine the fractional part of the cookies each girl should receive. Many students then diagram their understanding on paper. Many students use fraction equations to support their diagrams.

Time Required for Task

60 minutes

Interdisciplinary Links

This task was written to link to Little House on the Prairie, by Laura Ingalls Wilder. The task can also be linked to the study of Sweden and baking Swedish cookies.

Teaching Tips

Students may enjoy listening to a section of the book, Little House on the Prairie, by Laura Ingalls Wilder that references Mrs. Peterson. Consider having circle fractions sets or fraction bars available.

Suggested Materials

Fraction sets or fraction bars.

Possible Solutions

Each girl received 2/3 of one cookie or a total of 2/3 cookie from the two cookies.

More Accessible Version Solution:

Each girl receives 1/3 of the big cookie.

More Challenging Version Solution:

Each girl receives 1 1/3 cookies.

Task Specific Assessment Notes

Novice:
The Novice is unable to solve the task and might draw cookies on the paper or may diagram two cookies but show no conceptual understanding of fractional parts. The Novice does not communicate her/his understanding of mathematics, does not use any mathematical language or connections.

Apprentice:
The Apprentice does understand that fractional parts of two cookies needs to be considered but might not use the correct fractional part or might not find the fair share for three girls. The Apprentice attempts to communicate her/his reasoning but does not use more than one mathematical term. The Apprentice attempts a diagram or table to show the fractional part of the cookies each girl receives but the representation lacks a key, labels or displays incorrect fractional parts. The Apprentice attempts a connection but it is not a mathematically relevant observation.

Practitioner:
The Practitioner shows a correct strategy and reasoning that the cookies are fairly shared with each girl receiving 2/3 of the cookies. The Practitioner uses two or more mathematical terms which could include, but are not limited to, diagram, key, table, first, second, third..., whole, 1/2, 1/3, 1/4.... The Practitioner makes an appropriate and accurate diagram or table to support her/his solution. The Practitioner makes a connection(s) about her/his solution such as determining that using fourths as the fractional part of each cookie would not support a fair share or recreate the problem to have more cookies to include Ma and Pa in the fair share.


Expert:
The Expert meets all the criteria of the Practitioner and takes her/his reasoning further. The Expert uses consistent and precise mathematical language such as diagram, key, table, first, second, third..., whole, 1/2, 1/3, 1/4..., numerator, denominator, equivalent, lowest terms... The Expert could make a diagram to solve the problem and then the connection of verifying her/his solution by making a table to determine if the answer is correct. The Expert could also make the connection of showing equivalent fractions to determine that each girl could have 2/6 of the cookies or 3/9 of the cookies. The Expert could make the connection that each girl could have 1/2 of a cookie and 1/3 of the remaining half.

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