Filling up on Apples is a problem created for fifth graders on fraction addition and comparing fractions. In the task, two people eat multiple fraction amounts of apples and students are to use equivalent fractions and knowledge of fraction addition to determine how many apples were eaten. Scaffolding is used to break down the fractions and allow students to work on the problem one step at a time. Students are asked, through argumentation language, to critique the response on who ate more apples and show justification.
Microsoft Word version: 5_NF_FractionsAdditionComparing_Problem_Critique_FillingUpOnApples
PDF version: 5_NF_FractionsAdditionComparing_Problem_Critique_FillingUpOnApples
I used this task in my 5th grade classroom. It involves adding three fractions with unlike denominators. When the fractions are added, the sum is greater than one. The students also need to compare two mixed numbers to decide which mixed number is greater. The task requires them to decide who ate the most pie based on their comparison of two mixed numbers.
Microsoft Word version: 5_NF_FractionsAdditionComparing_Problem_Critique_EatingPies
PDF version: 5_NF_FractionsAdditionComparing_Problem_Critique_EatingPies
Stuffed with Pizza is a problem created for fifth graders on fraction addition. In the task, two people eat multiple fraction amounts of pizza and students are to use equivalent fractions and knowledge of fraction addition to determine how much pizza was eaten. Scaffolding is used to break down the fractions and lead up to the final question, which contains argumentative language as it asks students to critique the given response on who ate more pizza.
Microsoft Word version: 5_NF_FractionsAddition_Problem_Critique_StuffedWithPizza
PDF version: 5_NF_FractionsAddition_Problem_Critique_StuffedWithPizza
Lots of Pizza is a task in which fifth grade students must critique student responses to how much pizza was eaten by adding fractions of the whole. Students must be able to add three fractions with different denominators and determine if the value is equivalent to the addition of two fractions with different denominators. The task asks students to agree or disagree with student claims and explain reasoning.
Microsoft Word version: 5_NF_FractionsAddition_Problem_Critique_LotsOfPizza
PDF version: 5_NF_FractionsAddition_Problem_Critique_LotsOfPizza
Friends Who Run is a fraction addition problem designed for fifth grade. Students are given two people whose runs in a day are represented as fractions and are asked to mark distances on a number line, find the total number of miles run per person, and determine the difference between the two distances. Argumentation language is used, as well as scaffolding, to invoke the use of a claim and evidence in the critiquing the problem.
Microsoft Word version: 5_NF_FractionsAddition_Problem_Critique_FriendsWhoRun
PDF version: 5_NF_FractionsAddition_Problem_Critique_FriendsWhoRun
This task is designed for fifth graders working on fraction fluency. Students must know the vocabulary term “sum” and be able to add fractions, as they are asked to find the sum of two fractions with different denominators. Students must be able to determine if the fraction is closer to a half or whole by rounding, as well. Finding common denominators, creating equivalent fractions, and adding fractions are all skills necessary to complete this task. The problem allows space to solve as well as lines to justify a critique of student work.
Microsoft Word version: 5_NF_FractionsAddition_Problem_Construct
PDF version: 5_NF_FractionsAddition_Problem_Construct
Sharing Candy Bars Part 2 is an extension to Sharing Candy Bars, which is a fractions task designed for fifth graders with strong regards to mathematical standards. Students are asked if it is fair to divide a certain amount of candy bars amongst different amounts of people. Through pair and large group discussions, students critique each scenario, determine what fraction of candy bars each member receives, and identify the fairness.
Microsoft Word version: 5_NF_Fractions_ProblemLesson_Critique_SharingCandyBarsPart2
PDF version: 5_NF_Fractions_ProblemLesson_Critique_SharingCandyBarsPart2
Sharing Candy Bars Part 1 is a task designed for fifth grade students with strong skills in fractions and decimals. Students are given different scenarios in which candy bars are split amongst people. For example, 3 candy bars are split amongst 4 people, and 4 candy bars are split amongst 5 people. Students must use problem solving skills to decide how these candy bars would be divided equally. Students are asked to identify if the amount of candy bar that each person receives is fair. The task recommends use of manipulatives and provides a detailed outline and lesson plan for teachers to use, but offers a lot of freedom for students. Partner work is recommended, and the task can open the class to many discussions on problem solving methods.
Microsoft Word version: 5_NF_Fractions_ProblemLesson_Critique_SharingCandyBarsPart1
PDF version: 5_NF_Fractions_ProblemLesson_Critique_SharingCandyBarsPart1
In Breaking Apart a Candy Bar, fifth-grade students are given a problem on fractions. Students are asked if they agree that when four equal sections are split equally in half, then there are eight equal sections. Students must critique the given response and create a claim and provide evidence as to why they agree or disagree.
Microsoft Word version: 5_NF_Fractions_Problem_Critique_BreakingApartACandyBar
PDF version: 5_NF_Fractions_Problem_Critique_BreakingApartACandyBar
This is a task from Illustrative Mathematics. The students constructed an argument that described how they found equivalent fractions. The directions for this task were slightly modified for my fifth grade students. My fifth grade students we asked to come up with no more than six equivalent fractions for each of the diagrams on part b. Beyond what is already stated this task also met CSSSM:CCSS.MATH.CONTENT.4.NF.A.1:
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b)
by using visual fraction models, with attention to how the number and
size of the parts differ even though the two fractions themselves are
the same size. Use this principle to recognize and generate equivalent
Microsoft Word version: 5_NF_Fractions_Problem_Construct_IllustrativeMathematics
PDF version: 5_NF_Fractions_Problem_Construct_IllustrativeMathematics