I used this task to continue our 5th grade discussion about multiplying fractions. Prior to this talk frame, our class discussed the difference between multiplying whole numbers and multiplying fractions, and explored why fractions multiplied together result in a fraction that contains smaller pieces. Students struggled with the deeper conceptual understanding of why, and this talk frame supported that discussion.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Construct_AngelasIdea
PDF version: 5_NF_FractionsMultiplication_Problem_Construct_AngelasIdea
Dot Pattern is a scaffolded task in which students must create an expression to represent the number of dots in a figure at any given point in a pattern. Students are given a visual representation of the first three figures and asked to think about how the figures change each time, and how the next figures would look. Ultimately, students will generate an algebraic expression to represent any figure. Students must construct an argument in order to explain why an expression works and where it comes from.
Microsoft Word version: 5_OA_AlgebraPatterns_Problem_Construct_DotPattern
PDF version: 5_OA_AlgebraPatterns_Problem_Construct_DotPattern
Getting There is a problem created for fifth graders on adding numbers in different combinations. Students are given a distance a frog hops in three hops and a set of questions asking them about three numbers that will add up to the distance. The task provides a variation to include more argumentation language, specifically to explain their thinking, as they construct a response.
Microsoft Word version: 5_OA_AdditionCombinations_Problem_Construct_GettingThere
PDF version: 5_OA_AdditionCombinations_Problem_Construct_GettingThere
Making Hot Cocoa is a task on fraction multiplication and division for a fifth-grade classroom. Students are given a certain amount of cocoa powder and the fraction amount needed for each cup. Through a series of questions containing argumentative language, students are asked to construct a response to how many cups of cocoa they can make. Students are to construct a solution through a variety of methods, including pictures, mental thought, multiplication, and division. Sample solutions and commentary are provided.
Microsoft Word version: 5_NF_FractionsMultiplicationDivision_Problem_Construct_MakingHotCocoa
PDF version: 5_NF_FractionsMultiplicationDivision_Problem_Construct_MakingHotCocoa
This task was used with 4th and 5th graders because it focused on multiplying fractions by whole numbers and converting common measurements. The main objective was to use a real world situation so that students would develop a deeper understanding of multiplying fractions by whole numbers as well as converting ounces and cups.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Construct
PDF version: 5_NF_FractionsMultiplication_Problem_Construct
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
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
Birthday Balloons is a problem created for fifth graders to explore fractions. At a party, each guest takes a different proportion of remaining balloons until only a few are left. Students are to determine a way to find the original amount of balloons and construct an argumentative response.
Microsoft Word version: 5_NF_Fractions_Problem_Construct_BirthdayBalloons
PDF version: 5_NF_Fractions_Problem_Construct_BirthdayBalloons