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
This problem was used by students after working visually and conceptually to explain division with fractions. They use this problem as a transition to dividing fractions using the mulitplicative inverse. Students benefitted from constructing a diagram that showed the fence sections. Constructing the diagram on graph paper, using 20 squares for the length helped students divide equally and find the fraction they needed. Explaining the connections between the diagram and the equation are very important for constructing the argument.
Microsoft Word version: 6_NS_FractionsDivision_Problem_Critique
PDF version: 6_NS_FractionsDivision_Problem_Critique
Fraction differences is a task designed for fifth graders to critique a comparison of two differences of fractions. The task highlights the skills of finding a common denominator, finding equivalent fractions, subtracting fractions, and comparing fractions. Students must agree or disagree with the student’s comparison of the differences, and explain his or her answer.
Microsoft Word version: 5_NF_FractionsSubtraction_Problem_Critique_FractionDifferences
PDF version: 5_NF_FractionsSubtraction_Problem_Critique_FractionDifferences
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
Turkish Delight is a task developed for fifth graders working on multiplication of fractions. Students must understand how to take a fraction of a fraction by using multiplication. Students are then asked to compare the resulting fraction with a given fraction and critique a student’s comparison. The task asks the student to explain reasoning. When making the comparison, students must either convert fractions to decimals, or find common denominators, because the fractions will have different denominators, which may be an area for discussion with the class.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_TurkishDelight
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_TurkishDelight
Harvesting Corn is a problem on fraction multiplication for fifth graders. Students are given the number of acres harvested and amount of days in a mixed number. The questions are scaffolded to require transformation of the mixed number to improper fraction, subtraction, and the final multiplication question that asks students to critique the thinking of a worker through argumentative language.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_HarvestingCorn
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_HarvestingCorn
This task is created for fifth-grade students learning how to multiply fractions. Students are asked to critique the statement that half of a quarter is the same as a quarter of a half through multiple questions allowing for the problem to be visualized and broken down. A modification to the problem is presented to contain specific argumentation language, including as claim and evidence.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_5-11
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_5-11
This is a task designed for fifth graders learning how to multiply mixed numbers. Students are asked to critique a student’s strategy to multiply mixed numbers, which ends up addressing a common misconception in multiplication of mixed numbers. Students must determine if adding the product of the whole numbers to the product of the fractions is equal to multiplying the two mixed numbers. Students are asked to decide if this is a rule that works, and explain their answer.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_5-32
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_5-32
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 was used with fifth graders to critique argumentation. We had been working on multiplying fractions, so students had a solid understanding of the concept. This task was developed to help students identify the parts of a good argument in order for them to give feedback to their peers. We focused on claim, basis of argument, evidence, reasoning and mechanics. This aligned with the rubric we used when scoring the arguments.
Microsoft Word version: 5_NF_FractionsMultiplication_PeerFeedback_Critique
PDF version: 5_NF_FractionsMultiplication_PeerFeedback_Critique