construct

Gr 6_EE_ExpressionsOrderOfOperations_Problem_Construct

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This problem is meant for students developing their understanding of the distributive property in algebraic representations. A number trick is a series of calculations in which the person giving the directions always knows what number the players will end up with. When the students are asked to represent Step 3 in a different way, they will use the distributive property. When students use parentheses, the outside number is the number of groups. The expression inside the parentheses is what is in one group. When they write the expression without parentheses, they are saying how many total x tiles and total 1 tiles they have. Switching between these two representations gives a concrete, visual, and abstract expression of using the distributive property to group and ungroup terms in an expression.

Microsoft Word version: 6_EE_ExpressionsOrderOfOperations_Problem_Construct

PDF version: 6_EE_ExpressionsOrderOfOperations_Problem_Construct

Gr 6_EE_AlgebraRateOfChange_Problem_Construct

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This task is designed for sixth graders developing skills with rate of change. The task provides students with a distance travelled along with the amount of time taken. Students must use this information to determine how far someone could get in a given amount of time. Students must recognize that a rate of change is necessary. Students may solve the problem using a rate and creating an expression, or by creating equivalent fractions, which may open the class to discussion about different methods. Students are asked to provide an explanation and evidence for why a rate is necessary, which provides an opportunity for students to create a solid argument.

Microsoft Word version: 6_EE_AlgebraRateOfChange_Problem_Construct

PDF version: 6_EE_AlgebraRateOfChange_Problem_Construct

Gr 5_OA_AlgebraPatterns_Problem_Construct_DotPattern

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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

Gr 5_OA_AdditionCombinations_Problem_Construct_GettingThere

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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

Gr 5_NF_FractionsMultiplicationDivision_Problem_Construct_MakingHotCocoa

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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

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Gr 5_NF_FractionsMultiplication_Problem_Construct

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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

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Gr 5_NF_FractionsAddition_Problem_Construct

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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

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Gr 5_NF_Fractions_Problem_Construct_IllustrativeMathematics

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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
fractions.

Microsoft Word version: 5_NF_Fractions_Problem_Construct_IllustrativeMathematics

PDF version: 5_NF_Fractions_Problem_Construct_IllustrativeMathematics

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Gr 5_NF_Fractions_Problem_Construct_BirthdayBalloons

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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

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Gr 4_OA_Multiplication_ArgumentFrame_Construct

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Fourth graders are given this word problem to understand multiplication, though division can be used. This task is formatted as a graphic organizer, with a space for the problem, mathematical practice and vocabulary, claim, evidence, and warrants. Students are to use the graphic organizer to formulate their thoughts and construct an argument to complete the problem.

Microsoft Word version: 4_OA_Multiplication_ArgumentFrame_Construct

PDF version: 4_OA_Multiplication_ArgumentFrame_Construct