• MA.5.AR.1 Algebraic Reasoning

    Solve problems involving the four operations with whole numbers and fractions.

    Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context.

    Benchmark Clarifications:Clarification 1: Depending on the context, the solution of a division problem with a remainder may be the whole number part of the quotient, the whole number part of the quotient with the remainder, the whole number part of the quotient plus 1, or the remainder.


    Purpose and Instructional Strategies
    The purpose of this benchmark is for students to solve multistep word problems with whole numbers and whole-number answers involving any combination of the four operations. Work in this benchmark continues instruction from Grade 4 where students interpreted remainders in division situations (MA.4.AR.1.1) (MTR.7.1), and prepares for solving multi-step word problems involving fractions and decimals in Grade 6 (MA.6.NSO.2.3).

     To allow for an effective transition into algebraic concepts in Grade 6 (MA.6.AR.1.1), it is important for students to have opportunities to connect mathematical statements and number sentences or equations.

     During instruction, teachers should allow students an opportunity to practice with word problems that require multiplication or division which can be solved by using drawings and equations, especially as the students are making sense of the context within the problem (MTR.5.1).

     Teachers should have students practice with representing an unknown number in a word problem with a variable by scaffolding from the use of only an unknown box.

     Offer word problems to students with the numbers covered up or replaced with symbols or icons and ensure to ask students to write the equation or the number sentence to show the problem type situation (MTR.6.1).

     Interpreting number pairs on a coordinate graph can provide students opportunities to solve multi-step real-world problems with the four operations (MA.5.GR.4.2).

    Common Misconceptions or Errors

     Students may apply a procedure that results in remainders that are expressed as r for ALL situations, even for those in which the result does not make sense. For example, when a student is asked to solve the following problem: “There are 34 students in a class bowling tournament. They plan to have 3 students in each bowling lane. How many bowling lanes will they need so that everyone can participate?” the student response is “11 𝑟1 bowling lanes,” without any further understanding of how many bowling lanes are needed and how the students may be divided among the last 1 or 2 lanes. To assist students with this misconception, pose the question…“What does the quotient mean?”

    Instructional Tasks
    Instructional Task 1
    There are 128 girls in the Girl Scouts Troop 1653 and 154 girls in the Girl Scouts Troop 1764. Both Troops are going on a camping trip. Each bus can hold 36 girls. How many buses are needed to get all the girls to the camping site?

    Instructional Items
    Instructional Item 1
    A shoe store orders 17 cases each containing 142 pairs of sneakers and 12 cases each containing 89 pairs of sandals. How many more pairs of sneakers did the store order?

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