• MA.5.AR.1 Algebraic Reasoning

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


    Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
    Example: Shanice had a sleepover and her mom is making French toast in the morning. If her mom had 2 1/4 loaves of bread and used 1 1/2 loaves for the French toast, how much bread does she have left?

    Benchmark Clarifications:
    Clarification 1: Instruction includes the use of visual models and equations to represent the problem


    Purpose and Instructional Strategies
    The purpose of this benchmark is to connect division of fraction concepts to real-world scenarios (K12.MTR.7.1). This work builds on the multiplication of fractions by whole numbers in Grade 4 (MA.4.AR.1.3), and prepares them for Grade 6 (MA.6.NSO.2.3) where they will solve realworld fraction problems using all four operations with fractions (MTR.7.1).

     During instruction, it is important for students to have opportunities to extend their understanding of the meaning of fractions, how many unit fractions are in a whole, and their understanding of division of fractions as involving equal groups or shares and the number of objects in each.

     Students should use visual fraction models and reasoning to solve word problems involving division of fractions. For example, to assist students with solving the problem, “The elephant eats 4 lbs of peanuts a day. His trainer gives him 1/5 of a pound at a time. How many times a day does the elephant eat peanuts?” use the following diagram to show how 4 ÷ 1/5 can be visualized to assist students with solving.


     The expectation of this benchmark is not for students to use an algorithm (e.g., multiplicative inverse) to divide fractions.

     Instruction includes students using equivalent fractions to simplify answers; however, putting answers in simplest form is not a priority.

    Common Misconceptions or Errors
     Students may believe that division always results in a smaller number, which is true when dividing a fraction by a whole number, but not when dividing a whole number by a fraction. Using models will help students develop the understanding needed for computation with fractions.

    Instructional Tasks
    Instructional Task 1
    Sonya has 1/2 gallon of chocolate chip ice cream. She wants to share her ice cream with 6 friends. How much ice cream will each friend get?

    Instructional Items
    Instructional Item 1
    Betty has 12 sheets of tissue paper to add to her holiday gift bags. Each gift bag needs 1/3 sheet of tissue paper. How many holiday gift bags can Betty fill? 

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