• MA.5.AR.2 Algebraic Reasoning

Demonstrate an understanding of equality, the order of operations and equivalent numerical expressions

MA.5.AR.2.4

Given a mathematical or real-world context, write an equation involving any of the four operations to determine the unknown whole number with the unknown in any position. Example: The equation 250 − (5 × 𝑠) = 15 can be used to represent that 5 sheets of paper are given to 𝑠 students from a pack of paper containing 250 sheets with 15 sheets left over.

Benchmark Clarifications:
Clarification 1: Instruction extends the development of algebraic thinking where the unknown letter is recognized as a variable.
Clarification 2: Problems include the unknown and different operations on either side of the equal sign.

Purpose and Instructional Strategies
The purpose of this benchmark is for students to write equations that determine unknown whole numbers from mathematical and real-world contexts. In Grade 4, students wrote equations from mathematical and real-world contexts to determine unknown whole numbers (represented by letter symbols) (MA.4.AR.2.2). The extension in Grade 5 is that factors are not limited to within 12 and equations may use parentheses, implying students may have to use the order of operations to solve. In Grade 6, students extend this work to include integers and positive fractions and decimals (MA.6.AR.2.2/2.3/2.4).

 Instruction should focus on helping students translate mathematical and real-world contexts to equations. Instructional emphasis should be placed on students’ comprehension of the contexts to then translate to equations more easily. An instructional strategy that helps students translate from context to symbolic equations is to first present contexts with some or all their numerical information omitted. In a mathematical context, this may look like showing a data display with some numerical information covered. In a real-world context, this may look like a word problem with quantities covered. This allows students to comprehend what the problem trying to find and allows students to think deeper about what operations will be required to do so. It can also help students estimate reasonable solution ranges. Once students can predict an equation (or equations) to solve the problem, then the teacher can reveal all numerical information and allow students to solve (MTR.5.1).

 In each context, students may provide many examples of equations that can be used to solve. During instruction, teachers should have students compare their equations and evaluate whether they can be used to solve (MTR.4.1).

 During instruction, students should justify how their equations match the mathematical and real-world contexts through checking solutions. Students should substitute their solution for their letter symbol and use the order of operations to check that it makes the equation true.

Common Misconceptions or Errors

 When students have trouble comprehending contexts, they tend to just grab numbers from a given context and begin computing without justifying their arguments. Emphasis of instruction should be on the comprehension of problems through classroom discussion, sharing strategies, estimating reasonable solutions, and justifying equations and solutions.