Grade 1: Math Detectives! Using Properties of Operations to Find Change Unknown


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Operations and Algebraic Thinking

1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.B.3. Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

1.OA.B.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7=8-1, 5+2=2+5, 4+1=5+2.

Standards for Mathematical Practice

SMP.1 Make sense of problems and persevere in solving them.

SMP.2  Reason abstractly and quantitatively.

SMP.3 Construct viable arguments and critique the reasoning of others

SMP.4 Model with mathematics.

SMP.7 Look for and make use of structure.

English Language Arts and Literacy

Reading Informational Text

RI.2.1 Ask and answer such questions as who, what, where, why, how, and demonstrate understanding of key details in a text.

RI.2.2 Recount stories to determine the central message.


This Grade 1 unit titled “Math Detectives! Using Properties of Operations to Find Change Unknown” from the Massachusetts Department of Elementary and Secondary Education is intended to be completed in twelve 45+ minute lessons for approximately 3 weeks of mathematics instruction. As math detectives, first graders explore the mathematics behind having unknowns in “change positions” in equations. Through lesson activities students learn how to create situation equations that represent what occurs in a story problem and to use properties of operations to rearrange equation components to create solution equations. This unit is meant as a bridge between student proficiency with typical result unknown problem types and the much more difficult start unknown problems. Formative assessment opportunities are provided throughout the instructional phase of the unit. Two summative tasks end the unit. In the first, students are asked to solve an authentic problem by creating an equation to solve a mystery. In the second task, students take on the role of an evaluator to critique another student’s problem solving ability. They share feedback with each other to correct and defend each other’s answers to a problem.


Connecticut teachers should be aware that preparation materials and resources/charts for lessons will require familiarity to be used effectively. Prior knowledge is required for student success in all lessons, making it important to consider the variability of learners and make adaptations as necessary prior to instruction.


This exemplary unit includes clear and sufficient guidance to support teaching and learning of the targeted standards. It addresses instructional expectations and is easy to understand and use. The Standards for Mathematical Practice that are central to the lesson are identified, handled in a grade-appropriate way, and are well connected to the content being addressed. The unit plan provides opportunities for students to independently apply mathematical concepts in real-world situations and solve challenging problems with persistence. Unit materials include two curriculum-embedded assessments that are designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS. Rubrics for evaluating student work on the assessment tasks are included.

A video that captures first grade children as they engage with the Common Core Standard of Mathematical Practice: “Construct viable arguments and critique the reasoning of others.” →