Lesson 12

Equations with Unknowns

Lesson Purpose

The purpose of this lesson is for students to represent equations with an unknown in all positions on the number line and find the unknown values.

Lesson Narrative

In previous lessons, students found the value of sums and differences within 100, represented their thinking on the number line, and compared different methods.

In this lesson, students find the number that makes addition and subtraction equations true within 100 in equations with unknowns in all positions. They continue to think about the relationships between the numbers in each equation and reason about how they can use the structure of the number line, the relationship between addition and subtraction, and their understanding of place value to find the number that makes each equation true (MP7). The context of the first activity encourages all students to reason with the number line. In the second activity, students may use the methods and representations that make the most sense to them. The work of this lesson helps students make sense of the way the number line can be used to represent and solve story problems which will be useful in upcoming lessons.

  • Representation
  • MLR8

Learning Goals

Teacher Facing

  • Write equations and represent sums and differences on a number line.

Student Facing

  • Let’s represent equations with a ? for the unknown.

Required Materials

Materials to Copy

  • Number Line to 100

Required Preparation

CCSS Standards

Lesson Timeline

Warm-up 10 min
Activity 1 20 min
Activity 2 15 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

Reflect on how students work together during partner work. How are students supporting one another when reasoning together and sharing mathematical ideas?

Suggested Centers

  • Number Puzzles: Addition and Subtraction (1–4), Stage 4: Within 100 with Composing (Addressing)
  • Number Line Scoot (2–3), Stage 1: Twos, Fives, and Tens (Addressing)

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