Mathematics · 1st Grade

Active learning ideas

Solving for Unknowns in Equations

Active, hands-on learning turns abstract symbols into concrete reasoning for first graders. When students manipulate objects or pictures to find unknowns, they connect symbols like 5 + ? = 7 to real actions, building relational thinking that lasts beyond the activity.

• Common Core State Standards
• CCSS.Math.Content.1.OA.D.8

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: What Is Hiding?

Show an equation with a covered number (use a sticky note). Partners discuss possible strategies for finding the hidden value, then each partner tries their chosen strategy and compares results. Pairs share their methods with the whole class.

Analyze how a missing number changes the balance of an equation.

Facilitation Tip

During Think-Pair-Share: What Is Hiding?, sit with a small group to listen for how students describe their thinking about the hidden number rather than just the answer.

What to look for

Present students with three equations: one with the result unknown (e.g., 5 + 2 = ?), one with the change unknown (e.g., 5 + ? = 7), and one with the start unknown (e.g., ? + 2 = 7). Ask students to solve each and briefly explain their strategy for the second and third equations.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: Equation Stations

Set up three stations, each with unknowns in a different position (result, change, and start). Small groups rotate and must solve two equations per station using a different strategy at each one. Groups record which strategy worked best for each position.

Differentiate between finding a missing addend and finding a missing subtrahend.

Facilitation Tip

At Equation Stations, move between groups to redirect any student who starts counting from one for every problem.

What to look for

Give each student a card with a different equation, such as 8 - ? = 3 or ? - 4 = 5. Ask them to write the missing number and draw a picture or use a number line to show how they found it.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Peer Teaching
• 20 min · Pairs

Peer Teaching: Strategy Showcase

Each pair solves the same unknown equation using whichever strategy they prefer (counting on, using a known fact, drawing a bar model). Pairs present their method to another pair and explain why it works, then switch equations and try a new method.

Design a strategy to solve for an unknown in a simple equation.

Facilitation Tip

During Strategy Showcase, ask clarifying questions like 'How did you know 3 was hiding there?' to push students to articulate their process.

What to look for

Pose the problem: 'Sarah had some cookies, and she gave 3 to her friend. Now she has 5 cookies left. How many cookies did Sarah start with?' Ask students to share different ways they could solve this problem, encouraging them to use words like 'equation,' 'unknown,' and 'start unknown.'

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach this topic by starting with physical models: counters, number lines, or drawings. Ask students to represent equations like ? + 3 = 7 by placing seven counters and covering the unknown quantity with a cup. Avoid rushing to abstract symbols until students can explain the relationship. Research shows that first graders benefit from repeated exposure to equations with unknowns in all positions, not just result unknown, to build flexibility.

By the end of these activities, students will confidently identify the unknown in any position of an equation and explain their strategy using words like 'start unknown' or 'change unknown.' They will also hear multiple approaches from peers and choose methods that make sense to them.

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Watch Out for These Misconceptions

• During Think-Pair-Share: What Is Hiding?, watch for students who always assume the unknown is on the right side of the equation.

  Use the balance model at the station: place seven counters on one side and three on the other, then ask students to find the missing number that balances the scale. Ask, 'Where could the unknown be and still make both sides equal?'

• During Collaborative Investigation: Equation Stations, watch for students who only count all starting from one, even when they could use known facts.

  At the station, introduce a strategy-sharing routine where students must explain two ways to solve one equation, such as counting on and using a known fact like 5 + 2 = 7. Highlight efficiency by asking, 'Which way felt faster? Why?'

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Methods used in this brief

• Think-Pair-Share
• Inquiry Circle
• Peer Teaching