Mathematics · 2nd Grade

Active learning ideas

Writing Equations for Even and Odd

Active learning works for this topic because students need to physically manipulate objects and visualize groups to move beyond rote counting. Arrays provide a spatial bridge between addition and multiplication, making abstract ideas concrete through hands-on exploration.

• Common Core State Standards
• CCSS.Math.Content.2.OA.C.3

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

Activity 01

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: Array Architects

Groups are given 20 sticky notes and asked to create as many different rectangular arrays as possible. They must write the repeated addition equation for both the rows and the columns for every array they build.

Construct an equation to demonstrate that any even number can be formed by adding two identical numbers.

Facilitation Tip

During Array Architects, circulate with a tray of tiles and model how to arrange them into rows while naming each part aloud, e.g., 'I have 3 rows of 5 tiles.'

What to look for

Provide students with the number 14. Ask them to write an equation showing 14 as the sum of two equal addends. Then, ask them to write one sentence explaining why 15 cannot be written as the sum of two equal addends.

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

Activity 02

• Gallery Walk
• 25 min · Pairs

Gallery Walk: Real World Arrays

The teacher displays photos of real-world arrays (an egg carton, a muffin tin, a window pane). Students walk around in pairs, writing the 'row equation' and 'column equation' for each image on a recording sheet.

Analyze the relationship between an even number and its two equal addends.

Facilitation Tip

During the Gallery Walk, ask students to photograph one array they find and write its equation on an index card before moving to the next display.

What to look for

Display a collection of 10 objects. Ask students to draw two equal groups and write the equation that represents the total. Then, display 7 objects and ask them to explain why they cannot make two equal groups.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Array Flip

The teacher shows an array of 3 rows and 4 columns. Students solve for the total. Then, the teacher rotates the array 90 degrees. Pairs discuss whether the total changed and why the new equation (4+4+4) still equals the old one (3+3+3+3).

Predict what happens when you try to express an odd number as a sum of two equal addends.

Facilitation Tip

During the Think-Pair-Share for The Array Flip, give each pair two sticky notes to rotate their array and label both orientations with equations before sharing with the class.

What to look for

Pose the question: 'How can we use addition to show if a number is even or odd?' Guide students to share their equations for even numbers and their reasoning for odd numbers, focusing on the concept of equal addends.

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

A few notes on teaching this unit

Teachers should introduce arrays as a way to see equal groups, not just as a grid. Avoid rushing to multiplication; focus on repeated addition first. Research shows that students who physically build and manipulate arrays develop stronger number sense and retain the concept longer. Use consistent language: 'rows go left to right' and 'columns go top to bottom' to prevent confusion.

Successful learning looks like students confidently describing arrays with precise vocabulary, writing correct equations for even and odd totals, and explaining why rotating an array doesn’t change its total. They should also articulate why odd numbers cannot be split into two equal groups.

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Watch Out for These Misconceptions

• During Collaborative Investigation: Array Architects, watch for students mixing up the terms rows and columns.

  Pause the group work and have students trace the rows with their fingers while saying, 'Rows go across like a rowboat.' Then, have them trace the columns while saying, 'Columns go up and down like the columns on a tall building.' Repeat this cue before they continue building.

• During Think-Pair-Share: The Array Flip, watch for students thinking that rotating an array changes the total number of objects.

  Hand each pair their array and ask them to rotate it 90 degrees. Then, prompt them to write both equations (e.g., 3 rows of 5 and 5 rows of 3) and ask, 'Did the total change?' Guide them to recognize that the quantity stays the same even when the orientation changes.

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Methods used in this brief

• Inquiry Circle
• Gallery Walk
• Think-Pair-Share