Mathematics · 2nd Grade

Active learning ideas

Counting Tiled Squares

Active learning helps students move beyond abstract counting to concrete, visual strategies that build confidence in multiplicative thinking. When students physically mark, move, or compare squares during these activities, they develop reliable systems for accurate totals and see why different methods produce the same result.

• Common Core State Standards
• CCSS.Math.Content.2.G.A.2

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Predict Then Count

Students look at a partitioned rectangle and predict the total before counting. Pairs share predictions and their reasoning, then count using two different strategies to verify.

Explain how counting by rows and counting by columns both lead to the same total number of squares.

Facilitation Tip

During Think-Pair-Share: Predict Then Count, circulate and listen for students who justify their predictions with partial counts rather than guesses.

What to look for

Provide students with a drawing of a rectangle tiled with squares. Ask them to write down the number of rows and columns. Then, have them calculate and write the total number of squares, showing how they counted (e.g., by rows, by columns, or skip-counting).

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

Activity 02

• Inquiry Circle
• 25 min · Pairs

Inquiry Circle: Strategy Swap

Pairs solve a counting problem using their chosen strategy, then switch papers with another pair and re-count using a different strategy. The goal is to confirm they arrive at the same total.

Analyze the relationship between the number of rows, columns, and the total number of squares.

Facilitation Tip

During Collaborative Investigation: Strategy Swap, give pairs different rectangles so they must adapt their counting to new shapes.

What to look for

Draw a 3x5 grid on the board. Ask students to hold up fingers to show the number of rows. Then ask them to hold up fingers for the number of columns. Finally, ask them to write the total number of squares on a small whiteboard or paper.

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

Activity 03

• Gallery Walk
• 30 min · Small Groups

Gallery Walk: Strategy Museum

Students post their counting work for four different rectangles with annotations labeling the strategy used. The class walks through to identify which strategies appear and whether any led to errors.

Predict the total number of squares if a rectangle has 3 rows and 4 columns.

Facilitation Tip

During Gallery Walk: Strategy Museum, ask students to leave feedback notes on sticky pads that name the strategy they see and one thing that makes it clear.

What to look for

Present two rectangles: one with 2 rows and 4 columns, and another with 4 rows and 2 columns. Ask students: 'How are these rectangles the same? How are they different? How can we use counting by rows or columns to find the total number of squares in each?'

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

Activity 04

• Stations Rotation
• 40 min · Small Groups

Stations Rotation: Rows, Columns, Count

Three stations use the same rectangles but require students to count by rows at one, by columns at another, and by skip-counting at the third. Students record and compare totals at the end of the rotation.

Explain how counting by rows and counting by columns both lead to the same total number of squares.

Facilitation Tip

During Station Rotation: Rows, Columns, Count, ensure each station has unique materials like colored tiles or grid paper so students adjust to new visuals.

What to look for

Provide students with a drawing of a rectangle tiled with squares. Ask them to write down the number of rows and columns. Then, have them calculate and write the total number of squares, showing how they counted (e.g., by rows, by columns, or skip-counting).

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

A few notes on teaching this unit

Teach counting strategies explicitly by modeling how to mark or cover squares as you count, then have students practice while verbalizing their steps. Avoid rushing to multiplication symbols too soon; focus first on the reliable process of counting by groups. Research shows that students who physically interact with materials while verbalizing their process retain the concept longer and transfer it more easily to new shapes.

Students will confidently count squares using rows, columns, or skip-counting, explain their chosen strategy, and verify their totals match. They will also recognize that counting by different methods leads to the same answer, reinforcing the reliability of multiplicative reasoning.

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Watch Out for These Misconceptions

• During Think-Pair-Share: Predict Then Count, watch for students who make predictions without any counting method.

  After their initial prediction, ask them to point to one row or column and count it aloud. Then guide them to extend that count to the whole rectangle before revising their prediction.

• During Station Rotation: Rows, Columns, Count, watch for students who lose track when counting squares one at a time.

  Remind them to mark each counted square with a small check or cover it with a tile, and have their partner point while they mark to prevent skipping or double-counting.

• During Collaborative Investigation: Strategy Swap, watch for students who rely solely on guessing rather than applying a row or column count.

  Ask them to explain which row or column they counted first and how they used that count to find the total. If they can't explain, have them recount with a partner and verbalize each step.

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Methods used in this brief

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