Mathematics · 1st Grade

Active learning ideas

Partitioning Shapes into Quarters/Fourths

Active learning works for this topic because students need to physically manipulate shapes to see that four equal parts make a whole, not just hear about it. When they cut, fold, and label their own shapes, the abstract idea of quarters and fourths becomes concrete and memorable.

• Common Core State Standards
• CCSS.Math.Content.1.G.A.3

• 15–20 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inquiry Circle
• 20 min · Pairs

Inquiry Circle: Halves to Fourths

Partners start with a paper rectangle and fold it in half to create two equal halves, labeling each section. They then fold it in half again to create fourths and label again. Partners discuss what they notice about the size of each section before and after the second fold and write one sentence summarizing their observation.

How does dividing a shape into four equal parts compare to dividing it into two equal parts?

Facilitation Tip

During Collaborative Investigation: Halves to Fourths, circulate and ask groups to explain their folding or cutting process to ensure precision.

What to look for

Provide students with pre-drawn circles and rectangles. Ask them to draw lines to divide each shape into four equal shares. Then, have them label two of the shares as 'fourth' and two as 'quarter'.

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

Activity 02

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Same Name?

Present the words 'quarters' and 'fourths' on the board and ask pairs to discuss whether both words can describe the same thing and how they know. Pairs share their reasoning, and the class connects the everyday use of 'quarters' (coins, time) to the mathematical meaning.

Justify why 'quarters' and 'fourths' mean the same thing.

Facilitation Tip

During Think-Pair-Share: Same Name?, listen for students to notice that 'quarter' and 'fourth' name the same-sized piece to reinforce the vocabulary connection.

What to look for

Show students a circle divided in half and the same circle divided into fourths. Ask: 'Which circle has bigger pieces? Why do you think that is?' Guide the discussion towards the idea that more pieces mean smaller pieces.

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

Activity 03

• Gallery Walk
• 20 min · Pairs

Gallery Walk: How Many Parts?

Post a series of partitioned shapes showing different numbers of parts (2, 4, and some irregular non-equal divisions). Pairs walk through and sort shapes into 'halves,' 'fourths,' and 'neither,' writing a brief explanation on sticky notes before comparing their decisions with another pair.

Predict what happens to the size of each share when a shape is divided into more pieces.

Facilitation Tip

During Gallery Walk: How Many Parts?, point out that all shapes must start the same size to compare the size of the parts accurately.

What to look for

Give each student a paper rectangle. Ask them to fold it into four equal parts and then shade one part. On the back, they should write one sentence explaining why the shaded part is called a 'fourth'.

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

Activity 04

• Simulation Game
• 20 min · Small Groups

Simulation Game: Pizza Party

Use paper circles representing pizzas. Groups divide their pizza so four people get exactly the same amount. Groups compare different division strategies (two vertical lines, two perpendicular lines, diagonal lines) and verify that all methods produce four equal parts.

How does dividing a shape into four equal parts compare to dividing it into two equal parts?

Facilitation Tip

During Simulation: Pizza Party, use real pizza or paper models to show how four equal slices make one whole pizza.

What to look for

Provide students with pre-drawn circles and rectangles. Ask them to draw lines to divide each shape into four equal shares. Then, have them label two of the shares as 'fourth' and two as 'quarter'.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

A few notes on teaching this unit

Teachers should emphasize that the word 'quarter' is familiar from coins, but the math concept applies to any divided shape. Avoid rushing past the vocabulary connection, as it helps students see that formal and informal terms describe the same idea. Use identical starting shapes for all activities to prevent confusion about the total size of the whole changing.

Successful learning looks like students dividing shapes accurately into four equal parts and confidently using both 'quarters' and 'fourths' to label them. They should explain why the pieces are equal and how the words connect to the concept of four parts making one whole.

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Watch Out for These Misconceptions

• During Think-Pair-Share: Same Name?, watch for students who think 'quarters' and 'fourths' refer to different-sized pieces because of their real-world associations.

  Use the coin connection: hold up a dollar and ask how many quarters make a dollar. Then show a shape divided into four equal parts and ask how many fourths make one whole. Link the terms explicitly to reinforce that they describe the same division.

• During Collaborative Investigation: Halves to Fourths, students may believe that cutting a shape into more pieces makes the whole shape smaller.

  Give each group identical paper rectangles and have them fold the first into halves and the second into fourths. Ask them to compare the size of the halves and fourths directly to see that the whole shape remains the same size.

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Methods used in this brief

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