Mathematics · Year 1

Active learning ideas

Quarters of Shapes and Objects

Active learning helps Year 1 students grasp the concept of quarters by making abstract ideas concrete. When children fold paper, cut clay, or sort objects, they physically manipulate and see equal parts, which strengthens their understanding far more than passive observation. These hands-on experiences build a foundation for future fraction work by connecting visual, tactile, and spatial reasoning.

• ACARA Content Descriptions
• AC9M1N05

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

Activity 01

• Numbered Heads Together
• 20 min · Pairs

Pairs: Paper Folding Quarters

Give each pair square paper. Fold in half vertically, then horizontally to form four equal rectangles. Students unfold, color one quarter, and explain to partners why all parts match. Pairs swap papers to check equality.

Analyze the relationship between halves and quarters of a whole.

Facilitation Tip

During the Paper Folding Quarters activity, model precise folds by lining up edges carefully and ask students to check their partners' folds for accuracy.

What to look for

Give students a circle and a square. Ask them to draw lines to divide each shape into four equal quarters. Collect and check if the parts are equal in size.

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

Activity 02

• Numbered Heads Together
• 30 min · Small Groups

Small Groups: Clay Shape Quarters

Provide modeling clay and cutters for circles or squares. Groups divide each shape into four equal parts using strings or knives. They reassemble to verify wholeness and trade pieces to compare sizes visually and by touch.

Construct a shape that is divided into four equal quarters.

Facilitation Tip

For the Clay Shape Quarters activity, remind students to press gently to avoid distorting the original shape when dividing into quarters.

What to look for

Show students several shapes: one divided into four equal quarters, one divided into four unequal parts, and one divided into two halves. Ask students to point to the shape that shows quarters and explain why the other shapes are not quarters.

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

Activity 03

• Numbered Heads Together
• 25 min · Whole Class

Whole Class: Quartered Object Sort

Display images or real objects like quartered apples or pies. Class votes if each shows true quarters, discussing unequal examples. Students draw their own divided shapes on whiteboards to share justifications.

Justify why four unequal parts do not make quarters.

Facilitation Tip

When running the Quartered Object Sort, provide real objects like orange segments or paper pizzas so students can physically compare and confirm equal parts.

What to look for

Present a shape divided into two halves and another shape divided into four quarters. Ask: 'How many quarters do you need to make one half? How do you know?' Encourage students to use their hands or draw to demonstrate.

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

Activity 04

• Numbered Heads Together
• 15 min · Individual

Individual: Draw and Divide

Students draw a shape, divide into four equal quarters with lines, shade one, and label. They self-check by cutting out and comparing parts for equal size before gluing back together.

Analyze the relationship between halves and quarters of a whole.

What to look for

Give students a circle and a square. Ask them to draw lines to divide each shape into four equal quarters. Collect and check if the parts are equal in size.

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

A few notes on teaching this unit

Teachers should start with familiar objects like cakes or oranges to introduce quarters, then move to shapes with clear lines like squares and rectangles. Avoid using irregular shapes at this stage to prevent confusion. Use consistent language such as 'split into four equal parts' and link quarters to halves by asking students how many quarters make a half. Research shows that children learn fractions best when they can manipulate materials and discuss their observations with peers.

By the end of these activities, students will confidently partition shapes and objects into four equal parts, recognize quarters in different contexts, and explain why quarters must be equal in size and area. They will also begin to see the relationship between halves and quarters through folding, cutting, and discussion.

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Watch Out for These Misconceptions

• During Paper Folding Quarters, watch for students who fold paper into four unequal parts, believing any four sections are quarters.

  After folding, have students compare their quarters using a strip of paper to measure each part’s length or by folding again to check overlap and equal size.

• During Clay Shape Quarters, watch for students who believe quarters must look identical in shape, such as four identical triangles.

  Encourage students to cut or roll their clay into different quarter shapes (e.g., two triangles and two rectangles) and then stack the pieces to confirm equal area and volume.

• During Quartered Object Sort, watch for students who select pieces that are small but do not fill the whole shape, thinking they are quarters.

  Have students place the quartered pieces back onto the original shape outline to check for gaps or overlaps, reinforcing that quarters must completely and equally cover the whole.

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Methods used in this brief

• Numbered Heads Together