Mathematics · 3rd Class

Active learning ideas

Fractions of a Group

Today we're going to use our fraction skills in a new way, moving from cutting up shapes to sharing out groups of treasure!

• NCCA Curriculum Specifications
• PSMC: Number - Fractions (3rd/4th Class)

• 10–20 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Think-Pair-Share
• 20 min · Pairs

Sweet Shop Fractions

Give each pair a pot of 'sweets' (counters or cubes). Call out orders like, 'A customer wants half of your 14 sweets!' Pupils must count out the total, share them into the correct number of equal groups, and determine the answer.

Explain the steps to find one quarter of 12 counters.

Facilitation Tip

Use hoops or circles drawn on mini-whiteboards to help pupils physically organise their equal groups.

What to look for

Observe pupils during hands-on activities. Ask them to 'think aloud' and explain their steps for finding a fraction of the counters they are using.

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

Activity 02

• Think-Pair-Share
• 10 min · Whole Class

Human Fractions

Use the pupils themselves as the set. Ask questions like, 'If there are 20 pupils here today, how many are in one quarter of the class?' Have them form the correct number of equal groups to find the answer.

Identify half of a set of 16 objects and justify your answer.

Facilitation Tip

This is a great activity for a quick mental maths starter or to break up the lesson with movement.

What to look for

Provide a short worksheet with pictorial and numerical problems, e.g., 'Circle 1/4 of the cars' and 'What is 1/2 of 20?'.

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

Activity 03

• Think-Pair-Share
• 15 min · Individual

Play-Doh Partitioning

Give pupils a set number of small balls of Play-Doh (e.g., 12). Ask them to find half by squashing the correct amount. This provides a strong visual and tactile representation of the 'part' being taken from the 'whole group'.

Compare finding 1/2 of 10 with finding 1/5 of 10.

Facilitation Tip

Encourage pupils to arrange the balls in an array first, which can make visualising the equal groups easier.

What to look for

Pupils complete a 'two stars and a wish' slip, writing down two things they can do well (e.g., find half of 12) and one thing they still need help with.

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

A few notes on teaching this unit

Always start with physical objects. Have pupils physically move counters into circles to represent the equal groups. Constantly reinforce the language: 'To find one quarter, we share into four equal groups'. Once they are secure, you can move on to drawing pictures, and finally to solving problems with just numbers.

By the end of this, your pupils will be pros at finding half or a quarter of any group of items, like a bag of marbles or a box of crayons.

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Watch Out for These Misconceptions

• Confusing the denominator with the size of the group. For example, to find 1/4 of 12, a pupil might make groups of 4.

  Explain that the denominator tells us 'how many equal groups to share into'. Use the analogy of sharing with 4 friends, meaning you need to make 4 piles. Emphasise the language 'share 12 into 4 equal groups'.

• Thinking that the fraction with the larger denominator is bigger. For instance, believing 1/4 of 16 is more than 1/2 of 16 because 4 is greater than 2.

  Use concrete materials to demonstrate this directly. Show that when you share 16 sweets among 2 people, each person gets a large share (8). When you share among 4 people, the shares get smaller (4).

• Struggling to connect the action of sharing with the concept of division.

  Make the link explicit. After pupils find 1/2 of 10 is 5, write '10 ÷ 2 = 5' on the board beside it. Repeatedly show that finding a unit fraction of a number is the same as dividing by the bottom number.

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Methods used in this brief

• Think-Pair-Share