Chapter 3 • AC9MFN03

Foundation Counting and Comparing Collections to 20 Activities

Help Foundation students count, quantify and compare collections to at least 20 using practical materials, pictures, games and printable worksheets aligned with the Australian Curriculum Version 9.0.

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About This Foundation Maths Topic

Counting is more than saying number names in the correct sequence. Children also need to understand that every object must be counted once, the final number tells how many objects are in the collection, and rearranging the objects does not change the total.

In this chapter, students count collections to at least 20, compare groups of objects and explain how they know which collection contains more, fewer or the same number of items. They also use one-to-one correspondence to collect the correct number of objects for a practical purpose.

These activities support the Australian Curriculum Version 9.0 content descriptor AC9MFN03 and its associated elaborations.

Australian Curriculum Alignment

AC9MFN03

Quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning.

AC9MFN03_E1

Establish the language and process of counting, including counting each object only once and understanding that the final number counted tells how many objects are in the collection.

AC9MFN03_E2

Use counting to compare two or more collections of similar objects and explain which collection contains more or fewer items.

AC9MFN03_E3

Use counting and one-to-one correspondence to determine how many objects are required for a practical purpose.

AC9MFN03_E4

Explore different cultural methods of representing number and counting, including abacuses and hand gestures.

AC9MFN03_E5

Explore body-tallying and other First Nations Australians’ ways of representing and communicating quantities.

Learning Intentions

Students will learn to:

  • count collections accurately to at least 20;
  • touch, move or point to each object while counting;
  • understand that each object is counted only once;
  • recognise that the final counting number tells the total;
  • understand that rearranging objects does not change the quantity;
  • compare collections using more, fewer, less, equal and the same;
  • use one-to-one correspondence in practical situations;
  • explain or demonstrate how they found their answer.

Student Success Criteria

I can count each object once.

I can say how many objects are in a collection.

I can compare two groups of objects.

I can identify which group has more or fewer objects.

I can identify when two collections are equal.

I can match one object to one person or place.

I can explain how I worked out my answer.

Key Vocabulary

count collection quantity total more fewer less equal same compare one-to-one how many

Teacher Guide

Recommended Materials

  • counters, buttons, blocks or bottle caps;
  • number cards from 0 to 20;
  • ten-frames and twenty-frames;
  • small containers or sorting trays;
  • classroom objects such as pencils and crayons;
  • picture cards containing collections of objects;
  • an abacus or images of different counting systems.

Suggested Teaching Sequence

  1. Begin with small collections of up to five objects. Ask students to touch or move each object while counting.
  2. Gradually increase the size of the collections to 10 and then to 20.
  3. Rearrange a counted collection and ask whether the quantity has changed.
  4. Place two collections side by side and ask which has more, fewer or the same number of objects.
  5. Encourage students to match objects one-to-one before checking by counting.
  6. Ask students to explain their strategy using complete mathematical sentences.

Teacher Questions

  • How can you make sure every object is counted once?
  • What does the last number you said tell you?
  • How many objects are in this collection?
  • Which group has more? How do you know?
  • Which group has fewer objects?
  • Do the groups contain the same number?
  • Can you prove your answer by matching the objects?
  • Will the number change if the objects are moved?
  • Can you show your answer in another way?

Common Misconceptions

Counting an object more than once

Encourage the student to move each object into a new area after counting it.

Skipping objects

Arrange objects in a line or organised group before counting.

Believing that a spread-out collection has more

Count the same collection before and after rearranging it to demonstrate conservation of number.

Confusing “less” and “fewer”

Model both terms while comparing concrete collections. For countable objects, “fewer” is usually the more precise mathematical word.

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Foundation Counting and Comparing Activities

Activity 1: Count and Move

Place a collection of objects in front of the student. The student moves each object into a container while counting aloud.

Ask: How many objects are there altogether?

Curriculum connection: AC9MFN03_E1

Activity 2: Does the Number Change?

Count a row of objects together. Rearrange the same objects into a circle or spread them farther apart.

Ask students to predict whether the total has changed and then count to check.

Curriculum connection: AC9MFN03_E1

Activity 3: Which Collection Has More?

Display two collections of similar objects. Students count each collection and identify which contains more or fewer.

Encourage students to answer using a complete sentence: The button collection has more because it has 12 and the block collection has 9.

Curriculum connection: AC9MFN03_E2

Activity 4: Match Them One-to-One

Give students two collections. Ask them to place one object from the first collection beside one object from the second collection.

Students determine whether the collections are equal or whether one collection has objects left over.

Curriculum connection: AC9MFN03_E2

Activity 5: One for Each Student

Ask a student to collect one pencil, paintbrush or counter for every person in a small group.

The student counts the group members and then collects the required quantity.

Curriculum connection: AC9MFN03_E3

Activity 6: Set the Table

Create a pretend table-setting activity. Students provide one plate, cup or spoon for each toy or class member.

Ask students to explain how they know that they have collected enough items.

Curriculum connection: AC9MFN03_E3

Activity 7: Counting with an Abacus

Demonstrate how quantities can be represented by moving beads on an abacus.

Students represent selected numbers and compare two rows of beads.

Curriculum connection: AC9MFN03_E4

Activity 8: Different Ways to Show a Number

Choose a number between 1 and 20. Students show the number using objects, fingers, drawings, tally marks, an abacus or a number card.

Discuss how the representations look different but show the same quantity.

Curriculum connection: AC9MFN03_E4

Activity 9: Body Tally Counting

Introduce an age-appropriate example of body-tallying as a way of keeping track of quantities using parts of the body in a fixed sequence.

Present First Nations Australian knowledge respectfully, accurately and within its cultural context.

Curriculum connection: AC9MFN03_E5

Differentiation

Support

  • begin with collections containing no more than five objects;
  • arrange objects in straight lines;
  • use ten-frames to organise collections;
  • allow students to move objects as they count;
  • provide sentence starters for comparing collections.

Extension

  • compare three or more collections;
  • ask students to estimate before counting;
  • ask how many more or how many fewer;
  • represent the same collection in several arrangements;
  • ask students to create a collection for a partner to count;
  • ask students to explain two different comparison strategies.

Mathematical Sentence Starters

There are _____ objects altogether.

I counted each object by _____.

The _____ collection has more objects.

The _____ collection has fewer objects.

Both collections have the same number because _____.

I know my answer is correct because _____.

I matched one _____ with one _____.

Assessment Ideas

Observe whether the student can:

  • maintain the correct counting sequence;
  • count each object only once;
  • state the total after counting;
  • compare two collections accurately;
  • use words such as more, fewer and equal correctly;
  • use one-to-one matching;
  • explain or demonstrate their reasoning.

Quick Exit Ticket

  1. Count a collection of objects.
  2. Circle the collection that has more.
  3. Draw a collection with fewer objects.
  4. Explain how you checked your answer.

Printable Teacher and Student Resources

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Home Learning Ideas

Families can support this topic using familiar household objects. Children can count socks, spoons, toys, pegs, fruit or blocks and compare two collections.

Ask questions such as:

  • How many are there?
  • Which group has more?
  • Which group has fewer?
  • Can you make both groups equal?
  • How do you know?

Related Foundation Maths Chapters

Chapter 1: Numbers to 20 – AC9MFN01 Chapter 2: Subitising to 5 – AC9MFN02