Resources for the classroom | Australian Maths Trust

Resources for the classroom

Jump into a class of problem solving with these interesting and thought-provoking lesson cards, which offer multiple points of interest and ability for students in years 2 through 10.

Lesson Cards

Get your students exploring problem-solving tactics by basing a lesson on one of these cards. Each one features a problem and follow up challenges, and covers various levels of difficulty to suit a range of abilities in your classroom. 

You will also find the complete cards with solutions and links to the ACARA website (for full information on how each activity is linked to the Australian Curriculum).

Suitable years:

Animal, Vegetable, Mineral is suitable from years 2–12. This question is versatile in the sense that teachers can ask for either a simple answer or the intricate details within each answer.

Lesson Areas:

We have a rundown of the learning areas and descriptors taken from the Australian Curriculum so you’ll easily be able to drop these lesson cards into your schedule without deviating from the curriculum.

  • Year 2, ACMMG046 Identify and describe half and quarter turns
  • Year 3, ACMMG066 Identify symmetry in the environment
  • Year 4, ACMMG088 Compare and describe two dimensional shapes that result from combining and splitting common shapes
  • Year 4, ACMMG091 Create symmetrical patterns, pictures and shapes
  • Year 5, ACMMG114 Describe translations, reflections and rotations of two-dimensional shapes, and identify line and rotational symmetries
  • Year 6, ACMMG142 Investigate combinations of translations, reflections and rotations
  • Year 8, ACMMG200 Define congruence of plane shapes using transformations
  • Year 10, ACMMG244 Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes
Additional Resources:

We have created an interactive tool on GeoGebra as a visual aid to help. Click on the links below and walk your students through our visual aid.

  1. Squares
  2. Triangles
  3. Hexagons
Solutions Card:

Download the solutions card. The card contains all the items on the lesson card as well as the solutions to each question.

Suitable years:

Magic Dice is suitable from years 2–6. This question is versatile in the sense that teachers can ask for either a simple answer or the intricate details within each answer.

Learning areas:

Below is a rundown of the learning areas and descriptors are taken from the Australian Curriculum so you’ll easily be able to drop these lesson cards into your schedule without deviating from your class schedule.

  • Year 2, ACMNA029 Explore the connection between addition and subtraction
  • Year 3, ACMNA060 Describe, continue and create number patterns resulting from performing addition or subtraction
  • Year 4, ACMNA083 Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction
  • Year 5, ACMNA121 Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division
  • Year 6, ACMNA134 Explore the use of brackets and order of operations to write number sentences 

Additional Resources:

  1. Table
  2. Dice Templates

Solution Card:

Download the Solution card which contains all the items on the lesson card as well as the solutions to each question.

Suitable Years:

The Frobenius coin problem is suitable from years 7–12.

Learning areas:

Below is a rundown of the learning areas and descriptors taken from the Australian Curriculum so you’ll easily be able to drop these lesson cards into your schedule without deviating from the curriculum.

  • Year 7, ACMNA149 Investigate index notation and represent whole numbers as products of powers of prime numbers
  • Year 8, ACMNA183 Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies
  • Year 9, ACMNA208 Plot linear relationships on the Cartesian plane with and without the use of digital technologies
  • Year 10, ACMNA235 Solve problems involving linear equations, including those derived from formulas
Resources for the problem:
  1. Sliding graph
Supplementary Lesson Card:

Have a look at the Supplementary Lesson Card. It Provides you with extended questions for advanced students in your classroom.

Solution Card:

Download the solutions. The card provides all the items on the lesson card as well as the solutions to each question.

 
Suitable Years:

Scaly Tiles is suitable from years 5–12. This question is a playful investigation of how shapes fit together which leads to the sophisticated concepts of self-similarity.

Lesson Areas:

The following is not intended to be an exhaustive list, but indicates how the above activity aligns with various stages of the mathematics curriculum. Follow the links to the ACARA website for elaborations.

  • Year 5, ACMMG114 Describe translations, reflections and rotations of two-dimensional shapes, and identify line and rotational symmetries
  • Year 5, ACMMG115 Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original
  • Year 6, ACMMG142 Investigate combinations of translations, reflections and rotations
  • Year 7 ACMMG161 Draw different views of prisms and solids formed from combinations of prisms
  • Year 7 ACMMG163 Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal
  • Year 7 ACMMG166 Demonstrate that the angle sum of a triangle is 180◦ and use this to find the angle sum of a quadrilateral
  • Year 7 ACMMG181 Describe translations, reflections in an axis and rotations of multiples of 90◦ on the Cartesian plane using coordinates
  • Year 8, ACMMG200 Define congruence of plane shapes using transformations
  • Year 8, ACMMG201 Develop the conditions for congruence of triangles
  • Year 9, ACMMG220 Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
  •  Year 9, ACMMG221 Solve problems using ratio and scale factors in similar figures
  • Year 9, ACMMG222 Investigate Pythagoras’ Theorem and its application to solving simple problems involving right-angled triangles
  • Year 10, ACMMG243 Formulate proofs involving congruent triangles and angle properties
  • Year 10, ACMMG244 Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes
Additional Resources:
  1. Grid paper – isometric- small
  2. Grid paper – isometric- large
  3. Grid paper – square- small
  4. Grid paper -square- large
Solution Card:

Download the Solution Card. The card contains the above information as well as detailed solutions for all questions. 

AMC Practice Problems

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