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.

##### 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:

#### 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:

##### 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:

- Grid paper – isometric- small
- Grid paper – isometric- large
- Grid paper – square- small
- Grid paper -square- large

##### Solution Card:

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

The Sandpit is a free problem-solving platform that allows students to test their skill in mathematics and informatics. We’re still in the development stage but we would love for your students to test out the platform and send us some feedback.

## AMC Practice Problems Online

Choose your year level (3-12) and prepare for the AMC on our new platform. Users don’t need to log in to participate. Solutions for each question are supplied.

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## AMC Teacher's Handbook

Your guide to running the AMC. A step by step of instructions for the day and what to do afterwards.