Challenging Maths Tasks CD

Challenging Maths Tasks

The Challenging Maths Tasks are designed to extend Middle Years Mathematics Students. They are interactive and differentiated in nature. They expect students to apply the skills and knowledge learnt in the classroom to the new and different situations presented. In many cases students may need to ask further questions of themselves in order to be able to complete their investigations.

The tasks offer a huge variety of topics and mathematical concepts but all expect the student to work mathematically in order to be able to complete the tasks. Students are encouraged to present their responses by utilizing their computer skills. They should explain and justify each of their responses. (Can be used as e-maths tasks)

Responses will be judged on accuracy, clarity of explanation or justification; and complexity in regard to depth of investigation. Answers are provided where possible but due to the open ended nature of many of the questions, this cannot always be done.

Some sample answers or other assistance has been provided to help students if need be. An evaluation rubric has also been provided to both help direct students in what is expected and to assist the teacher. This resource can be used with the E-Maths program (©TMELA Education) but each one of the tasks provided on the CD is a stand-alone task and no particular order is required.

Curriculum Links are provided with the alphabetical index (main menu), and it is suggested that tasks be chosen to link with what others in the classroom are also studying at the time. All tasks provided on this CD promote the use of ICT and encourage students to use various computer applications to best present their work, but most tasks can also be simply printed off and worked on in pen and paper style if preferred.

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Task Explanations

Box Kites Rule

This task requires students to investigate diagonals of squares and calculate lengths of dowel and fabric required to build a box kite. Students need to work with ratios and fractions as well as costing materials. The task becomes more complex when students are asked to devise the most practical sized kite from given materials and also to propose the most efficient plan to mass produce the box kites.

Buildings

Students use the drawing, colouring, positioning and grouping techniques with the computer to represent their solutions in both 2D and 3D to the problems posed. A good understanding of the language of shape is needed to be able to construct the buildings correctly. Students then design and give clues for their own buildings and challenge other students with these.

Card Chances

This challenge uses a deck of cards to help students understand chance. It asks them to present the probability of events as fractions, decimals, ratios and percentages. It then asks them to apply their understanding of Chance into another situation

Centenary Formulae

Students are given a scenario of running an event for the school centenary. They are to present all the details on an Excel spreadsheet in order to ascertain costs, what is owing to suppliers, select the best ticket price and work out profits for anything from 1 – 200 guests. To achieve this task efficiently, students need to express instructions as formulae and use all the excel shortcuts they know. A sample answer is provided

Dice Chances

A look at probability using dices. Predicting, experimenting and proving outcomes using graphs are all part of this challenge.

Four, Three, Two, One

Manipulating numbers and processes to come up with required answers.

Furnishing the Office

This is a wordy challenge in its presentation but requires much computer drawing of shapes to scale for its response. Students have to represent various pieces of furniture and fit them into a room with specific dimensions.

The Games

Great activity to use at Commonwealth or Olympic Games times. Utilizes websites to give students up-to-date results to work with. Lots of work with decimals.

Handyman

Students are given a simple house plan and are asked to work out a quote for “an elderly client”. To do this, they need to work out area and perimeter and need to be able to cost a job. A sample quote is provided.

Land of the Giants

In this task students go to giant land. By using their knowledge of ratio, they work out how big the giant must be and how big other things in this land would have to be to cater for him.

Matching Tiles

A puzzle type problem where rotation is needed to manipulate various tiles in order to match them correctly.

Measurement Matching

Students must convert between units to be able to match the different measurements and descriptions given in the first part of this task. The second part involves a complex multi-stepped problem solving situation based on discovery and application of ratios between units of measurement.

The Petrol Station

Students interpret information from a graph and develop their own questions about the graph. Emphasis is on answering and developing complex questions. Students are expected to find out other information not explicit in the information provided, in order to answer the ‘complex’ questions posed.

Price Comparisons

Students are given a website to research their choice of grocery item prices for this task, but they can do their own research locally if they wish. They are then expected to use a table to compare products for their price value, and graph and interpret their findings. An example is worked through with them as part of the task.

Road Trip Around Australia

Students decide on places in Australia they would like to visit and plan a road trip. They must work out the best route, the distance and direction between places and time taken to travel to each. They must also present a budget for the trip.

Sports Ladders

An activity based on a local AFL football league ladder. Involves lots of percentages and interpretation of results. Students are then given results of the following round to make up the new ladder. Formulae using excel is encouraged.

Tessellations

An activity looking at the work of Escher. Students develop tessellated designs on the computer through the use of the various shapes provided in the word package.

Top Speed

Students have to work out speeds of various animals then apply this to solve various problems. They then apply their knowledge to work out their own heartbeats and speeds.

Travelling to School

This task presents students with a scenario and asks them to work out distances, times and costs of travelling to school over a period of time. It uses the Distance, Time and Speed Relationship formulae.

What’s my Number?

This task gives clues to 10 different numbers. Students use the tiles provided to make those 10 numbers. They then use the left-over digits to make another number. Good knowledge of the language of number is needed for this task.