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22nd May

22nd May: Problem Solving

Problem solving means engaging in a task for which the solution is not immediately obvious. Problem solving is integral to mathematical learning. In day-to-day life and in the workplace the ability to problem solve is a highly advantageous skill.
In the mathematics classroom problem solving should not be met in isolation, but should permeate all aspects of the teaching and learning experience. Problems may concern purely mathematical matters or some applied context.
In a mathematics problem-solving environment it is recognised that there are three things learners need to do:
• make sense of the problem
• make sense of the mathematics they can learn and use when doing the problem
• arrive at a correct solution to the problem

Problem Solving Resources and Presentations
GeoGebra Files
Interesting Videos and Links

Problem Solving Booklet

https://www.scoilnet.ieuploads/resources/33096/32840.pdf Added: 20 May 2020 Contributor: PDST Resource type: Guide/notes / Worksheet

The PDST Maths Development Team produced this booklet for Post-Primary students on the course content of 4.1 and 4.2. The booklet contains 19 pages of activities and questions for students to work on.

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Mathematics

Strand: 3. Number

Strand unit: 1. Number Systems (Complex Numbers,Sequences)

Suggestions for use: Useful for TY students or to help planning with problem solving in senior cycle.

Strand: Supplementary Resources

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Problem Solving Posters

https://www.scoilnet.ieuploads/resources/33098/32842.pdf Added: 20 May 2020 Contributor: PDST Resource type: Demonstration / Reference

A selection of problem solving posters for display in the classroom. Eight posters to choose from.

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Posters for display in the classroom

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Problem Solving Questions

https://www.scoilnet.ieuploads/resources/33099/32843.pdf Added: 20 May 2020 Contributor: PDST Resource type: Worksheet

Forty-seven problem solving questions that were originally created for Junior Cert students but links to the new strand unit 1.4.

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Strand: 1. Unifying

Strand unit: 4. Problem Solving

Suggestions for use: Useful resource for planning problem solving questions

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Problem Solving Questions for Leaving Cert

https://www.scoilnet.ieuploads/resources/33100/32844.pdf Added: 20 May 2020 Contributor: PDST Resource type: Worksheet

A selection of problem solving questions on the topic of statistics and probability. These questions would be suitable for students studying for the Leaving Cert Foundation Level.

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Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Suggestions for use: Useful resource for planning problem solving questions

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Problem Solving Questions Leaving Cert

https://www.scoilnet.ieuploads/resources/33102/32846.pdf Added: 20 May 2020 Contributor: PDST Resource type: Worksheet

A selection of problem solving questions containing ordinary and higher level Leaving Certificate questions.

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Strand: Supplementary Resources

Strand unit: Revision

Suggestions for use: Useful resource to help planning problem solving questions

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Solutions to Problem Solving Questions Junior Cert

https://www.scoilnet.ieuploads/resources/33103/32847.pdf Added: 20 May 2020 Contributor: PDST Resource type: Worksheet

Solutions to the Junior Cert problem solving activities. The problem solving worksheet can be accessed here >
https://www.scoilnet.ie/search/resource/entity/show/Lre/33099/

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Strand: 1. Unifying

Strand unit: 4. Problem Solving

Suggestions for use: Solutions to the problem solving Junior Cert document

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Solutions to Problem Solving Questions (Leaving cert Foundation Level)

https://www.scoilnet.ieuploads/resources/33104/32848.pdf Added: 20 May 2020 Contributor: PDST Resource type: Worksheet

Leaving Certificate Foundation Level students can review the solutions to the problem solving questions using this document. The problem solving worksheet without the solutions is available here>
https://www.scoilnet.ie/search/resource/entity/show/Lre/33100/

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Useful for planning problem solving questions

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Solutions to Problem Solving Questions (Leaving Cert OL and HL)

https://www.scoilnet.ieuploads/resources/33105/32849.pdf Added: 20 May 2020 Contributor: PDST Resource type: Worksheet

Leaving Certificate Ordinary and Higher Level students can review the solutions to the problem solving questions using this document. The problem solving worksheet without the solutions is available here>
https://www.scoilnet.ie/search/resource/entity/show/Lre/33102/

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Useful for planning problem solving questions

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Teaching through problem solving to promote Mathematical thinking.

https://www.scoilnet.ieuploads/resources/33106/32850.pdf Added: 20 May 2020 Contributor: PDST Resource type: Presentation

Presentation by Professor Takahaski at maths counts 2016

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Useful resource for teachers to help with planning problem solving in the classroom

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Number problems

https://www.scoilnet.ieuploads/resources/33107/32851.pdf Added: 20 May 2020 Contributor: PDST Resource type: Worksheet

Problem solving questions focused on number

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Strand: 3. Number

Strand unit: 1. Number Systems (Complex Numbers,Sequences)

Suggestions for use: Useful problems solving questions to help with planning

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Expanding Car park

https://www.geogebra.org/m/HBEKBcuN Added: 20 May 2020 Contributor: PDST Resource type: App/software

Use in conjunction with the corresponding activity from modular course 4 (Problem solving booklet)

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Use in conjunction with the corresponding activity from modular course 4 (Problem solving booklet)

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Net of a Cone

https://www.scoilnet.ie/pdst/maths/...perpendicular-lines/net-of-a-cone1/ Added: 26 Jun 2019 Contributor: PDST Resource type: Experiment / Guide/notes

The following applet can be used to explore the net of a Cone and it's surface area formula.Use slider to change the radius of the base and slider h to change height of the cone. Finally use the Net slider or press the play button to show how the cone unraps into its net.

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Strand: 3. Geometry & Trigonometry

Strand unit: 2. 2D Shapes and 3D Solids

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Net of a Cylinder

https://www.scoilnet.ie/pdst/maths/...pendicular-lines/net-of-a-cylinder/ Added: 26 Jun 2019 Contributor: PDST Resource type: Experiment / Guide/notes

The following applet can be used to explore the net of a Cylinder and it's surface area formula. Click on the formula to see the surface area formula for a cylinder. Change the height of the cylinder by dragging the h slider. Click play below the n slider to open the cylinder out.

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Strand: 3. Geometry & Trigonometry

Strand unit: 2. 2D Shapes and 3D Solids

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Net of a Cube

https://www.scoilnet.ie/pdst/maths/student/lc/lc-numbers/net/ Added: 09 Nov 2019 Contributor: PDST Resource type: Guide/notes / Simulation

Interactive GeoGebra files to visualise net of a cube.

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Strand: 3. Number

Strand unit: 4. Length, Area & Volume

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Arthur Benjamin: A performance of "Mathemagic" - Video

http://www.ted.com/talks/arthur_benjamin_does_mathemagic Added: 28 Jul 2016 Contributor: Scoilnet Resource type: Audio / Video

In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3-digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it?
See related video on more patterns in maths!

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Strand: 1. Unifying

Strand unit: 4. Problem Solving

Suggestions for use: Use the video when explaining squares to first year students. Students should check Arthur's answers using their calculators as a way to practice finding squares of numbers on a calculator.

Key Skills: Managing Information and Thinking

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Math class needs a makeover | Dan Meyer

https://www.youtube.com/watch?v=NWUFjb8w9Ps Added: 20 May 2020 Contributor: PDST Resource type: Audio / Video

At TEDxNYED, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Interesting perspective on teaching Mathematics that could be used to help plan

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Professor Takahashi keynote speech at Maths counts 2016

https://www.youtube.com/watch?v=k-HdYsq_xp4 Added: 20 May 2020 Contributor: PDST Resource type: Audio / Video

Professor Takahashi gives an overview of the success of teaching through problem solving

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Motivation for teaching through problem solving and how it can be a successful approach.

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Maths counts 2016 webpage

https://www.projectmaths.ie/for-tea...hers/conferences/maths-counts-2016/ Added: 20 May 2020 Contributor: PDST Resource type: Lesson Plan / Presentation / Reference / Other / Primary Source

further resources including lesson plans, worksheets and videos of Professor Takahashi teaching a lesson.

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Useful for teachers to help create lesson plans and resources based on problem solving for students

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Problem of the week web page

https://www.cemc.uwaterloo.ca/resources/potw.php Added: 22 May 2020 Contributor: PDST Resource type: Other

Website where you can sign up with your email to receive up to 4 problems every Thursday afternoon. Site also contains an archive of great problems.

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Strand: Supplementary Resources

Strand unit: Other

Suggestions for use: Problems that can be used for planning and creating resources for students from first year to sixth year.

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