1 / 17

A Problem Solving Guide for Grades 7 - 9

A Problem Solving Guide for Grades 7 - 9. Graeme Evans St John’s College evans@sjc.co.za. The Groundwork. Be well drilled in number basics such as: Prime factorisation LCM and HCF Ratio Remainders Exponents Number Patterns Understand the use of simple algebra

najila
Download Presentation

A Problem Solving Guide for Grades 7 - 9

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A Problem Solving Guide for Grades 7 - 9 Graeme Evans St John’s College evans@sjc.co.za

  2. The Groundwork • Be well drilled in number basics such as: • Prime factorisation • LCM and HCF • Ratio • Remainders • Exponents • Number Patterns • Understand the use of simple algebra • Can simplify difficult numerical calculations • Can generalise patterns

  3. Exposure • Give students a sheet of problems to try on their own • Don’t intervene with the method • Answers only are better than solutions • Enter Maths competitions • Have Maths competitions/Fun Days in school

  4. Developing skills • Review many maths Olympiad papers • Categorise questions • Note the skills which are often needed e.g. are there simple formulae for the following? • 1+2+3+4+5+6+….. • 1+3+5+7+9+11+…… • How many handshakes in a room of 20 people? • A solid grounding in basic numerical skills added to a knowledge of common results with experience of their application, are essential ingredients for the young problem solver. • As teachers, we can help the students with the above, without needing to be better problem-solvers than they are!

  5. Igniting the Passion • Get students and teachers to read around the subject: • Fermat’s Last Theorem – Simon Singh • The Code – Simon Singh • Conned Again Watson! – Colin Bruce • E = mc2 – David Bodanis • The Joy of Maths – Theoni Pappas • You are a Mathematician – David Wells • Hoard of Mathematical Treasures – Ian Stewart • Check out Top Documentaries: http://topdocumentaryfilms.com/fermats-last-theorem/ • Discuss mathematical theorems that have been proved ….. and those that have yet to be proved!

  6. Grade 7 and Grade 8 curriculum • Often difficult to apply to real world situations • Lots of great problem solving applications • Student’s often fail to make the link from what they learn in the classroom to application in problem-solving • As teachers, we need to help the learners to see the point in basic skills.

  7. Example 1(a) – Spot the pattern Questions to ask: What do you notice about the result of each expression? What is the next term in the sequence? How are the terms under the root sign related? What is the value of: What is the nth term of the sequence?

  8. Example 1(b) – Spot the Pattern Questions to ask: What do you notice about the result of each expression? Can you predict the answer to

  9. Example 2 - Simple Algebra Find the value of: without using a calculator. Notice how closely related the numbers are. Let x = 1234.

  10. Example 3 - Remainders A bug travels in a spiral as follows: 4+19 x 3 = 61 cm What distance will the bug travel on the 20th move? In what direction will the bug be facing during the 2014th move? 2014/4 =503 rem 2 Therefore, East

  11. 108o 108o Example 4 - A Geometry Application 36o 72o 72o

  12. Example 5 – Prime factors can be helpful

  13. Example 6 – Why put ratios in simplest form?

  14. Example 7 – Taxicab routes

  15. How many routes from A to X travelling only Right and Up?

  16. How many routes from top to bottom spell TAXICAB? 1 1 1 2 1 1 1 3 3 1 4 4 6 1 1 10 10 5 5 1 1 20 6 15 15 6 1 1 Total number of routes = 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64

  17. Example 8 - Counting techniques http://ed.ted.com/lessons/how-many-ways-can-you-arrange-a-deck-of-cards-yannay-khaikin

More Related