1 / 24

Thinking Mathematically

Thinking Mathematically. Jonathan Hall Maths Lead Practitioner Leeds City Academy @StudyMaths MathsBot.com. Problems and strategies to encourage mathematical thinking in the classroom. Workshop Aims:. Try a variety of Problems to encourage mathematical thinking in the classroom.

rinaldo
Télécharger la présentation

Thinking Mathematically

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. Thinking Mathematically Jonathan Hall Maths Lead Practitioner Leeds City Academy @StudyMaths MathsBot.com Problems and strategies to encourage mathematical thinking in the classroom

  2. Workshop Aims: Try a variety of Problems to encourage mathematical thinking in the classroom. Use the RUBRIC ‘ENTRY, ATTACK, REVIEW’ When Tackling a problem; Starting with specialised cases before working towards generalised solutions. Encourage use of rigorous mathematical language.

  3. 1089 Choose any 3 digits (At least 1 different from the rest). Write down the largest 3-digit number you can make. Write down the smallest 3-digit number you can make. Find the difference between them. Reverse the digits of your answer and add THEM Together. Why does this work?

  4. Thinking Mathematically J. Mason, L. Burton, K. Stacey

  5. Geoboards • Make a rectangle, triangle, parallelogram and trapezium. • The shapes must not be congruent to each other. • The shapes must each have an area of 16 square units. • The shapes must not touch each other. mathsbot.com/manipulatives/geoboard

  6. Geoboards mathsbot.com/manipulatives/geoboard

  7. Geoboards Make 4 rectangles, each with an area of 12 square units. The rectangles must not touch each other. The rectangles must not be congruent to each other. Can you do it for an area of 15 square units? Why is it harder? mathsbot.com/manipulatives/geoboard

  8. Geoboards How many different triangles with an area of 6 square units can you make on a 10 x 10 geoboard? Make a rectangle, triangle, parallelogram and trapezium all with an area of 16 square units. mathsbot.com/manipulatives/geoboard

  9. Chessboard Squares It was once claimed there are 204 squares on a chessboard. Can you justify this claim?

  10. Chessboard Squares • What about an n x n board? • What about rectangles? • What if we extend to work in 3 dimensions.

  11. Nearest Squares Is squared closer to squared or squared?

  12. Nearest Squares mathsbot.com/manipulatives/tiles

  13. Tethered Goat A goat is tied by a 6 metre rope to the outside corner of a rectangular shed. The shed measures 4 metres by 5 metres and is in the middle of a large grassy field. What area of grass can the goat eat?

  14. Tethered Goat + + In general, with rope (r), width (w) and length (l). Assuming r > w and r > l we have: + +

  15. Palindromes “All four-digit palindromes are divisible by 11” Is this true?

  16. Palindromes

  17. Paper Strip A long strip of paper is folded in half so the two ends meet. Now repeat the process with the new strip. How many creases are there once the paper is unfolded? How many creases will there be if the operation is repeated 10 times?

  18. Paper Strip What if you folded the paper into thirds each time? Quarters? N Parts?

  19. What is the length of the side of the square? How many ways can you solve the problem? Trigonometry, similar shapes, area, Pythagoras? What do you notice about the side lengths and your solution? What questions could you ask?

  20. What is the length of the side of the square? = Notice: 3 × 4 = 12 and 3 + 4 = 7? What questions do you ask yourself? Can you predict, conjecture, generalise?

  21. One Sum Choose two fractions which sum to 1. a) Square the larger and add it to the smaller. b) Square the smaller and add it to the larger. Which answer is the biggest?

  22. Specialising and Generalising

  23. Thinking Mathematically J. Mason, L. Burton, K. Stacey

  24. J. Mason, L. Burton, K. Stacey EEF RAG

More Related