This document provides information about problem solving and pattern blocks. It discusses goals of teaching problem solving such as improving willingness and abilities to select strategies. It also describes what pattern blocks are and how they can help students decompose shapes and see visual patterns. Examples are given of using pattern blocks to construct shapes based on a numeric sequence. Finally, it introduces the Tower of Hanoi puzzle and provides the rules and formulas to calculate the minimum number of moves needed for different numbers of disks.

5. PROBLEM
SOLVING
it is a higher order cognitive process
a process that provides the
that requires the modulation and
content in which concepts and
control of more routine or
skills can be learned.
fundamental skills

6. Goals when teaching
Problem Solving
Make pupils pupils’ willingness
Improve our aware that many to try
Improve pupils’ abilities to select
get more
Make pupils aware of the problem
problems and be solvedtheir
can improve in more than
correct strategies. problem.
appropriate solution strategies.
solving answers to solving problems.
one way.
perseverance when

8. Making a Picture
Working Backward
Intelligent Guessing and Testing
Finding a Pattern
Considering Extremes
Organizing Data

9. Using a Computer or Calculator
Using Logical Reasoning
Solving a simpler Analogous Problem
Accounting for all Possibilities
Adopting a Different Point of View

12. What are
Pattern Blocks?

13. PATTERN BLOCKS

14. They help students to see visual
support on extending number sequences.
They allow students to see how
shapes can be decomposed into other
They allow students to see how shapes
shapes and introduce them to tiling.
can be decomposed into other shapes
and introduce them to tiling.

15. They allow students to see how
ANIMALS
shapes can be decomposed into other
shapes and introduce them to tiling.
FLOWERS

16. Boats & Ships
Rockets & Planes
Cars

17. Find a pattern in the following
1
sequence of figures and use your tiles
3 the fifth and
They allow students to see how
to construct and sketch
shapes can be decomposed into other
sixth figures. 4
2
shapes and introduce them to tiling.
1
3
4
2th th
5 & 6 Figure

18. Fifth how
They allow students to see
Figure
shapes can be decomposed into other
9 tiles
shapes and introduce them to tiling.

19. Sixth how
They allow students to see
Figure
shapes can be decomposed into other
shapes and introduce themtiles
11 to tiling.

21. They allow students to see how
shapes can be decomposed into other
shapes and introduce them to tiling.
Figure 1
Figure 3
Figure 2
Figure 4
Figure 5
Figure 6

22. Figure Number of Tiles
1 1
2 3
3 5
4 7
5 9
6 11

24. tn = allow students tod how
They
t1 + (n-1) see
Where: can be decomposed into other
shapes
shapes and introduce them to tiling.
tn = last term (nth term)
t1 = first number in the sequence
n = number of term
d = common difference

25. Find the general formula for the
nth term:
They allow students to see how
shapes can be decomposed into other
1, 3, 5, 7, 9, 11
shapes and introduce them to tiling.
Given:
t1 = 1
d=2

26. Formula for the nth term:

27. Figure Number of Tiles
1 1
2 3
3 5
4 7
5 9
6 11

28. They allow students to see how
shapes can be decomposed into other
• Number of
39
shapes and introduce them to tiling.
tiles for the
20th figure

29. They allow students to see how
shapes can be decomposed into other
• Number of
199
shapes and introduce them to tiling.
tiles for the
100th figure

32. TOWER OF HANOI
They allow students to see how
shapes can be decomposed into other
shapes and introduce them to tiling.
The Tower of Hanoi, also called Tower
of Brahma, is a mathematical game or
puzzle.

33. It consists of three rods and a number of
disks of different sizesto see how slide
They allow students which can
onto any can be decomposed into other
shapes rod. The disks should be in
ascending order of size them torod, the
shapes and introduce on one tiling.
smallest at the top.

34. They allow students to see how
shapes can be decomposed into other
shapes and introduce them to tiling.

35. They allow students to see how
shapes can be decomposed into other
shapes and introduce them to tiling.

36. They allow students to see how
shapes can be decomposed into other
shapes and introduce them to tiling.

37. Rules of the Game:
They allow students to see how
Only one disk can be moved at a
shapes can be decomposed into other
time.
shapes and introduce them to tiling.
No disk can be placed on top of
a smaller disk.
No two corresponding disks
should have the same color.

38. No. of Disks No. of Moves
1 1
They allow students to see how
2
shapes can be decomposed into3other
3 7
shapes and introduce them to tiling.
4 15
5 31
6 63
7 ?
8 ?

39. 1, 3, 7, 15, 31, 63
n = number of terms to see how
They allow students
shapes can be decomposed into other
21 = 2 -and introduce them to tiling.
shapes 1 = 1
n
Formula
22 = 4 - 1 = 3 2
23 = 8 - 1 = 7
24 = 16 - 1 = 15
25 = 32 - 1 = 31
26 = 64 - 1 = 63

40. No. of Disks No. of Moves
1 1
They allow students to see how
shapes can be decomposed into3other
2
3 7
shapes and introduce them to tiling.
4 15
5 31
6 63
7 127
8 255

41. They allow students to see how
shapes can be decomposed into other
shapes and introduce them to tiling.