HOT Math-2

In the HOT Math series we publish a number of Hands-On Tasks for Mathematics. The practical activities link mathematics to other school subjects or to students’ experiences. Students’ age group: ± 12-14 yrs. No lesson plans are offered, as each idea will need adaptation to class level.

The students discover and learn to discover. Mathematics is not merely reproducing, but actively producing. The manipulative materials in this HOT Math series are learners’ materials and not demonstration aids for the teachers.

Activities with Click materials
Below are four tasks using the handy click-material. Tasks suitable for collaborative work are indicated with *.

Required material: PolydronTM, or Lokon, or any other system that is suitable for mconstructing geometrical figures/solids.

driehoekfiguren

Task 1: Build Solids with Triangles *
– Build as many different figures as you can, using only the triangles (max. 10).
– Make a sum-up of the figures, indicating their symmetries.

Assessment criteria for Task : Build Solids with Triangles

  • found at least 6 shapes
    # triangles max. # figures
    1, 2, 3, 5, 7, 9 0
    4, 6 1
    8 2
    10 6
  • quality of survey (e.g. with sketches)
  • indication of rotational and reflective symmetry

Task 2: Nets of a Cube
– Build a cube using squares and unfold it to make a net (cut-out).
– Make all possible different nets and sketch these clearly.

cubenetanim

Assessment criteria for Task 2: Nets of a Cube

  • mirrorred and rotated equivalents skipped
  • at least 8 (out of 11)  nets  found
  • all nets are correct
  • drawings are neat (with use of a ruler, squares are square and equal in size).

Task-3: Tiling
– Use only triangles and squares. Make a tiling pattern on the table.
– Draw a scetch of it.
– Describe which pieces come together at a corner point, and give an explanation for this.

planeby3by4

Assessment criteria for Task 3:

  • quality of sketch
  • explanation: 360° = 2 x 90° + 3 x 60°= 6 x 60°
  • Note: the pattern can be completely irregular

Task 4: Building Stairs
– Draw squares or use physical squares (or cubes) to build a staircase. Start with two steps and increase the height.
– Lay the figures of the growing stairs next to each other.
– Make a table of the number of squares required for each figure.
– How many extra squares are needed for each following figure?
– Predict how many squares will be needed for the 20-th figure?
– Explain how you reached this answer.

2dstairanim

Assessment criteria for Task 4: Building Stairs

  • quality of table (header, correct numbers).
  • formulation of increase
  • for 20-th figure: 210 squares (explanation)

More practical tasks and games can be found on the websites: gfsmath and NRICH

 

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