研習示範題

Sample demonstration questions PAMA uses across the four Teacher Training Seminars, organised by seminar stage.

1st Training Seminar

Is memorizing the formulae a pre-requisite for learning addition and subtraction well? Please share your opinions and give examples using 5's complement addition and 5's complement subtraction.

Please give examples using 10's complement addition and 10's complement subtraction formulae (include both 5's and 10's formulae and explain the differences).

Please give examples of 10's mixed addition and subtraction (list the 10 common examples before you demonstrate).

Please demonstrate how to conduct mental arithmetic with listening (one digit and two digits). Explain the focus and timing to start this exercise.

Please demonstrate how to conduct mental arithmetic with reading (one digit). Explain the focus and timing to start this exercise.

Please give an example of addition and subtraction where students make common mistakes — for example, a mistake of 1 or 2 in their answer.

Please explain the focus of abacus 2-digit addition (especially moving into 50, moving into 100, and mixed formulae addition).

Please explain the focus of 2-digit subtraction (especially subtracting from 50, 100, and mixed formulae subtraction).

Please demonstrate how to do multiplication on the abacus (setting place, 2 × 1, 3 × 1, and 2 × 2).

Please demonstrate how to do division on the abacus (setting place, 3 ÷ 1, 4 ÷ 1).

2nd Training Seminar

Please give examples of common mistakes students make when doing 2-digit addition and subtraction — a difference of 10 in answers, missing a number, repeating a number, wrong place, switching place, etc.

Please demonstrate how to do addition and subtraction with fractions on the abacus (explain the concept of dimes and cents, how to write answers).

Please demonstrate 4 ÷ 2 division (no over-quotient). Give examples of different quotient positions on the abacus for large and small divisors.

Please demonstrate 4 ÷ 2 division (over-quotient). Give examples of over-quotient by one, by two, and by three or more.

Please demonstrate 4 ÷ 2 division (same-first digit). Give examples where the second digit of the divisor is either big or small.

Please demonstrate 5 ÷ 2 division. Explain the difference between questions where the answer has a zero in the middle or at the end.

Please demonstrate 5 ÷ 3 division. Explain what to do when the third digit of the divisor is an over-quotient.

Please demonstrate 3 × 3, 2 × 4, 4 × 2 multiplication. Give examples of head-to-head multiplication and small-times-big multiplication.

Please explain the focus of 2 × 1, 3 × 1 mental multiplication and 3 ÷ 1, 4 ÷ 1 mental division.

Please demonstrate how to solve for square roots (2-digit integers). Explain the steps and the half-of-squares formula.

3rd Training Seminar

Please demonstrate addition and subtraction with fractions and negative numbers (focus on solving from the highest place and writing answers).

Demonstrate solving for square roots (3-digit integers).

Demonstrate solving for square roots (3-digit fractions).

Demonstrate Level 3 multiplication (name numbers). Explain setting place, rounding, and finding the answer to the requested place.

Demonstrate Level 3 multiplication (no name numbers). Explain setting place, rounding, and finding the answer to the requested place.

Demonstrate Level 3 division (name numbers). Explain setting place, rounding, and finding the answer to the requested place.

Demonstrate Level 3 division (no name numbers). Explain setting place, rounding, and finding the answer to the requested place.

Demonstrate consecutive multiplication and division, and primary operations questions.

Demonstrate mental multiplication 2 × 2, 2 × 3, 3 × 2. Explain the connection between mental addition/subtraction ability and mental multiplication ability.

Demonstrate mental division 4 ÷ 2. Explain the different methods for regular, over-quotient, and same-first-digit questions.

4th Training Seminar

Demonstrate Level 1 and 2 multiplication on the abacus. Explain the advantages and disadvantages of setting place last vs. small-times-big.

Demonstrate Level 1 and 2 division. Explain how to determine the place values of dividend and divisor, and how omission saves time.

Demonstrate omission techniques for multiplication (name number and no name number). Explain what to pay attention to.

Demonstrate omission techniques for division (name number). Explain what to pay attention to.

Demonstrate omission techniques for division (no name number). Explain the difference between numbers that are dividable and not.

Demonstrate solving for cubic roots (2-digit integers). Explain the steps and how returning works.

Demonstrate solving for cubic roots (3-digit integers). Explain the steps and what to do when the divisor is over 100.

Share your favourite mathematical or numerical games that can be played with students (2 to 3 games).

Explain how the one-way clear method works, compared with the current methods for addition, subtraction, multiplication, and division.

Share your special experience and inspiration when teaching — anything about teaching, competition, instructor training, or certification exams.