Resource 2: Fuller list of statements for Activity 1

This is an extensive (but not exhaustive) list of statements that could be used for Activity 1. Select the area (operations, which number systems, etc.) that you would like your students to work on. Students are asked which of the following statements are ‘always true’, ‘sometimes true’ or ‘never true’, and asked to explain why.

Working on the property of closure

  1. The sum/difference/product/quotient of two natural numbers is a natural number.
  2. The sum/difference/product/quotient of two whole numbers is a whole number.
  3. The sum/difference/product/quotient of two integers is NOT an integer.
  4. The sum/difference/product/quotient of two rational numbers is a rational number.
  5. The sum/difference/product/quotient of two irrational numbers is an irrational number.
  6. The sum/difference/product/quotient of two real numbers is a real number.

Working on inverses

  1. There are an infinite number of pairs of irrational numbers whose sum/product is 0 (or 1).
  2. There are an infinite number of pairs of rational numbers whose sum/product is 0 (or 1).
  3. There are an infinite number of pairs of integers whose sum/product is 0 (or 1).
  4. There are an infinite number of pairs of whole numbers whose sum/product is 0 (or 1).
  5. There exists a pair of whole numbers whose sum/product is 0 (or 1).

Working on decimal representations

  1. A terminating decimal can be expressed as a ratio of an integer to a non-zero integer.
  2. A non-terminating decimal can be expressed as a ratio of an integer to a non-zero integer.
  3. A repeating decimal can be expressed as a ratio of an integer to a non-zero integer.
  4. A non-repeating decimal can be expressed as a ratio of an integer to a non-zero integer.
  5. The sum of a rational and an irrational number is NOT a repeating decimal.
  6. The sum of two real numbers is a non-repeating, non-terminating decimal.
  7. The product of a rational and an irrational number is a repeating decimal.
  8. The product of two real numbers is NOT a non-repeating, non-terminating decimal.
  9. The product of a rational and an irrational number is a repeating decimal.
  10. The product of two real numbers is NOT a non-repeating, non-terminating decimal.

Locating numbers on a number line

  1. The exact location of a natural number/integer cannot be determined on a number line.
  2. The exact location of an integer cannot be determined on a number line.
  3. The exact location of a rational number can be determined on a number line.
  4. The exact location of an irrational number can be determined on a number line.
  5. The exact location of a real number can be determined on a number line.
  6. The sum of two natural numbers is to the right of each of the two numbers on a number line.
  7. The difference of two integers is to the left of each of the two integers on a number line.
  8. The sum of two real numbers is to the right of each of the two numbers on a number line.
  9. The quotient of two integers is always to the left of each of the two integers on a number line.
  10. There are infinite real numbers between any two real numbers on a number line.
  11. There are finite natural numbers between any two real numbers on a number line.
  12. There are infinite irrational numbers between any two rational numbers on a number line.
  13. There is at least one whole number between any two whole numbers.

Exponentiation

  1. The number a2 is a natural number if a is a natural number/integer.
  2. The number a2 is positive for every real number.
  3. The number ab is greater than both a and b.

Resources

Resource 3: Activity 1 in ‘card’ format