At a Glance...

B1.5 Generate fractions and decimal numbers between any two quantities.

Activity 1: The Sandwich (Comparing Decimal Numbers and Fractions)

Materials

• 1 whiteboard per student
• erasable felt-tip pen

Write a series of statements with 2 decimal numbers. The student is responsible for inserting 1 number between the 2 given numbers.

Examples of statements

Insert 1 number between the 2 given numbers.

• \(6.5\)

  \(7\)

• \(-0.1\)

  \(0\)

• \(3.6\)

  \(3.61\)

Do the same exercise with fractions.

• \(\frac{2}{3}\)

  \(\frac{20}{24}\)

• \(\frac{52}{100}\)

  \(\frac{6}{10}\)

• \(-3\)

  \(\frac{-11}{4}\)

Activity 2 : The Increasing Sequence (Inserting 1 Rational Number Between 2 Given Numbers)

Materials

• posters with rational numbers
• blank posters (30 cm x 30 cm)

Select 2 students to move to the front of the class. Give them a poster with a number. The choice of numbers must be strategic. The student with the smallest number moves to the left.

Invite another student to write on their poster a number located between the 2 initial numbers. Continue in this manner until all students have successfully inserted 1 number between 2 students in the front.

At the end of the activity, the number sequence should be ordered (increasing numbers, from left to right).

Challenge

Do the activity in silence using gestures only.

Consolidation Questions

• How difficult did you find the activity and why?
• What strategies did you use?
• How can you insert a number between two given numbers?

Examples

Posters with students and starting numbers.

• 6

  Student 1

  _____

  7

  Student 2

* Choose one student at a time to insert a number that meets the given conditions. Student 3 writes their number on their poster and places it in the correct spot. Student 4 must then decide if they will write a number that will be between students 1 and 2 or between students 3 and 2.

• 6

  Student 1

  _____

  6,1

  Student 2

Variations to the activity

Choose numbers that are closer together, change the form of the rational numbers (start with 2 fractions), and also incorporate irrational numbers.