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 two decimal numbers. The student is responsible for inserting one number between the two given numbers.
Examples of statements
Insert 1 number between the 2 given numbers.
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\(6.5\)
\(7\)
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\(-0.1\)
\(0\)
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\(3.6\)
\(3.61\)
Do the same exercise with fractions.
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\(\frac{2}{3}\)
\(\frac{20}{24}\)
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\(\frac{52}{100}\)
\(\frac{6}{10}\)
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\(-3\)
\(\frac{-11}{4}\)
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)
Provide two numbers and invite students to write on their poster a number that is located somewhere between them. Have all students work together to put themselves in the correct sequence at the front of the classe.
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.
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6
Student 1
_____7Student 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
_____6,1Student 2
Variations to the Activity
Choose numbers that are closer together, change the form of the rational numbers (start with two fractions), and also incorporate irrational numbers.