B1.3 Read, represent, compare, and order rational numbers, including positive and negative fractions and decimal numbers to thousandths, in various contexts.
Activity 1: The Human Number Line (Comparing and Ordering Rational Numbers)
Materials
- pieces of cardboard
- felt-tip pen
- calculator (if needed)
Cut cardboard boxes of \(30\;{\rm{cm}} \times 30 \;{\rm{cm}}\).
Write a rational number on each card. Be sure to have integers (positive and negative), mixed numbers, decimal numbers (terminating and repeating) and 0.
To begin the activity, determine a convenient location where all students can be next to each other to "build" the human number line. Distribute a card to each student. Each student must go to the "right place" in order to build this line.
Important criteria to mention:
Small numbers are on the left; numbers should be in ascending order from left to right.
Take a picture of the human number line and project it on the wall or whiteboard. Ask the students to analyze it. Following this analysis, ask them questions and invite them to move to the right place if necessary. Repeat the exercise if necessary. Note the vocabulary, discussions and strategies used by the students.
To help them order rational numbers correctly, here are some questions that might help their thinking:
- Is the number x to the right of the number y? Why is it so?
- Is the number x greater than the number y? How do you know that?
The goal is to have all the numbers (students) in ascending order (from left to right).
Review the activity by inviting students to share their thought processes about positioning themselves on the number line.
Activity 2: The Human Fraction Number Line (Comparing and Ordering Fractions)
Do the same exercise with only fractions.
(Suggestion: do this activity with small groups of four to five students before doing it with the class)
Start with fractions between -1 and 1. Choose simple denominators (half, third, fourth, fifth, tenth).
Discuss different ways to compare fractions (common denominator, convert to decimal, or other student strategies).
Activity 3: The Largest Number Wins (Reading and Comparing Numbers)
Prepare a set of 30 cards, with numbers from -10 to 10 for each student.
Be sure to have integers (positive and negative), mixed numbers, decimal numbers (terminating decimal).
Also make sure to have several equivalent numbers written in different forms (example: 0.5; \(\frac{1}{2}\); \(\frac{5}{10}\)) and also decimal numbers where place value comes into play (for example, 3.50; 3.05; 3.55).
Rules of the game
Both students receive the same amount of cards and place them in a deck face down on the desk, so they can't see the numbers written on the cards.
At the same time, both students will turn the card that is on top of their deck. The student with the highest value card wins the battle and keeps the 2 cards, placing them at the bottom of their deck.
*A battle occurs when both students turn over 2 cards that have the same value (number with equivalent value). Each student must then turn over the next 3 cards in their deck and compare who has the highest value on the third card.
The student who wins this battle then keeps the 6 turned cards.
The student who has the most cards at the end of the play period is the winner (or if a player has all the cards of their opponent).
Activity 4: The Surprise Bowl (Reading and Representing Rational Numbers)
Materials
- 5 cm x 5 cm cards
- felt-tip pen
- plastic bowl
Each student receives 3 blank cards. Each student writes a whole number on the first card, a fraction on the second and a decimal on the third. All students place their cards in the surprise bowl.
Ask a student to select a card from the bowl and ask all students to represent it in another equivalent form.
Select a few students to share their answers and strategies.
Challenges: 2 or 3 equivalent representations
Example
The chosen number is 0.8.
The student may write, for example, \(\frac{8}{{10}}\), \(\frac{4}{{10}}\) + \(\frac{4}{{10}}\) or \(\frac{4}{5}\).
Activity 5: Finding Temperatures (Comparing Integers and Decimal Numbers)
Materials
- one tablet or computer per student
Each student builds a 2-column chart like the one below.
|
Locations |
Average Temperature in January (oC) |
|---|---|
The students are to research the average temperature in January(oC) in 13 cities/locations in Canada. They must include one city from each province and territory (10 provinces and 3 territories).
*Alternatively, the average January temperature for the provinces or territories can be provided so that all students have the same answers; this may facilitate the analysis.
Individual analysis: The student answers the following questions.
- What do you notice about the average temperatures in January?
- Where is it warmer in January? How do you know?
- Where does it get colder in January? Explain.
- Which expression calculates the temperature difference in January between the warmest and the coldest city? Find this temperature difference.
- List the cities from the coldest to the warmest temperature. Do you notice a trend?
Consolidation of Learning
Ask students to construct a number line and place the 13 cities on it.
- Where on the number line will the city with the coldest January temperature be? Explain your thinking.
- Where on the number line will the city with the hottest January temperature be? Explain your thinking.
Explain.