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The Guides for Effective Instruction in Mathematics Revised

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B1.2 Compare and order whole numbers up to and including 1000, in various contexts.

Activity 1: Well-Ordered Numbers (Compare and Order)

Directions

Write the following numbers on pieces of paper: 426, 213, 889.

Ask students to represent these 3 numbers with base ten blocks and label them with the written numbers.

Ask the following questions:

  • Visualize these numbers on a number line. Which two numbers are closest? How do you know?
  • Which number is greater? How do you know?
  • Which number is closest to 1000? How do you know?
  • Which number is closest to 500? How do you know?

Ask students to place these three numbers and their representations in ascending order (from least to greatest)

Group students in pairs and give each group base ten blocks and a 3-digit number card.

Ask them to represent the number with the base ten blocks.

In turn, each group places their 3-digit representation in relation to the other three numbers already ordered and explains their reasoning.

Ask questions such as:

  • How did you know where to place your number?
  • Is your number close to 1000? How do you know?
  • How many more or less hundreds, tens and ones does your number have?"

Source: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 56.

Activity 2: The Joker

Identify sequences of numbers in ascending and descending order.

Directions

For each team you will create four sets of number cards including a Joker and 10 consecutive number cards (for example, 232 to 241, 376 to 385). Use a different colour for each set. For example, create a blue set with the numbers 232 to 241 and a Joker. (The image of a Joker will have to be printed). Each team will receive a total of 44 cards. Write the four number sequences from the different set of cards on the board so that the students can refer to them. For example, blue cards: 276 to 285; yellow cards 376 to 385.

Explain the rules of the game:

  • The objective of the game is to turn over as many cards as possible before the four Jokers are turned over.
  • The cards are shuffled and stacked face-down on the table to form four rows of 10 cards, each row containing only cards of the same suit. The remaining 4 cards are stacked face down on the table.
  • A team member turns over the top card from the stack of four, places it in the sequence in the appropriate position, and picks up the card it is replacing. For example, if one of the chosen sequences consists of the numbers 276 to 285 and the card turned over is 279, it should be placed in the 4th position of that sequence.
  • The next player takes the removed card and places it in the appropriate position in the appropriate sequence. For example, if the removed card is 276, it must be placed in the 1st position of the blue sequence that starts with 276.
  • When a Joker is turned over, another card must be taken from the stack.
  • The game continues until all four of the Jokers are turned over.

Provide number charts as needed to check numbers in a sequence.

Circulate and ask questions such as:

  • Name the number you just turned over. Which numbers come before and after in the sequence?
  • What would be the next number in the sequence if we added another card? 2 more cards? 5 more cards? 10 more cards?
  • What would be the 1st number if we added a card at the beginning of the sequence?
  • What is similar about the four number sequences?

Source: translated from Guide d'enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 22-23.

Activity 3: Numbers That Move

Ask students to write a number from 505 to 980 on their small whiteboard or on a piece of paper.

Divide the students into two groups.

One of the groups stands up and places themselves in ascending or descending order by looking at the numbers written on their board.

When the team is finished, the other students look at the numbers and determine how well the team did.

Repeat the same steps, alternating groups of students.

Activity 4: Number Strip Game

Number of players 2 teams of 2 players

Goal of the game to fill in all the squares on the board.

Materials

Directions

Place the cards face down on the table.

Teams take turns picking three cards (for example, 2, 1 and 4). Each team discusses how to form a number with these three numbers (for example, 124, 241, 412). They must consider where they want to place their number on their strip.

The team loses its turn when it cannot form a number that can be placed on the strip.

Note: It is important to model this game for students beforehand. Discuss with students why they decided to place their numbers in the different locations.

Variation

Play collectively by giving a strip to each student.

Vary the strips by changing the two numbers at the ends: 200 and 1000, 150 and 900, etc.

Source: translated from L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).