B1.4 Count to 1000, including by 50s, 100s, and 200s, using a variety of tools and strategies.
Activity 1: Throw and Count! (Connection Between Representations)
Directions
Prepare a tiled mat for each team (make about 3 squares per team member) and write in the squares the numbers that pose a problem for the students (for example, numbers having hundreds with a 0 in the tens position).
Distribute different coloured sandbags, a large sheet of paper and a marker, as well as base ten materials (or other materials) and place value mats to each team member.
Explain the rules of the game:
- Each team member throws their bag on a square, says the number on the square and leaves the bag there.
- Each student then writes the number on their large sheet of paper and represents it using the base ten materials (use the place value mats if needed).
- The game ends when all the numbered squares on the tiled mat are covered with sandbags.
Intervention
Circulate and ask the following questions:
- Name the number you threw your sandbag on.
- How many hundreds are there in this number? tens? ones?
- What is the number just before? just after?
- Represent it using your manipulatives.
- What would be the new number if we added 2? 5? 10? 100?
- Would your representation be different? Demonstrate it with your material.
- If the number has 9 ones (for example, 889) and another one is added, how would you change your representation?
- If the number has 9 tens (for example, 894) and another ten is added, how would you change your representation?
- Compare the numbers you have chosen.
- Did other students represent the number… in a different way? How did they do it?
- Name the numbers of another team member.
Source: Guide d'enseignement efficace des mathématiques de la 1re à la 3e année, p. 21-22.
Activity 2: Strategies for Counting
Provide opportunities to count beyond 100 in learning situations where number sense is emphasized and a relationship is established between numbers and their symbolic representation.
Provide problem-solving opportunities in contexts that encourage students to use combining as a counting strategy (for example, combining objects into sets of 50, 100, and 200).
Provide opportunities to participate in games that promote counting strategies (for example, games that include the use of money).
Provide counting activities related to daily life (for example, a fundraiser for a charity or preparation for a field trip).
Make manipulatives available to students (for example, tokens, hundreds charts and number lines).
Provide opportunities to use a variety of counting strategies that allow for larger numbers (for example, counting by 100s from 101, 201, 301…).
Provide opportunities to create and use an open number line to facilitate counting for problem solving (for example, to find the result of \(23 + 36\), they and they count 23, 33 , 43 and 53 on a number line, then add the remaining 6 of the 36 to get 59).
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 6, 7 & 9.
Activity 3: Counting and Counting Down by Intervals
Group the students in pairs and give each team a calculator.
Ask students to press the Delete key before starting the game.
The skip count
Explain the rules of the game:
- Student A enters a 2-digit number that the student shows to Student B.
- Student A then presses the + key and enters 10.
- Student B gives the answer without looking at the calculator display.
- Student A then gives the number that should follow in the sequence of counting in intervals of 10.
- Student B presses the = key and both students check this answer.
- Students continue to take turns predicting the number that the calculator will display.
- The game continues until students reach or exceed a given number (for example, 300).
Also play this game by counting in increments of 50, 100, and 200 to 1000.
Counting down
Explain the rules of the game:
- Student A enters a 3-digit number, presses the - key, then enters 10 (or 100).
- Student B presses the = key. The calculator then subtracts 10 (or 100) from the starting number.
- The game continues as in the previous game.
The numbers 2, 5 or 25 can also be used as counting intervals.
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 183.
Activity 4: At 100, We Sit Down
Invite students to form a circle.
Clarify that the game is similar to musical chairs and that the student who says "100" or a multiple of 100 (200, 300, 400, etc.) must sit down.
Ask:
- a student to start the game by saying "25";
- the next student in the circle to add 25 to the previous number to say "50";
- the 3rd to do the same and so on.
Continue counting until only one student is left standing.
Give different starting numbers each time students play this game and use different intervals (for example, intervals of 5, of 10). However, the starting number must make it possible to arrive at 100 or its multiples.
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 184.