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 mat with a grid for each team and make about three squares per team member. On the squares, write numbers that have been problematic for the students (for example, numbers in the hundreds that have 0 in the tens position).
Distribute different coloured bean bags, a large sheet of paper and a marker, as well as base ten blocks (or other materials) and place value mats to each team member.
Explain the rules of the game:
- Each team member throws their bag on the grid and says the number on the square where it lands. They leave the bean bag where it has landed.
- Each student writes the number on their large sheet of paper and represents it using the base ten blocks using the place value mats if desired.
- The game ends when all numbered squares on the mat are covered with bean bags.
Teacher Moves
Circulate and ask the following questions:
- Name the number you threw your bean bag 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? Represent 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: translated from Guide d'enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, 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, counters, 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 \(23 + 36\), count 23, 33 , 43 and 53 on a number line, then add the remaining 6 of the 36 to get 59).
Source: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 60.
Activity 3: Skip Counting Up and Down
Group the students in pairs and give each team a calculator and explain that today, it is going to be a skip counting machine.
Ask students to press the Delete key before starting the game.
Skip Counting Up
Explain the rules of the game:
- Student A enters a 2-digit number and shows it 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 in the skip-counting sequence (the next number when counting by 10s).
- Student B presses the = key and both students check this answer.
- Students continue to take turns predicting the next number that the calculator will display.
- The game continues until students reach or exceed a given number (for example, 300).
The game can also be played using 50, 100, and 200 as the skip-counting number with 1000 as the number to reach.
Skip 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: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 183.
Activity 4: One Hundred Sit-Down
Invite students to form a circle.
Explain 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.
- a student starts the game by saying "25";
- the next student in the circle adds 25 to the previous number to say "50";
- the third student says "75" 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 skip-counts (for example, skip count by 5s or 10s). However, the starting number must make it possible to arrive at 100 or its multiples.
Source: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 184.