B1.4 Estimate the number of objects in collections of up to 50, and verify their estimates by counting.
Activity 1: Welcome to Our Home (Estimating, Cardinality)
Directions
Explain to students that the principal has asked each class group to put a welcome sign on its door and that the number of students in the class should be indicated by symbols or drawings.
Ask students to estimate the number of students in the class.
Write the estimates on the board and discuss the likelihood of the answers.
Check the estimates by counting.
Group students into pairs and ask them to create a poster.
Intervention
Circulate among the students and ask them to explain their approach and reasoning.
When presenting the posters, compare two posters that students have created: one with the total number of students and one without.
Ask students the following questions:
- What is similar about the posters? What is different?
- What does the number 24 represent? (Point out the link between the number 24 and the stars: cardinality of a number.)
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 51-52.
Activity 2: Counting Strategies
Provide opportunities for students to solve problems, which include counting strategies; for example, a role-playing game set in a bank or buying food for a birthday party.
Provide opportunities for students to play games that promote counting strategies; for example, games that involve moving tokens along a line or path and keeping track of counts as you move forward or backward. These games should include numbers in the tens whenever possible; for example, games that use two-digit numbers on a hundreds mat.
Provide students with counting activities related to daily life; for example, counting the line at the door or getting ready to go home.
Make manipulatives available to students, such as tokens, grids of 100, and vertical and horizontal number lines.
Provide opportunities for students to explore the numbers 5 and 10 as benchmark numbers for all other numbers.
Provide opportunities for students to use a variety of counting strategies.
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 5.
Activity 3: Object Collections (Counting)
This collection varies from month to month and takes into account the days of the current month. The objects chosen can be related to a theme, a season, a show, etc.
Each day, a student puts an object in the bag or box.
Each object is linked to a day of the month, so there will always be 28 to 31 objects per month. On Mondays, have a student add the objects for Saturday and Sunday.
The objects can be placed in a small clear plastic bag, a cut-out box attached to the wall, etc.
When the collection reaches 11, 21, and in some cases 31 objects, add another bag or box to expose students to groupings of 10. The important thing is that students can see the objects.
Note: When a ten is formed, put the 10 objects in an opaque bag or closed box. Students know that there are 10 objects in the bag or box and are less likely to start counting again.
Display small cards on top of the bags or boxes to indicate the symbolic representation of the number. Explain to students what the numbers mean when you display them; for example, for 27, you would display a "2", which represents 2 groups of 10 objects, which makes 20, and a "7", which represents the extra objects in the other bag. So you can have them say, "2 groups of 10 and 7 more is 27".
At the end of each month, objects are removed and a new collection is started. By starting the collection of objects again each month, students have the opportunity to practice the pattern of numbers from 1 to 31 and associate an object with each day (one-to-one correspondence). Numbers that are more difficult to learn, such as 11, 12, 13, 14, 15, 16, are reviewed each month, and students build a better understanding of these numbers by seeing their different representations concretely and symbolically. Those with a more solid understanding make fewer digit reversal errors in numbers, such as 21 and 12, and can better explain their values.
Each day, count the objects with the students. During this counting activity, add noise when you say a multiple of 10 to remind students that a group of 10 has been formed. For example, snap your fingers, tap your thighs, or clap your hands. Towards the end of the month (for example, 29), ask students if there is another way to count other than in increments of 1. A student may suggest starting at 10. You can then do it together: 10 (snap), 11, 12… 29.
Ideas for Object Collections
Tokens, buttons, plastic animals, marbles, pumpkin-shaped erasers, straws, or pencils (bundled with an elastic band), stickers and 10 frames, self-inking stamps (paper plates), stamps, pasta, cotton balls, coins (1 cent and 10 cents), etc.
Source : L’@telier - Ressources pédagogiques en ligne (atelier.on.ca), p. 1-2.
Activity 4: Identify the Error
To play this game, students observe the teacher incorrectly count objects or a grouping of elements, identify the error, and correct the situation.
- Teachers count elements, such as money, books, blocks, or pencils, but get it wrong and get an incorrect count.
- The adult may forget a number or count an object more than once.
- Students must find the error.
- They can also take turns leading the game.
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 5.
Activity 5: Estimate the Number
Prepare two containers of the same size, one with larger objects and the other with smaller objects, such as golf balls in one and small marbles in the other. Count the golf balls with the students. Ask them if they think the amount of balls in the second container is smaller or larger. Ask them to think about it and discuss it with a peer, then justify their answer.
Another week, use the same containers. Fill one a quarter full with objects, such as small plastic dinosaurs, and fill the second one completely with the same objects. With the students, count the objects in the first container. Ask them to estimate the number of objects in the second container. Students can estimate the quantity in the second container by referring to the known quantity in the first. Ask them to explain their estimate, then count the objects in the container.
Another week, continue the estimation activities by preparing two containers of different sizes filled with the same objects.
With the students, count the objects in the first container.
Ask students to estimate the number of objects in the second container. Ask them if the known quantity of the first container can help them make their prediction. Check their predictions by counting the quantity in the second container.
Each week, discuss estimates and actual quantities. Vary how you check the number of elements in the containers:
- count them with the students;
- count them in the math centre in small teams;
- count them while projecting them onto the screen while placing the objects in 10 frames.
While counting the objects to check the accuracy of the estimates, ask if any students would like to change their original estimate once you approach half the container.
Discuss with students what estimating means so they do not worry about getting the right answer. Estimating should not be a competitive activity. Encourage students to feel comfortable estimating and to understand that estimating is not about getting the exact answer.
When you provide students with benchmarks and present them with strategies like the ones mentioned above, they can give plausible estimates instead of wild ones.
Source : L’@telier - Ressources pédagogiques en ligne (atelier.on.ca), p. 1-2.