B1.4 Count to 200, including by 20s, 25s, and 50s, using a variety of tools and strategies.
Skill: Interval Counting
Recognizing the sequence of numbers from 1 to 9 and understanding how it repeats throughout the base ten numbering system, namely, tens, hundreds, thousands, etc., helps students count and understand the concept of place value and master the decimal system. For example, patterns in multiples of numbers (for example, all multiples of 5 end in 5 or 0) provide a connection to divisibility (for example, all numbers that end in 0 or 5 are divisible by 5). Similarly, the regularity in the sequences of even (0, 2, 4, 6, …) and odd (1, 3, 5, 7,…) numbers allows one to establish that the difference between two consecutive even numbers or two consecutive odd numbers is always two. In addition, the patterns in numbers, when counting in intervals, allows one to recognize the factors of a number. For example, counting in intervals of 2 or 4 allows one to recognize some factors of a number (for example, 2, 4, 6, 8, and 12 are factors of 24).
Source : Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, p. 60.
To help students develop the ability to recognize relationships among large numbers, ask them to count up from a given number by 1 (for example, 98, 99, 100, 101 …) or by intervals (for example, 50, 75, 100 …) and to count backward by 1 (for example, 71, 70, 69 …) or by intervals (for example, 200, 150, 100…).
These activities help students recognize that when counting by 1s or intervals, any named number is greater than those before it and less than those after it, while when counting backwards by 1s or intervals, any named number is less than those before it and greater than those after it. While these relationships may seem obvious to adults, students often get them wrong because they do not consider the concept of grouping. When asked, for example, what number precedes 300, many students tend to spontaneously answer 399 because their attention is focused on the two 0's; they know that a number ending in two 0's is always preceded by a number ending in two 9's, and they forget to consider grouping by hundreds. In contrast, when the same problem is posed in context, students give more thoughtful responses; for example, in a situation where a person has 200 field hockey cards and loses one, students will readily respond that they have 199 cards left.
Using a homemade abacus or odometer (created using a toilet paper roll and the template below) helps students compare numbers, count in intervals, and discover changes related to grouping by tens, hundreds, etc.
Source : Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, p. 46-47.