B1.4 Count to 1000, including by 50s, 100s, and 200s, using a variety of tools and strategies.
Skill: Counting
Recognize and Understand Patterns
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., supports students in counting and understanding the concept of place value, including decimal numbers. Patterns in multiples of numbers (for example, all multiples of 5 end in 5 or 0) help students to make connections 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 skip counting, supports one to recognize the factors of a number. For example, skip counts of 2 or 4 allows helps to reveal factors of a number (for example, 2, 4, 6, 8, and 12 are factors of 24).
Source: translated from Guide d’enseignement efficace des mathématiques de la 1re à la 3e année, Numération et sens du nombre, p. 60.
To help students develop the skill of recognizing order relationships among large numbers, teachers may ask them to count up or down by 1s for a given number (for example, 898, 899, 900, 901…; 771, 770, 769, 768...) or by an interval (for example, 500, 600, 700, 800…; 650, 600, 550, 500...).
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 regrouping. 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 the regrouping by tens that occurs within the 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 or skip count, and discover changes related to regrouping by tens, hundreds, etc.
Source: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Numération et sens du nombre, Fascicule 1, Nombres naturels, p. 46-47.