At a Glance...

C1.4 create and describe patterns to illustrate relationships among whole numbers up to 50.

Skill: Creating and Representing Number Patterns Involving Whole Numbers Up To 50

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The base ten system includes multiple patterns that help deepen understanding of number relationships.

Source: translated from Curriculum de l'Ontario, Programme de mathématiques de la 1^re à la 8^e année, 2020, Ministère de l'Éducation de l'Ontario.

Students demonstrate their understanding of the concept of a pattern rule by creating and explaining number patterns, such as decompositions of numbers or sets of related operations. This is an opportunity for students to make connections related to place value, addition and subtraction, and to understand the inverse relationship between these two related operations.

Teachers can provide students with a whole number less than 50, such as 42, and ask them to decompose that number by place value to determine the pattern rule.

Example 1

This allows students to establish the relationship between place values (tens and ones), that is, that a ten is equal to 10 ones.

Teachers can also have students create a pattern of operations using concrete or visual (semi-concrete) materials (for example, a number strip, a ten frame, interlocking cubes, base ten materials). Students then exchange their set of operations with a partner's set. They can then construct the related set based on the associated facts and describe it.

Example 2

This allows students to establish the inverse relationship between addition and subtraction.

Skill: Describing Number Patterns of Whole Numbers Up To 50

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Recognizing patterns is an important problem-solving skill; it facilitates the acquisition of other concepts and the formulation of conjectures leading to generalizations. The concept of patterns is the cornerstone of algebraic reasoning.

By observing and analyzing the relationships between numbers within a pattern, within a number sentence, or within the base ten system, students discover patterns and can deepen their understanding of algebraic concepts.

Source: translated from Guide d’enseignement efficace des mathématiques de la maternelle à la 3^e année, Modélisation et algèbre, Fascicule 1, Régularités et relations, p. 16.

To get students to verbalize their observations, identify relationships, and explain how they determined the pattern rule, it is important that teachers ask relevant questions such as:

• What do you notice?
• What is repeated?
• What do you add? What are you taking away?
• What does this number represent?
• How could you represent this number differently?
• What is the link between your two representations?

To help students establish an intuitive understanding of the structure of the pattern, teachers should encourage them to verbalize the elements of the repeating pattern; for example, with the number facts of addition to 10 and associated subtraction facts, students can describe the pattern rule of the addition series. They can note that the sum always equals 10 and that, the first term increases by 1 and the second term decreases by 1. They can also describe the pattern rule of the subtraction series by explaining that the difference always increases by 1, the first term (minuend) always equals 10, and the second term (subtrahend) always decreases by 1.

In the example of the number 42, students can describe the pattern of operations by explaining that as ten decreases by 1 and the ones increase by 10.

Source: translated from Guide d’enseignement efficace des mathématiques de la maternelle à la 3^e année, Modélisation et algèbre, Fascicule 1, Régularités et relations, p. 44-46.