At a Glance...

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

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

The base-10 system includes multiple patterns that help deepen understanding of number relationships.

Source : The Ontario Curriculum. Mathematics, Grades 1-8 Ontario Ministry of Education, 2020.

Students demonstrate their understanding of the concept of 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 offer students a whole number less than 50, such as 42, and ask them to decompose that number by position value to determine the pattern rule.

Example 1

This allows students to establish the relationship between positional 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 semi-concrete materials (for example, a number strip, a 10 frame, interlocking cubes, base 10 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

\(\ 0 + 10 = 10\)

\(\ 10 - 10 = 0\)

\(\ 1 + 9 = 10\)

\(\ 10 - 9 = 1\)

\(\ 2 + 8 = 10\)

\(\ 10 - 8 = 2\)

\(\ 3 + 7 = 10\)

\(\ 10 - 7 = 3\)

\(\ 4 + 6 =10\)

\(\ 10 - 6 = 4\)

\(\ 5 + 5 = 10\)

\(\ 10 - 5 = 5\)

\(\ 6 + 4 = 10\)

\(\ 10 - 4 = 6\)

\(\ 7 + 3 = 10\)

\(\ 10 - 3 = 7\)

\(\ 8 + 2 =10\)

\(\ 10 - 2 = 8\)

\(\ 9 + 1 =10\)

\(\ 10 - 1 = 9\)

\(\ 10 + 0 = 10\)

10 - 0 = 10

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

Skill: Describing Number Patterns of Whole Numbers Up To 50

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 mathematical sentence, or within the base-10 system, students discover patterns and can deepen their understanding of algebraic concepts.

Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3^e année, p. 16.

To get students to verbalize their observations, identify relationships, and explain how they located 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 encourage them to verbalize the elements of the repeating pattern; for example, using the example of the number facts of addition of the number 10 and the facts associated with subtraction from the previous section, students can describe the pattern rule of the addition series. They can note that the sum always equals 10, the first term increases by 1, and the second term decreases by 1. They can also describe the rule of regularity of the subtraction series by explaining that the difference increases by 1, the first term always equals 10, and the second term decreases by 1.

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

Source : Guide d’enseignement efficace des mathématiques de la maternelle à la 3^e année, p. 44-46.