Algebra - Level 2

Achievement objectives

Exploring patterns and relationships
Within a range of meaningful contexts, students should be able to:

Exploring equations and expressions
Within a range of meaningful contexts, students should be able to:

Suggested learning experiences

Exploring patterns and relationships
Students should be:

• exploring, creating, describing, and continuing spatial and numerical sequential patterns, using calculators where appropriate, and developing the idea that some patterns continue without end;
• using a variety of diagrams to show relationships, drawn from familiar situations, for example,

• talking about and acting out ideas represented in their own and other graphs.

Exploring equations and expressions
Students should be:

• writing and talking about number sentences using =, <, >;
• using calculators and concrete materials to make statements involving = and the 4 operations, for example, 3 + 4 = 4 + 3, and 3x (4 + 5) = 3 x 4 + 3 x 5 and emphasising that these are alternative ways of expressing the same number;
• exploring the special properties of zero in the context of addition, and 1 in the context of multiplication

Sample assessment activities

These assessment activities are examples of the kinds of tasks which teachers could devise for their own assessment programme.

• Students describe and continue patterns such as:

Using this example, teachers could assess students' ability to:

• continue a sequential pattern and describe a rule for this (A2);
• use words and symbols to describe and continue patterns (MP2).

Students describe age relationships as number sentences in both directions. For example, "Jo's age plus two years gives John's age" is the same as "John's age minus two years gives Jo's age", and "Jo's age is less than John's age" is the same as "John's age is greater than Jo's age".

Using this example, teachers could assess students' ability to:

• use the mathematical symbols =,<,> for the relationships "is equal to", "is less than", and "is greater than" (A2);
• interpret information and results in context (MP2).

Students, working in groups, determine and record as many ways as possible of showing a particular number, for example, 16 = 4 x 4 = 2 x 2 + 12 = ...

Using this example, teachers could assess students' ability to:

• use the mathematical symbols =,<,> for the relationships "is equal to", "is less than", and "is greater than" (A2).

Students explain how to get the next numbers in a sequence. For example, what are the next two numbers in the sequence 3, 10, 17 ...? What is the rule?

Using this example, teachers could assess students' ability to:

• continue a sequential pattern and describe a rule for this (A2);
• devise and use problem-solving strategies to explore situations mathematically (MP2).

Sample development band activities

• Students investigate and report on number patterns resulting from operations they have chosen. For example, what happens when numbers are doubled, odd (or even) numbers are added, 4 is added to numbers ending in 7?
  
• Given sequences of objects, students predict what the 10th, 20th, etc., objects would be. They describe the starting sequence, write their prediction, and explain their reasoning.
  
• Students explore attribute games. For example:
  - They make a line which has a difference of three attributes between successive blocks.
  - They make lines in which the attribute differences between successive blocks vary according to a pattern.