Algebra - Level 3

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:

• investigating, creating, and continuing number and spatial sequential patterns, including figurate numbers (triangular, square, and so on), and expressing in words the rules which describe such patterns, using a calculator where appropriate;

• developing an understanding of relations and representing and interpreting them;
• using diagrams to show relationships;
• describing the rule for one- and two-stage "guess my rule" games, and graphing input and output pairs on a number plane, using a calculator where appropriate;
• sketching, interpreting, and writing stories about graphs of familiar situations.

Exploring equations and expressions
Students should be:

• finding, and explaining in words, simple formulae that can be used to solve a practical problem, for example, buying a number of chocolate bars given the price of one;
• creating and using rules for "think of a number" games, and solving number sentences, for example, + 5 = 12 and 6 x =18
• distinguishing between finite and infinite.

Sample assessment activities

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

Students investigate shape sequences and describe as many rules as they can for making them. For example, matches are used to make triangles. Describe a rule for finding the next member of the sequence.

Number of triangles 1 2 3 4 ...
Number of matches 3 5 7 9 ...

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

• describe in words rules for continuing number and spatial sequential patterns (A3);
• devise and use problem-solving strategies to explore situations mathematically (MP3).

Students talk about and sketch a graph showing their moods during the previous day.

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

• use graphs to represent number, or informal, relations (A3);
• use their own language, and mathematical language and diagrams, to explain mathematical ideas (MP3).

Students solve problems of the type: Judy has some marbles. She wins 17 more in a game from her friend Bruce. She then has 35 marbles. How many did she have at the start?

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

• solve problems of the type + 15 = 39(A3);
• write and solve problems which involve whole numbers and decimals and which require a choice of one or more of the four arithmetic operations (N3);
• devise and use problem-solving strategies to explore situations mathematically (MP3).

Sample development band activities

Students investigate number patterns, then explore related situations for other patterns. For example:

• What patterns can be found in the multiplication table of 9? Do similar patterns occur in other multiplication tables?
• After investigating triangular and square numbers, they explore the possibility of defining 3-dimensional figurate numbers, such as tetrahedral or cubic numbers.
• Observing that 1+3 = 4, 1+3+5=9, 1+3+5+7=16, they generalise and predict (then test) the sum of the first 10 odd numbers, then the first 20, then the first 200 odd numbers.