relationships

In this unit the students form collections of a 1000 objects.  In doing this they examine the relationship between 1000 and smaller numbers, specifically 100 and 10.

Visit ESOL Online for a version of this unit designed to support students for whom English is an additional language.

Techniques for drawing linear graphs are introduced via whole number problem situations where the focus is on the solutions rather than the technique. Only linear equations of the form ax±by=c are graphed by finding two or more points on the line. No attempt is made to link these equations by algebra to the gradient intercept form y=mx+c.

The initial focus of this unit involves students in gathering data from their investigation of squares that can be made on different sized geoboards, (an array of dots arranged on a square grid).  Students need to be systematic in their work, and to record their results in ways that are likely to help them notice patterns and relationships.

We have available a large range of activities that can be used for developing some basic concepts in algebra. Students often complain that they cannot see the point of learning algebra so all of the teaching of skills here is placed within contexts. The intention of this unit is not to teach skills in isolation, but rather to use each activity for developing all the concepts. It is not suggested that this unit should replace the skills practice traditionally used in the teaching of algebra. It does, however, provide the opportunities for discussion and development of concepts. As each learning outcome is explored there will probably be need for consolidation through more traditional exercises. With the first activities one will probably not wish to explore all aspects with the whole class, but the possibility is there for extending individuals. It would also be appropriate to use the first activity for diagnostic assessment.

The unit involves students in solving problems that can be modelled with algebraic equations or expressions. There are five sets of problems. Students should attempt one problem from each set each day. They increase in difficulty as the week progresses. Students are required to describe patterns and relationships using letters to represent variables.

 Students work out their own generalizations of the properties of number operations through their exploration of addition, subtraction, multiplication and division.

This week we explore the patterns in different types of staircases.