# relationships

## Puck's Girdle

- Problem Solving Activities
- Geometry and Measurement
- Level Five

Find the circumference of a circle;

Understand the relationship between changes in the circumference of a circle and changes in the radius.

Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).

## The Chicken Run

- Problem Solving Activities
- Geometry and Measurement
- Level Four

explain the relationship between the area and perimeter of rectangles

use a table to solve a problem

devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a table, make a drawing)

## The Castle

- Problem Solving Activities
- Geometry and Measurement
- Level Four

Construct 3-D shapes from 2-D drawings

Describe the symmetries of 3-D shapes

Draw 3-D shapes on isometric paper

Devise and use problem solving strategies to explore situations mathematically (guess and check, use equipment)

## Make 1000

- Units of Work
- Number and Algebra
- Level Two

In this unit the students form collections of 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. |

## Giant Mystery

- Units of Work
- Statistics
- Level Three

We have the hand print of a Giant…That’s all!! Can we find out how big this giant visitor was? By measuring other people, can we determine the relationship between hand size and body size, to help reconstruct the giant? The unit explores relationships between the hand length, width, span of a person and their height and other body measurements.

## Linear Graphs and Patterns

- Units of Work
- Number and Algebra
- Level Five

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.

## Tilted Squares and Right Triangles

- Units of Work
- Number and Algebra
- Level Five

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.

## Holistic Algebra

- Units of Work
- Number and Algebra
- Level Five

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.

## Balancing Acts

- Units of Work
- Number and Algebra
- Level Four

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.

## You Can Count on Squares!

- Units of Work
- Geometry and Measurement
- Level Four

The unit is presented as a scenario that includes five tasks that students engage in and explore to develop mathematical, specifically algebraic, ideas. Although the tasks are built around measurement, they are algebraic to the extent that they require ‘formulae’ to be derived form the geometric situations. It is sufficient at this Level for the students to express these formulae in words rather than in symbols.