NSW Syllabuses

# Stage 5 - Activity 3

### Midpoint

#### Description of activity

If the midpoint of an interval is (1,3), what might the endpoints of the interval be?
Students give reasons for their solution.
Possible prompts to assist student engagement:

• Could you draw a diagram?
• Is there only one possible answer?
• How could you summarise your findings?

#### Context

This assessment activity could be presented to students during a unit on Coordinate Geometry, after students have completed more traditional questions on finding the midpoint of an interval joining two given points.

#### Objectives

• develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning
• develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation.

#### Outcomes

MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts
MA5.1-2WM selects and uses appropriate strategies to solve problems
MA5.1-3WM provides reasoning to support conclusions that are appropriate to the context
MA5.1-6NA determines the midpoint, gradient and length of an interval, and graphs linear relationships

#### Criteria for assessing learning

(These criteria would normally be communicated to students with the activity.)
Students will be assessed on their ability to:

• find the endpoints of an interval, given the midpoint
• communicate mathematical ideas
• justify conclusions.