# Scaffolding numeracy in the middle years before you start

There are a number of ways that teachers can plan and prepare before starting the assessment:

## Find out about the Learning and Assessment Framework

The assessment tasks can be used to initially locate a student on the Learning and Assessment Framework for Multiplicative Thinking (LAF) and then to assess students’ progress after targeted teaching has taken place.

Through the LAF, you will be able to familiarise yourself with the key ideas and concepts within the zones of the framework where your students are located. You can then identify what a student currently understands, and what is needed to scaffold them to higher order multiplicative thinking.

Although the assessment tasks will help you to identify which zones of the LAF are specifically relevant to your students, it is important to review the framework in it’s entirety before you start the assessment to build a holistic view of the development of the multiplicative concepts.

## Access the booklets

All of the assessment tasks are contained within:

• one extended task and four to five supplementary or short tasks
• scoring rubrics
• student score sheet
• LAF
• raw score translator.

### Tables and Chairs

Introduce the task. Make sure that students understand what ‘end-to-end’ means (demonstrate using square tiles if needed). Provide small square tiles for students to use if needed.

### Butterfly House

Introduce the task. Make sure students understand what is meant by ‘making model butterflies’. Draw a model butterfly on the board to show four wings, one body and two feelers. For the last question, draw a model butterfly to illustrate what is meant by ‘all yellow wings’.

### Stained Glass Windows

Ensure students understand what is meant by ‘two triangles wide at the base and two triangles high’.

### Packing Pots

Students may draw on the diagram as necessary. Ensure students understand what is meant by the ‘35-pot tray’.

### Tiles, Tiles, Tiles / Adventure Camp / Speedy Snail / Canteen Capers

Teachers can answer questions of clarification as needed, but should not provide so much support that someone is able to complete the task with little understanding.

## Allocate enough time

One full session (at least 40 minutes) should be allocated for the extended task. Each Supplementary Task is designed to be completed in about 10 to 15 minutes.

While teachers may choose to do more than one supplementary task per session, it is suggested that no more than two tasks be attempted in any one session unless the session is more than one hour long.

## Prepare the materials

Students need their own copy of the assessment task booklet and whatever materials are specified for the particular task. Students should have access to pens, pencils and erasers. Rulers are not needed and calculators are not permitted.

One of the purposes of the assessment is to identify students’ computation strategies. Even rejected work can provide some clues to students’ thinking. Therefore:

• students are expected record all of their work on their copy of the assessment task booklet
• scrap paper or jotters are not required
• if extra working space is needed, students should use the back of the page
• rejected work should be crossed out, but not obliterated or rubbed out.

## Prepare the class

Treat this as you would a normal class assessment activity. If appropriate, avoid using the word ‘test’. Stress that the activity is about finding out what students know and can do, to inform future teaching decisions.

Many students are reluctant to write explanations or show their working at this level and need to be encouraged to provide as much evidence of their mathematical thinking as possible.

Before starting the assessment, teachers should explain how the tasks will be assessed and model what this might mean in practice.

The following table provides a guide as to how most tasks will be assessed.

No response or incorrect without any working or explanation

0

Incorrect with working and/or an explanation that indicates an understanding of what is required to solve the problem, or correct with little/no working or explanation

1

Correct, with working and/or an explanation that indicates some appropriate use of mathematics

2

Correct with working and/or an explanation that clearly supports conclusion(s) and uses as much mathematics as possible

3

## Work through the example

The worked example (shown below) should be discussed with students to make sure that they understand what is expected of them prior to the assessment.

In particular, it is important that students understand what is meant by the instructions:

• “Explain your reasoning using as much mathematics as you can.”
• “Use as much mathematics as you can to support your answer.”

WORKED EXAMPLE:

Here are two students’ responses to this problem.

Discuss with the students:

• The problem asked the students to show your working and explain your answer in as much detail as possible . Which one do you think did this best?
• Sometimes, the problem asks you to use as much mathematics as you can to support your answer. Which one do you think did this best? Could you use more mathematics?
• The following table provides a guide as to how most tasks will be assessed. What score would you give to each of these solutions?

No response or incorrect without any working or explanation

0

Incorrect with working and/or an explanation that indicates an understanding of what is required to solve the problem, or correct with little/no working or explanation

1

Correct, with working and/or an explanation that indicates some appropriate use of mathematics

2

Correct with working and/or an explanation that clearly supports conclusion(s) and uses as much mathematics as possible

3

## Conduct the assessment

The next step is to conduct the assessment with your students. You will then be able to score and locate your students on the LAF.