# LAF Zone 1: Primitive Modelling

The information below describes the key characteristics and teaching implications for Zone 1 of the Learning and Assessment Framework for Multiplicative Thinking (LAF), including:

## How to use this resource

There are eight zones in the LAF. If your students are across several zones, you should access information for each of the zones where they are located.

Where there is a reference to:

- an assessment task, the title is
*italicised,*and can be found in the Assessment Materials - an Authentic Task or task from a Learning Plan, the title is linked so you can download the relevant document.

## Key characteristics

Can solve simple multiplication and division problems involving relatively small whole numbers. For example,
*Butterfly House* parts a and b.

Tends to rely on drawing, models and count-all strategies. For example, draws and counts all pots for part a of
*Packing Pots*.

May use skip counting (repeated addition) for groups less than 5. For example, to find number of tables needed to seat up to 20 people in
*Tables and Chairs*.

Can make simple observations from data given in a task. For example,
*Adventure Camp a.*

Can reproduce a simple pattern. For example,
*Tables and Chairs*, parts a to e.

Multiplicative Thinking (MT) not really apparent as there is no indication that groups are perceived as composite units, dealt with systematically, or that the number of groups can be manipulated to support a more efficient calculation.

## Teaching implications – consolidation and establishment

#### Trusting the count for numbers to 10

For 6, as an example, this involves working with mental objects of 6 without having to model and/or count-all.

Use flash cards to develop subitising (the ability to say how many without counting) for numbers to 5 initially and then to 10 and beyond using part-part-whole knowledge. For example:

8 is 4 and 4, or 5 and 3 more, or 2 less than 10

Practice regularly.

**Simple skip counting**

Use simple skip counting to determine how many are in a collection and to establish numbers up to 5 as countable objects. For example:

count by twos, fives and tens, using concrete materials and a 0-99 Number Chart.

**Mental strategies for addition and subtraction facts to 20**

Count on from larger. For example:

for 2 and 7, think: 7, 8, 9.

Double and near doubles. Use ten-frames and a 2-row bead-frame to show that 7 and 7 is 10 and 4 more, 14.

Make-to-ten. For example:

for 6 and 8, think: 8, 10, 14, scaffold using open number lines

Explore and name mental strategies to solve subtraction problems such as 7 take 2, 12 take 5, and 16 take 9.

**2 digit place-value**

Work flexibly with ones and tens by making, naming, recording, comparing, ordering, counting forwards and backwards in place-value parts, and renaming (see Booker et al, 2004 ).

Play the Place-Value Game (pdf - 16.36kb)

## Teaching implications – introduction and development

**Doubling (and halving) strategies**

Use doubling and halving strategies for 2-digit numbers that do not require renaming. For example:

34 and 34, half of 46

Build to numbers that require some additional thinking. For example:

to double 36, think: double 3 tens, double 6 ones, 60 and 12 ones, 72

**Extended mental strategies for addition and subtraction**

Use efficient, place-value based strategies. For example:

37 and 24, think: 37, 47, 57, 60, 61

Scaffold thinking with open number lines.

**Efficient and reliable strategies for counting large collections**

Use strategies for large collections, for example:

counting a collection of 50 or more by 2s, 5s or 10s

Focus on how to organise the number of groups to facilitate the count. For example, by arranging the groups systematically in lines or arrays and then skip counting.

**Make, name and use arrays or regions**

Explain how to solve simple multiplication or sharing problems using concrete materials and skip counting. For example:

1 four, 2 fours, 3 fours …

Lead up to more efficient counting strategies based on reading arrays in terms of a consistent number of rows. For example:

4 rows of anything, that is, 4 ones, 4 twos, 4 threes, 4 fours …

**3 digit place-value**

Work flexibly with tens and hundreds by making with MAB , naming, recording, comparing, ordering, counting forwards and backwards in place-value parts, and renaming (see Booker et al, 2004 ).

**Strategies for unpacking and comprehending problem situations**

Read, re-tell and ask questions such as ‘What is the question asking?’ or ‘What do we need to do?’.

Use realistic word problems to explore different ideas for multiplication and division. For example:

3 rows, 7 chairs in each row, how many chairs (array)?

Mandy has three times as many…as Tom…, how many … does she have (scalar idea)?

24 cards shared among 6 students, how many each (partition)?

Lollipops cost 5c each, how much for 4 (‘for each’ idea)?

**How to explain and justify**

Present strategies for developing a solution orally and in writing through words and pictures. This is important for mathematical literacy.

## Learning plans

The following learning plans have been developed for this zone, to support targeted teaching after students have been assessed and located on The LAF

Zone 1 – Learning Plans Consolidating (pdf - 165.15kb)

Zone 1 – Learning Plans Introducing (pdf - 41.49kb)

## More information

Using the resources on this site, you can also:

- Look at the key characteristics and teaching implications for Zone 2
- Compare across the eight zones of the LAF
- Find out more about multiplicative thinking
- Read about how the LAF was developed through a research project
- Use the assessment materials with your class.

Last Update: 27 August 2017