Teaching students with numeracy learning difficulties

Mahli's teacher has described Mahli's existing knowledge and skills using the Victorian Curriculum F–10: Mathematics content descriptors 'Number and place value'. They have also identified the knowledge and skills that Mahli needs to learn next.  

The following comments have been taken from Mahli's numeracy profile.

Mahli understands the numerosity (number) of sets of up to 20 items. They can count smaller numerosities more accurately than larger sets. Mahli can count sets of up to 20 items by touching each item while saying its name. Mahli can read and write single-digit numbers and can assemble a set of items to match a spoken number up to 20 and a written number to 10. Mahli recalls some sequences of numbers up to 100.  

When Mahli sees a 10-grouped quantity, they know to count in tens. Mahli is capable of counting in tens and recalling the name of each decade number (10, 20, 30), but cannot easily count up or down a quantity of tens and ones (16, 26, 36). Mahli can group sets of units into tens.

Mahli needs to develop confidence with number sequences to and from 100 by ones, from any starting point. Skip count by twos, fives and tens, starting from zero.  

Given their importance to other aspects of 'Number and place value', the areas that Mahli has not achieved (counting on or down from any starting point up to 20) should be targeted first. It's important that these skills are taught in sequence.

For example:

• Read two-digit numbers less than 20.
• Count on from any starting number less than 20.
• Count down from 20.
• Count down from any starting number less than 20.

Teaching these intermediate steps will help to consolidate Mahli's understanding of counting and transition to skip counting, and other 'Number and place value' knowledge and skills.

Fatma's teacher has described Fatma's existing knowledge and skills using the Victorian Curriculum F–10: Mathematics content descriptors 'Number and place value'. They have also identified the knowledge and skills that Fatma needs to learn next.

Counting

Fatma can order numbers to 1,000 and continue number patterns by performing addition or subtraction for numbers up to 100.

Fatma's learning should be extended to order numbers to at least 10,000.

Place value

Fatma can use place value to describe quantities to 1,000.

They need to develop the skills to use place value to partition, rearrange and regroup numbers to at least 10,000 to assist calculations and solve problems.

Addition and subtraction

Fatma can solve simple addition and subtraction problems using mental and written strategies.

Their next step is to recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation.

Multiplication and division

Fatma recognises multiplication as repeated addition, groups and arrays, and division as grouping into equal sets and solving simple problems using these representations.

Fatma's next step is to learn to recall multiplication facts of 2, 3, 5 and 10 and related division facts. They will also need to develop skills to solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies.

Proportional reasoning

Fatma can recognise common uses of halves, quarters and eighths of shapes and collections.

They need to extend to modelling unit fractions including one half, one quarter, one third, one fifth and their multiples and simple fractions involving numbers greater than one.

Next steps

Given their importance to other aspects of 'Number and place value', a priority for Fatma's maths teacher is to:

• extend Fatma's understanding and skills in counting and place value to numbers above 1,000
• achieve Fatma's fluency in these 2 areas
• provide opportunities for Fatma to practise the application of skills gained in these areas as they will overlap with the Measurement and Geometry, and Statistics and Probability strands (such as when reading the scale on a ruler).

It's important that these skills are taught in sequence. For example:

• Recognise, understand, read and write four-digit numbers from a place value perspective and to transfer this to computations.
• Count up and down from any four-digit number in increments of 1, 10, 100 and 1,000.
• Recall addition, subtraction, multiplication and division facts for single-digit numbers.

Teaching these intermediate steps will help Fatma to consolidate their understanding of place value and 4-digit numbers, as well as other 'Number and place value' knowledge and skills.