# Additive strategies

## Learning intention

Students will learn to use mental and written strategies to add and subtract numbers up to five digits, selecting from a range of strategies.

### Syllabus outcome

• MA2-1WM uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-2WM selects and uses appropriate mental or written strategies, or technology, to solve problems

• MA2-3WM checks the accuracy of a statement and explains the reasoning used

• MA2-4NA applies place value to order, read and represent numbers of up to five digits

• MA2-5NA uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

• MA2-6NA uses mental and informal written strategies for multiplication and division

• MA2-8NA generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values.

### National Numeracy Learning Progression

#### Additive strategies

The full National Numeracy Learning Progression details are included in the resource, available for download on this page.
• AdS6: Flexible strategies with combinations to 10
• AdS7: Flexible strategies with two-digit numbers
• AdS8: Flexible strategies with three-digit numbers and beyond

### NAPLAN item descriptors

The relevant NAPLAN item descriptors are included in the resource, available for download on this page.

## Task outline

Full task descriptions are included in the resource, available for download on this page.

## Quantifying collections

### Task 1: Number busting

Students use an understanding of structure, number facts, counting principles and part-part-whole number knowledge to examine different ways of quantifying the same collection (two activities).

### Task 2: Handfuls

Students explore different ways of structuring a collection to answer the question: “how many?” (one activity).

### Task 3: Minute to win it

Students use an understanding of structure, number facts, counting principles and part-part-whole number knowledge to quantify a large collection (one activity).

## Developing flexible strategies with two-digit numbers and beyond

### Task 4: Bundling battle

Students aim to be the first pair of players to reach a target number, regrouping and renaming into tens and ones as they grow their collection (one activity).

### Task 5: Extending thinking

Students answer questions related to understanding place value (one activity).

### Task 6: Trading game

Students work with a partner to use their knowledge of regroup and renaming (‘trading’) to build their cumulative total (three activities).

## Doubling strategies

### Task 7: Near doubles bingo

Students use their understanding of doubles to derive facts with near doubles (two activities).

### Task 8: Double or near double?

Students choose to double, or almost double, a number to be the first person (or pair of students) to reach zero. This game draws on students use of flexible strategies whilst supporting their awareness of doubles and near doubles (three activities).

### Task 9: Doubles fill

A two versus two game supporting fluency with doubles facts and building number sense by connecting quantities with symbols and language (five activities).

### Task 10: Three tens in a row

This game can be played as two players versus two players to promote conversation and reasoning. Students use their understanding of patterns and additive strategies to combine two numbers that make ten (one activity).

### Task 11: 101 and you’re out!

Students use their understanding of place value and additive strategies to get as close to 100 as possible (five activities).

### Task 12: Dicey addition

Students use their number sense to create equations (number sentences) where the closest to a total of 100 wins (two activities).

### Task 12: Closest to 100

Students use their number sense to create a variety of equations (number sentences) totalling 100 (three activities).

### Task 13: Subtraction face off

Students apply their number sense and additive strategies whilst exploring the concept of difference (two activities).