**Core concept 2.1: **

**Arithmetic procedures**

**2.1.1.1***** ****Understand the mathematical structures that underpin addition and subtraction of positive and negative integers**

**2.1.1.2* Generalise and fluently use written addition and subtraction strategies, including columnar formats, with decimals**

**2.1.1.1 Understand the mathematical structures that underpin addition and subtraction of positive and negative integers**

**2.1.1.1 Understand the mathematical structures that underpin addition and subtraction of positive and negative integers**

●Use ‘zero pairs’ to partition a number.

●Expand understanding of addition and subtraction to include calculation with negative numbers.

●Solve problems where there is more than one answer and there are elements of experimentation, investigation, checking, reasoning, proof, etc.

See Integers for zero pairs and four operations on negative numbers

**2.1.1.2 Generalise and fluently use addition and subtraction strategies, including columnar formats, with decimals**

**2.1.1.2 Generalise and fluently use addition and subtraction strategies, including columnar formats, with decimals**

●Partition a number in multiple ways.

●Understand partitioning as a part of the columnar method with decimals.

●Manipulate place value correctly when calculating with integers and decimals.

Using the chart below, how would you partition the following numbers?

a) 3^{ }033 b) 33.03 c) 3.14 d) 31.4

What is the same and what is different about these sets of place-value counters?

Create your own with the MathsBot place value counters below.

2.1.2.1 Understand the mathematical structures that underpin multiplication and division of positive and negative integers

2.1.2.2 Factorise multiples of 10^{n} in order to simplify multiplication and division of both integers and decimals, e.g. 300 × 7000, 0.3 × 0.007, 0.9 ÷ 0.03, etc.

**2.1.2.3 Generalise and fluently use written multiplication strategies to calculate accurately with decimals**

2.1.2.4 Generalise and fluently use written division strategies to calculate accurately with decimals

**2.1.2.3 Generalise and fluently use written multiplication strategies to calculate accurately with decimals**

**2.1.2.3 Generalise and fluently use written multiplication strategies to calculate accurately with decimals**

●Appreciate the limitations of the (standard) written method for multiplying decimals

●Use place value to manipulate a calculation involving decimals to an equivalent calculation involving whole numbers

●Appreciate the (standard) written method for multiplying two whole numbers can be used as part of the strategy for multiplying decimals

●Solve problems where there is more than one answer and there are elements of experimentation, investigation, checking, reasoning, proof, etc

Area model for multiplying decimals.

2.1.3.1 Understand the mathematical structures that underpin the addition and subtraction of fractions

2.1.3.2 Generalise and fluently use addition and subtraction strategies to calculate with fractions and mixed numbers

**2.1.4.1* Understand the mathematical structures that underpin the multiplication of fractions**

**2.1.4.2* Understand how to multiply unit, non-unit and improper fractions**

2.1.4.3 Generalise and fluently use strategies to multiply with mixed numbers (e.g. 2 3/4 × 1 2/3)

2.1.4.4 Understand the mathematical structures that underpin the division of fractions

2.1.4.5 Divide a fraction by a whole number

2.1.4.6 Divide a whole number by a fraction

2.1.4.7 Divide a fraction by a fraction

The area model, a form of grid-multiplication, is used to display how the distributive law is used to multiply two numbers presented in mixed fraction form.

**Applet** (can be used without Cinderella)

**PROMOTING MATHEMATICAL THINKING ... THE HOME OF JOHN MASON & ANNE WATSON**

2.1.5.1 Know the commutative law and use it to calculate efficiently

2.1.5.2 Know the associative law and use it to calculate efficiently

2.1.5.3 Know the distributive law and use it to calculate efficiently

2.1.5.4 Calculate using priority of operations, including brackets, powers, exponents and reciprocals

**2.1.5.5* Use the associative, distributive and commutative laws to flexibly and efficiently solve problems**

2.1.5.6 Know how to fluently use certain calculator functions and use a calculator appropriately