# NA4-7: Form and solve simple linear equations.

This means students will form and solve simple linear equations in the form y = mx + c, where x and y are related variables and where m is a whole number and c is an integer, for example q = 3p – c, or a + 5 = 4b. When the value of one variable is given the value of the other can be found by solving the equation, for example 3p – 6 = 18. Students should understand the equals sign as a statement of balance and know what operations to both sides of an equation preserve that balance, for example take off the same number from both sides. At Level Four students should be able to find the required value using both sensible estimation and improvement, and by formal methods of applying inverse operations, for example 3p – 6 = 18 so 3p = 24 (adding six to both sides) so p = 8 (dividing both sides by three).

- Devise rules based on numerical patterns to solve triangular arithmagons.
- Explain the condition for the solution of any square arithmagon.
- Form and use linear equations to solve triangular arithmagons.
- Develop proofs of rules and conditions for the solution of arithmagons.

use a table to find a numbr pattern

use an equation to describe a patter

find unknowns to balance a linear equation represented by a balance scales diagram

- Predict further members in patterns of equations using relationships within the equations.
- Develop function rules to describe relationships.
- Find specific values for variables from given relationships.

use a table to find a rule for a geometric pattern

write the rule for relationship as a linear equation

use addition to sovle money problems

use multiplication and division to solve problems

find percentage of a number

solve problems involving ratios

find fraction of a number

Students develop their skills and knowledge on the mathematics learning progression, measurement sense, in a food technology context.

find a percentage of a decimal number

solve addition and subtraction problems

compare prices by using proportions

- Calculate the cost of hiring a taxi, hiring a car, and using a phone, and the cooking time for meat.
- Compare the costs of different plans.
- Represent linear relationships using graphs.
- Use graphs to make decisions about the best deal.

complete a table to find a pattern

use a linear equation to describe a relationship

sovle problems with possibilites and constraints

- Identify and find values for variables in context.
- Identify linear relationships in context.
- Represent linear relationships using tables, graphs and simple linear equations.
- Draw strip diagrams to represent linear equations and ratios.
- Solve problems in which two or more conditions must be300

- understand the concept of Fibonacci numbers and how they are generated
- find factors of a number
- make conjectures and attempt to prove them
- find generalisations

- Understand that an unknown amount or number can be represented with a symbol: a question mark, a shape or a letter.
- Recognise that to find the value of the missing number, you have to ‘undo’ what has been done to it.
- Write word problems of real-life situations and express these with equations300

- To write and calculate arithmetic expressions precisely using the order of operations.
- To realise the importance of the order of operations on a calculator.

use a table to find a pattern

use a linear equation to describe the relationship

Students develop their skills and knowledge on the mathematics learning progressions measurement sense and using symbols and expressions to think mathematically, in the context of time and motion in sports.

use a table to find a rule for a geometric patter

write the rule for a relationship as a linear equation

use a table to find a pattern

use a linear equation to describe the relationship

- Devise a rule for ensuring that sets of numbers can be arranged into 3-by-3 magic squares.
- Represent 3-by-3 magic squares algebraically.
- Devise rules for determining the Magic Number for magic squares.
- Represent magic squares using parametric equations.
- Solve equations that have been formed300

use a formula to solve calculations

write a linear formula to express a linear relationship

write the rule as a simple linear equation

use a rule to complete a number pattern