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
- Identify, quantify, and represent, using graphs and expressions, the effect of a scale in time contexts.
- Describe, apply, and graph linear relationships to solve problems involving time, temperature, and mass.
- Scale, convert, compare, and apply metric measurements to solve problems involving grams and300
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 be met.
- 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 equations that300
- Write and calculate arithmetic expressions precisely using the order of operations.
- Recognise the importance of the order of operations when using a calculator.
- Solve problems involving fractions and percentages.
- Devise and use problem solving strategies (guess and check, be systematic, look for a pattern, make a table).
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
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
write an equations to generalise a pattern