NA5-7: Form and solve linear and simple quadratic equations.
Students should be able to form the linear equation or simple quadratic (y = ax2 or y = x2 ± c, a and c are integers) to model a given situation (see patterns and relationships). They should understand that solving an equation involves finding the value of a variable when the other variable is defined, and interpret how the solution relates to the original context. Students should be able to solve linear and simple quadratic equations by applying inverse operations with an understanding of the equals sign as a statement of transitive balance, for example (3q + 7)/4 = 16, by multiplying both sides by four, subtracting seven, etc. They should also recognise where it is appropriate to solve an equation through trial and improvement, and find the missing value by systematic calculation.
use a table to find a pattern
write a quadratic equations to describe the relationship
- Represent algebraic expressions as array diagrams.
- Solve for specific unknowns, either areas or side lengths, from array diagrams.
- Expand quadratic expressions with the support of array diagrams.
- Factorise quadratic expressions with the support of array diagrams.
- Investigate situations involving ratios.
- Understand that there are many ways to solve ratio problems.
- Solve simple equations of the form ax = b.
- See the relevance of algebra to ratio problems.
- use algebra to generalise the results of a practical investigation.
- apply knowledge of circuits, power, voltage, currents, and resistance to problem solving.
- use graphical techniques to identify and describe a linear relationship found in a practical investigation.
- Apply algebra to the solution of a problem.
- Devise and use problem solving strategies to explore situations mathematically (be systematic, use a table, use algebra).
usea table to continue a pattern
use a rule to describe a prediction
write a rule as a quadratic equation
- Perform calculations with powers of numbers and square roots.
- Explain the relation between a square root and a square.
- Devise and use problem solving strategies to explore situations mathematically. This problem uses be systematic, draw a picture, and think.
- Describe a rule for the general term.
- Devise and use problem solving strategies to explore situations mathematically (be systematic).
- Make a table of one variable against another to represent a quadratic relationship.
- Represent a quadratic relationship between two variables in words and as an equation.
- Represent a quadratic relationship as a parabola on the Cartesian Plane.
- Recognise the key features of a parabola, including the300
write an equation to generalise an equation
- Form and solve linear equations.
- Use ratios.
- Devise and use problem solving strategies to explore situations mathematically (draw a diagram).
- Compare the volume of a sphere and a cylinder by measuring or applying a formula.
- Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).
- Make a table of one variable against another to represent a quadratic relationship.
- Represent a quadratic relationship between two variables in words and as an equation.
- Represent a quadratic relationship as a parabola on the Cartesian Plane.
- Recognise the key features of a parabola, including the300
- Solve problems involving the conservation of mechanical energy.
- Find elastic potential energy using graphs.
- Determine the nature of the relationship between physical quantities (height and elastic stored energy) using a graph.
- Use a physical property, elastic potential energy, to find an unknown300
- Identify and find values for variables in context.
- Identify linear relationships in context, including those with negative rates of change.
- Represent linear relationships using tables, graphs and simple linear equations.
- Draw strip diagrams to represent linear equations, including those with negative300
- Give a general expression for the nth term of a pattern.
- Describe the links between different patterns.
- Devise and use problem solving strategies to explore situations mathematically.
- Investigate situations involving quadratics.
- Understand that there are many ways to solve quadratic problems.
- Solve for unknowns in factorised quadratics.
- Appreciate the use of algebraic techniques in solving quadratic problems.
- Use algebra as required.
- Construct magic squares.
- Form and solve linear equations.
- Devise and use problem solving strategies to explore situations mathematically (be systematic, use algebra).
- Solve problems involving percentage increases and decreases
- Apply the area formulas for squares and rectangles.
- Devise and use problem solving strategies to explore situations mathematically (be systematic, use a diagram).
- Use their mathematical knowledge to invent problems.
- Devise and use problem solving strategies to explore situations mathematically.