GCSE Maths Lecture Notes

Overview

• Focus on Ratio, Proportion, Fractions, Decimals, and Percentages.
• Objectives for the week include understanding and using ratio notation, simplifying ratios, dividing quantities, and linking mathematical concepts.

Ratio

Definition

• Ratio is a way of comparing amounts.
• Expresses how much bigger one quantity is compared to another.

Writing Ratios

• Example: A ratio of 4:1 indicates a total of 5 parts.
• Important when dividing quantities.

Simplifying Ratios

• Example simplification: Blue to Yellow blocks 4:2 simplifies to 2:1.
• Always convert to the same unit before simplifying.
• Practicing conversion: 1mm to 5cm, etc.

Dividing Quantities

• Example: Sharing €10 between Mandy and Lara in a 3:2 ratio.
  • Total parts = 5, 1 part = €2.
  • Mandy = €6, Lara = €4.
• Orange drink made in a 4:3 ratio.
  • Total = 35 ml, 1 part = 5 ml.
  • Orange Juice = 20 ml, Water =15 ml.

Proportion

Definition

• Used in recipes; involves multiples for correctness.
• Similar to sharing in a ratio; all parts must be proportional.

Recipe Example

• Ingredients for 4 cupcakes: 2 eggs, 250g flour, 100g sugar.
• Calculating for 10 cupcakes by maintaining proportions.

Fruit Punch Example

• Original recipe for 20 glasses:
  • 1L orange juice, 600ml apple juice, 250ml cranberry juice, 350ml grapefruit juice.
• Adjusting for 75 glasses by scaling ingredients proportionally.

Skills Development

• Apply techniques comfortable with while solving problems.
• Practice is key to mastering maths skills.

Probability

• Use probability vocabulary.
• Express probabilities as fractions, decimals, or percentages.

Practice and Engagement

• Encouragement to work in groups to solve problems and discuss strategies.
• Apply learned techniques to past paper questions to reinforce learning.