Mastering Maths Model Drawing: Comparison Models
Corey CrossWhat Is the Comparison Model in Maths?
The comparison model is a visual method used to solve mathematical problems involving comparisons between two or more quantities. It is particularly useful in understanding relationships and differences, making it a popular choice for problem-solving in GCSE and A-Level Maths. This model often involves diagrams, such as bar models, to represent the problem clearly.
Why Is the Comparison Model Important?
Comparison models simplify complex word problems by providing a visual representation of relationships between quantities. This method enhances understanding and reduces errors, especially in exams where clarity is crucial.
Common Applications:
- Solving ratio problems
- Understanding proportional relationships
- Calculating differences between quantities
- Interpreting word problems
Step-by-Step Guide to Using the Comparison Model
Step 1: Understand the Problem
Start by reading the problem carefully. Identify the key quantities and their relationships. For example:
"A has twice as much money as B. Together, they have £90. How much does each person have?"
Step 2: Draw the Model
Represent the quantities using bar diagrams:
- Draw one bar for A, twice the length of B's bar.
- Label the total as £90.
Step 3: Solve the Problem
Use simple arithmetic to determine the value of each part:
- Total bars represent three parts (2 for A + 1 for B).
- Divide £90 by 3 to find the value of one part (£30).
- A has £60 (2 × £30), and B has £30.
Examples of Comparison Model Problems
Below are varied examples showcasing the versatility of the comparison model:
| Problem | Solution |
|---|---|
| John has three times the number of apples as Sarah. Together, they have 48 apples. How many apples does Sarah have? | Sarah has 12 apples, John has 36 apples. |
| A bag of sweets costs £15, which is twice the cost of a box of chocolates. What is the cost of the box? | The box costs £7.50. |
Exam Tips for Using Comparison Models
Understand Before You Draw
Spend time understanding the problem before attempting to draw the model. Misinterpretation can lead to incorrect diagrams and answers.
Label Your Diagrams
Always label the bars and quantities in your diagram. This helps you keep track of relationships and ensures clarity during exams.
Check Your Work
After solving, double-check your arithmetic and compare the solution to the question. Does it make sense?
Practice Exercises
Try these problems to sharpen your skills:
- "A has three times as much money as B. Together, they have £120. How much does A have?" (Answer: A has £90, B has £30)
- "The ratio of red to blue balls is 4:5. If there are 45 balls in total, how many are red?" (Answer: 20 red balls, 25 blue balls)
How RevisionGenie Can Help
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