Instructions
- Read Section 1: Review the core math concepts, their real-world uses, and related careers.
- Complete Section 2: Match the math concept to the correct real-world scenario.
- Solve Section 3: Apply the concepts to solve practical problems.
- Challenge Yourself: Attempt the final logic puzzle at the end.
Section 1: The KS4 Math Map
| Math Concept | Real-World Use | Careers |
|---|---|---|
| Standard Form | Writing very large (space) or small (atoms) numbers efficiently. | Scientists, Astronomers |
| Ratio & Proportion | Scaling recipes up/down or mixing chemicals/paint. | Chefs, Chemists, Painters |
| Compound Interest | Calculating how savings grow or how debt increases over time. | Bankers, Investors |
| Linear Equations | Finding an unknown value when other variables are constant. | Engineers, Programmers |
| Pythagoras/Trig | Calculating heights, distances, and angles for construction. | Architects, Pilots, Builders |
| Probability | Assessing risk and the likelihood of specific events occurring. | Game Designers, Insurance |
| Statistics | Analyzing trends in data to make future predictions. | Data Scientists, Marketers |
| Rearranging Formulae | Changing a rule to find a different starting variable. | Physicists, Software Devs |
Section 2: Scenario Matching
Draw a line (or write the letter) connecting the Scenario to the most relevant Math Concept.
| Scenario | Math Concept |
|---|---|
| 1. Calculating the trajectory of a rocket. | A. Probability |
| 2. Deciding if a 2-for-1 deal is actually a good price. | B. Pythagoras / Trigonometry |
| 3. Figuring out the slope of a wheelchair ramp. | C. Statistics |
| 4. Predicting the outcome of a coin toss in a game. | D. Ratio & Proportion |
| 5. Examining weather patterns over the last 10 years. | E. Linear Equations |
Section 3: Practical Application
Apply logic to these scenarios. Show your working clearly.
1. The Tech Setup (Ratio) An artist mixes blue and yellow paint in a 3:2 ratio to get the perfect green. If they use 15 liters of blue paint, how many liters of yellow paint do they need?
2. The Space Distance (Standard Form) The distance from Earth to the Sun is approximately 150,000,000 km. Write this number in standard form ($A \times 10^n$).
3. The Designer's Tool (Pythagoras) A carpenter needs to check if a frame is square. The sides are 3m and 4m. If the diagonal is exactly 5m, the corner is a right angle ($a^2 + b^2 = c^2$).
- Does $3^2 + 4^2 = 5^2$? (Show the math)
4. The Social Media Growth (Statistics) A YouTuber sees their views increase by 10% every month. This is an example of Compound Growth. If they have 1,000 views now, how many will they have after 2 months of 10% growth?
- Hint: Month 1: 1,000 + 10%. Month 2: (New Total) + 10%.
Section 4: The Logic Challenge
The Rule of Rearranging: The formula for speed is Speed = Distance ÷ Time ($S = D/T$).
If you are a Logistics Manager and you know the Distance is 120 miles and the Speed of the truck is 60 mph, rearrange the formula to find Time ($T$).
Calculation:
Answer Key
Section 2: Matching
- E (Linear Equations)
- D (Ratio & Proportion)
- B (Pythagoras/Trigonometry)
- A (Probability)
- C (Statistics)
Section 3: Practical Application
- 10 Liters. (15 ÷ 3 = 5. Then 5 × 2 = 10).
- $1.5 \times 10^8$ km.
- Yes. ($9 + 16 = 25$, which is $5^2$).
- 1,210 views. (Month 1: 1,100. Month 2: 1,100 + 110 = 1,210).
Section 4: Logic Challenge
- Formula: $T = D / S$
- Calculation: $120 / 60 = 2$
- Result: 2 Hours