Basic 9 · Mathematics · Term Project
Term Project: Investigating with Number
In this topic you will apply the term's learning through mathematical project work, using problem solving, reasoning, measurement, number and data skills.
By the end of these notes you should be able to:
- Plan a mathematical project on a real question
- Collect and organise data
- Use number skills to analyse results
What you already know
- All topics covered in Mathematics this term
Copy everything that has a blue line on its left into your notebook. The other parts are for reading.
Lesson 1
- Strand
- Number
- Sub-strand
- Term Project
Introduction
This project uses mathematics to answer a real question from your life.
1. Project Options
| Option | Question | Skills |
|---|---|---|
| household budget | How do families spend money? | percentages |
| best buy | Which shop is cheapest? | unit prices |
| school survey | What do learners think? | sets, percentages |
| land measuring | What is the area of the compound? | measurement |
| loan comparison | Which savings plan pays most? | interest |
| builder's corners | Is a building square? | surds |
2. Planning
- State a clear question.
- Decide what data you need.
- Plan how to collect it.
- Assign roles.
- Set a timetable.
- Estimate your expected result.
A clear question can be answered with data. "Is food expensive?" is vague. "How much does a 5 kg bag of rice cost in three local shops?" is clear. Include an estimate of what you expect to find, and compare it with your results later.
3. Making a Data Sheet
| Shop | Item | Size | Price (GH₵) | Price per kg |
|---|---|---|---|---|
| A | rice | 5 kg | 110 | 22 |
| B | rice | 2 kg | 48 | 24 |
| C | rice | 25 kg | 500 | 20 |
Set out your table before you begin. Include headings and units. Fill it in as you collect the information. If a value seems odd, check it again.
4. Fairness and Accuracy
Compare like with like. Compare prices for the same quality of rice and on the same day. In a survey, ask enough people, and include different groups. Asking only your friends will not represent your whole school. Record what people say, and do not change numbers to get the result that you want.
New words
- project
- A planned piece of work.
- data sheet
- A table for recording data.
- sample
- A small group that represents a larger one.
- unit price
- The price per unit.
Summary
- Choose a clear, measurable question.
- Plan your data collection with a table.
- Collect data fairly and accurately.
Class activity: Project Plan
- Choose a project.
- Prepare a data sheet.
- Show it to your teacher.
You need: Bottle tops, Number cards, Graph paper
Exercises
Answer in your exercise book first, then check your answers.
1. Which is a clear project question?
- A. How much does rice cost in three shops?
- B. Is life hard?
- C. Are things good?
- D. Who knows?
Show answer
Answer: How much does rice cost in three shops?Measurable.2. The price per kg of 5 kg of rice at GH₵100 is…
- A. GH₵20
- B. GH₵50
- C. GH₵5
- D. GH₵500
Show answer
Answer: GH₵20100 ÷ 5.3. A sample should represent the whole group.
- A. True
- B. False
Show answer
Answer: TrueFairness.4. A table for recording data is a data ______.
Show answer
Answer: sheetTerm.5. State three steps in planning a project.
Show answer
Answer: State a question, plan data collection and assign roles.Any three.6. Why is asking only your friends a poor survey?
Show answer
Answer: They may not represent the whole school.Sampling.
Lesson 2
- Strand
- Number
- Sub-strand
- Term Project
Introduction
Careful data collection is the backbone of any investigation.
1. Methods
| Method | Example |
|---|---|
| measuring | lengths with a tape |
| counting | vehicles passing the school |
| survey | a questionnaire |
| records | school or shop records |
| prices | visiting shops |
2. Tally Charts and Frequency Tables
Frequency table
A survey of 20 learners' transport gave: walk 9, bus 6, bicycle 3, car 2. Find the percentage who walk.
- Total: 9 + 6 + 3 + 2 = 20.
- Walk: 9/20 × 100.
Answer: 45%
A tally chart lets you record data quickly, with a mark for every item, and groups of five. Add up your tallies to form a frequency table. Check that your total matches the number of people surveyed.
3. Calculating Summaries
| Measure | Meaning | Example |
|---|---|---|
| mean | total ÷ number | 12 + 14 + 16 → 14 |
| median | middle value | 3, 7, 9 → 7 |
| mode | most common | 2, 2, 5 → 2 |
| range | largest − smallest | 12 − 5 = 7 |
| percentage | part ÷ whole × 100 | 9/20 = 45% |
4. Dealing with Problems
Sometimes data is missing, or a person refuses to answer. Note this honestly. If one value is far from the others, check it. It may be an error, or it may be real. Do not just delete it. Keep your original notes, and show them with your report. Use a calculator to check totals, and ask a partner to check your work. Round your answers sensibly, and state the accuracy used.
5. Choosing a Chart
Bar charts compare categories, pie charts show parts of a whole and line graphs show change over time. Give each chart a title and labelled axes, and choose a scale that fits the paper. A clear chart makes your results easy to understand. To make a pie chart, multiply each fraction by 360°. For example, 45% is 0.45 × 360 = 162°.
New words
- tally
- A mark used for counting.
- frequency
- How often something happens.
- median
- The middle value.
- mode
- The most common value.
Summary
- Choose a suitable method of collecting data.
- Use tally charts and frequency tables.
- Summarise data with the mean, median and mode.
Class activity: Data Day
- Collect your data.
- Make a frequency table.
- Find the mean and mode.
You need: Bottle tops, Number cards, Graph paper
Exercises
Answer in your exercise book first, then check your answers.
1. The middle value is the…
- A. median
- B. mode
- C. mean
- D. range
Show answer
Answer: medianTerm.2. The mean of 4, 8, 12 is…
- A. 8
- B. 24
- C. 4
- D. 12
Show answer
Answer: 824 ÷ 3.3. Pie charts show parts of a whole.
- A. True
- B. False
Show answer
Answer: TrueChart.4. How often something happens is its ______.
Show answer
Answer: frequencyTerm.5. Find the range of 5, 9, 2, 12.
Show answer
Answer: 1012 − 2.6. 25% of a class walks. What is the angle in a pie chart?
Show answer
Answer: 90°0.25 × 360.
Lesson 3
- Strand
- Number
- Sub-strand
- Term Project
Introduction
Data becomes useful when you ask what it means.
1. From Numbers to Meaning
Look at your results and ask: What is the biggest? What is the smallest? Is there a pattern? What surprises me? Calculate percentages or unit prices so that you can make fair comparisons. Compare your results with your first estimate. Explain any differences. These questions turn a table of numbers into a useful answer.
2. Worked Analysis
Best buy
Using the data sheet, find which shop gives the best value, and how much a family would save on 25 kg compared with the dearest.
- Unit prices: A = GH₵22, B = GH₵24, C = GH₵20.
- Cheapest: Shop C, dearest: Shop B.
- Saving on 25 kg: (24 − 20) × 25.
Answer: Shop C, saving GH₵100
But a poor family may not have GH₵500 to buy 25 kg at once. So the cheapest unit price may not be the best choice for everyone. Good analysis includes the real-life context.
3. Testing Results
| Question | Purpose |
|---|---|
| Are the calculations correct? | avoids errors |
| Is the sample big enough? | reliability |
| Could something else explain this? | fair thinking |
| Would it be true at another time? | limits |
| What should be done next? | recommendations |
4. Writing a Conclusion
State your answer to the question in clear words, using numbers. For example: "Rice costs least per kg at Shop C, at GH₵20, which is GH₵4 less than Shop B." Say how reliable your result is, and add a recommendation. Use terms such as "about" or "in our sample" where this is appropriate. A clear conclusion is the most valuable part of a project, and it shows that you have understood the mathematics.
5. Preparing to Present
Prepare a poster or a set of slides. Show your question, data, calculations and conclusion. Use one or two clear charts. Practise explaining your calculations in simple words. Next week, you will share your work and evaluate others.
New words
- analyse
- To examine in detail.
- reliable
- Able to be trusted.
- recommendation
- A suggestion for action.
- context
- The real-life situation.
Summary
- Turn numbers into meaning with comparisons.
- Test your results and consider context.
- Write a clear conclusion with numbers.
Class activity: Results Discussion
- Calculate your key results.
- Discuss what they mean.
- Write your conclusion.
You need: Bottle tops, Number cards, Graph paper
Exercises
Answer in your exercise book first, then check your answers.
1. A suggestion for action is a…
- A. recommendation
- B. tally
- C. mean
- D. mode
Show answer
Answer: recommendationTerm.2. 2 kg at GH₵48 has a unit price of…
- A. GH₵24
- B. GH₵96
- C. GH₵46
- D. GH₵12
Show answer
Answer: GH₵2448 ÷ 2.3. Context should be considered in analysis.
- A. True
- B. False
Show answer
Answer: TrueMeaning.4. Able to be trusted means ______.
Show answer
Answer: reliableTerm.5. Why might the cheapest unit price not suit every family?
Show answer
Answer: They may not have enough money to buy the large size.Context.6. Shop X sells 3 kg at GH₵75, and Shop Y sells 5 kg at GH₵120. Which is cheaper per kg?
Show answer
Answer: Shop Y, at GH₵24 against GH₵25.Unit price.
Homework
- Write up your results and your conclusion.