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Basic 9 · Mathematics · Term Project

Term Project: Presenting and Revising

In this topic you will present your mathematical project, evaluate your work and revise the term's topics in preparation for assessment.

By the end of these notes you should be able to:

  • Present mathematical findings clearly
  • Evaluate projects using criteria
  • Revise the term's number topics

What you already know

  • Investigating with number

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

Explaining your mathematics to others is one of the best ways to understand it.

1. Structure of the Presentation

  1. State your question and why it matters.
  2. Explain how you collected data.
  3. Show your table or chart.
  4. Explain one key calculation.
  5. Give your conclusion and your recommendation.
  6. Take questions.

2. Explaining Calculations

Choose one calculation and explain it step by step on the board. Use simple language. Say why you did each step. For example: "We divided the total by the number of learners to find the mean, because we wanted a typical value." Showing that you understand matters more than showing many numbers. Check that your charts are large enough for all to see.

3. Evaluation Checklist

Evaluation checklist
CriterionQuestion
questionWas it clear and useful?
dataWas it accurate and fair?
calculationsWere they correct, with working shown?
displayWere tables and charts clear?
conclusionDid it answer the question?
teamworkDid all members contribute?
A student explaining a chart
Figure 1: Explaining a chart Evaluate another group's project.

4. Responding to Questions

Your audience may ask how you got a number. Be ready to show your working. If someone finds a mistake, thank them, and say how you will fix it. Mathematicians check each other's work all the time, and this is how knowledge improves. Do not feel ashamed. Spotting and correcting an error shows understanding.

5. Making a Difference

Share your recommendation with those who could use it. Tell your family which shop is cheapest. Tell your head teacher how much water could be saved. If your measurements show that a corner is not square, tell the builder. Mathematics can help people to make wise decisions, and that is why it is worth learning.

New words

criterion
A standard used for judging.
evaluate
To judge how good something is.
working
The steps in a calculation.
present
To share with an audience.

Summary

  • Present your question, data, calculations and conclusion.
  • Explain one calculation well.
  • Use findings to help real decisions.

Class activity: Project Fair

  1. Present your project.
  2. Evaluate two others.
  3. Share a recommendation.

You need: Bottle tops, Number cards, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. Which belongs in a presentation?

    • A. your conclusion
    • B. your bus fare
    • C. your shoe size
    • D. your phone number
    Show answer
    Answer: your conclusionContent.

  2. 2. If someone finds an error, you should…

    • A. thank them and fix it
    • B. get angry
    • C. hide it
    • D. leave
    Show answer
    Answer: thank them and fix itAttitude.

  3. 3. Explaining mathematics deepens understanding.

    • A. True
    • B. False
    Show answer
    Answer: TrueLearning.

  4. 4. The steps in a calculation are the ______.

    Show answer
    Answer: workingTerm.

  5. 5. State three evaluation criteria.

    Show answer
    Answer: Data, calculations and conclusion.Any three.

  6. 6. How can a project on shop prices help a family?

    Show answer
    Answer: It shows where to buy at lower cost and saves money.Application.

Lesson 2

Strand
Number
Sub-strand
Term Project

Introduction

Now let us look back over the first half of the term's work.

1. Key Ideas

Summary of number topics
TopicKey points
significant figurescount from the first non-zero digit
decimal placescount after the point
rational numberscan be written as a/b
recurring decimalsuse 10x or 100x to convert
setsn(A ∪ B) = n(A) + n(B) − n(A ∩ B)
powers of 10multiply left, divide right
propertiescommutative, associative, distributive

2. Practice Questions

Mixed revision 1

Express 0.0506 to 2 s.f. and 12.358 to 2 d.p.

  1. 0.0506: the digits 5, 0 and then 6 give 0.051.
  2. 12.358: next digit 8 gives 12.36.

Answer: 0.051 and 12.36

Mixed revision 2

Write 0.272727... as a fraction.

  1. Let x = 0.2727...
  2. 100x = 27.2727...
  3. 99x = 27.

Answer: x = 27/99 = 3/11

Mixed revision 3

Solve 2(3x − 1) + 4 = 20.

  1. Expand: 6x − 2 + 4 = 20.
  2. 6x + 2 = 20.
  3. 6x = 18.

Answer: x = 3

Students revising with past papers
Figure 2: Revising past papers Solve five past questions.

3. Examination Technique

Read each question twice. Show your working. Use a pencil and ruler for diagrams. Check that your answer is reasonable, and that it includes units. If you get stuck, leave a space, and come back to the question. Manage your time, and aim to finish with a few minutes left to check your work.

4. Making a Revision Plan

Make a list of the topics you have studied, and rate each as strong, fair or weak. Spend the most time on weak topics, but do not ignore the others. Practise a little daily. Use past questions, and mark them. Form a study group, and explain ideas to each other. Teaching someone else is one of the best forms of revision.

New words

revision
Studying again.
past question
A question from an earlier examination.
technique
A skilled way of doing something.
study group
Learners who revise together.

Summary

  • Review rounding, rationals, sets and properties.
  • Practise questions from each topic.
  • Plan revision around weak topics.

Class activity: Revision Stations

  1. Rotate through four topics.
  2. Solve one problem at each.
  3. Note what you need to practise.

You need: Bottle tops, Number cards, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 0.0506 has how many s.f.?

    • A. 3
    • B. 2
    • C. 4
    • D. 5
    Show answer
    Answer: 35, 0, 6.

  2. 2. 0.333... as a fraction is…

    • A. ⅓
    • B. ⅔
    • C. 1/30
    • D. 3/10
    Show answer
    Answer: ⅓9x = 3.

  3. 3. Showing working can earn marks.

    • A. True
    • B. False
    Show answer
    Answer: TrueMethod.

  4. 4. a(b + c) = ab + ______.

    Show answer
    Answer: acDistributive.

  5. 5. Find n(A ∪ B) if n(A) = 12, n(B) = 9, n(A ∩ B) = 4.

    Show answer
    Answer: 1712 + 9 − 4.

  6. 6. Write 0.1 repeating as a fraction, with x = 0.111...

    Show answer
    Answer: 1/99x = 1.

Lesson 3

Strand
Number
Sub-strand
Term Project

Introduction

The second half of the term was full of useful rules. Let us bring them together.

1. Key Ideas

Summary of operations topics
TopicKey points
surdssimplify using perfect squares
surd rules√a × √b = √(ab); add only like surds
rationalisingmultiply by the surd or conjugate
fractionscommon denominators; multiply by the reciprocal
decimalsline up points; count places
percentagesuse the correct base
BODMASbrackets, orders, ÷ ×, + −

2. Practice Questions

Revision 1

Simplify √18 + √50 − √8.

  1. 3√2 + 5√2 − 2√2.

Answer: 6√2

Revision 2

Rationalise 5/(2 + √3).

  1. Multiply by 2 − √3.
  2. Top: 5(2 − √3).
  3. Bottom: 4 − 3 = 1.

Answer: 10 − 5√3

Revision 3

Simplify ⅔ of 1½ + 0.5 × 4.

  1. ⅔ × 3/2 = 1.
  2. 0.5 × 4 = 2.
  3. 1 + 2.

Answer: 3

Revision 4

A trader's price rises from GH₵240 to GH₵270. Find the percentage increase.

  1. Increase: 30.
  2. 30/240 × 100.

Answer: 12.5%

Students at the end of the school term
Figure 3: End of term Write a list of formulas to remember.

3. Common Errors to Avoid

Errors to avoid
ErrorCorrect idea
√a + √b = √(a + b)Only like surds add.
½ + ⅓ = 2/5Use a common denominator.
wrong percentage baseUse the original amount.
leaving a surd in the denominatorRationalise.

4. Looking Ahead

Keep practising during the holidays. Do a little mathematics every day, using a small set of past questions. Notice mathematics in the world: shop prices, percentages in the news and the shape of buildings. When you return, you will build on these number skills in algebra, geometry and statistics. Be proud of what you have achieved this term.

New words

formula
A rule written with symbols.
increase
A rise in amount.
simplify
To write in a simpler form.
reciprocal
A number turned upside down.

Summary

  • Review surds, fractions, decimals and percentages.
  • Avoid the common errors.
  • Keep practising each day.

Class activity: End-of-Term Quiz

  1. Answer ten mixed questions.
  2. Mark your work.
  3. List two topics to practise.

You need: Bottle tops, Number cards, Graph paper

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. √16 + √9 =

    • A. 7
    • B. 5
    • C. 25
    • D. √25
    Show answer
    Answer: 74 + 3.

  2. 2. The percentage rise from 80 to 100 is…

    • A. 25%
    • B. 20%
    • C. 80%
    • D. 100%
    Show answer
    Answer: 25%20/80.

  3. 3. Only like surds can be added.

    • A. True
    • B. False
    Show answer
    Answer: TrueRule.

  4. 4. ½ + ⅓ = ______.

    Show answer
    Answer: 5/6Common denominator.

  5. 5. Simplify 3√2 × √2.

    Show answer
    Answer: 63 × 2.

  6. 6. Rationalise 3/(√5 − 2).

    Show answer
    Answer: 3√5 + 6Bottom = 1.

Homework

  1. Solve ten mixed revision questions, and mark them.
Term Project: Presenting and Revising – Basic 9 Mathematics Notes | sirbus