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Basic 9 · Mathematics · Term Preparation

Preparing for the Term in Mathematics

In this topic you will prepare for the term by recalling key number skills, reviewing problem-solving strategies and planning how to use mathematics in project work.

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

  • Recall key number skills from Basic 8
  • Apply problem-solving strategies
  • Plan a simple mathematical investigation

What you already know

  • Mathematics, Basic 8

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 Preparation

Introduction

Your B.E.C.E. year has begun. Strong number skills make every other part of mathematics easier.

1. Key Ideas from Basic 8

Review of number
IdeaExample
place valueIn 4,562,000 the 5 is worth 500,000.
standard form4,500 = 4.5 × 10³
significant figures7,862 to 2 s.f. is 7,900
indices2³ × 2⁴ = 2⁷
HCF and LCMHCF of 12 and 18 is 6; LCM is 36
percentages15% of 200 = 30

2. Quick Review Questions

Mixed review

Calculate: (a) 3⁴ ÷ 3² (b) 20% of 350 (c) the LCM of 6 and 8.

  1. (a) 3⁴⁻² = 3² = 9.
  2. (b) 0.2 × 350 = 70.
  3. (c) Multiples of 8: 8, 16, 24. 24 is divisible by 6.

Answer: 9, 70 and 24

A student solving a mathematics problem on the board
Figure 1: Maths at the board Make a list of topics you find difficult.

3. Finding Your Gaps

Mathematics is built in layers. If a lower layer is weak, the next will be shaky too. Try past questions without help, and mark them honestly. List the topics in which you lost marks, and revise those first. Do not just read worked examples. Cover the solution, try the question yourself and compare. Doing mathematics is the only way to get better at it.

4. Working Without a Calculator

Some B.E.C.E. questions must be worked by hand, so keep your mental skills sharp. Know your multiplication tables up to 12 × 12, your squares up to 15² and the common fractions, decimals and percentages. Knowing that ⅛ = 0.125 = 12.5% will save you time. Show each step of your working, because marks are given for method. A neat page helps you to find your own mistakes.

New words

review
To study again.
standard form
A number written as A × 10ⁿ.
significant figure
A digit that carries meaning in a number.
method
The steps used to solve a problem.

Summary

  • Number skills form the base of mathematics.
  • Find your weak topics by trying past questions.
  • Show your working and keep your mental skills sharp.

Class activity: Review Stations

  1. Rotate through stations on place value, indices and percentages.
  2. Solve two problems at each.
  3. Record what you need to revise.

You need: Bottle tops, Number cards, Graph paper

Exercises

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

  1. 1. 4,500 in standard form is…

    • A. 4.5 × 10³
    • B. 45 × 10²
    • C. 4.5 × 10²
    • D. 0.45 × 10⁴
    Show answer
    Answer: 4.5 × 10³Standard form.

  2. 2. 2³ × 2⁴ =

    • A. 2⁷
    • B. 2¹²
    • C. 4⁷
    • D. 4¹²
    Show answer
    Answer: 2⁷Add indices.

  3. 3. Marks can be given for method.

    • A. True
    • B. False
    Show answer
    Answer: TrueShow working.

  4. 4. The LCM of 4 and 6 is ______.

    Show answer
    Answer: 12Multiples.

  5. 5. Find 15% of GH₵240.

    Show answer
    Answer: GH₵360.15 × 240.

  6. 6. Write ⅜ as a decimal and a percentage.

    Show answer
    Answer: 0.375 and 37.5%3 ÷ 8.

Lesson 2

Strand
Number
Sub-strand
Term Preparation

Introduction

Many learners freeze when they see a word problem. A clear strategy gives you a place to start.

1. Four Steps

  1. Understand: read carefully and note what is given and asked.
  2. Plan: choose a strategy.
  3. Solve: carry out the steps.
  4. Check: ask whether the answer makes sense.

2. Strategies

Problem-solving strategies
StrategyWhen to use it
draw a diagramshapes, sets and distances
make a tablepatterns and comparisons
work backwardswhen the end result is known
guess and checksmall whole-number answers
find a patternsequences
simplifylarge or hard numbers

3. Worked Example

Working backwards

A trader spends half of her money on cloth and GH₵20 on transport. She has GH₵80 left. How much did she start with?

  1. Before transport she had 80 + 20 = 100.
  2. That was half of her money.
  3. So she started with 100 × 2.

Answer: GH₵200

Check: half of 200 is 100, take away 20 to leave 80. The check agrees with the question, so the answer is right. Always check your answer, using the original numbers.

A trader counting money at a stall
Figure 2: Trader counting money Make up a working-backwards problem.

4. Reasoning

Reasoning means explaining why something is true. Mathematicians do not simply say an answer. They give reasons. If you say that the sum of two odd numbers is always even, can you explain why? An odd number is one more than an even number, so two odd numbers contain two extra ones, which make a pair. Giving reasons like this deepens your understanding, and it prepares you for higher mathematics. Use words like "because", "therefore" and "since" when you explain.

New words

strategy
A plan for solving a problem.
reasoning
Explaining why something is true.
pattern
A regular arrangement.
estimate
A rough calculation.

Summary

  • Understand, plan, solve and check.
  • Choose a strategy that suits the problem.
  • Explain your reasoning.

Class activity: Strategy Match

  1. Read five word problems.
  2. Choose a strategy for each.
  3. Solve them and compare.

You need: Bottle tops, Number cards, Graph paper

Exercises

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

  1. 1. The last step in problem solving is to…

    • A. check
    • B. read
    • C. plan
    • D. guess
    Show answer
    Answer: checkSteps.

  2. 2. Which strategy suits a sequence?

    • A. find a pattern
    • B. draw a map
    • C. use a ruler
    • D. divide by zero
    Show answer
    Answer: find a patternStrategy.

  3. 3. Reasoning explains why something is true.

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

  4. 4. A plan for solving a problem is a ______.

    Show answer
    Answer: strategyTerm.

  5. 5. I think of a number, double it and add 6 to get 20. Find it.

    Show answer
    Answer: 7Work backwards.

  6. 6. Explain why the sum of two even numbers is even.

    Show answer
    Answer: Each even number divides into pairs, so together they still form pairs.Reasoning.

Lesson 3

Strand
Number
Sub-strand
Term Preparation

Introduction

Mathematics can answer real questions about your school, your family and your town.

1. What Is an Investigation?

An investigation starts with a question, then uses data and calculation to answer it. For example: How much water does our school use each day? How far do learners walk to school? What is the cheapest way to buy a bag of rice? Unlike a textbook exercise, an investigation may not have one correct answer. You must decide what to measure, and how to interpret the results.

2. Steps

  1. Ask a clear question.
  2. Decide what data you need.
  3. Collect the data.
  4. Organise it in a table.
  5. Calculate totals, averages and percentages.
  6. Draw a chart.
  7. State your conclusion.

3. Sample Data

Walking distance

Five learners walk 1.2 km, 0.8 km, 2.5 km, 1.5 km and 1.0 km to school. Find the mean distance.

  1. Total: 1.2 + 0.8 + 2.5 + 1.5 + 1.0 = 7.0 km.
  2. Mean: 7.0 ÷ 5.

Answer: 1.4 km

The mean tells us a typical value. If the school has 300 learners, we could estimate that they walk about 300 × 1.4 = 420 km each morning. That is about the straight-line distance from Accra to Tamale. Numbers like this make a report memorable.

Students walking to school along a road
Figure 3: Walking to school Write a question you could investigate.

4. Measuring Accurately

Use the right tool and unit. A ruler is suitable for a book, and a tape measure for a classroom. Record your measurements right away, with units. Repeat them to check. Round your answers sensibly: there is no need to give a walking distance to six decimal places. Say how you found your results, and whether they might be inaccurate. Honest reporting matters as much in mathematics as it does anywhere else.

New words

investigation
A study to answer a question.
data
Facts and numbers collected.
mean
The total divided by the number of items.
conclusion
What the results show.

Summary

  • An investigation answers a real question with data.
  • Organise data and calculate the mean and totals.
  • Measure carefully and report honestly.

Class activity: Class Survey

  1. Choose a question.
  2. Collect data from ten learners.
  3. Find the mean and state a conclusion.

You need: Bottle tops, Number cards, Graph paper

Exercises

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

  1. 1. The mean of 2, 4 and 6 is…

    • A. 4
    • B. 12
    • C. 6
    • D. 2
    Show answer
    Answer: 412 ÷ 3.

  2. 2. Which tool suits measuring a classroom?

    • A. tape measure
    • B. thermometer
    • C. compass
    • D. protractor
    Show answer
    Answer: tape measureTool.

  3. 3. An investigation begins with a question.

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

  4. 4. Facts and numbers collected are ______.

    Show answer
    Answer: dataTerm.

  5. 5. Find the mean of 10, 12, 14 and 16.

    Show answer
    Answer: 1352 ÷ 4.

  6. 6. If 4 learners use 60 litres a week, estimate the use of 300 learners.

    Show answer
    Answer: 4,500 litres15 × 300.

Homework

  1. Choose a question for an investigation and write a plan for it.
Preparing for the Term in Mathematics – Basic 9 Mathematics Notes | sirbus