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Basic 8 · Mathematics · Term Preparation

Preparing for the Term in Mathematics

In this topic you will review number work from Basic 7, including place value, operations, powers and fractions, and apply your knowledge in short problem-solving tasks.

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

  • Recall place value, rounding and significant figures
  • Recall the four operations, powers and prime factors
  • Recall fractions, decimals and percentages

What you already know

  • Mathematics, Basic 7

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

Mathematics builds step by step, so the skills from Basic 7 are the foundation for this year. Let us begin with place value and rounding.

1. Place Value Review

Large numbers are read in periods of three digits: ones, thousands, millions and billions. The number 5,204,060,300 is read as five billion, two hundred and four million, sixty thousand, three hundred. The value of a digit is the digit multiplied by its place value, so the 2 is worth 200,000,000.

Rounding and accuracy review
SkillRuleExample
roundinglook at the digit to the right; 5 or more rounds up4,768 to the nearest hundred is 4,800
decimal placesdigits after the point3.1416 to 2 d.p. is 3.14
significant figurescount from the first non-zero digit0.04567 to 2 s.f. is 0.046
powers of ten× moves digits left; ÷ moves digits right3.5 × 1,000 = 3,500
A chalkboard with large numbers and place value headings
Figure 1: Place value on the board Write three large numbers in words and in expanded form.

2. Worked Review

Mixed review

Round 7,496,312 to the nearest ten thousand and write 0.003782 to 2 significant figures.

  1. Ten-thousands digit: 9; next digit: 6, so round up. 49 ten thousands become 50 ten thousands.
  2. 7,496,312 becomes 7,500,000.
  3. First significant figures: 3, 7; next digit: 8, so round up.

Answer: 7,500,000 and 0.0038

3. Why Estimation Matters

Rounding lets us check answers quickly. Before calculating 4,987 × 21, estimate 5,000 × 20 = 100,000. If your exact answer is not close to this, check your working. Good mathematicians estimate before they calculate.

New words

period
A group of three digits in a large number.
place value
The value given to a digit by its position.
estimate
A sensible approximate answer.
significant figure
A digit counted from the first non-zero digit.

Summary

  • Large numbers are read in periods, and each digit's value depends on its position.
  • Rounding, decimal places and significant figures use the digit to the right.
  • Estimating first helps you check answers.

Class activity: Review Stations

  1. Use place-value cards to build three large numbers.
  2. Round each number to the nearest thousand and hundred thousand.
  3. Check another group's answers.

You need: Bottle tops, Number cards, Graph paper

Exercises

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

  1. 1. The value of 6 in 6,300,000,000 is…

    • A. 6,000,000,000
    • B. 600,000,000
    • C. 60,000,000
    • D. 6,000,000
    Show answer
    Answer: 6,000,000,000Billions.

  2. 2. 0.05678 correct to 2 s.f. is…

    • A. 0.057
    • B. 0.056
    • C. 0.05
    • D. 0.06
    Show answer
    Answer: 0.057Next digit 7.

  3. 3. Estimating helps to check answers.

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

  4. 4. 3.25 × 100 = ______.

    Show answer
    Answer: 325Two places left.

  5. 5. Round 3,482,915 to the nearest hundred thousand.

    Show answer
    Answer: 3,500,000Next digit 8.

  6. 6. Estimate 398 × 52 and explain your method.

    Show answer
    Answer: 400 × 50 = 20,000; round each number to one significant figure.Estimation.

Lesson 2

Strand
Number
Sub-strand
Term Preparation

Introduction

Addition, subtraction, multiplication and division are the tools of mathematics. Powers and prime factors give us short ways of working with numbers.

1. Operations Review

Key operations ideas
TopicKey points
mental strategiespartitioning, compensation, doubling and halving
number propertiescommutative, associative, distributive, identity
column methodsline up place values; regroup when needed
long divisiondivide, multiply, subtract, bring down
decimalsline up points when adding; count places when multiplying

2. Powers Review

A power is a short way of writing repeated multiplication: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. The base is 2 and the index is 5. Any non-zero number to the power 0 equals 1. BODMAS tells us the order of operations: brackets, orders, division and multiplication, then addition and subtraction.

Evaluate

Find the value of 3² + 2⁴ × 5⁰.

  1. Orders: 3² = 9, 2⁴ = 16, 5⁰ = 1.
  2. Multiply: 16 × 1 = 16.
  3. Add: 9 + 16.

Answer: 25

3. Prime Factors and HCF

Find the HCF

Find the HCF of 48 and 180.

  1. 48 = 2⁴ × 3.
  2. 180 = 2² × 3² × 5.
  3. Common primes with lowest powers: 2² and 3.

Answer: HCF = 4 × 3 = 12

Students solving mathematics problems in exercise books
Figure 2: Maths practice Write 72 and 96 as products of primes and find their HCF.

4. Using Calculators Wisely

A calculator is a useful tool, but it does exactly what you press. Estimate first, enter numbers carefully and check that the answer is reasonable. Many examination papers do not allow calculators, so keep your written and mental skills strong.

New words

index
The small number showing repeated multiplication.
HCF
The highest common factor.
BODMAS
The order of operations.
prime factor
A factor that is a prime number.

Summary

  • Mental strategies and number properties make calculations easier.
  • Powers are repeated multiplication, and BODMAS gives the order of operations.
  • The HCF uses common primes with their lowest powers.

Class activity: Operations Relay

  1. Each member solves one step of a multi-step problem.
  2. Pass the answer to the next member.
  3. Check the final answer together.

You need: Bottle tops, Number cards, Graph paper

Exercises

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

  1. 1. 2³ =

    • A. 8
    • B. 6
    • C. 9
    • D. 5
    Show answer
    Answer: 82 × 2 × 2.

  2. 2. The HCF of 18 and 24 is…

    • A. 6
    • B. 3
    • C. 12
    • D. 72
    Show answer
    Answer: 62 × 3.

  3. 3. Any non-zero number to the power 0 equals 1.

    • A. True
    • B. False
    Show answer
    Answer: TrueZero index.

  4. 4. In BODMAS, the B stands for ______.

    Show answer
    Answer: bracketsFirst.

  5. 5. Evaluate 5 + 3 × 2².

    Show answer
    Answer: 175 + 3 × 4 = 5 + 12.

  6. 6. Use the distributive property to calculate 6 × 98.

    Show answer
    Answer: 6 × (100 − 2) = 600 − 12 = 588Distributive.

Lesson 3

Strand
Number
Sub-strand
Term Preparation

Introduction

Fractions, decimals and percentages are three ways of showing parts of a whole. Being able to move between them is an essential skill.

1. Equivalents

Common equivalents
FractionDecimalPercentage
½0.550%
¼0.2525%
¾0.7575%
⅕0.220%
1/100.110%
⅓0.333...33⅓%

2. Operations with Fractions

To add or subtract fractions, use a common denominator from the LCM. To multiply, multiply numerators and denominators, cancelling first where possible. To find a fraction of a quantity, divide by the denominator and multiply by the numerator.

Mixed review

Calculate 2⅓ + 1¾ and find ⅗ of GH₵450.

  1. 2 4/12 + 1 9/12 = 3 13/12 = 4 1/12.
  2. 450 ÷ 5 = 90; 90 × 3 = 270.

Answer: 4 1/12 and GH₵270

A fraction wall chart in a classroom
Figure 3: Fraction chart Draw a fraction wall up to tenths.

3. Problem-Solving Review

In a short practical task, measure the length and width of your desk in centimetres, calculate its perimeter and area and express the width as a fraction, decimal and percentage of the length. This links number skills to measurement, and shows why mathematics is useful.

4. Planning for the Term

This term you will work with very large numbers, standard form, sets, laws of indices and real-life problems. Keep a neat exercise book, try every question, and ask when you do not understand. Regular practice is the secret of success in mathematics.

5. Using Mathematics at Home

Look for mathematics in daily life. When you shop, work out the change. When you cook, double a recipe. When you travel, estimate the distance and time. The more you use numbers outside the classroom, the stronger and more confident you become.

New words

equivalent
Having the same value.
denominator
The bottom number of a fraction.
percentage
A number out of 100.
perimeter
The distance around a shape.

Summary

  • Fractions, decimals and percentages are different forms of the same value.
  • Use the LCM to add fractions, and multiply tops and bottoms when multiplying.
  • Regular practice builds success in mathematics.

Class activity: Desk Measurement Task

  1. Measure the length and width of your desk.
  2. Calculate its perimeter and area.
  3. Express the width as a fraction, decimal and percentage of the length.

You need: Bottle tops, Number cards, Graph paper

Exercises

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

  1. 1. ¾ as a percentage is…

    • A. 75%
    • B. 34%
    • C. 25%
    • D. 43%
    Show answer
    Answer: 75%0.75 × 100.

  2. 2. ⅖ + ⅓ =

    • A. 11/15
    • B. 3/8
    • C. 2/15
    • D. 5/15
    Show answer
    Answer: 11/15Common denominator 15.

  3. 3. 0.5 = ½.

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

  4. 4. ¼ of 80 is ______.

    Show answer
    Answer: 2080 ÷ 4.

  5. 5. Find 15% of GH₵600.

    Show answer
    Answer: GH₵90600 × 15/100.

  6. 6. Order from least to greatest: ⅜, 0.4, 35%.

    Show answer
    Answer: 35%, ⅜, 0.40.35, 0.375, 0.4.

Homework

  1. Solve ten mixed revision questions from your Basic 7 work.
Preparing for the Term in Mathematics – Basic 8 Mathematics Notes | sirbus