Grade 10 Mathematics Unit 1

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TOPIC 1: NUMBERS

Lesson 1: Whole Numbers - Revision

This lesson reviews basic operations with whole numbers, including addition, subtraction, multiplication, and division.

  • Addition Example: Adding 123 and 456.
  • Subtraction Example: Subtracting 78 from 154.
  • Multiplication Example: Multiplying 7 by 8.
  • Division Example: Dividing 144 by 12.

Lesson 2: Fractions - Revision

Covers the basics of fractions, including simplification, addition, subtraction, multiplication, and division of fractions.

  • Simplification Example: Reducing the fraction 12/16 to 3/4.
  • Addition Example: Adding 1/4 and 2/3 (find a common denominator).
  • Subtraction Example: Subtracting 3/8 from 5/6.
  • Multiplication Example: Multiplying 2/5 by 3/7.
  • Division Example: Dividing 4/9 by 2/3.

Lesson 3: Decimals - Revision

Reviews operations with decimals, including addition, subtraction, multiplication, and division.

  • Addition Example: Adding 3.75 and 2.68.
  • Subtraction Example: Subtracting 5.4 from 8.6.
  • Multiplication Example: Multiplying 0.6 by 0.4.
  • Division Example: Dividing 7.2 by 0.3.

Lesson 4: Percentages - Revision

Focuses on converting between percentages, fractions, and decimals, and solving percentage-related problems.

  • Conversion Example: Converting 25% to a decimal and a fraction (0.25 and 1/4).
  • Problem Example: Finding what percentage 30 is of 150 (20%).

Lesson 5: Decimals, Fractions, and Percentages

Explores the relationships between decimals, fractions, and percentages and how to convert between them.

  • Conversion Example: Converting 0.75 to a fraction (3/4) and a percentage (75%).

Lesson 6: Mixed Word Problems

Provides practice with word problems that involve a combination of whole numbers, fractions, decimals, and percentages.

  • Example: Calculating the total cost after a 15% discount on a $200 item and adding a 5% tax.

TOPIC 2: ESTIMATION

Lesson 7: Rounding Off

Teaches rounding numbers to the nearest ten, hundred, thousand, etc.

  • Example: Rounding 356 to the nearest hundred results in 400.

Lesson 8: Significant Figures

Focuses on identifying and using significant figures in calculations.

  • Example: Rounding 0.0076543 to three significant figures results in 0.00765.

Lesson 9: Addition and Subtraction with Significant Figures

Explores performing addition and subtraction while considering significant figures.

  • Example: Adding 12.345 (five significant figures) and 0.067 (two significant figures) results in 12.41 (rounded to two decimal places).

Lesson 10: Multiplication and Division with Significant Figures

Covers multiplication and division while maintaining the correct number of significant figures.

  • Example: Multiplying 4.56 (three significant figures) by 0.0042 (two significant figures) results in 0.019 (rounded to two significant figures).

Lesson 11: Word Problems

Involves solving word problems that require estimation using rounding and significant figures.

  • Example: Estimating the cost of 12 items priced at $8.75 each when rounded to the nearest dollar.

Lesson 12: The Calculator

Reviews how to use a calculator effectively for performing estimations and rounding correctly.

  • Example: Using a calculator to approximate the product of 234 and 56 by rounding to the nearest hundred.

TOPIC 3: DIRECTED NUMBERS

Lesson 13: Integers

Introduces integers, including positive and negative numbers, and their representation on a number line.

  • Example: Identifying -3 and 5 on a number line.

Lesson 14: Adding & Subtracting Integers

Teaches rules for adding and subtracting integers, including handling negative numbers.

  • Addition Example: Adding -5 and 3 results in -2.
  • Subtraction Example: Subtracting -7 from 4 results in 11.

Lesson 15: Multiplying Integers

Explains how to multiply integers, including rules for determining the sign of the product.

  • Example: Multiplying -4 by 7 results in -28.

Lesson 16: Dividing Integers

Covers the rules for dividing integers, focusing on sign rules for positive and negative results.

  • Example: Dividing -24 by 6 results in -4.

Lesson 17: Order of Operations

Reviews the order of operations (PEMDAS/BODMAS) with a focus on problems involving integers.

  • Example: Solving 3 + 4 × (-2) results in -5.

TOPIC 4: NUMBER SEQUENCE AND PATTERNS

Lesson 18: Sequences

Introduces number sequences, teaching how to identify and continue arithmetic and geometric sequences.

  • Arithmetic Sequence Example: Finding the next term in 2, 5, 8, 11... (next term is 14).
  • Geometric Sequence Example: Finding the next term in 3, 6, 12, 24... (next term is 48).

Lesson 19: A Rule for a Sequence

Focuses on identifying and creating rules that define arithmetic and geometric sequences.

  • Example: Determining the nth term formula for an arithmetic sequence like 2, 5, 8, 11 (rule is an=2+(n−1)×3a_n = 2 + (n-1) \times 3an​=2+(n−1)×3).

Lesson 20: More Sequences

Explores more complex sequences, including Fibonacci and other non-linear sequences.

  • Example: Continuing the Fibonacci sequence 1, 1, 2, 3, 5, 8... (next terms are 13, 21).

Lesson 21: Patterns in Graphs

Teaches how to recognize and interpret patterns that emerge when sequences are plotted on graphs.

  • Example: Plotting an arithmetic sequence like 2, 5, 8, 11 on a graph shows a straight line.

Lesson 22: The Graph of Square Numbers

Covers the specific patterns that emerge when plotting square numbers on a graph.

  • Example: Plotting the graph of 1, 4, 9, 16 shows a parabolic curve.

 

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