What is a Number Line? - Year 7 PDF Download

Key Points

• Number Line: A number line is a straight line marked with numbers at equal intervals. These lines typically run horizontally but can also be represented vertically, as seen in graphs and thermometers. When moving right on a number line, numbers increase; when moving left, numbers decrease. Integers, decimals, and fractions can all be positioned on a number line.
• Representation: In mathematics, representation denotes the various forms in which mathematical concepts are presented, such as expressions, tables, or graphs. This includes both horizontal and vertical displays seen in different mathematical contexts like graphing and measuring temperature.
• Increase and Decrease: Progressing rightward on a number line results in number increase, while moving left leads to number decrease. This fundamental principle is crucial for understanding numerical relationships on a number line.
• Integers on a Number Line: Integers, which encompass positive, negative whole numbers, and zero, can be accurately located on a number line alongside decimals and fractions. This visual representation aids in understanding their relative positions and magnitudes.

How to Use a Number Line

• A number line serves as a visual representation of a single value or a range of values in mathematics.
• It offers an ordered view, indicating positions within a sequence such as first, second, third, and so forth.
• Number lines are a fundamental tool for understanding and working with numerical values.

Importance of Number Line Representation

• Number lines help in grasping the concept of order and magnitude in mathematics.
• They provide a tangible way to comprehend the relative positions of numbers.

Examples of Using a Number Line

• Example 1: Comparing Fractions - By plotting fractions on a number line, students can visualize and compare their relative sizes.
• Example 2: Addition and Subtraction - Number lines aid in adding and subtracting integers by moving along the line.

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Understanding Number Lines

• The concept of division on a scale, such as a ruler, where each division may represent a unit like a millimeter.
• Number lines can accommodate various values, including integers, decimals, and fractions.
• Comparison between numbers is facilitated by representing them on a number line.

Benefits of Using Number Lines

• Number lines aid in calculating or estimating readings on the same scale by using marked values.
• Conversion between different units is possible using number lines, with the double number line being a useful tool.

Double Number Line

• A double number line comprises two number lines with corresponding value pairs, often depicted as a single line with values on both sides.

Understanding Number Lines

Number lines are visual tools that help us understand the concept of numbers and their relationships. They are particularly useful for grasping the concept of integers, decimals, fractions, and even unit conversions.

Integer Values on a Number Line

• When representing integer values on a number line, each number is evenly spaced.
• To indicate a value like 2 on the number line, you start at zero and move two steps to the right.
• For example, a number line from 0 to 10 helps visualize integer values.

Decimal and Fraction Values

• Decimal values on a number line, like between 4 and 5, show increments by tenths (0.1).
• Similarly, fractions can be represented on a number line, such as values between 0 and 1 in tenths (1/10).

Double Number Lines for Conversions

• Double number lines are beneficial for converting between different units, for instance, miles and kilometers.
• They provide a visual representation of how values in one unit correspond to values in another unit.
• For instance, if 10 miles aligns with 16 kilometers on a double number line, it signifies the equivalence between the two units.

Image caption: This number line shows integer values. The numbers are evenly spaced on the number line. Each step increases by 1.	Image caption: To mark a value on the number line, e.g., the number 2, start at zero and take 2 steps to the right.	Image caption: Number lines can show decimals as well as integers. This number line represents the values between 4 and 5. Each step increases by 0.1.	Image caption: Number lines can also show fractions as values. This number line represents the values between 0 and 1. Each step increases by 1/10 (one tenth).	Image caption: A double number line can be helpful when converting between different units. E.g., this double number line shows miles and kilometers (km). 10 miles is in the corresponding position to 16 km. This means that 10 miles is the same as 16 km.

How to work out a missing value on a number line

Not all numbers on a number line have a value written next to them. Sometimes it is necessary to calculate these missing values in order to interpret the number line accurately.

There are several methods to calculate a missing value on a number line:

• Find the difference:
  • The numerical difference between two numbers is determined by comparing the quantities. It is always a positive value. For instance, the difference between 3 and 5 is 2, and vice versa, between 5 and 3 on the number line.
• Count the number of steps between the two values.
• Divide the difference by the number of steps.
• This calculation provides the size of each step, which can be used to fill in the missing values on the number line.

Sometimes, identifying a missing value can be expedited without calculating each step. For example, it may be quicker to determine a value that lies halfway between two known points on the number line.

Topic: Working out the Missing Value on a Number Line

Explanation:

• On a number line ranging from 0 to 10, with 5 equal steps, understanding the value represented by a question mark involves division and basic arithmetic.

Steps to Determine the Missing Value:

• Review the values on the number line; in this case, 0 and 10 are the endpoints.
• Count the number of steps between the values, which should be 5 in this scenario.
• Divide the total difference by the number of steps to ascertain the value each step represents (10 ÷ 5 = 2).
• Start at 0 on the number line, take the required number of steps to the right, with each step representing the calculated value.

Illustrative Example:

• Consider a scenario where starting at 0, taking 3 steps to the right on the number line indicates a missing value of 6.

Visual Representation:

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Number Line Examples

• Image caption: This number line has 30 and 50 identified. What is the value represented by the question mark?
• Explanation: The missing value is exactly halfway between the values of 30 and 50. Halfway between 30 and 50 is 40. The value of the question mark is 40. The value represented by the question mark can be identified here without calculating the size of each step.

Question

• Slide 1 of 7, Example 1: A number line going from zero and ten. There are five steps. An arrow points to a question mark positioned on the 3rd value of the number line. What is the value represented by the question mark?

Practise number lines

Practice reading number lines and determine missing values with this interactive quiz. Grab a pen and paper to work through the questions.

Quiz

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Real-world maths

Number lines play a crucial role in everyday scenarios. Typically depicted as horizontal lines, they can also be vertical or curved. These lines aid in converting between various units of measurement.

• Number lines, like rulers and tape measures, are essential tools for measuring distances or lengths. Rulers are divided into equal increments such as millimeters (mm) and centimeters (cm).
• Thermometers, another form of number line, gauge temperature, representing how hot or cold something is. For instance, water freezes at 0°C and boils at 100°C.
• Scales, often shown as curved lines, are utilized to measure weight, such as quantities of produce like fruits or vegetables, commonly measured in grams (g) or kilograms (kg).
• Measuring jugs function as number lines for measuring liquid volumes, e.g., milliliters (ml).

Measurement Tools

• Thermometers
• Scales
• Measuring Jugs

Thermometers

• Thermometers are instruments used to measure temperature, indicating how hot or cold something is. For instance, water freezes at 0°C and boils at 100°C.

Scales

• Scales are tools that represent weight as a curved line. They measure the weight of items like fruits or vegetables, usually in grams (g) or kilograms (kg).

Measuring Jugs

• Measuring jugs are devices used to measure the volume of liquids, typically in milliliters (ml).

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