Learning Activities

• Students in groups research the history of measurement and propose instruments that can be used to grade, a particular measurement
• Students as a class, discuss the different units of measurement and their abbreviations
• Students practice math skills involved in real-life applications, integrating the use of approximate measures and their relationships using charts. They should calculate on those relationships together
• Each pupil work in pairs to solve simple problems

Embedded Core Skills

• Communication and collaboration
• Critical thinking and problem solving
• Leadership skills and Personal Development

Content

Measurement: is one of the most important areas of mathematics, as people use it in day-to-day life on a regular basis. It is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of measurement are dependent on the context and discipline.

For example: “the length of an object,” the “weight of an object,” and the “time it takes to complete an activity.” Units are used to determine different types of measurements such as units of length, units of weight, units of time, units of capacity, and units of temperature.

Standard of measurement of objects as:

• Mass or weight of different objects
• Length (Dimension) of different objects
• Temperature of different places
• Volume of containers/capacity
• Capacity of different things
• Calculation of different measurements
• Time calculations
• Height of tree (tall) of mountains/people
• Length of distance between two specific places (long/approximate distance)

Some of the Terminologies used in Measurement:

• Grams (mass) – (g)
• Kilograms – (Kg)
• Meters (distance) – (m)
• Kilometers – (Km)
• Centimeters – (cm)
• Millimeters – (mm)
• Capacity – (Liters) – (l)
• Degrees – Temperature – (°C)
• Capacity – (milliliters) – (ml)
• Time – Hours (Hrs)
• Minutes (min) – (min)
• Seconds (sec) – (sec)
• Years – (yrs)
• Weeks – (wks)
• Days

Problem Solving in Daily Activities

• Measure in estimating measuring and calculating amounts, weighty
• Measure in estimating duration, time and movements of objects
• Measurement help daily work, be dealt with properly
• Measuring area and volume of different objects
• How (long) to travel and deal with the requirement (not trip)
• Measuring things help to have organized to organize and clean tools
• Measurement units all have their values

The importance of measurement that affects our daily routine including shopping products, measuring time schedules, calculating, estimating among others. How children learn about measuring through hands-on activities and active learning process. For instance, they would practice through hands-on using instruments of measurements (rulers, scales and clocks measuring) using real world problems. Practical session in measurements helps demonstrate the power of measurement in solving real problems.

ABBREVIATIONS OF UNITS OF MEASUREMENTS. How to solve APPROXIMATE Measurements and Some Problems

Approximations are used to estimate values, particularly when precision is not necessary or when working with large numbers. The procedure described above, which is to round of time to reasonable values, can be extremely useful.

How to make measurements close to the real value by investigating the given values.

Examples:

• 547 km ≈ 550 km (rounded)
• 35 kg = 35 kg = 40 kg (rounded)
• 4.7 liters ≈ 5 liters (rounded)

The above rounding helps us estimate sums, products, and differences. But it is important that the approximate result the question is asking to look at it like the unit of measurement asked and the level.

Estimating Weights

An apple might weigh about _____ grams:

• 10 grams = 150 grams
• 150 grams = 150 grams
• 100 grams = 100 grams

Worked Examples with Estimations and Measurements:

Simple Examples of Approximation. Rounding the metric of measurement, we are working with to get the nearest hundred or nearest ten:

Conversion:

Weight: 1 kilogram = 1000g = 1 Kg = 1000 gram = 1000g

Length: 1 kilometer = 1000m = 1 Km = 1000 meter = 1000m 1 meter = 100cm = 1 m = 100 centimeter = 100cm 1 centimeter = 10mm = 1 cm = 10 millimeter = 10mm

Capacity: 1 liter = 1000ml = 1 l = 1000 milliliter = 1000ml

From above examples one can use conversion of mathematical operation such as division, multiplication, addition etc. to solve approximation problems.

Example Questions in Measurements:

2 Kg = _____ grams? 2 Kg = 2000g (2 × 1000g = 2000g)

5 meters = _____ centimeters? 5m = 500cm (5 × 100cm = 500cm)

Profit and Loss

Profit and loss is one of the most important concepts in mathematics and economics that explores finding profits and losses.

Profit: When the selling price of an object is greater than its cost price, we have a profit. Profit = Selling Price – Cost Price

Loss: When the selling price is less than the cost price, we have a loss. Loss = Cost Price – Selling Price

Examples:

A man bought a bag for ₦200 and sold it for ₦250. Find his profit. Given: Cost Price = ₦200, Selling Price = ₦250 Since Selling Price > Cost Price, he made a profit Profit = Selling Price – Cost Price = ₦250 – ₦200 = ₦50

A woman bought a dress for ₦500 and sold it for ₦400. Find her loss. Given: Cost Price = ₦500, Selling Price = ₦400 Since Selling Price < Cost Price, she made a loss Loss = Cost Price – Selling Price = ₦500 – ₦400 = ₦100

Percentage Profit and Loss:

Percentage Profit = (Profit ÷ Cost Price) × 100 Percentage Loss = (Loss ÷ Cost Price) × 100

Examples:

If a book cost ₦200 and was sold for ₦240, find the percentage profit. Profit = ₦240 – ₦200 = ₦40 Percentage Profit = (₦40 ÷ ₦200) × 100 = 20%

If a phone cost ₦800 and was sold for ₦600, find the percentage loss. Loss = ₦800 – ₦600 = ₦200 Percentage Loss = (₦200 ÷ ₦800) × 100 = 25%

Profit and Loss

The concept we introduced by those from business and commerce, profit and loss is a financial term used in business. If anything, after anything is bought and sold and it is money (more profit) or lower cost, based on the purchasing price.

When the selling price is more than the cost price, we get profit. When the selling price is less than the cost price, we get loss.

When the selling price is equal to the cost price, there is no profit or loss.

Important Formula:

If the cost price < selling price, then there is a profit. If the cost price > selling price, then there is a loss. If the cost price = selling price, then there is no profit or loss.

Some Calculations:

Profit = selling price – cost price Loss = cost price – selling price Cost Price = selling price – profit Cost Price = selling price + loss
Selling Price = cost price + profit Selling Price = cost price – loss

Real Estate Problems:

A trader bought a land at the cost of ₦120,000 and sold it at ₦180,000. Find his profit and profit percentage.

Given: Cost Price = ₦120,000, Selling Price = ₦180,000 Since Selling Price > Cost Price, there is profit Profit = Selling Price – Cost Price = ₦180,000 – ₦120,000 = ₦60,000 Profit % = (Profit ÷ Cost Price) × 100 = (₦60,000 ÷ ₦120,000) × 100 = 50%

Food Market Problem:

A fruit seller bought oranges for ₦50 per dozen and sold them for ₦60 per dozen. If he sold 20 dozens, find his total profit.

Cost Price per dozen = ₦50 Selling Price per dozen = ₦60 Profit per dozen = ₦60 – ₦50 = ₦10 Total dozens sold = 20 Total Profit = 20 × ₦10 = ₦200