Lesson Notes By Weeks and Term v3 - Junior Secondary 1
Estimation
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Estimation
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: General Mathematics
Class: Junior Secondary 1
Term: 3rd Term
Week: 4
Theme: Basic Operations
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Estimate the dimensions and distances with in the school; Estimate the capacity and mass of given objects; Estimate other things in day to day activities; Solve problems on quantitative reasoning in estimation
one short row. There are about 8 such rows across the tray." Estimated Number of Oranges: $5 \times 8 = 40 \text{ oranges}$.
Note: The teacher can use real items like groundnuts, pebbles, or bottle tops for this activity. D. Solving Problems on Quantitative Reasoning in Estimation These problems require students to apply estimation in multi-step scenarios, often involving comparison or simple arithmetic with estimated values.
Techniques: Identify the quantities to be estimated. Make reasonable individual estimates for each quantity. Perform the required operation (addition, subtraction, multiplication, division) using the estimated values. Consider if the final estimate is reasonable in the context of the problem.
Worked Example 6: Quantitative Reasoning Problem Problem: Mr. Emeka is driving from Lagos to Ibadan, a distance of about 120 km. If he estimates his average speed to be 60 km/h, approximately how long will the journey take?
Explanation:
1. Identify Knowns and Unknowns: Distance (D) = approximately 120 km Average Speed (S) = approximately 60 km/h Time (T) = unknown (to be estimated)
2. Recall Relationship: Time = Distance / Speed.
3. Perform Calculation with Estimates: $T = 120 \text{ km} / 60 \text{ km/h} = 2 \text{ hours}$.
4. Check Reasonableness: If he drives at 60 km/h, 2 hours for 120 km seems very reasonable.
Estimated Journey Time: Approximately 2 hours.
Worked Example 7: Quantitative Reasoning Problem (Cost Estimation)
Problem: A primary school wants to buy new exercise books for its 250 pupils. Each exercise book costs N
1
8
5. Estimate the total cost of buying the books for all pupils.
Explanation:
1. Estimate Pupil Count: The number 250 is already an exact number, but it could be rounded for easier mental math if it were, say, 247 (round to 250).
2. Estimate Cost per Book: N185 is close to N
2
0
0. This makes multiplication easier.
3. Perform Calculation with Estimates: Estimated total cost = (Number of pupils) $\times$ (Estimated cost per book) Estimated total cost = $250 \times N200$ $250 \times 200 = 50000$
4. Check Reasonableness: If each book were N100, it would be N25,
0
0
0. If it were N200, it would be N50,
0
0
0. So N50,000 is a good estimate.
Estimated Total Cost: Approximately N50,
0
0
0. Estimation is the process of finding an approximate value for a quantity or magnitude, rather than an exact one. It involves making a reasonable guess based on available information, prior knowledge, and common sense. Estimation is useful when exact measurements are difficult, impossible, or unnecessary. A. Estimating Dimensions and Distances Dimensions refer to length, width, and height. Distances refer to the space between two points.
Techniques for Visual Estimation: Using Reference Units: Students should be taught to use familiar objects or their own body parts as reference points.
Length/Width/Height: A standard ruler (30 cm), a meter stick (1 m), the length of a student's stride (approximately 0.5m to 1m), a standard door height (approx. 2m), the height of an average adult (approx. 1.7m), or the length of a standard school desk (approx. 0.6m - 0.7m).
Example: To estimate the length of the classroom, students can imagine how many standard school desks would fit end-to-end along its length, then multiply by the approximate length of one desk. Alternatively, they can walk the length of the room, counting their strides and multiplying by their estimated stride length.
Breaking Down Large Distances: For longer distances, students can estimate shorter segments and then add them up.
Example: To estimate the distance from the classroom to the principal's office, students can estimate the length of the corridor, then the distance across an open space, and sum these estimates.
Worked Example 1: Estimating Classroom Dimensions Problem: Estimate the length and width of the JSS1 classroom.
Explanation: The teacher should guide students to use visual references.
1. Length: Instruct students to stand at one end of the classroom and look to the other. Ask them to imagine a standard 1-meter stick or the length of a large blackboard (typically 2-3 meters). How many "meter sticks" or "blackboards" would fit along the length?
Student A's approach: "I think about 10 standard 1-meter rulers would fit along the length." Estimated Length: $10 \times 1 \text{ meter} = 10 \text{ meters}$.
2. Width: Instruct students to do the same for the width of the classroom.
Student B's approach: "The width looks like about 6 standard desks. Each desk is about 0.6 meters long." Estimated Width: $6 \times 0.6 \text{ meters} = 3.6 \text{ meters}$.
Note: Actual measurements can be done afterward to compare estimates and refine skills. A reasonable estimate for a classroom could be 8m-12m in length and 4m-7m in width.
Worked Example 2: Estimating Distance within the School Problem: Estimate the distance between the JSS1 classroom and the school gate.
Explanation: This involves a longer distance, so students might use strides or segment estimation.
1. Stride Method: Students estimate their average stride length (e.g., 0.7 meters). Then, they can visually (or actually) walk the distance, counting their steps.
Student C's approach: "My stride is about 0.7 meters. I think it would take me about 150 steps to get to the school gate." Estimated Distance: $150 \times 0.7 \text{ meters} = 105 \text{ meters}$.
2. Segment Method: Break the journey into smaller, more manageable parts (e.g., classroom to assembly ground, assembly ground to administrative block, administrative block to gate).
Student D's approach: "From my classroom to the assembly ground is about 50m. From assembly ground to admin block is about 30m. From admin block to the gate is about 40m." Estimated Distance: $50 \text{m} + 30 \text{m} + 40 \text{m} = 120 \text{ meters}$.
Note: The teacher should emphasize that different students may have different but equally valid estimates, as long as the reasoning is sound. B. Estimating Capacity and Mass Capacity refers to the amount a container can hold (usually liquids or granular solids). Units include litres (L) and millilitres (mL). Mass refers to the amount of matter in an object, often loosely referred to as weight. Units include kilograms (kg) and grams (g).
Techniques for Estimation: Using Known Containers/Objects: * Capacity: A standard sachet of pure water (0.5 L or 500 mL), a 1-litre bottle of soft drink, a common bucket (often 10-20 valid estimates, as long as the reasoning is sound. B. Estimating Capacity and Mass Capacity refers to the amount a container can hold (usually liquids or granular solids). Units include litres (L) and millilitres (mL). Mass refers to the amount of matter in an object, often loosely referred to as weight. Units include kilograms (kg) and grams (g).
Techniques for Estimation: Using Known Containers/Objects: Capacity: A standard sachet of pure water (0.5 L or 500 mL), a 1-litre bottle of soft drink, a common bucket (often 10-20 L), a small cup (approx. 200 mL).
Mass: A sachet of pure water (approx. 500g or 0.5kg), a 1 kg bag of sugar, a 50 kg bag of rice/cement, a standard textbook (approx. 1 kg).
Visual Comparison: Comparing the size of an unknown object/container to a known one. "Feeling" the Weight: For mass, students can hold an object and compare its perceived heaviness to an object of known mass.
Worked Example 3: Estimating Capacity Problem: Estimate the capacity of a typical water bucket used in the classroom (e.g., for fetching water or cleaning).
Explanation:
1. Reference: Ask students to recall the size of a 1-litre bottle. How many of those bottles would fill the bucket?
Student E's approach: "A sachet of water is 0.5 litres. I think about 20 sachets of water would fill this bucket." Estimated Capacity: $20 \times 0.5 \text{ litres} = 10 \text{ litres}$.
2. Direct Comparison: If a known 5-litre jerrycan is available, students can compare the bucket's size to it.
Student F's approach: "This bucket looks like it could hold about two 5-litre jerrycans, plus a little extra." Estimated Capacity: $2 \times 5 \text{ litres} + 2 \text{ litres} = 12 \text{ litres}$.
Note: Typical buckets can range from 8L to 20
L. Worked Example 4: Estimating Mass Problem: Estimate the mass of a JSS1 General Mathematics textbook.
Explanation:
1. Reference: Students should consider known masses. A 1 kg bag of sugar or rice is a good reference. A sachet of pure water is 0.5 kg.
Student G's approach: "I'm holding the textbook. It feels lighter than a 1 kg bag of sugar but heavier than two sachets of water (1 kg total). It feels like about one sachet and a half." Estimated Mass: $1.5 \times 0.5 \text{ kg} = 0.75 \text{ kg}$. (Or 750g).
2. Comparison: If an empty 500g Milo tin is available, students can compare.
Student H's approach: "The textbook feels a bit heavier than an empty 500g Milo tin." Estimated Mass: Possibly 600g to 800g (0.6 kg to 0.8 kg).
Note: A JSS1 textbook often weighs between 0.5 kg and 1.2 kg. C. Estimating Other Things in Day-to-Day Activities This includes estimating numbers of items, time, money, speed, etc.
Techniques: Grouping and Counting: For a large number of items, estimate the number in a small, countable section, then multiply by the number of such sections.
Rounding: Rounding numbers to the nearest tens, hundreds, or thousands simplifies mental calculations.
Known Rates: If a task takes a certain time for a small portion, estimate total time by multiplying.
Worked Example 5: Estimating Number of Items Problem: A tray of oranges is brought to the class. Estimate the number of oranges on the tray.
Explanation:
1. Visual Grouping: Students should be encouraged to quickly count oranges in a small, visible section (e.g., one row or column).
Student I's approach: "I can see about 5 oranges in one short row. There are about 8 such rows across the tray." Estimated Number of Oranges: $5 \times 8 = 40 \text{ oranges}$.
Note: The teacher can use real items like groundnuts, pebbles, or bottle tops for this activity. D. Solving Problems on Quantitative Reasoning in Estimation These problems require students to apply estimation in multi-step scenarios, often involving comparison or simple arithmetic with estimated values.
Techniques: Identify the quantities to be estimated. Make reasonable individual estimates for each quantity. Perform the required operation (addition, subtraction,
A. Introduction (10 minutes)
Teacher Activity: Begin by asking students about situations in their daily lives where they make "guesses" or "rough calculations" without using exact measuring tools. For example, "How much rice do you think is in this bag?", "How far is it from your house to the market?", "How many students do you think are in the assembly hall today?". Introduce the term "estimation" as a mathematical way of making such reasonable guesses. Explain that estimation is a valuable skill in real life.
Student Activity: Students share their experiences with making guesses or approximations. They listen attentively and respond to questions.
B. Development - Core Concepts and Practical Estimation (30-40 minutes)
Activity 1: Estimating Dimensions and Distances within the Classroom/School Teacher Activity: Explain the concept of length, width, height, and distance.
Introduce common reference units: meter rule, blackboard length, average student stride, teacher's height (approx. 1.7m). Guide students to estimate the length and width of their classroom. Demonstrate by "walking out" the length and width using strides, or pointing out how many meter sticks might fit. Guide students to estimate the distance from their classroom door to another prominent location (e.g., the school gate, the principal's office, the assembly ground) using similar methods (e.g., number of strides). Facilitate comparison of estimates among students and encourage discussion on why estimates vary.
Student Activity: In groups of 3-4, students visually estimate the length and width of the classroom. They record their group's estimates. Students visually estimate the distance from their classroom to a designated point within the school compound. They record their estimates. Groups present their estimates, and students engage in a class discussion about their methods and the variations in their estimates.
Activity 2: Estimating Capacity and Mass of Given Objects Teacher Activity: Present various everyday objects for estimation: Capacity: An empty water bucket, a small cup, an empty 1-litre soft drink bottle, an empty sachet of pure water.
Mass: A JSS1 General Mathematics textbook, a small bag of sand/stones, a full water sachet, a pen. Explain the concepts of capacity (how much it holds) and mass (how heavy it is).
Introduce reference units: a sachet of water (0.5L / 500g), a 1-litre bottle, a 1 kg bag of sugar (if available). Guide students to estimate the capacity of the bucket using the sachet of water or 1-litre bottle as a reference. Guide students to estimate the mass of the textbook by holding it and comparing its perceived weight to a known reference (e.g., a 1 kg sugar bag, or a 500g sachet of water).
Student Activity: Students, individually or in pairs, pick up and examine the provided objects. They estimate the capacity of the water bucket. They estimate the mass of the textbook and other objects. Students record their estimates and compare them with peers.
Activity 3: Estimating Other Things in Day-to-Day Activities & Quantitative Reasoning Teacher Activity: Present scenarios or actual items for estimation: e.g., a pile of bottle caps, a handful of beans, or a picture of a crowded market. Guide students to estimate the number of items by visually grouping them and multiplying (e.g., estimate number in one row/section and multiply by number of rows/sections). Present simple word problems involving estimation and quantitative reasoning (e.g., estimating total cost after rounding prices, estimating time for a journey based on speed and distance). Demonstrate step-by-step problem-solving using estimated values.
Student Activity: Students estimate the number of items in a given collection (e.g., bottle caps in a jar). Students work in groups to solve 1-2 quantitative reasoning problems requiring estimation. They discuss their strategies and present their estimated solutions.
C. Conclusion (5 minutes)
Teacher Activity: Summarize the importance of estimation in various aspects of life. Reiterate that a good estimate is not necessarily exact but is reasonable and close to the actual value. Encourage students to practice estimation regularly.
Student Activity: Students ask any clarifying questions and reflect on the usefulness of estimation.
Market and Shopping: Application: When buying foodstuffs like rice, beans, or garri from a vendor, people often estimate the quantity (e.g., "This looks like enough for my family for a week"). Estimating the total cost of multiple items before reaching the cashier helps in budgeting (e.g., "A sachet of Maggi is about N50, I need 10, so N500").
Integration: Students can be given hypothetical shopping scenarios with rounded prices to estimate total costs, or shown pictures of market stalls and asked to estimate quantities of goods.
Construction and Home Improvement: Application: Builders and carpenters frequently estimate dimensions of rooms, lengths of wood needed, or the amount of paint required for a wall before getting exact measurements. For example, estimating the number of bags of cement needed for a small project or the length of fencing required for a compound.
Integration: Discuss with students how their parents or local artisans estimate materials for building or repairing items at home or in the community. Teachers can bring in simplified blueprints (drawings) of a room and ask students to estimate its area or the perimeter.
Travel and Time Management: Application: Estimating journey duration and distance when travelling (e.g., "It's about 200 km from here to the next town, and if we drive at 80 km/h, it will take roughly 2.5 hours"). Estimating time needed for daily tasks (e.g., "I need about 30 minutes to get ready for school").
Integration: Ask students to estimate the time it takes them to get from home to school, or to estimate the distance to their hometown if they travel for holidays. Use maps (even simplified ones) to estimate distances between Nigerian cities.