Concept of estimation and values , capacity ,volumes and mass Mathematics JSS 1 First Term Lesson Notes Week 10

Subject: Mathematics
Class: JSS 1
Term: First Term
Week: 10
Age: 12 years
Topic: Estimation
Sub-topic: i. Concept of Estimation and Reasons ii. Estimation of Dimensions and Distance iii. Estimation of Capacity, Volumes, and Mass of Objects iv. Estimation of Other Things (e.g., Age, Time, etc.)
Duration: 40 minutes

Behavioural Objectives

By the end of the lesson, students should be able to:

1. Understand the concept of estimation and its importance.
2. Estimate dimensions and distances accurately.
3. Estimate the capacity, volumes, and mass of objects.
4. Estimate other quantities such as age and time.

Keywords

Estimation, Dimensions, Distance, Capacity, Volume, Mass, Age, Time

Set Induction

Begin with a discussion on why estimation is useful in daily life, such as guessing the amount of time needed for an activity or estimating the cost of items.

Entry Behaviour

Students should be familiar with basic measurements and have some understanding of units of measure.

Learning Resources and Materials

1. Measuring tapes
2. Rulers
3. Scales
4. Containers of various sizes
5. Clocks and calendars

Building Background/Connection to Prior Knowledge

Students should recall previous lessons on measurement and have basic knowledge of units for length, volume, and mass.

Embedded Core Skills

1. Measurement skills
2. Approximation
3. Practical application of mathematical concepts

Content

1. Concept of Estimation and Reasons:
   • Estimation involves making an approximate calculation or judgment.
   • Useful when exact measurements are not necessary or possible.
   • Example: Estimating how long it will take to travel a certain distance.
2. Estimation of Dimensions and Distance:
   • Use benchmarks or reference objects to estimate length and width.
   • Example: Estimating the length of a classroom by comparing it to the length of a desk.
3. Estimation of Capacity, Volumes, and Mass of Objects:
   • Estimate the volume of liquids using container sizes.
   • Estimate mass using scales or comparison with known weights.
   • Example: Estimating the volume of water in a jug.
4. Estimation of Other Things:
   • Age: Estimate age based on appearance or life stages.
   • Time: Estimate how long it takes to complete tasks.
   • Example: Estimating how much time is left before a class ends.

Evaluation

1. Estimate the length of a classroom.
2. Estimate the volume of a water bottle.
3. Estimate the mass of a bag of flour.
4. Estimate how many people are in a room.
5. Estimate the time needed to complete a homework assignment.

• Rounding Off Numbers:
  • To the Nearest Ten:
    • Example: 1234 rounds to 1230.
  • To the Nearest Hundred:
    • Example: 1834 rounds to 1800.
  • To the Nearest Thousand:
    • Example: 3512 rounds to 4000.
    • Example: 4265 rounds to 4000.
• Rounding Decimal Numbers:
  • To the Nearest Whole Number:
    • Example: 13.73 rounds to 14.
    • Example: 34.245 rounds to 34.
  • To a Specific Number of Decimal Places:
    • Example: 474.4547 correct to:
      • Nearest tenth: 474.5
      • Nearest hundredth: 474.45
      • Nearest thousandth: 474.455
• Rounding to Significant Figures:
  • Example: 5754 correct to:
    • 1 significant figure: 6000
    • 2 significant figures: 5800
    • 3 significant figures: 5750
  • Example: 147.006 correct to:
    • 1 significant figure: 100
    • 2 significant figures: 150
    • 3 significant figures: 147
    • 4 significant figures: 147.0
    • 5 significant figures: 147.01

Class Activity Discussion

1. What is estimation?
   • Making an approximate calculation or judgment.
2. Why is estimation important?
   • Helps in making quick decisions when exact numbers are not required.
3. How can you estimate dimensions?
   • Compare with known lengths or use measuring tools.
4. How do you estimate volume?
   • Use reference containers or known volumes for comparison.
5. What methods can you use to estimate mass?
   • Use scales or compare with objects of known weight.
6. How do you estimate time?
   • Compare with known durations or use a timer.
7. Can you give an example of estimating age?
   • Based on appearance or milestones.
8. How does estimating distance help in daily life?
   • Helps in planning travel time or space needs.
9. What tools can assist in estimating capacity?
   • Measuring cups and containers.
10. How accurate does estimation need to be?
    • Accuracy depends on the context and need.
11. What is a benchmark in estimation?
    • A reference point used for comparison.
12. How can you practice estimating?
    • Regularly practice with different objects and measurements.
13. Can estimation be used in budgeting?
    • Yes, to estimate costs and manage expenses.
14. What is a practical example of estimating volume?
    • Estimating the amount of paint needed for a wall.
15. How can estimation improve problem-solving?
    • Helps in making quick decisions and planning.

Presentation

1. Step 1: Review basic measurement concepts and their importance.
2. Step 2: Introduce the concept of estimation with practical examples.
3. Step 3: Demonstrate various estimation techniques and practice with students.

Teacher’s Activities

1. Explain the concept and importance of estimation.
2. Demonstrate how to estimate dimensions, volume, and mass.
3. Provide practice exercises and guide students through them.

Learners’ Activities

1. Estimate dimensions of objects in the classroom.
2. Practice estimating volume and mass using provided materials.
3. Discuss and share their estimation results with the class.

Assessment

1. Review student estimates for accuracy.
2. Provide feedback and correct any misunderstandings.
3. Round 95 to the nearest ten.
4. Round 127 to the nearest ten.
5. Round 3.9998 to 1 significant figure.
6. Round 3.9998 to 2 significant figures.
7. Round 0.007025 to 1 significant figure.
8. Round 0.007025 to 2 significant figures.
9. Round 0.007025 to 3 significant figures.
10. Round 0.0007004 to 2 significant figures.
11. Round 0.0007004 to 3 significant figures.
12. Round 1234 to the nearest thousand.

Evaluation Questions

1. Estimate the height of a door.
2. Estimate the capacity of a milk carton.
3. Estimate the mass of a book.
4. Estimate the number of chairs in a room.
5. Estimate how long it will take to walk a mile.
6. How do you estimate the volume of a fish tank?
7. What methods do you use to estimate mass?
8. How accurate was your estimation of the classroom length?
9. Estimate the time to bake a cake.
10. How can estimation help in daily planning?

• Units of Measurement:
  • Length:
    • Small distances: millimeters (mm), centimeters (cm)
    • Larger distances: meters (m), kilometers (km)
    • Example: Measuring the height of a person (meters) vs. the length of a fingernail (millimeters).
  • Mass:
    • Small masses: grams (g)
    • Larger masses: kilograms (kg), tonnes (t)
    • Example: Measuring the weight of an object (grams) vs. a person (kilograms).
  • Capacity:
    • Small capacities: milliliters (ml), centiliters (cl)
    • Larger capacities: liters (l)
    • Example: Measuring the amount of liquid in a cup (milliliters) vs. a bottle (liters).
  • Time:
    • Seconds, minutes, hours
    • Example: Timing an event (seconds) vs. the duration of a trip (hours).
• Costing:
  • Example 1: James bought 5 exercise books at N50.50 each. Calculate the total cost.
    • Cost: N50.50 x 5 = N252.50.
  • Example 2: One candle costs 19C. Calculate the cost of 5 candles.
    • Cost: 19C x 5 = 95C.
  • Example 3: Find the cost of 3 tins of margarine at N48.00 per tin.
    • Cost: N48.00 x 3 = N144.00.

Evaluation Questions:

1. State the metric units of length for:
   • (a) The height of a desk.
   • (b) The height of yourself.
2. State the units of mass for:
   • (a) A parcel.
   • (b) A large land area.
3. State the units of capacity for:
   • (a) A cup.
   • (b) A car’s petrol tank.
   • (c) A tin of peak milk.
   • (d) The amount of water in a reservoir.
4. State the appropriate metric units of time for:
   • (a) The time to fill an empty tank.
   • (b) The time to travel from Lagos to Ado Ekiti.

Solution to Evaluation Questions:

1. (a) cm (b) cm
2. (a) g or kg (b) t
3. (a) ml (b) liter (c) ml (d) ml
4. (a) min (b) hour

Reading Assignment:

1. New General Mathematics by J.B. Channon, pg. 24 Ex 24C nos 2 c-d
2. Essential Mathematics by Oluwasanmi, pg. 170 Ex 16.7 nos 1 c-d

Weekend Assignment:

1. Round 567 to the nearest hundred:
   • (a) 500 (b) 520 (c) 540 (d) 580 (e) 600
2. What is 1.99961 rounded to 2 decimal places?
   • (a) 1.99 (b) 2.00 (c) 3.00 (d) 4.00 (e) 5.00
3. Write 7.0149 rounded to the nearest thousandth:
   • (a) 7.000 (b) 7.014 (c) 7.015 (d) 7.0145 (e) 7.0146
4. Give 0.000057891 rounded to 4 significant figures:
   • (a) 0.00005789 (b) 0.00005790 (c) 0.00005781 (d) 0.000057892 (e) 0.00005793
5. Give 45698 rounded to 3 significant figures:
   • (a) 45600 (b) 45700 (c) 45800 (d) 45690 (e) 45000

Theory Questions:

1. A sack of rice holds 64 basins. If each basin sells for N48.50, calculate the total amount if the sack is sold.
2. Calculate the total cost for:
   • (i) 3 textbooks at N400.00 each.
   • (ii) 9 mathematical sets at N2500.50 each.
   • (iii) 3 pens at N120.25 each.
   • (iv) 5 pencils at N20.00 each.

Solution to Theory Questions:

1. Total cost = 64 basins x N48.50 = N3104.00
2. (i) Total cost = 3 x N400.00 = N1200.00
   (ii) Total cost = 9 x N2500.50 = N22504.50
   (iii) Total cost = 3 x N120.25 = N360.75
   (iv) Total cost = 5 x N20.00 = N100.00

Conclusion

The teacher will review students’ work, address any errors, and discuss the importance of accurate estimation in various contexts.