Decimals (Rounding off) – SCOPES-DF

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Chwee Tin Priscilla Chua
Chwee Tin Priscilla Chua
K-12 teacher
Hi! I am Priscilla Chua. I am an educator from Singapore. I teach English and Mathematics in a primary school. Currently I am teaching Grade 4 students who are about 10 years old. Read More

Summary

In this lesson, students explore rounding off decimals using number lines.

In the past, number lines was drawn on the whiteboard to help students

visualise rounding positions.

 

To enhance engagement and understanding, this activity was upgraded using

laser-cut magnetic number bars which are placed on the whiteboard, allowing

students to physically manipulate and align decimals by pointing arrows and

writing the decimals on the board.

What You'll Need

Whiteboard and markers

Magnetic Number bars (Laser-cut) – Computers with vector software (e.g. Inkscape), Laser cutter

 

Learning Objectives

  1. Students develop the skill in rounding decimals to the nearest whole number, I decimal place and 2 decimal places with the help of number lines (laser-cut magnetic bars)
  2. Students to compare decimals to determine which way to round.
  3. Students to discuss connections to real-world examples (e.g. money, measurement, temperature).

 

Reflection

I used to do this activity or rounding off numbers by drawing lines on the whiteboard. The lines have to be redrawn each time and is time-consumng.Visual clarity may depend on drawing accuracy.

 

As a beginner to digital fabrication, I have no idea how I should start. Inspired by the Snake Decimals, I developed this simple idea of magnetic bars to start with, not too complicated for me to design and cut. At first, I wanted to further cut one part of the whole bar into 10 parts. With advice from a colleague teaching Maths that it may too confusing for the young ones to visualise, I aborted the idea of dividing further. I just divide the one part into half as shown in Fig 3.

 

The use of digital fabrication (laser-cut bars) transformed an abstract concept into a hands-on experience, deepening conceptual understanding and engagement. Students can see and feel decimal intervals and rounding positions. It also provides precision and consistency as it ensures precise measuring measurement and spacing, aiding accurate mathematical reasoning.

These number bars are durable, reusable, and adaptable for multiple lessons or levels (e.g. whole numbers, decimals, fractions).

More pieces can be cut for individuals (e.g. manipulates for small group teaching or even the whole class of 40).

 

Process of the laser-cut the Number Bar:

 

Fig. 1 Using Inkscape to design the number bar

 

By designing the number bar, I have learnt the various features of this software. This is what we always mean by learning through making. It is quite challenging at first (especially drawing the lines), but getting better each time I design.

 

 Fig 2 Generating the code online for cutting

 

I had used a Lionforge laser cutter to cut the number bar. This was challenging as I had to generate the code online and download the code and send to the cutter. At the website, I needed to manually assign the engrave path (those lines that turned orange). Maybe there is a way, hopefully. I will try to find out later if there is one.

 

 

Fig 3 Final product – Magnetic bars

 

 

This is the final product that I used in class. I would like to make it bigger though it is visible by the last row in the class.

 

From this lesson, I learned not only about enhancing mathematical understanding but also about the process of digital fabrication. Designing and laser-cutting the magnetic number bars required accuracy, planning, and testing, which deepened my understanding of how digital tools translate ideas into tangible learning aids. I realized the importance of design iteration—ensuring correct sizing, alignment, and materials for safety and usability. Through this process, I experienced how digital fabrication supports creativity, problem-solving, and innovation, transforming traditional teaching materials into interactive tools that engage students more deeply in hands-on, meaningful learning experiences.

The Instructions

Introduction (15 minutes)

Prior Knowledge - Recap decimals using the number bars Making connections - Students to share how they can use rounding off decimals in daily lives

  1. Recap decimals using the number bars especially comparisons of decimals
  2. Create awareness on how and why rounding off of decimals are used in daily lives. For example, we need to estimate the amount of money to use for grocery in the supermarket.

 

Rounding off decimals to the nearest whole numbers using the number bars. (45 minutes)

Students to round a 1-place decimal to the nearest whole number.

Using the number bars, students to:

  1. round a 1- place decimal, such as 4.9 to the nearest whole number
  2. mark the two whole numbers that are near to 4.9 below the number bar using arrows.
  3. state the number representated by each marking between 4 and 5 (4.1, 4.2, 4.3 ….4.9)
  4. identify the mid-point between the whole numbers.
  5. mark 4.9 below the number bar using arrow.
  6. state the whole number nearer to 4.9 which is 5
  7. know that 4.8 is 5 when rounded off to the nearest whole number or 4.8 is approximately equal to 5.
  8. round a 1- place decimal, such as 3.3 nearer to the other whole number
  9. mark the two whole numbers that are near to 3.3 below the number bar using arrows.
  10. state the number representated by each marking between 3 and 4 (3.1, 3.2, 3.3 ….3.9)
  11. state the mid-point between the whole numbers.
  12. mark 3.3 below the number bar using arrow.
  13. state the whole number nearer to 3.3 which is 3
  14. know that 3.3 is 4 when rounded off to the nearest whole number or 3.3 is approximately equal to 3.
  15. round a 1- place decimal, such as 6.5 to the nearest whole number
  16. mark the two whole numbers that are near to 6.5 below the number bar using arrows.
  17. see that 6.5 is halfway between 6 and 7 and they should round off to the higher whole number which is 7.
  18. round off 1.8 to the nearest whole number on their own.

 

 

 

 

Round off decimals to 1 decimal place or to the nearest tenth using the number bars (30 minutes)

Students to round off decimals to 1 decimal place or to the nearest tenth

Using the number bars, students to:

  1. round a 2- place decimal, such as 5.78 to 1 decimal place.
  2. mark the two 1-place decimals that are near to 5.78 below the number bar using arrows.
  3. state the number representated by each marking between 5.7 and 5.8 (5.71, 5.72,5.73 ….5.79)
  4. identify the mid-point between the two 1-place decimals.
  5. mark 5.78 below the number bar using arrow.
  6. state the 1-place decimal number nearer to 5.78 which is 5.8
  7. know that 5.78 is 5.8 when rounded off to 1 decimal place or 5.78 is approximately equal to 5.8.
  8. round a 1- place decimal, such as 4.32 nearer to the other whole number
  9. mark the two 1-place decimals that are near to 4.32 below the number bar using arrows.
  10. state the number representated by each marking between 4.3 and 4.4 (4.31, 4.32, 4.33 ….4.39)
  11. identify the mid-point between the two 1-place decimals.
  12. mark 4.32 below the number bar using arrow.
  13. state the 1-place decimal number nearer to 4.32 which is 4.3
  14. know that 4.32 is 4.3 when rounded off to 1 decimal place or 4.32 is approximately equal to 4.3.
  15. round a 1- place decimal, such as 6.55 to 1-decimal number.
  16. mark the two 1-decimal numbers that are near to 6.55 below the number bar using arrows.
  17. see that 6.55 is halfway between 6.5 and 6.6 and they should round off to the higher 1-decimal place number which is 6.6.
  18. be aware that rounding off decimals to 1 decimal place is the same as to the nearest tenth.
  19. round off 3.85 to 1 decimal place on their own.

 

 

 

Round off decimals to 2 decimal places or to the nearest hundredth using the number bars. (30 minutes)

Students to round off decimals to 2 decimal places or to the nearest hundredth

Using the number bars, students to:.

  1. round a 3-place decimal, such as 7.763 to 2 decimal places.
  2. mark the two 2-place decimals that are nearer to 7.763 below the number bar using arrows.
  3. state the number representated by each marking between 7.76 and 7.77 (7.761, 7.762, 7.763, 7.764 ….7.769)
  4. identify the mid-point between the two 2-place decimals.
  5. mark 7.763 below the number bar using arrow.
  6. state the 2-place decimal number nearer to 7.763which is 7.76
  7. know that 7.763 is 7.76 when rounded off to 2 decimal places or 7.763 is approximately equal to 7.76.
  8. round a 3- place decimal, such as 2.817 nearer to the other whole number
  9. mark the two 2-place decimals that are near to 2.817 below the number bar using arrows.
  10. state the number representated by each marking between 2.81 and 2.82 (2.811, 2.812, 2.813….2.819)
  11. identify the mid-point between the two 2-place decimals.
  12. mark 2.817 below the number bar using arrow.
  13. state the 2-place decimal number nearer to 2.817 which is 2.82
  14. know that 2.817 is 2.82 when rounded off to 2 decimal places or 2.817 is approximately equal to 2.82.
  15. round a 3-place decimal, such as 6.565 to 2 decimal places
  16. mark the two 2-decimal numbers that are near to 6.565 below the number bar using arrows.
  17. see that 6.565 is halfway between 6.56 and 6.57 and they should round off to the higher 2-decimal number which is 6.57.
  18. be aware that rounding off decimals to 2 decimal place is the same as to the nearest hundredth.
  19. round off 5.996 to 2 decimal places on their own.

 

 

 

Lesson Closure (30 minutes)

Consolidation of Learning

 

  • Students are given a 1-decimal place number 8.8 to round off to the nearest whole number.
  • Using the number bar, ask the students to identify the possible decimals that give 9 when rounded off to the nearest whole number.
  • Highlight the smallest possible decimal that gives 9
  • Get students to round off 2-decimal places to the nearest whole number.

 

Rounding Quiz

http://www.topmarks.co.uk

1.Click on ‘Learning Games’

Click on ‘7-11 Years’ – ‘Fractions and Decimals’ – ‘Daily 10’

2. Select ‘Level 5’ – ‘Rounding’ – ‘To nearest Whole Number’ or ‘To 1 dp’

3. Start the game to round the decimals.

 

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