Chapter III – Writing Numbers in the Decimal System

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Understanding the decimal system is a foundation of mathematics education in grades 1–3. A child who can consciously use the concepts of ones, tens, and hundreds gains not only computational fluency but also the ability to think logically, organize, and analyze numerical information. These skills make it possible to efficiently add and subtract larger numbers and, in later years, to multiply, divide, and solve complex word problems.

Due to the abstract nature of mathematics, especially when working with larger numbers where the use of counters becomes very difficult or impossible, a strong understanding of number components is essential. Children should understand the difference between the concepts of a “digit” and a “number,” as well as what the value of each digit represents depending on its position in the number.

The early primary stage of education is a time when children learn through action, movement, manipulation, and play. Therefore, it is very important that mathematical content is presented not only symbolically (on paper) but also in a concrete, tangible, and visual way.

Korbo blocks perfectly support learning the positional value of digits in a three-digit number because they:

  • allow specific values to be assigned to individual elements: a gear wheel as a unit, a cylinder as a ten, a platform as a hundred,

  • enable the physical construction of numbers using elements corresponding to their values, which strengthens understanding rather than rote memorization,

  • support counting, exchanging, comparing, and observing how the value of a number changes when a digit shifts to a different position,

  • engage children in building, encoding, exchanging, and decoding numerical values, which promotes a deeper understanding of the structure of the decimal system.

All the mathematical activities with Korbo blocks proposed in this chapter enable children to experience numerical operations in practice. They teach logical thinking and prepare students for more abstract operations, allowing for a better understanding and performance of more complex mathematical operations with larger numbers, and providing a strong introduction to written calculations (“column methods”).

After completing the tasks in this chapter, the student:

  • Recognizes and names the digits in a three-digit number as ones, tens, and hundreds.

  • Assigns positional value to digits (e.g. in the number 243: 2 hundreds, 4 tens, 3 ones).

  • Builds a three-digit number using Korbo block elements assigned with specific values.

  • Breaks down a three-digit number into hundreds, tens, and ones, representing it as a construction.

  • Compares three-digit numbers based on the number and type of elements used.

  • Exchanges ones for tens and tens for hundreds (and vice versa), observing the impact of these changes on the value of the number.

  • Writes the value of a number represented by a block construction as an Arabic numeral.

  • Creates numbers based on verbal instructions, e.g. “Build a number with 3 hundreds, 2 tens, and 5 ones.”

  • Solves simple word problems related to exchanging and counting tens and hundreds.

  • Communicates and presents numerical constructions verbally, orally, and in graphical or symbolic form (e.g. numerical notation).

Exercise 1:

Educational objective: Explaining the position of a digit in a number in relation to its value.

Materials: Korbo blocks.

Procedure:

The teacher draws a table on the board with eight rows and four columns. In the first row, the teacher places printed images of gear wheels in four colors (red in the first column, yellow in the second, purple in the third, blue in the fourth). Then the teacher labels each gear wheel (red—thousands, yellow—hundreds, purple—tens, blue—ones). The teacher explains to the students that each column will contain one digit, represented by the number of gear wheels in the corresponding color.

The teacher writes the digit 4 in the fourth column of the second row and asks a student to read its value. The teacher builds a tower of four blue gear wheels and places it on a mat built from two platforms (2×4), in the far-right position.

Next, in the third row, the teacher fills the third column with the digit 6 and the fourth column with the digit 4, and asks a student to read the value of the number—64. The teacher explains that this number consists of six tens and four ones, and places six purple gear wheels and four blue gear wheels on the mat. The teacher explains to the students that the number 64 contains 6 tens and 4 ones.

Similarly, the teacher fills in the remaining fields in the table on the board with any values, asking students to read the numbers, build towers from gear wheels in the appropriate colors and quantities, and place them in the correct positions on the mat.

Prepare images of gear wheels.

Exercise 2:

Educational objective:

Materials: Korbo blocks, cards with digits 1–9.

Procedure:

The teacher prepares a mat made of two connected platforms (4×2).

Next, the teacher assigns a positional value to each gear wheel color (ones, tens, hundreds—colors can be assigned in the same way as in Exercise 1). The teacher draws a table on the board similar to the one used in the previous task. The teacher places the mat in front of them and creates any number using four digits. The students are asked to work together to build towers using the correct number of gear wheels in the appropriate colors and place them in the correct positions on the mat.

The exercise can be repeated several times, each time asking the rest of the class whether they think the task was completed correctly.

Prepare digit cards.

Exercise 3:

Educational objective: Reinforcing the values of individual digits in their correct positions in three-digit numbers.

Materials: Korbo blocks.

Procedure:

The teacher divides the children into pairs. Each pair receives a Korbo set and a worksheet with written numbers. The children build towers from gear wheels according to the given scheme (similar to Exercises 1 and 2).

Variation:

– Guessing game: “What number is this?” based on the construction.

Exercise 4:

Educational objective: Practicing the names of numerical place values in three-digit numbers.

Materials: Korbo blocks, digit cards, worksheets.

Procedure:

The teacher prepares a mat made of two platforms (4×2), printed digits, and places several gear wheels in different colors into a non-transparent bag or box. The teacher asks a student to draw 10 gear wheels, then arrange a number on the mat according to the scheme from Exercise 1. Next, the teacher asks another student to “read” the constructed number and place the appropriate digits underneath it.

The teacher writes the number created by the student on the board in words. During this activity, the teacher can explain the rules of writing number words.

The teacher divides the children into pairs. Each pair receives a Korbo set and worksheets. One student selects one number from each worksheet (e.g. three hundred, fifty, eight), and the other builds the number using Korbo towers based on what was read.

Variation:

The teacher divides the children into pairs. Each pair receives worksheets with numbers written in words. One student builds towers in specific colors, while the other assigns each tower to the appropriate value on the worksheets and then reads the value of the entire number.

Prepare three worksheets containing:
A) digits 1–9 written in words,
B) tens written in words from 10 to 90,
C) hundreds written in words from 100 to 900.

Exercise 5:

Educational objective:

Materials: Korbo blocks.

Procedure:

The teacher prepares four containers labeled respectively: “1000”, “100”, “10”, and “1”. All red gear wheels are placed in the “1000” container, yellow gear wheels in the “100” container, purple gear wheels in the “10” container, and blue gear wheels in the “1” container. A mat made of two connected platforms (4×2) is placed in front of the containers.

The teacher asks a student to build a number consisting of 4 thousands, 5 hundreds, 2 tens, and 3 ones and place it on the mat. The exercise can be repeated several times.

The teacher divides the children into teams of four. Each team receives a mat made of two connected platforms (4×2). Each child in the group is assigned a role: one is “thousands,” one “hundreds,” one “tens,” and one “ones” (if a group has fewer than four children, one child may take on two roles). The teacher reads a number aloud in the following way: “The number I am thinking of has 6 thousands, 3 hundreds, 8 tens, and 2 ones.” Each child must run to the appropriate container, select the correct number of gear wheels, and the group works together to place the number read by the teacher on the mat.

Exercise 6: Encode a Three-Digit Number

Objective: Reinforcing number notation in the form of ones–tens–hundreds.

Required elements:

– Gear wheels = 1 (one),
– Cylinders = 10 (ten),
– Platforms = 100 (hundred).

Procedure:

The teacher gives a number, e.g. 243. The student’s task is to build a construction whose blocks add up to that number (e.g. 2 platforms, 4 cylinders, and 3 gear wheels). The children present their numbers and read them aloud.

Variation:

– Students randomly draw blocks, for example from a bag, and write down the number that can be built using them.

Exercise 7: Construction with Tens and Hundreds

Objective: Creating numbers using tens and hundreds without ones.

Required elements: cylinders and platforms, connectors.

Procedure:

The teacher assigns a value of 100 to the platform and a value of 10 to the cylinder.

Then the teacher asks the children to build a construction consisting of, for example, 3 platforms and 5 cylinders. After building the number, the children convert the number of platforms and cylinders into numerical values and write the number according to the pattern: 300 + 50 = 350.

Exercise 8: Moving Tens

Objective: Converting ones into tens.

Required elements: gear wheels, cylinders, connectors.

Procedure:

The teacher explains to the children that a tower made of 10 gear wheels has a value of 10. Similarly, one cylinder also has a value of 10.

Each child receives 15 gear wheels. Their task is to build a construction and exchange 10 gear wheels for 1 cylinder (i.e. one ten). Then they count the remaining ones.

Next, the teacher pours out a larger number of gear wheels (the class can also be divided into groups, with each group assigned one color of gear wheels). The students count the gear wheels and then analyze how many cylinders they can exchange the counted wheels for (10 gear wheels = 1 cylinder).

Variation:

– Reverse tasks – breaking tens into ones.

Exercise 9: Korbo Market – Buying Numbers

Objective: Reading and creating numbers in the decimal system.

Required elements: sets of blocks, cards with prices (e.g. 146, 203).

Procedure:

Assign numerical values to individual Korbo elements, for example: a platform = 100, a cylinder = 10, a gear wheel = 1.

Children are given a “budget” (e.g. 150) and “buy” items (price cards) by building the corresponding value using blocks (e.g. 1 platform, 4 cylinders, 6 gear wheels = 146).

Next, they check which child managed to buy the most items and who has the smallest “remainder” left. The activity can also be done in pairs or groups, where children discuss and calculate values together before making a purchase.

Variations:

– Calculating the remainder – how much is left from 150?
– Creating their own prices and shopping between groups.

Exercise 10: Number Obstacle Course

Objective: Reinforcing the order and value of digits.

Required elements: blocks, cards with three-digit numbers, a platform as a base.

Procedure:

The teacher places cards with three-digit numbers around the classroom. Then, together with the students, assigns values to individual elements, for example:

platform = 100, cylinder = 10, gear wheel = 1.

At each station, students build the value of the number and then move on to the next one.

Variations:

– This task works very well as a timed activity.
– Additional tasks can be added to the cards (e.g. add 10, exchange a ten for ones).

Exercise 11: Construction with a Recorded Value

Objective: Understanding the place value of digits in a three-digit number.

Required elements: boards labeled (O, T, H), gear wheels, platforms.

Procedure:

Pair activity. One child creates a “number board” with three fields. In each field, they place the appropriate number of gear wheels (e.g. 3 wheels in “O”, 2 in “T”, 1 in “H”). The child reads the number aloud. Then they rearrange the gear wheel towers by swapping their positions and ask the partner to read the new number. The partner is also asked to explain what has changed (e.g. the ones and tens have swapped places or are now in different positions).

Variation:

– Adding or removing gear wheels and observing how the number changes.

Exercise 12: Block Bank

Objective: Exchanging numbers in the decimal system.

Required elements: a large set of blocks, “task cards” (e.g. “exchange 1 hundred”).

Procedure:

The teacher places cards with three-digit numbers around the classroom. Then, together with the students, assigns values to individual elements, for example:

platform = 100, cylinder = 10, gear wheel = 1.

A child receives a card such as “exchange 1 hundred into tens” and performs the operation: 1 platform → 10 cylinders. Then the child can continue exchanging tens.

Variations:

– Introducing the concept of a “remainder,” e.g. 1 ten and 3 ones.

Exercise 13: Number Comparison Game

Objective: Comparing the value of numbers based on constructions.

Required elements: sets for building numbers, cards with the symbols >, <, =.

Procedure:

Children build constructions using Korbo blocks. Then the teacher explains: each platform represents one hundred, each cylinder represents one ten, and each gear wheel represents one unit (elements such as connectors or cranks are not counted). The children calculate the value of their structure and compare it with another pair’s construction. They place both constructions on the floor and put the appropriate comparison symbol between them (this construction has a greater numerical value than the other).

Variations:

– Teamwork: who can build the larger number using 12 elements.
– Increased difficulty: each time, the children first build a tower, and then the teacher draws cards determining which element represents a hundred, a ten, etc.

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