Chapter IV – Addition and Subtraction
Table of Contents:
- 1. Connecting Towers
- 2. Colorful Addition
- 3. Chain of Operations
- 4. How Many Wheels Are Missing?
- 5. Read, Build, Complete.
- 6. Add and Build
- 7. Subtracting from a Construction
- 8. Addition Machine
- 9. Number Stick
- 10. Block Shop
- 11. Tower Operations
- 12. Gear Equations
- 13. Movable Block Number Line
- 14. Block Operation Towers
- 15. Block Operation Pyramids
Addition and subtraction are the basic arithmetic operations that mark the beginning of learning mathematics. Understanding and mastering them forms the foundation for further calculations, as well as for solving word problems, planning expenses, making measurements, and many everyday activities. Curiosity stimulated in a child by frequently asking the question “how many” encourages action and the discovery of mathematical relationships.
In early primary education, it is extremely important that a child not only knows the symbolic notation of an operation but also understands what it represents: addition means joining and increasing a set, while subtraction means taking away and reducing it. Children learn most effectively through action, experience, and play—not through abstract symbols alone.
Korbo blocks perfectly support this stage of learning because they enable:
manipulating concrete elements while building models of operations,
physically adding and removing blocks within a construction,
visually comparing quantities and differences in height, length, and number of elements,
introducing operations through movement, building, rotating, and shifting, which activates different learning styles.
Activities using Korbo blocks help children feel and understand mathematics with their whole bodies, not only “in their heads” or “on paper.” This chapter provides a foundation for further learning and prepares children for mathematical thinking in a natural, dynamic, and engaging way.
1. Connecting Towers
Educational objective: Introducing the concept of a sum.
Materials: Korbo blocks.
Procedure:
The teacher builds a tower from 10 blue gear wheels and asks one student to count the gear wheels in the tower out loud. The teacher reminds the children that the tower consists of 10 gear wheels and writes this number on the board (under a picture of a blue gear wheel). Next, the teacher builds a tower from 3 red gear wheels and asks another student to count the red gear wheels aloud. The teacher asks how many gear wheels the second tower consists of and writes the number on the board (under a picture of a red gear wheel).
The teacher then asks another student to count all the gear wheels in both towers together and give the result using the phrase: “What is the sum of all the gear wheels?” The teacher writes the result on the board and places the addition and equality symbols between the values. The teacher also points out that the sum represents the total number of all elements in this operation.
Variation:
The teacher asks the student how much taller the blue tower is than the red tower.
The teacher moves one gear wheel from the blue tower to the red tower and asks the student how many gear wheels there are in total, how many are in the taller tower, and how many are in the shorter tower (by how many gear wheels the two towers differ).
2. Colorful Addition
Educational objective:
Materials: Korbo blocks, a sheet of paper and a pencil for each group.
Procedure:
The teacher divides the children into groups of four. Each group receives a worksheet with instructions and space to write down the results. All Korbo sets are placed in a box under the board. The teacher informs the children that each of them is assigned one color (one person in the group has purple, one yellow, one blue, one red). Only the person assigned a given color may collect the required gear wheels for the group.
The teacher gives the following instructions:
Build a tower from 10 yellow gear wheels.
Build a tower from 4 purple gear wheels and connect it to the yellow tower.
Count the gear wheels in each tower and then add them together.
Write down the operation and finally give the sum of all gear wheels.
Return 2 yellow gear wheels to the box.
Bring 4 red gear wheels and build a tower from them.
Count the gear wheels in each tower, write the equation, and calculate the total number of gear wheels. Write down the result.
Return 1 purple, 1 red, and 1 yellow gear wheel to the box.
Bring 5 blue gear wheels and build a tower from them. Count the gear wheels in each tower, write the equation, and calculate how many gear wheels there are in total. Write down the result.
After completing all the instructions, return all gear wheels to the box.
3. Chain of Operations
Educational objective: Practicing addition and subtraction.
Materials: Korbo blocks.
Procedure:
The teacher divides the children into pairs and places a box with gear wheels under the board. The teacher tells the children that they will take turns going to the box to collect the required gear wheels. The children follow the instructions written on the worksheet:
Bring 10 purple and 6 yellow gear wheels and build one tower from them. Give the sum of all the gear wheels in the tower. Write down the operation.
Return 4 purple gear wheels and count how many gear wheels remain. Write down the operation.
Return 2 yellow and 1 purple gear wheel. How many gear wheels remain? Write down the result.
Subtract the result of the second operation from the result of the first operation.
How many yellow gear wheels did you return in total, and how many purple gear wheels did you return?
4. How Many Wheels Are Missing?
Educational objective:
Materials: Korbo blocks.
Procedure:
The teacher asks a student to build a tower of 6 gear wheels in one color of their choice. Then the teacher asks another student to say how many gear wheels are missing for the tower to reach a height of 10 gear wheels. The student adds the missing number of gear wheels in a different chosen color and checks whether the total equals 10. The teacher writes the equation on the board.
Next, the teacher asks a student to build a tower of 10 gear wheels in any color, and then asks the student to remove enough gear wheels so that 6 remain in the tower. The teacher writes the equation on the board.
The teacher divides the students into pairs. Each pair receives a Korbo set and a worksheet. The students take turns building towers according to the pattern on the worksheet and completing each tower to 10 gear wheels. They write the number of missing gear wheels on the worksheet.
5. Read, Build, Complete.
Educational objective: Reading comprehension and completing to a given value.
Materials: Korbo blocks, worksheets.
Procedure:
The teacher asks a student to build a tower of 11 gear wheels in one color of their choice. Then the teacher asks another student to say how many gear wheels are missing for the tower to reach a height of 20 gear wheels. The student adds the missing number of gear wheels in a different chosen color and checks whether the total equals 20. The teacher writes the equation on the board.
Next, the teacher asks a student to build a tower of 20 gear wheels in any color, and then asks the student to remove enough gear wheels so that 11 remain in the tower. The teacher writes the equation on the board.
The teacher divides the students into pairs. Each pair receives a Korbo set and a worksheet. The students take turns building towers according to the pattern on the worksheet and completing each tower to 20 gear wheels. They write the number of missing gear wheels on the worksheet.
6. Add and Build
Objective: Reinforcing the addition of single-digit numbers.
Required elements: gear wheels, cylinders, platforms, connectors, cards with digits.
Procedure:
A child draws two digit cards (e.g. 4 and 3) and selects blocks from the box—first the number shown on the first card, then the number shown on the second card. The child counts how many elements were selected in total and builds a construction consisting of that many elements, equal to the sum (7).
Variations:
– When working with younger children, it is advisable to use only gear wheels, first selecting the appropriate number in one color and then in another, and then building a single tower.
7. Subtracting from a Construction
Objective: Developing a practical understanding of subtraction.
Required elements: Korbo blocks.
Procedure:
The teacher asks each child to build a construction using 10 elements. Then the teacher asks them to remove, for example, three elements. Next, the students count how many elements remain.
Variations:
– The teacher creates a chain of operations (e.g. add three more elements, how many blocks are there now? subtract 5, etc.).
8. Addition Machine
Objective: Illustrating addition as a process.
Required elements: two connected platforms for each student, gear wheels.
Procedure:
The child builds a “machine” on the platforms. First, the teacher asks the children to add, for example, 4 gear wheels to their machine, and then add two more in such a way that all of them rotate. After connecting them, the machine “adds” (the wheels rotate), and the child states the result. The children can then continue adding more wheels. The wheels can be stacked on top of each other (rotating towers)—it is important that the children can always count all the wheels that are rotating.
Variations:
– Reversing the role – the machine subtracts.
9. Number Stick
Objective: Developing mathematical and spatial thinking through addition.
Required elements: cross connectors, cylinders.
Procedure:
The child’s task is to build a “stick” using as many elements as the teacher specifies. The first number indicates the number of cylinders, and the second indicates the number of connectors. For example, the teacher says: “Build a stick that consists of 6 cylinders and 3 connectors. What is the total number of blocks?”
Variations:
– As an extension of the activity, gear wheels can be added to the stick, placed on the connectors like “flowers” on branches.
10. Block Shop
Objective: Adding values and finding the remainder.
Required elements: blocks as “goods,” cards with constructions of different point values (e.g. 3, 6, 10), a worksheet with block values.
Important rule:
In one turn, each child may either go to the box to take one block or go to the board to take one card with a value.
Procedure:
Children collect blocks of different values, building constructions which they can then exchange for a card with a picture and points. In each round:
The children go together to the box, and each child selects one block with the value they need. Then they add it to their construction. Once everyone has added a block to their construction, the next round begins—children may again go to the box or exchange their construction for points.
11. Tower Operations
Objective: Comparing sums and differences in operations.
Required elements: gear wheels.
Procedure:
Children build towers representing the sums of different operations (e.g. 4 + 2 vs. 5 + 1). Then they compare the heights of the towers. The teacher asks: what is the difference in the number of blocks between the first and the second tower?
Variations:
Group work – each child builds a tower with as many gear wheels as indicated on a card. Then, working in pairs, they combine towers to further check the difference in the number of blocks between two groups (two towers).
12. Gear Equations
Objective: Completing missing components of an operation.
Required elements: cylinders.
Procedure:
The teacher says: Everyone takes three cylinders. Now I want you to have seven cylinders each. Check how many more cylinders you need to add so that everyone has seven.
Variations:
Subtraction tasks (You have seven and I would like you to have three).
Creating equations for one another in pairs.
13. Movable Block Number Line
Objective: Spatial addition and subtraction on a number line.
Required elements: a long platform (10 platforms connected in a line), a cylinder as a token made from blocks. Two pairs can work at each platform (one in the top row, one in the bottom row), and a die.
Procedure:
Each point (peg) on the platform represents a consecutive position. Working in pairs, children take turns moving the token according to the number rolled on the die and perform the operation, for example:
They roll a 5 and move to the fifth position. Then they roll a 3. They say 5 + 3 and move three positions forward. They count how many positions they have moved from the start (five and three is 8), and so on.
Variations:
Instead of dice, students create stories related to addition to be performed on the line, e.g. “Janek took four steps, stopped, and then took two more steps. How many steps did he take in total?”
Drawing operations from cards.
14. Block Operation Towers
Objective: Reinforcing addition and subtraction operations.
Required elements: gear wheels, cards with gear wheels (for assigning values).
Procedure:
The teacher places cards with gear wheels on the board and assigns a specific value to each color, for example:
a yellow gear wheel has a value of three,
a blue gear wheel has a value of four,
a red gear wheel has a value of five,
a green gear wheel has a value of six.
Next, the teacher asks the students to build a tower with a value of, for example, 10.
Different challenge variants:
build a tower using three blocks that has a value of 10,
build a tower that has a value of 12 and is made of four blocks,
build a tower that has a value of 15 and includes at least two yellow gear wheels,
build a tower that has a value of 12 where one block is yellow and one is blue,
build a tower that has a value of 16 and includes three green gear wheels.
15. Block Operation Pyramids
Objective: Reinforcing addition and subtraction operations.
Required elements: cylinders, cards with cylinders (for assigning values).
Procedure:
The teacher places cards with cylinders on the board and assigns a specific value to each color, for example:
a yellow cylinder has a value of three,
a blue cylinder has a value of four,
a red cylinder has a value of five,
a green cylinder has a value of six.
Next, the teacher asks the students to each take, for example, two blue cylinders, two green cylinders, one red cylinder, and one yellow cylinder, and build a specific pyramid, for example:
in the first row: blue, red, blue;
in the second row: two green cylinders;
in the third row: one yellow cylinder.
Then the teacher asks questions and sets challenges:
What is the sum of the first row?
What is the sum of the first and second rows?
What is the sum of the entire pyramid?
Change the first row so that its sum is 16.
Change the second row so that its sum is eight (the first row may also be modified).
Arrange the pyramid so that the sum of the first two rows is, for example, twenty-two.
