Multiplication and Division

The teacher builds three identical towers, each from two gears. The teacher asks a pupil to say how many towers there are, and then to write the number on the board. The teacher asks another pupil to count how many gears are in one tower and write it on the board. The teacher says that there are three identical towers, in each tower there are two gears, and asks the pupils how many gears there are in all the towers. The teacher writes the operation 3 × 2 = 6. The teacher explains to the pupils what the multiplication sign means.

The teacher gives one more example (e.g. 4 × 3 = 12), stressing that the towers are the same.

The teacher divides the children into groups; each pair gets a set of blocks and worksheets with operations to solve. The children build towers and solve the tasks.

The teacher builds an 8×8 mat from platforms. Then the teacher places three gears in the first row and asks a pupil how many gears there are on the mat, writes the operation on the board (three gears in a row 1 × 3 = 3), then takes the gears off and places four gears in the first row and four gears in the second row, saying: we have four gears in the first row and we will add a second row with the same number of gears, that is two rows of four gears, 2 × 4 = 8. The teacher shows two more examples (e.g. 5 × 4 = 20 and 8 × 3 = 24).

The teacher divides the children into teams of four; each team gets worksheets. The children build an 8×8 mat and number the rows and columns. The children solve the tasks by placing the matching numbers of gears in rows and columns on the mat, according to the written operation.

The teacher builds three towers consisting of two gears, the first tower from red gears, the second from blue gears, the third from yellow gears. The teacher asks the children how many towers there are, how many gears in each tower, and how we will write the equation. A child writes the equation on the board (3 × 2 = 6). Then the teacher rebuilds the towers so that two identical towers of three gears are created; each gear in a tower is a different color. The teacher shows the towers to the children and asks them to check whether the number of gears in both towers has not changed. The teacher explains that from three towers two were built, but from the same gears, so 2 × 3 = 6. The teacher gives two more simple examples explaining the commutative property of factors in multiplication.

The teacher divides the children into pairs; each pair gets a set of blocks and worksheets with operations to solve. The children build and rebuild towers and solve the tasks.

The teacher builds an 8×8 mat, places five gears in the first, second, and third row on the mat, asks a child to count the gears and write the operation (3 × 5 = 15). Then the teacher takes the gears off and arranges them five at a time in the first, second, and third column, asks a child to count the gears and write the operation (5 × 3 = 15).

The teacher divides the children into teams of four; each team gets two sets of blocks and worksheets. The children build an 8×8 mat and number the rows and columns. The children solve the tasks by placing the matching numbers of gears in rows and columns on the mat, according to the written operation.

The teacher places graphics of four gears on the board, each in a different color. To each gear the teacher assigns a given numerical value, e.g.:
● red gear = 3
● blue gear = 5
● purple gear = 6
● yellow gear = 7

Then the teacher asks a pupil to draw one gear; the teacher draws a second gear and hands it to the pupil for the other hand; the pupil writes on the board the values matching both gears and the result of the multiplication.

The teacher divides the children into pairs; each pair gets several gears in different colors. Children take turns drawing gears, similarly to the pupil–teacher setup (one child takes one gear, the other chooses theirs and hands it to the first); the first pupil calculates the result and gives it to the second, who checks whether it is correct.

The teacher builds a tower from eight gears. The teacher shows it to the children and writes 8 on the board, then divides the tower into two equal parts of four gears each and asks the children into how many towers the large tower was divided and how many gears both towers have, writes the equation 8 ÷ 2 = 4 on the board. The teacher explains the “÷” sign to the children. Then the teacher puts the tower of eight gears together again, but this time divides it into four towers of two gears each. The teacher asks the children to count the towers and say how many gears each of them consists of, and writes the equation 8 ÷ 4 = 2.

The teacher divides the children into pairs. The teacher says a number of pieces that the children are to take together from the container and a number of groups that the children are to arrange (in each group there is to be the same number of blocks).

The teacher points to a box in which there are 22 cylinders and asks three pupils to share them among themselves. The pupils conclude that they are not able to share the blocks equally among themselves. The teacher writes the operation 22 ÷ 3 and explains to the children what division with a remainder means. Then the teacher asks one pupil to add as many cylinders to 22 as needed so that they can be shared equally among three people, and to write the equation.

The teacher divides the children into pairs; each pair gets a worksheet with division. Using cylinders, the children solve the equations and record the results of operations with and without a remainder.

In pairs, children receive worksheets with equations in which the divisor is replaced by a graphic of a colorful gear. Helping themselves with cylinders, the children are to assign the correct value of the divisor to the color of the gear in the graphic. The teacher explains that the divisor is another way of saying into how many groups the total number of all the blocks should be divided.

The teacher has a prepared tower of twelve gears, places it on a platform, and writes the equation 12 ÷ 4 = 3 on the board (asks a pupil to give the result). The teacher divides the tower of gears into four parts, then asks a pupil to say how many towers they see and how many gears they consist of. The teacher writes the equation 4 × 3 on the board, then asks a pupil to say how many gears there are altogether, and writes 12. In the same way, the teacher presents the operations 15 ÷ 5 = 3, 5 × 3 = 15, and so on, and explains to the pupils that the result of division can be checked through multiplication.

The pupil receives 12 gears and is to share them equally onto 4 pegs of the platforms. Conclusion: 12 ÷ 4 = 3.

The pupil has 12 “team members” (cylinders). They divide them into, e.g., 3 teams — 4 people each. Then 4 teams — 3 people each.

Work in pairs / groups. The group chooses a number (e.g. 5), builds a “machine” from 5 gears turning in a row. Then onto each gear they place 3 more: 5 × 3 = 15. They count the number of blocks.

The pupil draws a card with an operation (e.g. 6 ÷ 2). They are to build a construction from 6 pieces and divide it equally into 2 parts.

In pairs, children draw operations, carry them out with blocks, and compare the result — who has more?

The pupil tries through building to find the missing value — e.g. they arrange 4 blocks in groups until they reach 16.