Writing Numbers in the Decimal System

The teacher draws a table on the board with eight rows and four columns. In the first row the teacher places printed graphics of gears in four colors (in the first column a red one, in the second a yellow one, in the third a purple one, in the fourth a blue one). Then each gear is labeled (red — thousands, yellow — hundreds, purple — tens, blue — ones). The teacher explains to the pupils that each column will contain one digit, which will be shown by the number of gears of the matching color.

The teacher writes the digit 4 in the fourth column, in the second row, and asks a pupil to read the value. The teacher builds a tower from four blue gears and places it on a mat built from two platforms (2×4) in the last space on the right.

Then, 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 pupil to read the value of the number — 64. The teacher explains that this number contains six tens and four ones and arranges six purple gears and four blue ones on the mat. The teacher explains to the pupils that the number 64 contains 6 tens and 4 ones.

In the same way the teacher fills the remaining cells in the table on the board with chosen values, asking pupils to read the number, build towers from gears of the matching color and number, and place them in the correct place on the mat.

Prepare graphics of gears.

The teacher prepares a mat from two joined platforms (4×2). Then each gear of a given color is assigned a place (ones, tens, hundreds — colors can be assigned in the same way as in the first activity).

The teacher draws a table on the board similar to the one in the previous task. The teacher places the mat in front of themselves and from four digits arranges any number, then asks the pupils to build towers together from the given number of gears in the correct color and place them in the matching place on the mat.

The activity can be repeated several times, each time asking the rest of the class whether they think the activity was carried out correctly.

Prepare the cards.

The teacher divides the children into pairs; each pair gets a set of blocks and a worksheet with written numbers; the children build towers from gears according to a scheme written earlier (similarly to activities 1 and 2).

The teacher prepares a mat made from two platforms (4×2), printed digits, and pours a dozen or so gears in different colors into an opaque bag or box. The teacher asks a pupil to draw 10 gears, then arrange a number from them on the mat according to the scheme from the first task. Then the teacher asks the next pupil to “read” the arranged number and place the matching digits under it.

The teacher writes the number arranged by the pupil in words on the board. During this activity the teacher can also explain the rules for writing number words.

The teacher divides the children into pairs; each pair receives a set of blocks and worksheets. One pupil chooses one number from each worksheet (e.g. three hundred, fifty, eight); the other arranges the number they have read in the form of towers from blocks.

The teacher prepares four containers labeled in order: “1000”, “100”, “10”, and “1”; into the “1000” container go all the red gears, into “100” the yellow gears, into “10” the purple ones, into “1” the blue ones. In front of them the teacher places a mat arranged from two platforms (4×2). The teacher asks a pupil to build a number consisting of 4 thousands, 5 hundreds, 2 tens, and 3 ones and place it on the mat. The activity can be repeated several times.

The teacher divides the children into teams of 4; each team receives a mat from two joined platforms (4×2). All the children in the group have an assigned role: one is “thousands”, one “hundreds”, one “tens”, one “ones” (if it happens that not all groups have 4 children, one child may have two “roles”). The teacher reads a number 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 matching container, choose the right number of gears, and the group together arranges on the mat the number read by the teacher.

The teacher gives a number, e.g. 243. The pupil's task is to build a construction whose blocks add up to that number (e.g. 2 platforms, 4 cylinders, and 3 gears). Children present their numbers and read them.

The teacher assigns a platform the value 100, and a cylinder the value 10. Then the teacher asks the children to build a construction consisting of, e.g., 3 platforms and 5 cylinders. After building the given number, the children convert the number of platforms and cylinders into numerical values and write the number according to the model: 300 + 50 = 350.

The teacher explains to the children that a tower of 10 gears has the value 10. In the same way, one cylinder has the value 10.

Each child gets 15 gears. Their task is to build a construction and exchange 10 gears for 1 cylinder (that is, one ten). Then they count the remaining ones.

Then the teacher pours out a larger number of gears (the class can also be divided into groups and each group assigned one color of gears). Pupils count the gears and then analyze how many cylinders they can exchange the counted gears for (10 gears — 1 cylinder).

We assign particular pieces a numerical value, e.g. a platform is 100, a cylinder is 10, a gear is 1.

Children have their “budget” (e.g. 150) and “buy” items (cards), building the matching value from blocks (e.g. 1 platform, 4 cylinders, 6 gears = 146). Then they check which child managed to buy the most and had the least “change” left.

The activity can also be run in pairs and groups (where children can discuss and calculate values together before buying).

The teacher spreads cards with three-digit numbers around the whole classroom. Then, together with the pupils, the teacher establishes a value for particular pieces, e.g. platform — 100, cylinder — 10, gear — 1. At each station pupils build the value of the number and move on.

An activity in pairs. One child creates a “number board” with three fields. Into each field they place the matching number of gears (e.g. 3 gears in “Ones”, 2 in “Tens”, 1 in “Hundreds”). They read the number. Then they swap the towers of gears and ask the partner to read the number that has been created. They also ask the partner to explain what changed (e.g. the ones and tens swapped places / were in different positions).

The teacher spreads cards with three-digit numbers around the whole classroom. Then, together with the pupils, the teacher establishes a value for particular pieces, e.g. platform — 100, cylinder — 10, gear — 1.

The child gets a card, e.g. “exchange 1 hundred for tens”, and carries out the operation — 1 platform — 10 cylinders. Then they may continue exchanging tens.

Children build constructions from blocks. Then the teacher says: each platform is one hundred, a cylinder is one ten, a gear is one one (we do not count, e.g., connectors or cranks). Children calculate the value of their tower and compare its value with another pair. They place both constructions on the floor and between them they place the matching comparison sign (this construction has a greater numerical value than the other).