Chapter VIII

Coding Values, Money Calculations

Why is it worth teaching value coding?

In early-school education children get to know the value of a number not only as a sign written with a digit, but also as something concrete — something that can be counted, compared, exchanged, built, or coded. Understanding numerical value in a practical context is the basis of fluent counting, logical thinking, and introducing children to the world of mathematics and programming.

The chapter “Coding Values” is based on the idea that each piece can be assigned a given numerical value — and then a concrete number can be built from them, the value can be read from a construction, compared with others, or even mathematical operations can be carried out on sets of blocks. In this way pupils learn both the decimal place-value system and the meaning of mathematical operations — through something concrete, and not only a symbolic record.

Blocks are an excellent tool for learning to code values:

different pieces can represent ones, tens, and hundreds (e.g. a gear = 1, a cylinder = 10, a platform = 100),
constructions from blocks allow children to build numbers physically and understand them better,
activities involving comparing, reading, and coding develop algorithmic thinking and early programming competencies.

The activities in this chapter teach not only mathematics, but also precision, planning, strategies for action, and cooperation.

After completing the tasks in this chapter, the pupil:

Understands the idea of the value of a number and can assign a numerical value to a concrete object (e.g. a gear = 1, a cylinder = 10).
Builds numbers using blocks with assigned values (e.g. 2 cylinders and 3 gears = 23).
Reads the numerical value from ready-made constructions of blocks.
Compares the values of different constructions, using the signs: <, >, =.
Exchanges numbers for matching sets of blocks in different combinations (e.g. 100 = 1 platform or 10 cylinders).
Uses the decimal system in practical action (e.g. 3 blue gears and 2 green gears = 32).
Creates different constructions of blocks with the same value — understands the idea of numerical equivalence.
Solves word problems using value coding.
Creates and reads simple “number codes” from blocks — introducing early programming thinking.
Works in a team on solving logic and coding tasks, using constructions as a form of record.

Encode a Number

Learning goal

Assigning a numerical value to blocks and representing numbers.

Needed elements

Blocks

How it goes

The teacher gives a number, e.g. 134. Pupils build a construction from 1 platform, 3 cylinders, and 4 gears.

Variants

Pupils draw a number from cards and code it with blocks.
Decoding a value: the teacher builds a construction from blocks (e.g. 2 platforms, 4 cylinders, 6 gears). Pupils read its value: 246.
Pupils create constructions for classmates, who must read them.

Coded Decimal System

Learning goal

Understanding the value of ones, tens, and hundreds in three-digit numbers.

Needed elements

Gears
Two platforms per pair/group/person (depending on how we divide the class)

How it goes

The teacher assigns a value to the colors of the gears, e.g.:
● Green — 100
● Blue — 10
● Yellow — 1

Then the teacher explains that, e.g., two green gears arranged as a tower are 200. Next the teacher asks the pupils to arrange the value 321 from gears on the platform (in the last position on the right there will be one yellow gear, to its left two blue ones, and to the left of the blue ones three green ones).

Then the teacher creates challenges for the children. Example challenge: build a number in which the hundreds digit is smaller than 3, the tens digit is smaller than 4, and the ones digit is greater than six.

Variants

Children create challenges for one another.

Block Safe

Learning goal

Creating numerical codes and logical arrangements.

Needed elements

Blocks

How it goes

The teacher assigns a value to the colors of the gears, e.g.:
● Green — 100
● Blue — 10
● Yellow — 1

The teacher tells the pupils that a special CODE for a safe has been created. To decode it, the blocks must be arranged in the matching configuration. At the same time the teacher writes “the code on a card”, which is kept hidden from the pupils. Then the teacher tells them that the code consists of three digits, which are, e.g., 4, 2, 5.

Pupils must “open the safe” by building a correct combination of values (that is, e.g., they arrange on the platform, similarly to the previous task, the values: 425 or 245 or 452 or 254 or 542 or 524).

Variants

Extending the cipher with an extra, fourth position (e.g. red gears).

Money Values

Learning goal

Translating money values into an arrangement of blocks and the other way around.

Needed elements

Blocks as symbols

How it goes

The teacher prepares values for particular pieces on the board. Then the teacher asks the pupils to build a construction worth 12 dollars.

Variants

Pupils create values without using gears.
Or, e.g., pieces in the color green.

We Build a Bank of Values

Learning goal

Calculating the values of different sets.

Needed elements

All the blocks
Cards with “price” values

How it goes

Pupils receive an “account” with a starting value (e.g. 250). Their task is to build, for that amount, e.g. three independent constructions.

Variants

A game: who will spend the whole amount completing the task in a given time.
Calculating change — e.g. I built a construction for 187, how much do I have left?

A Construction for a Task

Learning goal

Using value coding in a word problem.

Needed elements

Blocks
Cards with the wording of tasks (e.g. “Build a vehicle worth 142”)

How it goes

Variants

Pupils create their own tasks.
Adding constraints such as: “you may not use more than 2 platforms”.
Cards with the wording of tasks: build a vehicle worth 142 dollars, build a flower worth 220 dollars, build a windmill worth 500 dollars, and so on.

Block Comparisons

Learning goal

Comparing the values of different sets and recording them symbolically.

Needed elements

Blocks

How it goes

The teacher prepares values for particular pieces on the board, e.g.: platform — 50 dollars, gear — 15 dollars, cross connector — 1 dollar, cylinder — 5 dollars, tire — 4 dollars, and so on. We ask each pupil to take 15 pieces of their choice. Then the pupil builds two constructions and records the comparison: “Construction A (145) > Construction B (123)”.

Variants

Children place their constructions in increasing/decreasing order.
Using only one color of blocks in each construction.

Who Encodes Faster?

Learning goal

Automating the assignment of values to blocks.

Needed elements

Sets of blocks
Cards with numbers

How it goes

The teacher prepares values for particular pieces on the board, e.g.: platform — 50 dollars, gear — 15 dollars, cross connector — 1 dollar, cylinder — 5 dollars, tire — 4 dollars, and so on. A team game — the teacher writes a number on the board (e.g. 417), and the children as quickly as possible must arrange as a group a construction of that value.

Variants

Adding extra conditions, e.g. in the construction at least 5 pieces must turn.

Reverse Block Mathematics

Learning goal

Creating different sets with the same value.

Needed elements

All the pieces.

How it goes

Variants

A task with a ban on using platforms.
Adding extra conditions, e.g. 4 pieces turn in the construction.

Exchange It Differently

Learning goal

Creating equivalent constructions for the same value.

Needed elements

All types of blocks.

How it goes

The teacher prepares values for particular pieces on the board, e.g.: platform — 50 dollars, gear — 15 dollars, cross connector — 1 dollar, cylinder — 5 dollars, tire — 4 dollars, and so on. The teacher builds a construction, asks the pupils to reproduce it, and then to calculate its value. Then the teacher asks the pupils to take away one piece (e.g. a platform) and they are to create a different combination that gives the same value (e.g. exchanging a platform for 4 gears and one cylinder).

Variants

Looking together for as many variants of the same value as possible.