Chapter II
Comparing Numbers
Why is it worth teaching number comparison?
Comparing numbers is one of the key mathematical skills developed in early-school education. It lies at the heart of understanding the idea of number, its value, order, and the relations between numbers. A child who can point out which number is greater, smaller, or equal to another gains foundations not only for calculating, but also for solving word problems, logic tasks, and practical everyday problems.
In grades 1–3 this competence should be developed in a concrete way, using tangible, countable objects. Only then does the pupil have a chance to understand what it really means that there is “more” or “fewer” of something — not as an abstract record, but as a concrete action and observation.
Blocks support the development of this skill very well, because they:
- make it possible to build number sets and compare them in action,
- allow the child to count, arrange, order, and match pieces in an active and independent way,
- introduce the possibility of modeling number ideas by assigning values to particular pieces (e.g. a cylinder as 5, a platform as 10),
- also support the development of logical, spatial, and language thinking when pupils describe their constructions and comparisons.
Construction activities with blocks make it possible to meet educational goals aligned with the curriculum, and at the same time give children the joy of acting, experimenting, and discovering the rules of mathematics in practice.
After completing the tasks in this chapter, the pupil:
- Compares natural numbers in the range appropriate to the grade, using the terms: more, fewer, the same number.
- Records comparisons of numbers using the mathematical signs: >, <, =.
- Creates and reads sets with the same number of elements, using different types of pieces (e.g. cylinders, gears).
- Orders numbers in increasing and decreasing order based on the number of pieces in a set or construction.
- Creates constructions from a given number of pieces and compares them with other pupils' constructions.
- Builds sets with a given numerical difference (e.g. a set that is 3 greater).
- Makes approximate and exact comparisons of the number of pieces in sets or of the height of constructions.
- Creates models of numbers with blocks, assigning values (e.g. cylinder = 5, platform = 10).
- Solves simple word problems involving comparison of the number of pieces, e.g. “How many more?”, “How many fewer?”.
- Communicates the results of comparisons verbally and graphically, e.g. orally, on paper, using symbols or buildings.
Who Has More
Learning goal
Comparing the numerosity of sets.
Needed elements
- Gears
- Cylinders
- Connectors
- Dice / math dice
How it goes
Children work in pairs. Each of them rolls a die and takes the indicated number of pieces. Then they compare their sets and point out who has more, who has fewer, and who has the same number / by how many more, by how many fewer.
Variants
Children may roll two dice, first adding the values they rolled and then taking the blocks. An activity in pairs. Children can be given cards: >, <, =, to place the matching sign between their own blocks and their partner's.
We Build and Compare
Learning goal
Comparing the number of pieces in constructions.
Needed elements
- Gears
- Cylinders
- Platforms
How it goes
In pairs, children build constructions from any number of blocks in a given time (e.g. 30 seconds). They count how many pieces they used and compare their buildings — which has more, fewer, or the same number of parts.
Variants
Children build only a pyramid from cylinders, stacking them one on another (like a pyramid).
Tower with Comparison
Learning goal
Comparing height as a result of the number of pieces.
Needed elements
Cylinders.
How it goes
Each child builds a tower from chosen pieces. They compare the towers by the number of blocks and by height — which is taller, which has more pieces.
Variants
On each cylinder, first place (do not press into the hole) a gear, and only then place the next cylinder. Building towers with a given difference (e.g. “the teacher's tower has 3 blocks; your towers should be 2 blocks taller”).
Scale on the Platform
Learning goal
Matching numbers to the length of a construction.
Needed elements
- Platforms
- Gears
How it goes
Children build rows of gears on a platform, placing them horizontally. Each row corresponds to a number (e.g. a row of 4 gears = 4). Children compare the lengths.
Variants
Building increasing or decreasing sequences on a large platform (10 by 10 platforms).
Who Is Faster? — Gear Clock
Learning goal
Comparing time and the number of turns.
Needed elements
- Gears
- 1 platform
- A marker built from cylinders, a straight connector, and a cross connector (an inverted L)
How it goes
Children turn a gear and count how many turns they made in 30 seconds. They compare the numbers — who more, who fewer.
Variants
Change the time, change the hand (10 sec., 1 minute).
Add word problems: “If I made 5 turns and you made 7, who made more and by how many?”.
Number Battle
Learning goal
Comparing randomly chosen numbers.
Needed elements
- A box of blocks
- Slips of paper with numbers
How it goes
They go to the box and take a “handful” or a “bucket” of blocks, then count how many they have of a given type. They compare the results in groups. A points game — the person with the greater number wins.
Variants
The teacher may draw challenges for counting, e.g. (which group has the most cylinders / connectors / red gears, and so on).
Encode a Number
Learning goal
Coding and comparing numbers.
Needed elements
- Gears
- Cylinders
- Platforms
How it goes
Together with the children we establish a value for particular pieces, e.g.: a straight connector has the value 1, a gear has the value 2, a cylinder = 3, a cross connector has the value 4, a platform has the value 5, and so on. You can use the proposed coding cards.
The children's task is to build a construction whose value is, for example, 35. Then we compare the constructions, checking which is taller, which is wider, and so on.
Variants
While building a construction we can introduce constraints — e.g. “you may not use more than 2 cylinders”.
Increasing Queue
Learning goal
Ordering numbers in increasing and decreasing order.
Needed elements
Different numbers of blocks placed in bags, one bag for each group.
How it goes
Each group arranges its number of blocks next to one another in a single row. Then the children arrange their rows in increasing or decreasing order. We count the blocks.
Variants
We rearrange the rows, setting them in increasing order, but we take into account the number of cylinders that were in the bags.
Equal, but Different
Learning goal
Creating sets with the same number of elements from different pieces.
Needed elements
- Gears
- Cylinders
- Platforms
How it goes
Children are to create two sets that have the same number of pieces but differ in the type of blocks (e.g. 3 cylinders = 3 gears).
Variants
A task in pairs — the partner guesses whether the sets are equal (we first compare “by eye”, first without counting and then we check).
Build the Difference
Learning goal
Determining the difference between numbers.
Needed elements
Various pieces.
How it goes
The pupil is given two numbers (e.g. 8 and 5). They build two sets from that many pieces and show the difference — by adding or taking away the missing blocks.
Variants
Reverse tasks — the child builds the difference, and a classmate guesses the numbers.
Change the number range — up to 20, up to 50.