Chapter VII
Measuring the Length of Segments
Why is it worth teaching length measurement?
The skill of measuring length is one of the basic mathematical competencies developed in early-school education. A child who can determine the length of an object or a segment not only learns to use a unit of measure, but above all understands size relationships, develops spatial orientation, and logical thinking.
In grades 1-3 measurement should not be only a record in a notebook - it is first of all action, handling materials, comparing, and experimenting. Measuring with a ruler, comparing lengths using the body (e.g. steps), or creating one's own measuring tools are actions that allow pupils to fully understand the idea of length.
Blocks support this stage of learning very well. Thanks to the different sizes and shapes of the pieces (gears, cylinders, connectors, platforms) children:
- can build segments and measure them using measuring tools they have constructed themselves,
- understand that length depends not only on the number of pieces, but also on their type,
- learn to estimate, convert, and compare lengths in concrete situations,
- develop the skill of spatial thinking and organization.
Activities involving measuring length with blocks teach children a practical approach to mathematics - one that makes sense and has use in everyday life.
After completing the chapter, the pupil:
- Understands the idea of length as a feature of a segment or object that can be measured using a unit.
- Measures the length of simple segments using standard units (e.g. a ruler) and non-standard units (e.g. blocks).
- Builds segments of a given length, using a chosen type of piece.
- Compares the lengths of different segments, using the terms: longer, shorter, the same.
- Uses the mathematical signs >, <, = in the context of comparing lengths.
- Measures lengths using different units of measure, understanding that units may have a different value.
- Creates and uses their own measuring tools from blocks to measure the length of objects.
- Makes measurements of the length of broken and straight segments and can record them as a sum.
- Solves word problems about length (e.g. by how much is segment A longer than segment B?).
- Uses length measurement in the context of building spatial constructions and routes (e.g. marking a route from point A to B).
We Measure Length
Learning goal
Introducing the idea of the length of a segment and a unit of measure.
Needed elements
- Cylinders and straight connectors
- Painter's tape
How it goes
The teacher marks segments of different lengths on the floor with painter's tape. Pupils in groups (e.g. the red, blue, green, yellow group) join cylinders in their group's colors using connectors into a measuring tool that should be the length of the measured segment. Then they count how many cylinders they used to measure the length.
Variants
Change of unit: measuring with gears arranged one next to another along the tape line.
Comparing the results with a ruler or a meter tape.
Which Segment Is Longer
Learning goal
Comparing the lengths of different segments.
Needed elements
- Blocks
- Paper and a pencil for each group
How it goes
Children build two segments from cylinders and straight connectors. Then they compare the lengths by placing them next to each other or by counting.
Variants
Introducing the signs >, <, =.
Building segments from the same number of pieces (e.g. one segment from joined cylinders, another from gears arranged next to one another, another from platforms joined together).
We Build to Size
Learning goal
Creating constructions of a given length.
Needed elements
- All types of blocks
- A ruler (or paper meter tapes)
How it goes
The teacher gives a length (e.g. 35 cm). Children are to build a segment from blocks arranged next to one another of that length - using any pieces.
Variants
Building in teams, who comes closest to the target.
From Point A to Point B
Learning goal
Measuring the length of a segment between two points.
Needed elements
- A platform with points A and B marked
- Connectors
How it goes
Children build a route from point A to B, then count its length - how many pieces they used to join the two points (e.g. from a desk to the door). The result can be recorded as an operation (e.g. 25 cylinders plus 15 gears plus 5 connectors is 45 pieces altogether).
Variants
Different routes between the same points.
The shortest / longest possible route / exchanging pieces so that there are as few of them as possible.
Block Measuring Line
Learning goal
Building one's own measuring tool from blocks and measuring with it.
Needed elements
- Cylinders and connectors
- e.g. 4 platforms
How it goes
Pupils create a measuring line from pieces (e.g. 1 unit = 1 cylinder). Then they measure various things in the classroom or constructions they have built.
Variants
Comparing the lengths of different measuring tools.
Converting into centimeters (using a paper measure 1 m long).
Chain of Lengths
Learning goal
Adding the lengths of successive segments.
Needed elements
- Platforms
- Gears
- Cylinders
- Connectors
How it goes
Children build 3 short segments and measure each one separately. Then they join them into a whole and measure the total length.
Variants
Building the longest measuring tool using all the cylinders and connectors.
Length and the Number of Pieces
Learning goal
Understanding that length is not always the number of pieces.
Needed elements
- Gears
- Cylinders
- Connectors - of different lengths
How it goes
Children build two segments from different numbers of pieces (e.g. 5 gears vs. 3 cylinders). They measure and compare: more pieces is not the same as longer.
Variants
Observing the relationship: length of one piece - number of pieces.
Recording it as multiplication operations.
We Measure Turns
Learning goal
Estimating the length of a broken line.
Needed elements
- Cross connectors and cylinders
- Platforms
How it goes
Children build a broken line (e.g. the shape of the letter L) and measure the length of each part, then add them up. Different units can be used (blocks, a ruler).
Variants
Reproducing the route as a robot (10 cylinders - 10 steps), checking how large the line would be if each piece were the length of one step.
Comparing broken and straight segments of the same total length or made from the same number of pieces in a straight line.
Your Step, Your Length
Learning goal
Comparing lengths using non-standard units (e.g. the length of a step).
Needed elements
- Platforms as a path
- Painter's tape
- A measuring tape
- Cylinders and connectors
How it goes
The teacher marks a segment using tape. Children measure how many steps or elbows are needed to walk the given route. Then they build their own measuring tool. They may build their own step measure from 3 joined cylinders and check how many such measures fit into the marked segment. Children may then change the step measure to a larger or smaller one to compare again.
Variants
Comparing their own results (steps, elbows) with other children.
Measuring different routes in the classroom.
Length Game
Learning goal
Using the idea of length in play.
Needed elements
- Blocks
- A die
- Cards with tasks
How it goes
A board game - the child rolls a die and builds a segment from as many pieces as the number of pips. We check which segment is the longest. Segments can also be built upward, placing a platform as a base. Two dice can also be used, to practice addition or, in older grades, multiplication.
Variants
A game: the teacher marks a longer segment on the floor with painter's tape. By rolling a die, children get information about how many pieces they must join in a given round. The winner is the person who first builds a measuring tool equal to the marked route.
Adding extra challenges, e.g.: if your measuring tool consists of 5 pieces of the same color, you may take two extra blocks.