# Trains

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Purpose

This problem solving activity has a measurement focus.

Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
Student Activity

Niko makes a train from three different coloured rods. ​

Kaia does too.

Niko's train is longer than Kaia's.

What coloured rods might each person have used?

Specific Learning Outcomes
• Compare two lengths (either directly or by calculation).
• Devise and use problem solving strategies to explore situations mathematically.
Description of Mathematics

This is an opportunity for the students to compare lengths. It can be done by calculation if students know the "value" of the Cuisenaire rods or by using the rods and comparing the lengths. Prior to beginning this unit, your students should have some experience with exploring number values with Cuisenaire rods.

Required Resource Materials
Activity

### The Problem

Niko makes a train from three different coloured rods.
Kaia does too.
Niko's train is longer than Kaia's.
What coloured rods might each person have used?

### Teaching Sequence

1. Begin the lesson by forming trains with Cuisenaire rods.  Show a train using 2 rods and ask the students to make a longer one (you could also demonstrate this digitally - search for interactive Cuisenaire rods). If the students have used the number values for the rods ask them to explain their working.
2. Pose the problem.
3. Brainstorm for ways to solve the problem (use equipment, addition) and ask how they can record their ideas.
4. Let the students work on the problem in groups of 2-3. As they work ask questions that focus their thinking on measurement:
Which is the longer train?
How do you know?
Can you think of another way that you could have found out which train was longer?
5. Share solutions.

#### Extension

Kaia's train is twice as long as Niko's. What coloured rods might each person have used? Incorporate fraction language (e.g. half, double).

### Solution

There are many possibilities. Have students refer to their recording and take turns to demonstrate their findings to the group/class.

#### Solution to the Extension

Have students demonstrate their findings by showing that two of Niko's trains can fit alongside Kaia's train.

If students know, and have used number values, listen for the language of half and double as they demonstrate their findings.

Attachments
Trains.pdf124.58 KB