The purpose of this unit of two lessons is to develop relational thinking through the exploration and expression of the relationship between two related number patterns.
In mathematics, a function is the relationship between two number sets, often referred to as inputs and outputs. What characterises this relationship is that one ‘input’ is paired with one single ‘output’.
Through exploring functional relationships, students are introduced to ways of expressing these relationships, including function diagrams (or machines), tables, graphs, equations, and ‘mapping’ diagrams. All of these provide a visual image of the relationship between two number sets. The early introduction of this enables students to show relationships between important elements in their lives, such as their relationship to other family members.
Students may also encounter this expression of a relationship in a pictorial mind map of ideas, where the relationship between one idea and another is depicted with an arrow or similar ‘mapped’ connection.
In relationship diagrams such as this:
2→4
3→6
4→8
5→10
This means one value is matched with, or mapped onto, one other value. In exploring the number relationships in these diagrams, students develop their understanding of a unique paired relationship between variables.
The mapping diagram is a clear visual representation of the special relationship that exists between the pairs of numbers, as demonstrated by arrows. When looking at the whole set of mapped values, students must consider the relationship that is common to all pairs. They should look for the ‘rule’ that explains what is happening between the numbers. This will explain how the variables in one set are related to the variables in the other set.
It is important for students to have opportunities to both interpret and create sets of mapped pairs. When students create their own diagrams for others to interpret, they must generate the values of the mapped pairs, thinking about the relationship that connects the numbers.
This exploration of mapped values is essential to a student’s understanding of coordinate pairs. As a student interprets and represents a situation on a relationship graph, they apply this understanding. Locating uniquely paired numbers on the (xy) coordinate system allows them to represent the relationship in another way. Students need opportunities to identify the connections between ‘mapped pairs’, ‘mapping’, coordinate systems and graphs that show relationships. These two lessons introduce these concepts.
Links to the Number Framework
Advanced counting (Stage 4)
Early additive (Stage 5)
Early multiplicative (Stage 6)
The learning opportunities in this unit can be differentiated by providing or removing support to students and varying the task requirements. Ways to support students include:
The contexts for this unit can be adapted to suit the interests and experiences of your students. For example:
Te reo Māori kupu such as tauira (pattern), ture (rule), and tatau (count) could be introduced in this unit and used throughout other mathematical learning.
Session 1
Activity 1
Activity 2
Activity 3
Session 2
Activity 1
Activity 2
Dear families and whānau,
In class we have been mapping relationships between data sets and making relationship graphs. Talk about the two attached pictures with your child and have them explain what they have been doing. They will show you how to make a mapping diagram and a graph related to one of the pictures. Take your turn to complete the task with the other picture and ask your child for their feedback on your work.
Enjoy the challenge and the discussion.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/mapping-relationships at 8:39pm on the 26th February 2024