Displays the Getting started on page 163.
You could extend this by looking at other Fibonacci patterns in nature.
Teaching ideas
This link displays three growing patterns, three tables and three expressions that give the rule for the pattern. Ask students to match each pattern with its table and expression.
You could display this activity on a write-on surface and draw lines to match them up.
Students could substitute some of the values into the expressions to see which ones work.
Once the correct matches have been made, students are asked “What do you notice about the number multiplying n and the difference between the numbers in the table?”
Teacher notes
- You may need to recap how to write expressions and remind students that a multiplication sign is not written between a number and a letter.
- Encourage students to look at both the patterns and the numbers in the table to help work out the expression.
Teaching ideas
Ask students to draw a simple two-step function machine like the one on page 173.
Ask them to choose two operations to put into the boxes.
Give them five numbers to put into the machine and work out what will come out the other end.
Ask them to draw their own input/output table for their machine.
Group the students and ask them to play “Guess my rule” by looking at the input/output table of one of the students.
The first person who guesses correctly explains how they worked it out.
It is then someone else’s turn to show their input/output table.
Teacher notes
- Emphasise that the order of the operations is important and that x 3 + 2 is different from + 2 x 3.
- The relationship between two variables can be represented by a table, a rule or a graph.
A linear relationship is characterised by a straight line on a graph or a regular amount added on or taken off between terms on a table. Example: Cost of Mr Fixit = 50h + 30 will be a straight line.
Teaching ideas
This link displays the instructions for students to gather the information to draw their own distance-time graph and answer questions about it.
This link displays some photos of dogs which are all different shapes and sizes. Students are asked to represent each dog by putting dots on a graph of height versus weight.
Discuss the relative positions of the dots.
Other resources
This link is to “turtle maths”. You can make patterns using Logo.
https://nrich.maths.org/1532
Teacher notes
- Guess (or estimate) and check is a useful technique for students to know.
