Waiters’ Nightmare A single rectangular table can seat 6 hungry humans

Waiters’ Nightmare However, two rectangular tables can seat various numbers of hungry humans depending on the layout

You need to find the minimum and maximum number of hungry humans that can be fed, using different numbers of tables Number of Tables Smallest Number of Seats Largest Number of Seats 2 3 4 5 6 10

Your Mission Complete the layouts of seats on the diagram for two tables Fill in the results table Draw as many different layouts as possible for three tables. Add the seats, fill in the table with your results. Repeat for layouts of four tables and five tables. Investigation Tips Extension Tasks Clearly presented. Draw diagrams to help you. Use a pencil and ruler. Record your results in the table as you go. Look for patterns. Try and identify the term to term rule for the smallest number of seats Repeat for the largest number of seats Use these rules to predict the numbers for 6 & 7 tables. Draw out the tables for 6 & 7 to see if your predictions were right.

The Staircase Investigation This is the start of a sequence… How many cubes do you need for the 5th staircase? How many cubes for the 6th staircase? Can you find a rule linking the pattern number to the number of cubes used? Use your rule to find how many cubes you would need for the 10th staircase.

The Staircase Investigation This is the start of another sequence… How many cubes do you need for the 4th and 5th staircase? Can you find a rule linking the pattern number to the number of cubes used? Test your rule… Use your rule to find out how many cubes you need for the 10th staircase.

The Staircase Investigation Here is yet another type of stairway sequence… How many cubes do you need for the 4th and 5th staircase? Can you find a rule linking the pattern number to the number of cubes used? Test your rule… Use your rule to find out how many cubes you need for the 10th staircase.

Hints… Hints…. These are some quick ways you can use to count the total cubes used each time

Handshake Investigation Hints… Handshake Investigation If everybody in this classroom today shook hands with every other person, how many handshakes would there be? Begin by making a table and testing it out for 1 person, 2 people, 3 people, etc. You may like to try it out amongst you. Try and spot any patterns you may notice. There are a few different methods you can use to organise your working and record your results. Ask me for hint sheets if unsure.

Bunny Rabbits Investigation Hints… Bunny Rabbits Investigation In 1202, Fibonacci investigated about how fast rabbits could breed in ideal circumstances. One male and one female rabbit are put in a field after birth. Rabbits can mate at the age of one month, and it takes one month until the new bunnies are born. Hence, at the end of its second month a female can produce another pair of rabbits. Assume your rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. How many pairs will there be in one year?

Bunny Rabbits Investigation Hints… Bunny Rabbits Investigation At the end of the first month, they mate, but there is still one only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5….

Hailstone Sequence Investigation Hints… Hailstone Sequence Investigation

Hailstone Sequence Investigation Hints… Hailstone Sequence Investigation Investigation 1 Collatz believed that whatever number you start with, you will always end up with a 1. However, this has not been proven yet. Try out different ‘seeds’ and see if you agree or disagree with Collatz. Why? How long does it take for each of your sequences to reach 1? Can you predict the length of the sequence from the ‘seed’ chosen? Create at least one graph, with three different seeds, to show how the numbers ‘bounce’ around like a hailstone. Your graphs should look similar to this one 

Hailstone Sequence Investigation Hints… Hailstone Sequence Investigation Investigation 2

Hailstone Sequence Investigation Hints Hints for Investigation 2