Fish and Chips
This is a level 4 algebra strand activity from the Figure It Out series.
use a formula to continue a pattern
In this activity, students develop rules or formulae that can be used to determine the total prices for meals of fish and chips.
In question 1, the students use the Fresh Fish Shop’s display of their prices to make a “double-entry table” or ready reckoner that can be used to read off the price of a range of fish and chip orders. In question 2, however, only the formula for the total cost is given. The students must make a ready reckoner table from this formula and search the table to locate total charges of $24. Note that the table will need to be extended to 8 fish x 12 scoops of chips to cover every possibility. Some students will discover this by trial and error, but others may reason that 24 can be divided by both 3 and 2, which gives the possible orders 8 fish x $3 = $24 and 12 chips x $2 = $24 respectively.
Some students may argue that neither of these orders are orders of fish and chips and that there are really only three possible orders; strictly speaking, they are correct!
The table in the Answers shows five entries representing purchases of $24. These are:
Note the pattern in this table. For every 2 additional pieces of fish, 3 fewer scoops of chips can be bought for a purchase price of $24.
Answers to Activities
1. a $9.60
b. $21.00 (8 x 1.50 + 9)
c. t = 1.50 x f + 1.80 x c
2. a. i. $3.00
b. There are five possible solutions that give a total cost of $24: 8 fish and 0 scoops of chips, 6 fish and 3 scoops of chips, 4 fish and 6 scoops of chips, 2 fish and 9 scoops of chips, and 0 fish and 12 scoops of chips. A table similar to Andy’s
would look like the one on the following page (the $24 totals have been highlighted).