Lesson Plan
Number Crunching Machines
“WHAT’S MY RULE?”
Curriculum Outcomes
Introduce the concept of variables as a way of representing numbers using letters
Create algebraic expressions and evaluate them by substituting a given value for each variable
Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point
Equipment
Rewards, whiteboard markers, graph paper, students will need pens, pencils, ruler and working
paper
1. Introduction
Begin lesson by introducing the concept of the number crunching machine. A “IN” number
goes in and then the machine follows a rule and produces an “OUT” number.
The rules will be linear made up of multiplying by a number and then adding or subtracting
another number. We will start with whole numbers however can be extended to fractions and
directed numbers
Question to students
The rule will not be add 6 then subtract 2 or x2 x3 ? WHY?
So the rule will be X ___ add or subtract ___
Students should pick whole numbers up to 10
Ex 0, 1, 2…..9, 10
If they have prior knowledge of operations on directed numbers they could choose IN
numbers between -10 and 10
2. Start playing the Game
WHAT’S MY RULE???
Draw a table on the board as below or
IN
OUT
Interactive websites with number crunching machines
http://www.shodor.org/interactivate/activities/WholeNumberCruncher/
http://www.mathplayground.com/functionmachine.html
Think of a rule: start with something simple like x2 +3
write down the rule on a scrap of paper so you don’t forget the rule used each game
Students give you an IN number, write it on the board, then calculate the corresponding OUT
number
For example using the rule above IN number 3 would give OUT number 9
Repeat this with various numbers until one of the students are able to find the rule. Give this
student a reward (class star, sticker etc). The student will probably say “x2 +3” write this on the
board as
OUT = 2 X IN + 3
Repeat with other rules adjusting the difficulty of the rules depending on how the students
are picking it up. Some examples in increasing difficulty are below
OUT = 3 X IN + 4
OUT = 5 X IN + 10
OUT = 2 X IN - 7
OUT = 7 X IN
OUT = 1/2 X IN + 1/4
Students may start to look for strategies to find the rule as they play, these are some
below
What happens when the IN number is ‘0’. When we multiply any number by 0 the answer
is 0 so the answer must be what we add or subtract
By choosing consecutive IN numbers the OUT numbers have a difference of the number
we are multiplying by. This is called the first difference and it is constant for linear rules.
3. Introduce Variables
Replace IN and OUT with x and y, and play some more rounds of the game using
variables.
4. Consolidate Activity in Pairs
Students to rule up about three tables each in their books (x and y) and in pairs play the
game with each other. Walk around the room, seeing if pairs of students are
understanding what to do, informative assessment
5. Plotting values in a Cartesian Plane
Hand out graph paper to students. Draw a Cartesian plane 0 < x < 10 and 0 < y < 20
On the board for students to copy. Give an example how to transfer the table values as
graph points. Get students to repeat with one of their own graphs. What do they notice
about the points.
SUGGESTED FOLLOW ON LESSONS (Australian Curriculum)
This introductory activity gives students an introduction to variables. From here students could
begin measurement – using formulas for areas of rectangles, triangles and parallelograms and
use these in problem solving
Access to Algebra Unit 1 Pages 27 - 29
Worksheet from enrich–e–matics Anne Joshua