Mathematics
Intermediate
50 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

Tables of Values: Input to Output

Explore how function machines transform numbers using rules. Build tables of values by working out input-output pairs for different rules, then practise reading and completing tables independently.

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    1 - Getting Started ~4 mins

    Here is a number machine with a rule inside it: × 3. When you put 4 in at the top, what number comes out the bottom? And what about 7?

    2 - Watch and Notice ~10 mins

    Watch four different machines, each with its own rule. The rule sits inside the machine and tells it what to do to every number you put in. The table beside each machine records the input-output pairs as they happen.

    Example 1: the × 3 rule

    Watch the table fill in: 4 goes in and 12 comes out, 7 goes in and 21 comes out, 10 goes in and 30 comes out, 0 goes in and 0 comes out.

    Example 2: the + 5 rule

    The rule changes. Now every input has 5 added on. Watch how the gap between input and output stays the same on every row.

    Example 3: a two-step rule, × 2 then + 1

    This machine does two things in a row. First it doubles the input; then it adds 1. So when 3 goes in, the machine doubles it to 6, then adds 1, and 7 comes out.

    Now watch what would happen if the machine did the two steps in the opposite order. If it added 1 first, 3 becomes 4. Then it doubles, and 8 comes out instead of 7. Same numbers, different order, different answer. That's why the order matters.

    Example 4: × 10 with a decimal input

    The same machine works on decimals too. When you put 0.5 into a × 10 machine, you get 5 out.

    3 - Try It Together ~9 mins

    Now you drive the × 3 machine together. You choose an input, the machine sends it through the × 3 rule, and the input-output pair lands in the table. The class watches the table grow, row by row, into the table of values for the × 3 rule.

    × 3 machine: try any input

    4 - Draw the Tables in Your Copy ~7 mins

    COPYBOOK MOMENT

    In your maths copy, draw two input/output tables. Write the rule at the top of each table, then fill in four input-output pairs underneath, using the inputs given.

    • Rule: × 3 — use the inputs 2, 5, 8, 10
    • Rule: × 2 then + 1 — use the inputs 3, 5, 7, 10

    5 - Class Challenge ~12 mins

    Today's challenge: build the table of values for five different rules in turn. The rule is shown at the top of each machine; your job is to work out what comes out for each of the four given inputs.

    Build the table for each rule

    Pupil practice
    Module 8 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 103 · Tables of Values: Input to Output
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