Inputs and outputs | MathIsland

Can you find an output without the previous row?

Under the rule “add 2”, add two to each input. Reordering the rows does not change the pairs.

Imagine a box that adds two blocks to whatever you put in. An input of three gives five. The input 3 and output 5 form a pair.

Input means the number put in; output means the number that comes out. Input 0 corresponds to output 2; input 1 to output 3. Write inputs and outputs in separate table columns.

For input 4, compute 4+2=6 without reading any previous row. The two is added to the input. It is not automatically added to the previous output.

Reorder the inputs as 4, 0, 2, and the outputs are 6, 2, 4. The correspondence is unchanged. Check the rule within each row instead of memorizing the rows in order.

Adding two and doubling differ. Both give 4 from input 2, but input 3 gives 5 and 6 respectively. Agreement on one example does not make two rules identical.

This activity assigns one output to each input, a useful idea for functions later. An add-two correspondence is not direct proportion. Proportion requires a constant multiplier, which must be checked separately.

Listen one paragraph at a time

1 / 6

2 / 6

3 / 6

4 / 6

5 / 6

6 / 6

Hold on to this distinction

Point to input 4 and output 6 in one row. Two was added to 4, not to the previous row’s answer.

Change it and check

Switch between add-two and double, choose an input, and match it to its output in the table.

Rule applied to the inputInput

3 + 2 = 5

Reordered rows: apply the rule to this row’s input, not the previous output.
Input	Output
4	6
0	2
2	4
5	7
1	3
A: 3	5

Try input 3 in both rules. Are the outputs equal?

Compare these rules on integer inputs 0 to 5. Formal lessons on functions, coordinate graphs and proportions follow later.

Try with paper and objects

Lay input cards 4, 0, 2 and attach outputs under add-two. Shuffle the rows and check that the pairs remain the same.

Check and explain another example

Check your idea 1

The rule is add 2. What is the output for input 5?

Check your idea 2

After reordering an add-two table, what is the output for 0?

Apply it in a new setting

There are two sweets per bag and three bags. Under doubling, what output matches input 3?

Write an answer yourself

Return to the explanation

Compare with a solution

6 · number only

4+2=6.

Does your explanation include these ideas?

Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.

Name an input-output pair.Use the rule after rows are reordered.Distinguish adding from multiplying.

Continue, or pause here

Choose a reference zero and unit, then read negative positions.