# 6.B.7. Circuits & venn diagrams

### 0. ABOUT

How can **Digital Making** take place at the intersection of Science, Math, and Computational Thinking?

We start with a look at Venn Diagrams, to give a mindset for the similarity of the Logic involved in each of the following components:

- circuits
- Boolean algebra
- logical operators and gates

### 1. VENN DIAGRAMS

A Venn diagram shows relationships among sets.

**1.A. An example with shapes**

For example, here are some shapes that belong to the set "quadrilaterals":

Remember that a quadrilateral is a 4-sided shape.

And here are some shapes that belong to the set "regular polygons":

Remember that a regular polygon is a shape with equal sides and equal angles.

Which shapes belong to the set of "regular quadrilaterals"?

We can represent this visually with a Venn diagram:

**1.B. An example with song lyrics**

In 1971, the singer-songwriter John Denver released his song: Sunshine on my shoulders.

The first line of this song is:

Sunshine on my shoulders makes me happy

We can represent this as:

sunshineAND shoulders = happy

And as a Venn diagram:

**1.C. Make your own Venn diagram**

Use your imagination to create your own Venn diagram relationship:

### 2. CIRCUITS

Let's build the Venn diagram below with a circuit.

We fold a piece of cardstock in half, and draw the following on the top side.

Then, inside the fold, we build this circuit, using: conductive tape, an LED, a 3V battery, and a clip to hold the battery in place.

We also add 2 short strips to close the switches when pressed from the other side.

When you close the fold and press on the dots (switches), the LED lights up.

If you close only one OR the other switch, the LED does not turn on.

If you close the first switch AND the second swirtch, the LED turns on.

This circuit is called a SERIES circuit.

Notice that all the components are in a single loop, so the current from the battery has only one path to follow.

### 3. WHAT'S THE BIG DEAL?

Venn diagrams and series circuits connect to mathematics, science and digital electronics.

**3.A. Mathematics** - Boolean algebra

Sets (like "all the quadrilaterals" or all the "regular polygons") and their relationships are an important part of math.

Let's look at sets A and B:

A = {1, 2, 3, 4}

B = {3, 4, 5, 6}

Here are 3 examples of relationships:

A

ANDB = {3, 4}A

ORB = {1, 2, 3, 4, 5, 6}A

NOTB = {1, 2}

**AND**, **OR** and **NOT** are 3 examples of how we can create relationships between sets.

Let's look at two new sets, C and D:

C = {20, 30, 40}

D = {40, 50, 60, 70}}

What would be the resulting sets in each of these relationships?

C

ANDD = { ................}C

ORD = { ................}C

NOTD = { ................}

All of this is part of the brach of mathematics called Boolean Algebra.

**3.B. Science** - electricity & circuits

In science you study electricity and circuits.

The SERIES circuit we looked at above is one example.

Another example is a PARALLEL circuit, which is shown below.

Notice that closing either switch will complete the circuit, and turn on the LED.

So, in the **SERIES** circuit, both the first switch **AND** and second switch must be closed.

And, in the **PARALLEL** circuit, either the first switch **OR** the second switch must be closed.

**3.C. Digital electronics** - logic gates

What makes smartphones smart?

Smartphones are smart because they can make decisions.

Let's consider the built-in alarm clock. Suppose you set it for 7 AM.

In order for the alarm to sound:

the clock must be set for 7 AM

ANDthe time must be 7 AM

This decision is made using an **AND logic gate**, illustrated below.

Boolean Algebra, circuits, and logic gates are different forms of similar ideas.

### 5. MAKING DECISIONS IN SCRATCH

Here is Scratch program that decides if the number you enter is **greater than 10** **AND**** less than 20**.

See and edit the code at scratch.mit.edu/projects/125851999/#editor

### REFERENCES

- Based on ideas discussed in: Hughes, J., Gadanidis, G. and Yiu, C. (2016). Digital making in elementary mathematics education.
*Digital Experiences in Mathematics Education*.