What do kids think about equality? Let's ask!

What number would you put in the box to make this a true number sentence?

$$8+4 = \square + 5$$Source: Thinking Mathematically

Percentage of various responses per grade level

Response | 7 | 12 | 17 | 12 and 17 | |

Grade | |||||

1st and 2nd | 5 | 58 | 13 | 8 | |

3rd and 4th | 9 | 49 | 25 | 10 | |

5th and 6th | 2 | 76 | 21 | 2 |

The correct answer is certainly $7$,

but $12$ is not exactly an unreasonable response

What's the difference between $$8+4 = \square + 5$$ and $$8+4 = x + 5?$$

Not much that I can see.

to solving $x+5=12$

Subtract $5$ from both sides.

If $x+5=12$, then $(x+5)-5=12-5$ so $x=7$.

In relational thinking, we consider the relationship between quantities. Often, we can solve algebraic expressions without doing significant computation.

What value of $x$ makes the following statement true?

$$123-115 = 54-x$$

Sometimes, we simply think about whether an expression is true or false.

- $3-8 = 42-47$
- $2x-7x = x-6x$
- $2x-7 = x-6$
- $2x-7 = 2x-6$

$=$ vs $==$

Javascript uses `=`

to set a variable to a value.

```
In :
x = 2;
x
Out:
2
```

```
In :
x + 3;
Out:
5
```

Javascript uses `==`

to check if a variable has a certain
value. The result is either `true`

or `false`

.

```
In :
x == 2
Out:
true
```

```
In :
x + 3 == 4;
Out:
false
```

You don't have to take my word for any of this!

Let $x=3$. Then, $x+7=10$.