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|
|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.
$=$ vs $==$
= to set a variable to a value.
In : x = 2; x Out: 2
In : x + 3; Out: 5
== to check if a variable has a certain
value. The result is either
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, $x+7=10$.