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.
$=$ 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, $x+7=10$.