Upon completion of the Balanced and Equal pages, ask:
- What combination of gram masses could you use to
show 136 grams? (Possible responses: [list number
sentences as students share them]
100 + 10 + 10 + 10 + 5 + 1; 50 + 50 + 20 + 10 + 5 + 1; 50 + 10 + 50 + 10 + 10 + 5 + 1)
- In Question 8D, Sam says the order in which you
add numbers in a number sentence matters. He says
if you start with a larger number, you will get a larger
sum than if you start with a smaller number. Do you
agree with Sam? Does the order in which you add
the numbers in the sentence matter? Give an example.
(The order doesn’t matter. Possible response:
For example, 50 + 50 + 20 + 10 + 5 + 1 + 1 = 5 + 10 + 20 + 50 + 50. You can add the numbers
in any order and still get the same sum.)
Display the number sentence 50 + 10 + 50 + 10 + 10 + 5 + 1.
- Look at this number sentence. Does the way in
which you group and add the numbers in the sentence
matter? How would you group and add the
numbers? (No. you can group the numbers in a
way that makes sense to you. Possible response:
I’d group the 50s to make 100, the three 10s to
make 30, and then add on the 5 + 1.)
Combine two of the suggested number sentences to
make a true number sentence and ask:
- Does [100 + 10 + 10 + 10 + 5 + 1 = 50 + 50 + 20 + 10
+ 5 + 1]? How do you know? (Possible
response: Yes, because I can add up all the numbers
and each side is the same.)
- Can you tell that these number sentences are true
without adding the numbers? Explain. (Possible
response: I know they are true because I can match
up equal values on both sides of the equal sign.
100 matches with two 50s. Two 10s match with 20.
Then there is 10 + 5 + 1 on both sides. I don’t
have to add them up because I know the same
value is shown on each side of the equal sign.)
To emphasize relational thinking, display number sentences such as the following
and ask:
- Is this number sentence true:
10 + 5 + 10 + 5 = 9 + 6 + 9 + 6? How can you
tell without adding? (Possible response: There are
10s and 5s on one side of the equal sign. There are
9s and 6s on the other side. The 10 is one more
than the 9 on the other side, but the 6 is one more
than the 5 on the other side so it balances out. Both
sides end up showing the same value.)
- Is this number sentence true: 987 + 50 + 12 + 100 = 50 + 987 + 12 + 100? How can you tell without
adding? (Both sides show the same amounts, so it is a true number sentence.)
- What would make this number sentence true:
100 + 200 + 300 = 300 + 200 + ? (100)
- Why do you think this lesson is called “Balanced
and Equal”? (Possible responses: If the pans on the
scale balance, the values of the masses in each pan
are equal; the equal sign in the expression is like a
balance. Whatever is on one side of the equation
“balances” or equals what is on the other side.)
