Algebra Readiness Made Easy Grade 6

BLOCKY BALANCE

• What does it mean that two pans are balanced? (The total

weight of the blocks in each pan is the same.)

• What do you need to find out? (How many cubes will bal-

ance 12 spheres.)

• How many spheres will balance 1 cylinder? (2)And 4

cylinders? (8)And 6 cylinders? (12)

• Why did Ima start with the first pan balance? (She could

figure out that the weight of 1 cylinder equals, or balances,

2 spheres.)

• Inthe second pan balance, if you substitute 2 spheres for

each cylinder, how many spheres will be in the pan on

the left? (12)

Work together as a class to answer the questions in “Solve the Problem: Blocky

Balance.”

Math Chat With the Transparency

Display the “Make the Case: Blocky Balance” transparency

on the overhead. Before students can decide which char-

acter’s “circuits are connected,” they need to figure out

the answer to the problem. Encourage students to work in

pairs to solve the problem, then bring the class together

for another whole-class discussion. Ask:

• Who has the right answer? (CeCe Circuits)


• How did you figure it out? (In the first pan balance, 3 cubes

balance 6 spheres. So, 1 cube (3 ÷3) balances 2 spheres (6 ÷3).

In the second pan balance, substitute 1 cube for every 2 spheres.

Then 2 cubes balance 2 cylinders. So,8 cubes (4 x2) will bal-

ance 8 cylinders (4 x2).)

• How do you think Boodles got the answer 12? (Boodles

may have multiplied both the number of cylinders and the number of cubes shown by 4. So,

in the second pan balance, Boodles multiplied the 2 cylinders by 4 to get 8 cylinders, and then

multiplied the 3 cubes in the first pan balance by 4 to get 12 cubes.)

• How do you think Mighty Mouth got the answer of 9 cubes? (He may have added 6

cylinders to the cylinders in the second pan balance to get 8 cylinders, and likewise added the 6

cubes to the number of cubes in the first pan balance to get 9 cubes.)

43

BLOCKY BALANCE

Name _____________________________________________ Date __________________

44

I’ll start with the first pan balance. Since

4 spheres weigh the same as 2 cylinders,

then 2 spheres (4 ÷ 2) will balance 1 cylinder

(2 ÷ 2). Now I can substitute spheres for

cylinders in the second pan balance.

1 .Why did Ima start with the first pan balance?

__________________________________

__________________________________

2.How many cubes balance 12 spheres? _______

3.How did you figure it out? __________________________________

______________________________________________________

4.If 1 cylinder weighs 12 pounds, what’s the weight of 1 sphere? _______

5 .If 1 cube weighs 6 pounds, what’s the weight of 1 sphere? _______

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How many cubes will balance 12 spheres?
All objects of the same shape are equal in weight.
Ima Thinker
BLOCKY BALANCE
Name _____ Date __
Whose circuits are connected?
MAKE
CASETHE How many cubes will balance 8 cylinders?
All objects of the same shape are equal in weight.
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Mighty Mouth
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CeCe Circuits
No way.
It’s 12 cubes.
You’re wrong.
I am sure
it’s 8 cubes.
The answer is
9 cubes.
Algebra Readiness Made Easy: Grade 6 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources