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# 4.1: Which Boxes

Difficulty Level: At Grade Created by: CK-12

You have lots of these boxes. If you wanted to make the pans balance, which boxes will you put in the empty pan? Can you solve this problem in more than one way?

### Guidance

In order to balance pans like the one above, use the problem solving steps to help you.

• First, describe what you see and what information you are given.
• Next, identify what your job is and what you are trying to solve. In all of these problems, your job will be to figure out which boxes to put in the pan. You want to make sure that the pans will balance.
• Third, make a plan for how you will solve.
• Fourth, solve the problem.
• Last, check your answer by making sure that the combinations of boxes you found add up to the amount that you needed.

For the problem above, since the left side weighs 10 pounds, you want to make sure the right side will also weigh 10 pounds.

#### Example A

Put boxes in the empty pan.

Make the pans balance.

Which boxes will you use?

Can you use a different set of boxes? Explain.

Solution:

We can use the problem solving steps to help us solve this problem.

#### Example B

Put boxes in the empty pan.

Make the pans balance.

Which boxes will you use?

Can you use a different set of boxes? Explain.

Solution:

We can use the problem solving steps to help us solve this problem.

#### Concept Problem Revisited

We can use the problem solving steps to help us solve this problem.

### Vocabulary

To be equal means to be the same. In this concept, we are trying to make weights equal. This means we are trying to make each side of the pan balance have the same weight.

### Guided Practice

For each problem, put boxes in the empty pan to make the pans balance. Can you find more than one answer?

1.

2.

3.

1. \begin{align*}J + J + J + J + J + J = 12 \ pounds\end{align*}

\begin{align*}K + K + K + K = 12 \ pounds\end{align*}
\begin{align*}J + J + J + K + K = 12 \ pounds\end{align*}
\begin{align*}J + L + L = 12 \ pounds\end{align*}
\begin{align*}J + J + K + L = 12 \ pounds\end{align*}

2. \begin{align*}R + R + R + R + R = 15 \ pounds\end{align*}

\begin{align*}R + R + R + S = 15 \ pounds\end{align*}
\begin{align*}R + S + S = 15 \ pounds\end{align*}
\begin{align*}R + R + Q = 15 \ pounds\end{align*}
\begin{align*}Q + S = 15 \ pounds\end{align*}

3. \begin{align*}W + W + W + W = 16 \ pounds\end{align*}

\begin{align*}Y + Y = 16 \ pounds\end{align*}
\begin{align*}W + X + X = 16 \ pounds\end{align*}
\begin{align*}W + W + Y = 16 \ pounds\end{align*}

### Explore More

For each problem, put boxes in the empty pan to make the pans balance. Can you find more than one answer?

## Date Created:

Jan 18, 2013

Dec 29, 2014
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