# 3.2: How Many Pounds

**At Grade**Created by: CK-12

Look at the pictures below.

Can you figure out the total number of pounds for the scale in the third picture (C)? In this concept, we will practice finding the total weight of collections of blocks.

### Guidance

In order to solve the problem above, use the problem solving steps.

- Start by
**describing**what information is given. - Then, identify what
**your job**is. In these problems, your job will be to figure out the total weight of the blocks in the third scale. - Next, make a
**plan**for how you will solve. In these problems, write the weight of each block on the block and then add the weights together to find the total weight. - Then,
**solve**the problem. - Finally,
**check**your solution.

#### Example A

Figure out the total number of pounds. Write the number on the scale.

**Solution:**

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

\begin{align*}& \mathbf{Describe:} && \text{Three scales with blocks.}\\ &&& \mathbf{1st:} \ \text{the orange shape is} \ 5 \ \text{pounds.}\\ &&& \mathbf{2nd:} \ \text{the green shape is} \ 2 \ \text{pounds.}\\ &&& \mathbf{3rd:} \ \text{one orange shape and} \ 1 \ \text{green shape. No number of pounds.}\\ & \mathbf{My \ Job:} && \text{Figure out the total number of pounds for the third scale.}\\ & \mathbf{Plan:} && \text{Write the numbers of pounds on the blocks on the third scale}.\\ &&& \text{Add to figure out the total number of pounds.}\\ & \mathbf{Solve:} && \text{There are 5 pounds for the orange shape and 2 pounds for the green shape}.\\ & \mathbf{Check: } && \ 5 + 2 = 7 \end{align*}

#### Example B

Figure out the total number of pounds. Write the number on the scale.

**Solution:**

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

\begin{align*}& \mathbf{Describe:} && \text{Three scales with blocks.}\\ &&& \mathbf{1st:} \ \text{the orange shape is} \ 5 \ \text{pounds.}\\ &&& \mathbf{2nd:} \ \text{the green shape is} \ 2 \ \text{pounds.}\\ &&& \mathbf{3rd:} \ \text{one orange shape and} \ 3 \ \text{green shapes. No number of pounds.}\\ & \mathbf{My \ Job:} && \text{Figure out the total number of pounds for the third scale.}\\ & \mathbf{Plan:} && \text{Write the numbers of pounds on the blocks on the third scale}.\\ &&& \text{Add to figure out the total number of pounds.}\\ & \mathbf{Solve:} && \text{There are 5 pounds for the orange shape and 2 pounds for the green shapes}.\\ & \mathbf{Check: } && \ 5 + 2 + 2 + 2 = 11 \end{align*}

#### Example C

Figure out the total number of pounds. Write the number on the scale.

**Solution:**

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

\begin{align*}& \mathbf{Describe:} && \text{Three scales with blocks.}\\ &&& \mathbf{1st:} \ \text{the orange shape is} \ 5 \ \text{pounds.}\\ &&& \mathbf{2nd:} \ \text{the green shape is} \ 2 \ \text{pounds.}\\ &&& \mathbf{3rd:} \ \text{2 orange shapes and} \ 2 \ \text{green shapes. No number of pounds.}\\ & \mathbf{My \ Job:} && \text{Figure out the total number of pounds for the third scale.}\\ & \mathbf{Plan:} && \text{Write the numbers of pounds on the blocks on the third scale}.\\ &&& \text{Add to figure out the total number of pounds.}\\ & \mathbf{Solve:} && \text{There are 5 pounds for the orange shapes and 2 pounds for the green shapes}.\\ & \mathbf{Check: } && \ 5 + 5 + 2 + 2 = 14 \end{align*}

#### Concept Problem Revisited

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

\begin{align*}& \mathbf{Describe:} && \text{Three scales with blocks.}\\ &&& \mathbf{A:} \ \text{one cube is} \ 4 \ \text{pounds.}\\ &&& \mathbf{B:} \ \text{one cylinder is} \ 2 \ \text{pounds.}\\ &&& \mathbf{C:} \ \text{one cube and} \ 2 \ \text{cylinders. No number of pounds.}\\ & \mathbf{My \ Job:} && \text{Figure out the total number of pounds for scale} \ C.\\ & \mathbf{Plan:} && \text{Write the numbers of pounds on the blocks on} \ C.\\ &&& \text{Add to figure out the total number of pounds.}\\ & \mathbf{Solve:} \end{align*}

\begin{align*}\mathbf{Check: } \ 4 + 2 + 2 = 8 \end{align*}

### Vocabulary

** Substitution** is when you replace one object or value with an equal object or value. In this concept, we used substitution when we recorded the weight of each block on the actual block.

### Guided Practice

Figure out the total number of pounds on each scale. Write the number on the scale.

**Answers:**

- 20 pounds
- 18 pounds
- 22 pounds

### Practice

Use the following picture for problems 1-3.

Figure out the total number of pounds. Write the number on the scale.

Use the following picture for problems 4-6.

Figure out the total number of pounds. Write the number on the scale.

Use the following picture for problems 7-9.

Figure out the total number of pounds. Write the number on the scale.

Use the following picture for problems 10-12.

Figure out the total number of pounds. Write the number on the scale.

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### Image Attributions

Students determine the total weight of various collections of blocks by recording the weight of each block and adding these weights together. They will use the problem solving steps to solve. This is an early introduction to the concept of substitution, a key skill in algebra.