Question

1. stem connection an ocean engineer used a sonar system to count fish populations of four schools of fish.

\

$$\begin{array}{|c|c|} \\hline \\text{school} & \\text{number of fish} \\\\ \\hline 1 & 234 \\\\ \\hline 2 & 536 \\\\ \\hline 3 & 1,112 \\\\ \\hline 4 & 189 \\\\ \\hline \\end{array}$$

a. how many fish were counted?

b. the sonar used to count the fish is not always accurate, it can have an error of counting 10 fish too many or 10 fish too few for every 1,000 fish. would it be reasonable to say that there could be 2,090 fish in all four schools? explain.

1. extend your thinking gina used the following equations to solve a multi-step problem. write a word problem that can be represented by the equations.

step 1: \\(5,700 - 2,200 = 3,500\\)
step 2: \\(3,500 - 1,545 = 1,955\\)
step 3: \\(5,700 + 3,500 + 1,955 = 11,155\\)

reflect
how do you decide whether to write an addition equation or a subtraction equation for each step in a problem?

Explanation:

Sum the fish counts

Using the Multi-digit Addition knowledge point, we calculate the total number of fish counted across all four schools:

$$ 234 + 536 + 1,112 + 189 = 2,071 $$

Determine the error range

Using the Word Problems knowledge point, we analyze the sonar error. The error is \(\pm 10\) fish for every \(1,000\) fish. Since the total count is \(2,071\) (which is approximately \(2,000\) fish), the maximum expected error is:

$$ 2 \times 10 = 20\text{ fish} $$

This gives a reasonable range of:

$$ 2,071 - 20 = 2,051 \quad \text{to} \quad 2,071 + 20 = 2,091 $$

Since \(2,090\) falls within this range \([2,051, 2,091]\), it is a reasonable estimate.

Create a word problem

Using the Multi-step Word Problems knowledge point, we write a scenario matching the three given equations:

• Step 1: \(5,700 - 2,200 = 3,500\)
• Step 2: \(3,500 - 1,545 = 1,955\)
• Step 3: \(5,700 + 3,500 + 1,955 = 11,155\)

Scenario: A store has three branches. Branch A has \(5,700\) books. Branch B has \(2,200\) fewer books than Branch A. Branch C has \(1,545\) fewer books than Branch B. How many books do all three branches have in total?

Explain equation choice

We decide based on the action described in the problem:

• Use addition when combining groups, finding a total, or increasing an amount.
• Use subtraction when taking away, comparing differences, or finding a remaining amount.

Answer:

Question 5a

\(2,071\) fish

Question 5b

Yes, it is reasonable. The total counted is \(2,071\) fish. Since \(2,071\) is about \(2,000\), the sonar can have an error of up to \(20\) fish too many or too few. This makes the reasonable range \(2,051\) to \(2,091\) fish. Since \(2,090\) is within this range, it is a reasonable estimate.

Question 6

A library system has three branches. Branch A has \(5,700\) books. Branch B has \(2,200\) fewer books than Branch A. Branch C has \(1,545\) fewer books than Branch B. How many books do the three branches have altogether?

Reflect

You write an addition equation when you need to combine groups, find a total, or show an increase. You write a subtraction equation when you need to take away an amount, compare two quantities, or find a remaining part.