Lesson 2: Use multiplication, addition, or subtraction to solve multi-step word problems.

Property

Deconstruct a multi-step word problem by first identifying the final question and then finding the "hidden question" that must be answered first. Use a model, like a tape diagram, to visualize the relationship between the parts and determine the correct sequence of operations to solve the problem.

Examples

Property

To model a multi-step problem involving 3-digit by 1-digit multiplication, a tape diagram can be used to visualize the relationship between quantities. For a problem where you have $n$ equal groups of size $X$ and another part $Y$, the total $T$ can be represented as:

Examples

• A school bought 4 printers. Each printer cost 125 dollars. They also bought paper for 45 dollars. What was the total cost?
• Tape Diagram: A tape with four equal units labeled 125 and one smaller unit labeled 45. The total is marked with a question mark.
• Equation: $(4 \times 125) + 45 = T$
• Javier had 500 dollars. He bought 3 video games for 110 dollars each. How much money does he have left?
• Tape Diagram: A whole tape labeled 500. A part of the tape is sectioned into three equal units labeled 110. The remaining part is marked with a question mark.
• Equation: $500 - (3 \times 110) = M$

Explanation

A tape diagram helps you visualize and organize the information in a complex word problem. For problems involving multiplication of a 3-digit number, you can draw equal-sized boxes to represent the repeated groups. This visual model makes it easier to see what operations are needed, such as adding an extra amount or subtracting from a total, to find the final answer.