## Lesson Objective

The lesson is aligned to the Common Core State Standards for Mathematics – 4.OA.3 Operations and Algebraic Thinking – Solve multistep word problems posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

## Materials Required

Calculators

## Using Multiplication to Solve Word Problems involving Multiplicative Comparisons

**Part A**

Look at the word problem below.

Daniel’s dog weighs 2 times as much as Edward’s dog does. Edward’s dog weighs 28 pounds. How many more pounds does Daniel’s dog weigh than Edward’s dog?

To solve this word problem you will need to use two operations. You will need to use multiplication and then subtraction.

First, the weight of Daniel’s dog is unknown. Let *d* represent the weight of Daniel’s dog.

*d* = 2 x 28

*d* = 56

Daniel’s dog weighs 56 pounds.

Second, find the difference between the weight of Daniel’s dog and the weight of Edward’s dog. Let *w* = the difference.

*w* = 56 – 28

*w* = 28 pounds

Daniel’s dog weighs 28 more pounds than Edward’s dog.

**Part B**

Look at the word problems below. Write the equations for each word problem. Solve the equations and label your answers.

- Nathan’s dog weighs 72 pounds. Nathan’s dog weighs 3 times as many pounds as Thomas’ dog. What is the combined weight of Nathan’s dog and Thomas’ dog?
- Kevin’s dog weighs 4 times as many pounds as Gene’s dog. Gene’s dog weighs 15 pounds. What is the difference, in pounds, between the weight of Kevin’s dog and Gene’s dog?

**Answers:**

- First, let
*t*= the weight of Thomas’ dog.*t*= 72 / 3, t = 24, Thomas’ dog weighs 24 pounds.

Second, let *c* = the combined weight of Nathan’s dog and Thomas’ dog. *c* = 72 + 24, *c* = 96, The combined weight of Nathan’s dog and Thomas’ dog is 96 pounds.

- First, Let
*k*= the weight of Kevin’s dog.*k*= 4 x 15,*k*= 60, Kevin’s dog weighs 60 pounds.

Second, let *d* = the difference, in pounds, between the weight of Kevin’s dog and Gene’s dog. *d* = 60 – 15, *d* = 45 pounds, The difference between the weight of Kevin’s dog and Gene’s dog is 45 pounds.

## Individual or Group Work

Use the four operations to solve the multistep word problems about a video game. Write the equation for each word problem. Solve the equations and label your answers.

- Ms. Fisher is planning a field trip to an amusement park for the fourth grade students. She plans to order buses to take the students and the adults to the amusement park. Each bus can carry 22 passengers. There are 58 students and 5 adults going on the field trip. How many buses will Ms. Fisher need to order? Explain your answer.
- At the amusement park, Fred scored 3 times as many points as Gary on a video game. Gary scored 227 points. How many more points did Fred score than Gary did?
- Tanya scored 4 times as many points as Stella on a video game. Tanya scored 284 points. What is the combined number of points for Tanya and Stella?
- Eric’s score on a video game is 1200 points. Eric’s score is 3 times as many points as Mike’s score. Brian’s score is 4 times as many points as Mike’s score. How many points is Brian’s score?
- Angela’s score on a video game is 435. Angela’s score is 5 times as many points as Sheila’s score. Tina’s score is 3 times as many points as Sheila’s score. What is the combined number of points Angela, Sheila, and Tina scored?

**Answers:**

- First, find the number of passengers by adding the number of students and the number of adults. Let
*p*= the number of passengers.*p*= 58 + 5,*p*= 63 passengers.

Second, find how many buses Ms. Fisher needs to order. Let *b* = the number of buses. *b* = 63 / 22, *b* = 2 with a remainder of 19.

Ms. Fisher needs to order 3 buses. Two buses will carry 22 passengers and the third bus will carry 19 passengers.

- First, find the number of points Fred scored. Let
*f*= the number of points Fred scored.*f*= 3 x 227,*f*= 681 points.

Second, find the difference, in points, between Fred’s score and Gary’s score. Let *p* = the difference, in points, between Fred’s score and Gary’s score. *p* = 681 – 227, *p* = 454, Fred scored 454 more points than Gary did.

- First, find the number of points Stella scored. Let
*s*= the number of points Stella scored.*s*= 284 / 4,*s*= 66, Stella scored 71 points.

Second, find the combined number of points both Tanya and Stella scored. Let *c* = the combined number of points for Tanya and Stella. *c *= 284 + 71, *c* = 355 points.

- First, find the number of points Mike scored. Let
*m*= the number of points Mike scored.*m*= 1200 / 3,*m*= 400, Mike scored 400 points.

Second, find the number of points Brian scored. Let *b* = the number of points Brian scored. *b* = 4 x 400, *b* = 1600, Brian’s score is 1600 points.

- First, find the number of points Sheila scored. Let
*s*= the number of points Sheila scored.*s*= 435 /5,*s*= 87, Sheila scored 87 points.

Second, find the number of points Tina scored. Let *t* = the number of points Tina scored. *t* = 3 x 87, *t* = 261, Tina scored 261 points.

Third, find the combined number of points Angela, Sheila, and Tina scored. Let *c* = the combined number of points Angela, Sheila and Tina scored. *c* = 435 + 87 + 261, *c* = 783, The combined number of points Angela, Sheila, and Tina scored is 783 points.

## This post is part of the series: Mathematics Lesson Plan

- Multiplicative Comparisons
- Word Problems Involving Multiplicative Comparisons
- Multistep Word Problems
- Factors and Multiples
- Teaching About Patterns
- Assessment on Math Series