Lesson 29 Module 4 Gr. 6 EngageNY Math

Lesson 29 Module 4 Gr. 6 EngageNY Math

Multi-step Problems - All Operations

Student Outcomes:

• Students will be able to use their knowledge of simplifying expressions, order of operations, and properties of equality to calculate the solution of multi-step equations.

• Students will be able to use tables to determine their answers

• Students check to determine if their solutions make the equations true.

Example 1

The school librarian, Mr. Marker, knows the library has 1,400 books but wants to reorganize how the books are displayed on the shelves. Mr. Marker needs to know how many fiction, nonfiction, and resource books are in the library. He knows that the library has four times as many fiction books as resource books and half as many nonfiction books as fiction books. If these are the only types of books in the library, how many of each type of book are in the library?

Example 1

• Draw a tape diagram to represent the total number of books in the library.

• Draw two more tape diagrams, one to represent the number of fiction books in the library and one to represent the number of resource books in the library.

Multiple Choice

This tape diagram represents...

• the total number of books

• the number of resource books

Multiple Choice

The top portion of this diagram represents which part of the problems?

• the total number of books

• the resource books

What variable should we use throughout the problem?

• We should use r to represent the number of resource books

• The resource books are the smallest number of books

• This will eliminate the need for working with fractions in this problem.

Multiple Choice

Which expression shows the relationship between the resource books, and the number of fiction books.

• $\frac{r}{4}$

• $4r$

Fill in the Blank

If there are twice as many nonfiction books as resource books, how many sections would be needed to show the relationship between the resource books and the nonfiction books?

There are half as many nonfiction books.

• the tape diagram has four section

• since the tape diagram has four secgtions the portion for the nonfiction book should have two sections

Fill in the Blank

Write an equation that represents the tape diagram

Steps to solve. 4r+2r+r=1400

• 1. combine like terms (remember there is a 1 with the r.)

• 7r=1400

• divide both sides of the equation by 7

•  $7r\div7=1400\div7$  

•  $r=200$  

Multiple Choice

How many fiction books are in the library? (remember there are 4 times as many fiction books as resource books .)

• 1400

• 400

• 200

• 800

Multiple Choice

How many nonfiction books are in the library? (remember there are twice times as many fiction books as resource books (200).)

• 1400

• 400

• 200

• 800

A different way to solve..

Use a table

Fill in the Blank

If we use a table, how many columns will we need?

Example 1

The school librarian, Mr. Marker, knows the library has 1,400 books but wants to reorganize how the books are displayed on the shelves.

Mr. Marker needs to know how many fiction, nonfiction, and resource books are in the library. He knows that the library has four times as many fiction books as resource books and half as many nonfiction books as fiction books.

If these are the only types of books in the library, how many of each type of book are in the library?

How many categories of books are there?

• Fiction

• Nonficion

• Resource

• Total

This information gives us the scale factor that we can use to find the totals for each category of books.

When we know there are 1,400 total books, how can we use the ratios to determine how many of each category of books.

We can fill out another row of the table using any number to multiply by the base ratio we know from our description of the story.

What if we use the number 200 to multiply the various categories of books.

We would also need to multiply the number of fiction books, which are times as many as the resource books)

Then divide that answer by two, as we are told that there are half as many fiction books.

Steps to solve word problems CUBED(S)

• C. circle important numbers and labels

• U. underline the question (assign a variable)

• B. box the operations (identify the operations that need to be considered)

• E. examine the question- what information do I have? What information do I need?

• D. Draw a model (tape diagram) or make a table

• S. solve - create and use an equation to find the answer

Conclusion

Using tape diagrams or tables are helpful ways to solve these relationship or ratio problems.