Multi-Digit Division

Lesson 11


Apply the formulas for area and perimeter in real-world and mathematical problems involving all four operations.

Common Core Standards

Core Standards


  • 4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

  • 4.OA.A.3 — 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.

Foundational Standards


  • 3.MD.C.5

  • 3.MD.C.6

  • 3.MD.C.7

  • 3.MD.D.8

  • 3.OA.D.8

Criteria for Success


  1. Solve real-world and mathematical problems involving area and perimeter that require multiplication, division, addition, and/or subtraction to solve (MP.4).

Tips for Teachers


  • This lesson provides an opportunity to connect two domains in the grade, 4.OA and 4.MD, since students will be solving multi-step word problems that involve area and perimeter, thus connecting standards 4.OA.3 and 4.MD.3.
  • “When engaging in the mathematical practice of reasoning abstractly and quantitatively (MP.2) in work with area and perimeter, students think of the situation and perhaps make a drawing. Then they recreate the “formula” with specific numbers and one unknown number as a situation equation for this particular numerical equation” (GM Progression, p. 22)
  • “’Apply the formula’ does not mean write down a memorized formula and put in known values because at Grade 4 students do not evaluate expression (they begin this type of work in Grade 6). In Grade 4, working with perimeter and area of rectangles is still grounded in specific visualizations and numbers” (GM Progression, p. 22). Thus, students are not asked to “plug-and-chug” to solve, but rather should “recreate the ‘formula’ with specific numbers” (GM Progression, p. 22).

Remote Learning Guidance

This lesson does not have any identified priority Anchor Tasks, but students should complete the Problem Set independently rather than skipping the lesson entirely. Find more guidance on adapting our math curriculum for remote learning here.

Fishtank Plus

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  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package


Anchor Tasks


Problem 1

Edris wants to build a rectangular garden in his backyard to grow vegetables. He buys 60 yards of fencing to put around the garden to keep animals out. He wants the garden to be 12 feet long. What should the width of his garden be so that he uses all of the fencing he bought? 

Guiding Questions

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Problem 2

Now Edris wants to retile the rectangular patio in his backyard. He uses 128 tiles that are each one square foot. His patio is 8 feet wide. He wants to edge the patio with metal tape to make sure the tiles don’t move or shift at all. How many feet of metal tape should Edris buy? 

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • Did you use the formula given in #3 to solve? If so, how did you use it? If not, how did you solve? 
  • What made #6 more challenging than many of the other problems? 
  • In #7, what measurement did the amount of carpet correspond with, area or perimeter? How do you know? 
  • How did you determine how many tulips were in the garden in #8?
  • In the challenge in #10, how did you interpret the word “bigger”? Is there another way to interpret that word that would result in a different answer? How does this help demonstrate the importance of attending to precision (MP.6)? 

Target Task


A bulletin board in the hallway is 3 feet tall and 45 square feet. What is the perimeter of the bulletin board?

Mastery Response


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Additional Practice

Unit Practice

With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.

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