The Lesson 3 Exit Ticket 4.3 Answer Key provides solutions to multi-step real-world problems involving area and perimeter. It specifically addresses a problem where a rectangular poster and a banner have defined relationships between their lengths and widths. Students can use this answer key to verify their calculations and understand the underlying mathematical concepts. Ideal for educators and students in grades 3-5 focusing on geometry and measurement. This resource enhances comprehension of perimeter and area formulas through practical application.

Key Points

  • Solves a problem involving a rectangular poster and banner with specific length-width relationships
  • Demonstrates understanding of area and perimeter formulas in real-world contexts
  • Provides step-by-step solutions for multi-step mathematical problems
  • Aids students in grades 3-5 in mastering geometry concepts related to perimeter and area
newtopiccyclegrowin
1 page
Language:English
Type:Worksheet
Algebra
newtopiccyclegrowin
1 page
Language:English
Type:Worksheet
Algebra
152
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Lesson 3 Exit Ticket
NYS COMMON CORE MATHEMATICS CURRICULUM
4 3
Lesson 3: Demonstrate understanding of area and perimeter formulas by solving
multi-step real world problems.
Date: 7/23/14
3.A.41
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Name Date
Solve the following problem. Use pictures, numbers, or words to show your work.
A rectangular poster is 3 times as long as it is wide. A rectangular banner is 5 times as long as it is wide. Both
the banner and the poster have perimeters of 24 inches. What are the lengths and widths of the poster and
the banner?
W
Length =3W
The perimeter is W + 3W + W + 3W and that
would equal 8W.
The perimeter is 8 widths and it says it is 24
inches sooooo... 8W = 24 oh, W must be 3
inches because 8 x 3 is 24. I'm not done yet. If
W is 3 inches then the length is 3 times W which
mean 3x3=9 the length is 9 inches
(3 + 9 + 3 + 9) =24 inches
or
2(3+9)=24
POSTER
3 in
9 in
Now the next one will be easy. We have a "W" and the other side is 5 times as long so "5W"
Perimeter = (W + 5W) x 2 so that's 6W x 2 = 12W
(that was two of the widths and two of the lengths)
so 12W = 24 soooo W must be 2 inches. That
makes the length 5 times longer than 2 or 10
inches.
Check the perimeter: 2+10+2+10=24 inches
W
Length = 5W
2 in
10 in
That is a tiny poster!
Banner
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End of Document
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FAQs

What are the dimensions of the rectangular poster in the lesson?
The rectangular poster is described as being 3 times as long as it is wide. If we let the width be represented by 'W', then the length of the poster would be 3W. Given that the perimeter of the poster is 24 inches, we can use the formula for perimeter (P = 2L + 2W) to find the specific dimensions.
How is the perimeter of the rectangular banner calculated?
The rectangular banner is stated to be 5 times as long as it is wide. If we denote the width of the banner as 'W', then its length would be 5W. The perimeter is also given as 24 inches, allowing us to use the perimeter formula (P = 2L + 2W) to derive the width and length of the banner.
What formula is used to find the perimeter of the poster and banner?
The formula used to find the perimeter of both the poster and the banner is P = 2L + 2W, where 'L' is the length and 'W' is the width. This formula allows for the calculation of the dimensions based on the given perimeter of 24 inches for both shapes.
What steps are taken to solve for the dimensions of the poster?
To solve for the dimensions of the poster, we start by letting the width be 'W' and the length be 3W. The perimeter is set at 24 inches, leading to the equation 2(3W) + 2W = 24. Simplifying this equation allows us to solve for 'W', which can then be used to find the length.
What are the specific dimensions of the rectangular banner?
To find the dimensions of the rectangular banner, we denote its width as 'W' and its length as 5W. Using the perimeter formula and the given perimeter of 24 inches, we derive the dimensions. After solving the equation, we can determine both the width and length of the banner.
How do the dimensions of the poster and banner compare?
The dimensions of the poster and banner differ in their length-to-width ratios. The poster is 3 times longer than its width, while the banner is 5 times longer than its width. This relationship affects their respective dimensions when calculated using the same perimeter of 24 inches.
What is the significance of using multi-step problems in this lesson?
The significance of using multi-step problems in this lesson is to enhance students' understanding of area and perimeter formulas. By applying these concepts to real-world scenarios, learners develop critical thinking and problem-solving skills, which are essential in mathematics.

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