Problem Solving
How do you use what you have learned to problem solve?
Goal:
Goal:
Practice!
Goal: Apply what you have learned about using the distributive property to find area to solve a word problem.
When using the distributive property of multiplication to solve for area, you add the product of two areas to find the total area.
An area. The width is labelled with a w and the length of the first section is labelled with Length l \({_{1}}\) and the length of the second section is labelled l\({_{1}}\) The Area \({=}\) \({(w \times l_{1}) + (w \times l_{2}))}\)
Let’s practice using the distributive property to find the area of a rectangular shape. Remember to use these problem-solving steps to help you find the answers to word problems.
Word Problem Solving Steps
- Read the problem.
- Look for important information.
- Write a math sentence.
- Choose a way to solve.
- Solve and label your answer.
Write the multiplication sentences for the following problem, and solve for the total area.
Todd and his friends are marking off an area for a party. They need an area for tables that is 4 feet by 8 feet. Then, they decide to add a dance floor that is 3 feet by 4 feet. What is the total area that needs to be marked off for the party?
That is right! \({4 \times (8 + 3) = 44}\)!
That is incorrect. Remember, \({(4 \times 8) + (4 \times 3) = 32 + 12 = ?}\)
Write the multiplication sentences for the following problem, and solve for the total area.
Marsha is measuring the amount of space that her house and garage cover. Her house is 9 units by 7 units, and the garage is 7 units by 4 units. What is the total area of the property?
That is right! \({7 \times (9 + 4) = 91}\)!
That is incorrect. Remember, \({(7 \times 9) + (7 \times 4) = 63 + 28 = ?}\)
Write the multiplication sentences for the following problem, and solve for the total area.
Twins Sam and Stan want to plant some vegetables and herbs in a garden. Their mom gives each of them the same amount of land to use. If each of them gets a plot of land 5 units by 6 units, how much total area is being used?
That is right! \({5 \times (6 + 6) = 60}\)!
That is incorrect. Remember, \({(5 \times 6) + (5 \times 6) = 30 + 30 = 60}\).
Write the multiplication sentences for the following problem, and solve for the total area.
Jose and his family are going on a camping trip. Jose’s tent is 4 feet by 3 feet. His parents’ tent is 4 feet by 6 feet. They need to place a tarp under both tents to protect them from the dirt. What is the area of the tarp?
That is right! \({4 \times (6 + 3) = 36}\)!
That is incorrect. Remember, \({4 \times 6}\) + \({4 \times 3}\) = 24 + 12 = 36.
Write the multiplication sentences for the following problem, and solve for the total area.
Zoe is covering two walls with wallpaper. The first wall is 8 feet by 12 feet. The second wall is 8 feet by 8 feet. What is the area that will be covered?
That is right! \({8 \times (12 + 8) = 160}\) square feet!
That is incorrect. Remember, \({(8 \times 12) + (8 \times 8) = 96 + 64 = 160}\).