TEKS 6.6A Worksheets — Grade 6 Identify independent and dependent quantities from tables

Victoria is planting a garden in her backyard in Marfa, Texas. She has a rectangular flower bed that is 2 meters long and has a width that is the sum of 1/2 meter and 3/4 meter. What is the width of the flower bed in meters?

1. 1 1/4 ✓
2. 1 3/4
3. 2
4. 2 1/4

Why: To find the width of the flower bed, we need to add 1/2 meter and 3/4 meter. First, convert 1/2 to a fraction with a denominator of 4, which is 2/4. Now, add 2/4 and 3/4: 2/4 + 3/4 = 5/4. This can be expressed as 1 1/4 meters. Therefore, the correct answer is 1 1/4.

Sanaa is planting a garden in her backyard in San Antonio, Texas. She has two types of plants: 3/4 of the space is dedicated to live oaks, while the remaining space is used for mesquite trees. If Sanaa has a total of 12 square feet of garden space, how much space is dedicated to planting live oaks?

1. 9 square feet ✓
2. 6 square feet
3. 3 square feet
4. 4 square feet

Why: To find the amount of space dedicated to live oaks, we calculate 3/4 of the total garden space. First, we find 3/4 of 12 square feet by multiplying: 12 * (3/4) = 12 * 3 / 4 = 36 / 4 = 9. Therefore, 9 square feet of the garden space is dedicated to planting live oaks.

During the Bluebonnet season in Texas, Gabriela wants to plant bluebonnet flowers in her garden. She decides to plant 2/3 of her garden area with bluebonnets and the rest with sunflowers. If her garden is 9 square meters in total, how much area will Gabriela use for the bluebonnet flowers?

1. 6 square meters ✓
2. 3 square meters
3. 5 square meters
4. 4 square meters

Why: To find the area Gabriela will use for bluebonnet flowers, we need to calculate 2/3 of her total garden area. First, we convert the total area into a fraction: 2/3 * 9 = 18/3 = 6 square meters. Thus, the correct answer is 6 square meters.

Tomas is helping his dad sell lemonade at a fundraiser in Palo Duro Canyon. They sell each cup of lemonade for $2.50. If they sell 12 cups in the first hour and the amount they earn is represented in a table that shows the number of cups sold and the total earnings, which quantity is the independent variable in this scenario?

1. number of cups sold ✓
2. total earnings
3. price per cup
4. time of sale

Why: In this scenario, the number of cups sold is the independent variable because it is the quantity that Tomas can control by selling more or fewer cups of lemonade. The total earnings depend on the number of cups sold (earnings increase as more cups are sold), making total earnings the dependent variable.

Daniel is planning a field trip to the Houston Museum of Natural Science. The museum charges a $10 admission fee for students and a $5 admission fee for each adult. If Daniel is bringing 3 adults and 12 students, what will be the total cost for the group to enter the museum?

1. $135 ✓
2. $150
3. $110
4. $140

Why: To find the total cost, we first calculate the cost for the adults and students separately. The cost for 12 students is 12 * $10 = $120. The cost for 3 adults is 3 * $5 = $15. Adding these two amounts gives us $120 + $15 = $135. Therefore, the total cost for the group to enter the museum is $135.

During the Bluebonnet season in Texas, Alejandro is planting a flower bed in his backyard. He wants to plant bluebonnets and sunflowers in a ratio of 3 to 2. If he has a total of 25 flowers to plant, how many bluebonnet flowers will Alejandro plant?

1. 15 ✓
2. 10
3. 20
4. 12

Why: To solve the problem, first recognize that the ratio of bluebonnets to sunflowers is 3:2, which means for every 3 bluebonnets, there are 2 sunflowers. The total parts in the ratio are 3 + 2 = 5. To find out how many flowers each part represents, divide the total number of flowers (25) by the total parts (5). So, 25 / 5 = 5. Each part represents 5 flowers. To find the number of bluebonnets, multiply the number of parts for bluebonnets (3) by the number of flowers per part (5). Thus, 3 * 5 = 15. Therefore, Alejandro will plant 15 bluebonnet flowers.

Olivia is organizing a school fundraiser to support the local wildlife rehabilitation center in Austin. She created a chart that shows the number of baked goods sold compared to the amount of money raised. The table below displays this information: | Baked Goods Sold | Money Raised ($) | |------------------|------------------| | 10 | 25 | | 20 | 50 | | 30 | 75 | | 40 | 100 | Which quantity in this scenario is the independent variable?

1. Baked Goods Sold ✓
2. Money Raised
3. Total Cost
4. Number of Volunteers

Why: In this context, the independent variable is 'Baked Goods Sold' because it is the quantity that Olivia can control or change when organizing the fundraiser. The amount of money raised depends on how many baked goods are sold, making it the dependent variable.

Camila is planning a trip to Big Bend National Park with her family. They want to hike 3/4 of a mile along a trail that is 2 1/2 miles long. After completing that portion of the trail, they will take a break for 1/3 of an hour before continuing on their hike. How much of the trail will they have left to hike after their break?

1. 1 3/4 miles ✓
2. 1 1/4 miles
3. 1/2 mile
4. 2 miles

Why: To find out how much of the trail Camila and her family will have left to hike, we first need to determine how much of the trail they complete. The total length of the trail is 2 1/2 miles, which is equal to 5/2 miles. They hike 3/4 miles, so we subtract that from 5/2 miles. First, we convert 5/2 to a common denominator with 3/4: 5/2 = 10/4. Now, we calculate: 10/4 - 3/4 = 7/4 or 1 3/4 miles left of the trail to hike.