TEKS 6.7C Worksheets — Grade 6 Determine if two expressions are equivalent using

DeAndre is helping his family plant bluebonnets in their garden in Fredericksburg. They have a garden area that measures 15 feet by 10 feet. Each packet of bluebonnet seeds covers an area of 30 square feet. If DeAndre uses 1/2 of a packet for the garden, how much of the garden area will be covered by the seeds from the packet he used?

1. 10 square feet
2. 15 square feet ✓
3. 20 square feet
4. 25 square feet

Why: To find out how much of the garden area will be covered by the seeds from the packet, we first determine the total area DeAndre is planting. The total area of the garden is 15 feet * 10 feet = 150 square feet. Since 1 packet covers 30 square feet and DeAndre uses 1/2 of a packet, we calculate 30 square feet * 1/2 = 15 square feet of coverage. However, since he will only cover the area he planted, which is less than the entire packet, we can directly get the correct area covered by the 1/2 packet as 15 square feet. Thus, DeAndre will cover 15 square feet of the garden area with seeds.

Wren is helping her family sell fresh oranges at a market in McAllen, Texas. They started with 120 oranges. If they sold 3/5 of them, how many oranges do they have left to sell?

1. 48 ✓
2. 72
3. 60
4. 36

Why: To find out how many oranges Wren has left, we first need to calculate how many they sold. They sold 3/5 of 120 oranges. First, calculate 3/5 of 120: (3/5) * 120 = 72. This means 72 oranges were sold. Now, subtract the number of oranges sold from the original amount: 120 - 72 = 48. Therefore, they have 48 oranges left to sell.

Aisha is helping her family set up a booth at the San Antonio River Walk for their taco business. They need to create a sign that is 4 feet tall and 8 feet wide. If each square foot of the sign costs $3 to make, what is the total cost for the sign?

1. $96 ✓
2. $72
3. $48
4. $24

Why: To find the total cost for the sign, first calculate the area of the sign. The area is 4 feet tall multiplied by 8 feet wide, which is 4 * 8 = 32 square feet. Since each square foot costs $3, multiply the area by the cost per square foot: 32 * 3 = $96. Therefore, the total cost for the sign is $96.

Paola is helping her family run a booth at the San Antonio River Walk during a festival. They are selling tacos for $2.50 each and drinks for $1.75 each. If Paola sells x tacos and y drinks, which expression represents the total amount of money earned from selling both items if she sells 4 tacos and 3 drinks?

1. (2.50 * 4) + (1.75 * 3) ✓
2. (2 * 4) + (1.75 * 3)
3. (2.50 * 4) + (1 * 3)
4. (2.50 + 1.75) * (4 + 3)

Why: To find the total amount earned from selling tacos and drinks, we need to use the expression for each item sold. Since Paola sells 4 tacos at $2.50 each and 3 drinks at $1.75 each, the expression for the total amount is (2.50 * 4) + (1.75 * 3). This correctly calculates the total earnings based on the quantities sold.

Avery is helping out at the State Fair of Texas. She sets up a booth that sells fried pies. If Avery sells 3/4 of her 12 pies in the morning and then buys 8 more pies to sell in the afternoon, how many pies does she have left after selling 6 pies in the afternoon?

1. 6
2. 5 ✓
3. 4
4. 3

Why: Avery starts with 12 pies and sells 3/4 of them in the morning. 3/4 of 12 is 9 pies, so she has 12 - 9 = 3 pies left. Then, she buys 8 more pies, giving her a total of 3 + 8 = 11 pies. After selling 6 pies in the afternoon, she has 11 - 6 = 5 pies left.

Sofia is planning a trip to Fredericksburg, Texas, where she wants to visit a local vineyard. The vineyard charges $45 per person for a tour. Sofia is inviting 3 friends to join her. If she has a budget of $200, how much money will she have left after paying for the tour for herself and her friends?

1. $20 ✓
2. $15
3. $25
4. $30

Why: First, calculate the total cost for Sofia and her 3 friends. The total number of people is 4 (Sofia + 3 friends). The cost for the tour is 4 * $45 = $180. Next, subtract the total cost from her budget: $200 - $180 = $20. Therefore, Sofia will have $20 left after paying for the tour.

Camila is participating in a school project where she is planting a garden in her backyard in Austin, Texas. She plans to plant 2 types of flowers: roses and sunflowers. If she has 3/4 of a garden bed for roses and 1/2 of a garden bed for sunflowers, which equation can be used to find the total area of the garden bed she is using for both types of flowers?

1. 3/4 + 1/2 ✓
2. 3/4 - 1/2
3. 3/4 * 1/2
4. 3/4 / 1/2

Why: To find the total area of the garden bed that Camila is using, you need to add the area used for roses and sunflowers together. The equation that represents this is 3/4 + 1/2. To solve this, convert 1/2 to a fraction with a denominator of 4, which is 2/4. Then, 3/4 + 2/4 equals 5/4 or 1 and 1/4 garden beds total.

Imani is planting a garden in her backyard in Austin, Texas. She has two expressions for calculating the total number of plants she can fit. The first expression is 3 * (2 + 4) and the second expression is 18. Which statement about these two expressions is true?

1. The expressions are equivalent. ✓
2. The first expression is greater than the second.
3. The first expression is less than the second.
4. The expressions are not comparable.

Why: To determine if the expressions are equivalent, evaluate the first expression: 3 * (2 + 4) simplifies to 3 * 6, which equals 18. Since both expressions equal 18, they are equivalent. Therefore, the correct answer is that the expressions are equivalent.