7th Grade Math: Unit 1

Unit 1 – Item 1
The city of Derinkuyu is an underground city in present-day Turkey. While on vacation in Turkey, Olamide began the tour alongside the other adventurers at the entrance of one of the burrows and walked down 46m with the rest of the tour group. Along the tour he wanted to make a video to post on social media when he noticed that he had lost his phone. Olamide quickly turned around and ascended 8m to where he saw his phone laying on the ground and then ran to catch up with his tour group who had traveled an additional 34m.

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What is the total distance that Olamide traveled during his tour? Provide a visual representation and written explanation as your solution.

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Unit 1 – Item 2
An eight-pack of fine tip pens costs $10.50. The pack of pens are on sale for 1/3 off the
original price. What is the sale price of an individual pen?

Unit 1 – Item 3
Tremaine has a coupon for one of his favorite clothing stores that is going out of business. He walks into the store, and he sees a discount sign that can be applied to everything in the store.

He would like to buy two pairs of pants for his new job and notices that the price has been marked down as well. Using the information below, determine whether Tremaine should use his coupon or not.

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Tremaine should use the store's 30% discount because it will reduce the total cost to $22.75, which is less than the total with the member coupon.

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Tremaine should use the member coupon because it will reduce the total cost to $22.75, which is less than the total with the store's discount.

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Tremaine should use the member coupon because it will bring the cost of the second pair to $9.75, making the total for both pairs $26.00, a better deal than the store's discount.

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Tremaine should not use any discounts, as the store's 30% discount and the member coupon would both result in the same total cost of $32.50 for two pairs of pants.

Unit 1 – Item 4
Jayden is a cyclist who has dreams of one day competing in the Tour de France. He begins his training on the Silver Comet Trail in Georgia which is 61.5 miles long. Jayden is training on 20% of the trail and his goal is to cover that distance in 30 minutes.

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If he trains and improves consistently each week, what average speed increase must Jayden maintain over the next 9 weeks if the average for his first week was 14 miles per hour.

Unit 1 – Item 5
Jonathan contracted Connie’s Kitchen Consulting to help him remodel his kitchen and dining room. Below is a listing of different charges.

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While balancing his account, Jonathan forgot to write down his balance. What are the balances for the missing account entries?

Unit 1 – Item 6
Amari is a teacher at Downton Middle School. Her salary is $42,205.00 annually. The governor announced that all teachers would receive a 4.4% increase in pay, plus a one-time $2,000.00 bonus for the holidays.

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How much money would Amari gross this year teaching?

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Unit 1 – Item 7
A research team aboard an underwater research vessel descends 1,350 feet beneath the
surface of the water. They then rise 155 feet and descend again 175 feet. Where are they
currently located?

Unit 1 – Item 8
For Field Day, each 7th grade teacher was asked to bring a case of water for their class.

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There are sixteen 7th grade teachers. If each case of water costs $7.52. How much money will the teachers spend on water for Field Day if they each purchase one case?

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Mr. Parsh has 27 students in his class. He goes to the local Drop N Shop to purchase his water. Drop N Shop sells two brands of water. Wet Water is $8.74 for a case of 24 bottles while
Aquarius Water is $11.00 for a case of 32 bottles. Which brand of water is the better buy for Mr. Parsh’s class? Justify your answer.

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Unit 1 – Item 9
What is the distance between a dwelling located underground at a depth of 50 2/3 feet and a building located at an altitude of 717 feet above sea level?

Unit 1 – Item 10
Miranda and Nikki are working on the puzzle below collaboratively.

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Using the digits 1 to 9, at most one time each, place a digit in each box to make a true statement.

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How might Miranda respond to Nikki’s thinking? Help Miranda construct a viable argument to support her thinking.

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Unit 1 – Item 11
Mikal had 1 3/4 pounds of trail mix. She ate 1/6 pound of the trail mix each day of a 5 day clean eating challenge. How many pounds of trail mix did she have left after the challenge?

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Unit 1 – Item 12
Mali, a computer analyst with a large internet company, makes $40,000 a year. He is slated to receive a bonus that is 2% of his total salary quarterly this year. What will Mali’s total earning be at the end of the year?

Unit 1 – Item 13
For his 12th birthday, Michael received tickets to see his favorite artist in concert. The total cost was $260.24 for 2 adults and 3 children, including Michael. Adult tickets were $63.60 each.

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What was the price for Michael’s ticket?

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If Michael’s 4 grandparents went to the concert along with the rest of his family, what would have been the total price?

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If Michael’s grandparents received a 44% discount on concert tickets for being senior citizens, what would be the price for each senior citizen ticket?

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Unit 1 – Item 14
Planning a Group Outing: Budgeting with Discounts
Your school is organizing a field trip to a museum located in a nearby city. The principal has asked your class to help with creating a budget plan that takes into account potential discounts for booking a large group.

1. Research and Cost Estimation:
Research the costs associated with the field trip, including transportation, museum admission fees, meals, and any other expenses.
Estimate the cost per person for each expense category based on your research.
2. Discount Calculation:
Inquire about potential discounts for booking a large group at the museum and transportation services.
Calculate the percentage discount offered for the group booking.
3. Budget Planning:
Create a budget plan detailing the estimated costs for each expense category, considering the potential discounts.
Determine the total budget needed for the trip, factoring in the discounts.
4. Budget Allocation:
Allocate the total budget among the participating students evenly.
Calculate the amount each student needs to contribute to cover their share of the expenses, taking into account the discounted total budget.
5. Budget Adjustment:
If the total estimated costs exceed the discounted budget, revise your budget plan to reduce expenses while ensuring essential aspects of the trip are covered.
Make necessary adjustments to the budget allocation per student based on the revised plan.
6. Reflection:
Write a reflection on the budgeting process, including the budget that you will propose to the principal.

What is the total distance that Olamide traveled during his tour? Provide a visual representation and written explanation as your solution.

Unit 1 – Item 2An eight-pack of fine tip pens costs $10.50. The pack of pens are on sale for 1/3 off theoriginal price. What is the sale price of an individual pen?

Tremaine should use the store's 30% discount because it will reduce the total cost to $22.75, which is less than the total with the member coupon.

Tremaine should use the member coupon because it will reduce the total cost to $22.75, which is less than the total with the store's discount.

Tremaine should use the member coupon because it will bring the cost of the second pair to $9.75, making the total for both pairs $26.00, a better deal than the store's discount.

Tremaine should not use any discounts, as the store's 30% discount and the member coupon would both result in the same total cost of $32.50 for two pairs of pants.

If he trains and improves consistently each week, what average speed increase must Jayden maintain over the next 9 weeks if the average for his first week was 14 miles per hour.

While balancing his account, Jonathan forgot to write down his balance. What are the balances for the missing account entries?

How much money would Amari gross this year teaching?

Unit 1 – Item 7A research team aboard an underwater research vessel descends 1,350 feet beneath thesurface of the water. They then rise 155 feet and descend again 175 feet. Where are theycurrently located?

There are sixteen 7th grade teachers. If each case of water costs $7.52. How much money will the teachers spend on water for Field Day if they each purchase one case?

Unit 1 – Item 9What is the distance between a dwelling located underground at a depth of 50 2/3 feet and a building located at an altitude of 717 feet above sea level?

Using the digits 1 to 9, at most one time each, place a digit in each box to make a true statement.

How might Miranda respond to Nikki’s thinking? Help Miranda construct a viable argument to support her thinking.

Unit 1 – Item 11Mikal had 1 3/4 pounds of trail mix. She ate 1/6 pound of the trail mix each day of a 5 day clean eating challenge. How many pounds of trail mix did she have left after the challenge?

Unit 1 – Item 12Mali, a computer analyst with a large internet company, makes $40,000 a year. He is slated to receive a bonus that is 2% of his total salary quarterly this year. What will Mali’s total earning be at the end of the year?

What was the price for Michael’s ticket?

If Michael’s 4 grandparents went to the concert along with the rest of his family, what would have been the total price?

If Michael’s grandparents received a 44% discount on concert tickets for being senior citizens, what would be the price for each senior citizen ticket?

Unit 1 – Item 2
An eight-pack of fine tip pens costs $10.50. The pack of pens are on sale for 1/3 off the
original price. What is the sale price of an individual pen?

Unit 1 – Item 7
A research team aboard an underwater research vessel descends 1,350 feet beneath the
surface of the water. They then rise 155 feet and descend again 175 feet. Where are they
currently located?

Unit 1 – Item 9
What is the distance between a dwelling located underground at a depth of 50 2/3 feet and a building located at an altitude of 717 feet above sea level?

Unit 1 – Item 11
Mikal had 1 3/4 pounds of trail mix. She ate 1/6 pound of the trail mix each day of a 5 day clean eating challenge. How many pounds of trail mix did she have left after the challenge?

Unit 1 – Item 12
Mali, a computer analyst with a large internet company, makes $40,000 a year. He is slated to receive a bonus that is 2% of his total salary quarterly this year. What will Mali’s total earning be at the end of the year?