Worksheet

Inside the Gym: Memberships and Climbing Routes

Describe gym memberships and climbing routes with ordered ratios, part-to-part comparisons, and part-to-whole comparisons.

Grade 6MathInteractive · Printable

Aligned to6.RP.A.1

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What’s included

Single worksheet
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1 Common Core standard
Printable answer key
14 questions
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Details

Format: Interactive · Printable
Grade: Grade 6
Subject: Math
Question types: Fill in the blank, Multiple choice, Matching, Circle the answer, Sorting, Short answer

About this worksheet

What students practice

Students describe relationships between two quantities using ratio notation and ratio language.
Students distinguish part-to-part comparisons from part-to-whole comparisons.
Students interpret the order of quantities in membership and climbing-route ratios.

How to use

Have students label the two quantities before writing each ratio. Discuss how changing the order or using a total changes the comparison.

Curriculum

Common Core standard covered

6.RP.A.1

Use ratio language to describe how two quantities are related, such as 3 wings for every 1 beak.

Preview

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Name Date

Inside the Gym: Memberships and Climbing Routes

Use ratio language to describe an indoor skate and climbing gym.

Membership Desk

Use the membership table. Each member appears in exactly one row. For all ratio blanks, use the recorded counts without simplifying.

Current Gym Memberships
Membership type	Members
Skate only	14
Climbing only	21
Both activities	7

There are climbing-only members for every skate-only members.

Which comparison does the ratio 7 : 21 describe in the table?

A. Climbing-only members to members with both activities
B. Members with both activities to climbing-only members
C. Members with both activities to skate-only members
D. Skate-only members to climbing-only members

A welcome display compares members with both activities to all current members.

Write that ratio: : .

Members with either a skate-only membership or a both-activities membership may use the skate area. Select both accurate statements.

There are 21 members with skate access for every 42 members in all.There are 14 members with skate access for every 42 members in all.There are 7 members with both activities for every 21 members with skate access.There are 21 skate-only members for every 7 members with both activities.

A staff note says, “The ratio of climbing-only members to skate-only members is 21 : 14.” Which sentence reverses this comparison correctly?

A. There are 14 skate-only members for every 35 climbing-only members.
B. There are 21 skate-only members for every 14 climbing-only members.
C. There are 14 skate-only members for every 7 climbing-only members.
D. There are 14 skate-only members for every 21 climbing-only members.

Climbing Route Board

Each climbing route is either open or closed. Use the table, and write ratio blanks with the actual counts, without simplifying.

Today's Climbing Routes
Difficulty	Open	Closed
Beginner	5	2
Intermediate	7	3
Advanced	4	1

Match each comparison of intermediate routes to its ratio.

Open routes to closed routes
Closed routes to all intermediate routes
All intermediate routes to open routes

A. 10 : 7
B. 7 : 3
C. 3 : 10

A maintenance report combines all three difficulty levels.

The ratio of closed routes to open routes is : .

A visitor guide compares open beginner routes with all open routes. Which sentence should it use?

A. There are 5 open beginner routes for every 16 open routes.
B. There are 5 open beginner routes for every 7 open routes.
C. There are 7 open beginner routes for every 16 open routes.
D. There are 5 open beginner routes for every 22 open routes.

Sort each route comparison. A part-to-part ratio compares two separate groups. A part-to-whole ratio compares one group with the entire group containing it.

Open advanced routes to closed advanced routesClosed beginner routes to all beginner routesOpen beginner routes to open intermediate routesOpen advanced routes to all open routes

Part-to-part	Part-to-whole

10.

Jules says, “There are 4 open advanced routes for every 1 advanced route in all.” Explain the mistake and write a correct sentence comparing open advanced routes with all advanced routes.

Check the Gym Updates

Read each new situation separately. Identify the quantities and their order before answering. Use the stated counts without simplifying.

11.

During an orientation, 8 visitors choose the skate tour and 11 choose the climbing tour. Each visitor chooses exactly one tour. Which sentence correctly compares the climbing tour group with all visitors?

A. There are 11 climbing-tour visitors for every 8 visitors in all.
B. There are 8 climbing-tour visitors for every 19 visitors in all.
C. There are 11 climbing-tour visitors for every 19 visitors in all.
D. There are 19 climbing-tour visitors for every 11 visitors in all.

12.

A route-setting plan says, “For every 9 routes with blue holds, there are 4 routes with orange holds.”

Using the numbers in the plan, the ratio of routes with orange holds to routes with blue holds is : .

13.

Of 18 new members this week, 5 choose both activities. Every other new member chooses just one activity. A signup report compares members choosing just one activity with members choosing both. Which ratio belongs in the report?

A. 5 : 13
B. 13 : 5
C. 18 : 5
D. 13 : 18

14.

A gym survey reports a ratio of 6 members who prefer morning visits to 13 members who prefer evening visits. These are the only two choices, and each member selects one. Select all three statements supported by the report.

For every 13 members who prefer evening visits, 6 prefer morning visits.The ratio of morning preferences to evening preferences is 13 : 6.For every 19 members surveyed, 6 prefer morning visits.The ratio of evening preferences to all survey responses is 13 : 19.For every 13 members surveyed, 6 prefer morning visits.