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Swim Practice: From Pace Triangles to Equations

Use swimming practice models to explain constant slope with similar triangles and derive equations through and above the origin.

Grade 8MathInteractive · Printable

Aligned to8.EE.B.6

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
14 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Matching, Short answer

About this worksheet

What students practice

Students use similar right triangles to explain why rise divided by run is constant on a line.
Students derive y = mx and y = mx + b from slope-triangle relationships.
Students interpret slopes and intercepts in swimming practice models.

How to use

Use after teaching angle-angle similarity. Have students mark corresponding triangle legs and show algebra beside each equation before comparing answers.

Curriculum

Common Core standard covered

8.EE.B.6

Use similar triangles to explain why slope is the same anywhere on a line, and derive y = mx and y = mx + b.

Preview

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Swim Practice: From Pace Triangles to Equations

Use similar triangles to connect practice times, lap counts, and linear equations.

One Pace, Different Triangles

The team uses straight-line models for steady swimming. A lap count can include part of a lap. On each graph, horizontal distance represents minutes and vertical distance represents laps.

Use this graph for Questions 1–5. Points A, B, and C lie on the same straight pace line. Sketch segments AH, HB, and BA to form triangle AHB. Sketch segments BK, KC, and CB to form triangle BKC. Both triangles have horizontal and vertical legs.

Compare the horizontal and vertical legs when moving from triangle AHB to triangle BKC.

The horizontal leg is multiplied by . The vertical leg is multiplied by .

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