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Practice sheet · Hockey Path · Lens 1: Math

Solving for x

Algebra practice for The Math of Hockey, Algebra Level Up A1–A2 (book pp.17–18). Players, teams and stats here are made-up examples unless a page of the book is named.
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Do the same thing to both sides. Undo + with −, × with ÷, and a square with a square root, until x is alone.

Check by plugging it back in. Then ask: does it make sense in hockey? You can't make 37.7 saves, so round to what's possible.

Warm-up

One step

Undo one thing. The equation is given.
1

Box score

Points = goals + assists (p.8). A player has 41 points and 17 goals. Solve 17 + a = 41 for the assists.

2

Goals-against average

GAA = goals against × 60 ÷ minutes (p.8). A goalie played 3,000 minutes with a 2.40 GAA. Solve GA × 60 ÷ 3,000 = 2.40.

3

Save percentage

A goalie faced 25 shots and finished with a .880 save percentage (p.9). Solve s ÷ 25 = 0.880 for her saves.

4

On pace

A player scores 0.5 points per game. Solve P ÷ 82 = 0.5 to find the points they are on pace for over an 82-game season.

Core

Two steps, or x on both sides

Write the equation yourself, then solve.
5

Pace needed

A player has 22 points after 30 games and wants 60 points. There are 52 games left. What pace (points per game) does that need? Compare it with their pace so far.

6

Standings points

In the NHL a win is worth 2 standings points and an overtime or shootout loss is worth 1. A team finished with 95 points and 9 overtime losses. How many wins?

Algebra Practice · Hockey Path · Unizon1/2
Hockey Path · Unizon · PracticeAlgebra · solving for x
7

Zones on the rink

An NHL rink is 200 ft long and the neutral zone between the blue lines is 50 ft (p.13). The two end zones are the same length, z. Solve 2z + 50 = 200. Check it with p.13 (11 ft + 64 ft).

8

Catching up

Player A has 12 goals and scores 0.5 a game. Player B has 20 goals and scores 0.3 a game. If both keep those paces, after how many more games are they tied?

9

Shot attempts

Corsi share = CF ÷ (CF + CA) (p.10). Your team took 48 shot attempts and had a 60% share. Solve 48 ÷ (48 + CA) = 0.60 for the attempts against.

10

A save percentage target

A goalie has 720 saves on 800 shots (.900). Next game she faces 40 shots. How many saves does she need to reach at least .902? Could she reach .905?

Level Up

Squares and square roots

From A2 (p.18). Use a calculator for the roots.
11

How far out?

The net is at (0, 0). A shot from 26 ft away was taken 10 ft to the side. Solve x² + 10² = 26².

12

Same out as across

A shot is 30 ft from the net and just as far out as it is across, so x² + x² = 30². Find x to one decimal place.

13

Falling puck

A puck falls d = 4.9t² metres in t seconds, ignoring air (p.18). One pops off a stick about 1.6 m up (example). Solve 1.6 = 4.9t² to two decimal places.

14

Turning force

For the Michigan model (pp.16, 18), F = 0.1375v² newtons. What blade speed v (m/s) needs a turning force of 5.5 N? Two decimal places.

Make your own problem

Your turn to be the stats analyst

  1. Pick a stat from the book: points, save %, shooting %, Corsi, GAA, pace or shot distance.
  2. Write a short hockey story with one number missing, and turn it into an equation.
  3. Solve it on a separate line, check it, and swap problems with someone (or try it on a family member).

My problem, and my worked answer:

Algebra Practice · Hockey Path · Unizon2/2
Hockey Path · Unizon · PracticeAlgebra · solving for x

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Your steps can look different and still be right: what matters is that both sides stay equal.

Warm-up
1
a = 24 assists Subtract 17 from both sides: a = 41 − 17 = 24.
2
GA = 120 goals Multiply both sides by 3,000: GA × 60 = 7,200. Divide by 60: GA = 120.
3
s = 22 saves Multiply both sides by 25: s = 0.880 × 25 = 22 (3 goals against).
4
P = 41 points Multiply both sides by 82: P = 0.5 × 82 = 41.
Core
5
r ≈ 0.73 per game 22 + 52r = 60 → 52r = 38 → r = 38 ÷ 52 ≈ 0.73. That is about the pace so far (22 ÷ 30 ≈ 0.73), so the player just has to keep it up.
6
w = 43 wins 2w + 9 = 95 → 2w = 86 → w = 43. Check: 2 × 43 + 9 = 95.
7
z = 75 ft 2z = 150 → z = 75. Matches p.13: 11 ft (boards to goal line) + 64 ft (goal line to blue line) = 75 ft.
8
g = 40 games 12 + 0.5g = 20 + 0.3g → 0.2g = 8 → g = 40. Both then have 32 goals.
9
CA = 32 48 = 0.60(48 + CA) = 28.8 + 0.6CA → 0.6CA = 19.2 → CA = 32. Check: 48 ÷ 80 = 0.60.
10
38 saves · no (720 + x) ÷ 840 = 0.902 → 720 + x = 757.68 → x = 37.68, so 38 saves (2 goals against): 758 ÷ 840 ≈ .902. For .905 she would need 40.2 saves on 40 shots, which is impossible.
Level Up
11
x = 24 ft x² + 100 = 676 → x² = 576 → x = √576 = 24. (Only the positive root makes sense as a distance.)
12
x ≈ 21.2 ft 2x² = 900 → x² = 450 → x = √450 ≈ 21.2. Check: √(21.2² + 21.2²) ≈ 30.
13
t ≈ 0.57 s t² = 1.6 ÷ 4.9 ≈ 0.3265 → t = √0.3265 ≈ 0.57. About half a second: not much time to react.
14
v ≈ 6.32 m/s v² = 5.5 ÷ 0.1375 = 40 → v = √40 ≈ 6.32. (0.1375 comes from m ÷ r = 0.165 ÷ 1.2.)
Make your own: check that your equation matches your story, that your answer works when you plug it back in, and that it is possible in a real game (whole saves, whole goals).
Algebra Practice · Hockey Path · UnizonAnswer key