Hopscotch HattieFunction Machines · functions, their graphs, and sequences

Flat squares, then a jump: step functions.

Step Functions

Step functions. In MathBound, the free Algebra I adventure game, Hopscotch Hattie asks these problems, and the only way past is to solve them.

Part of Radicals and More Functions: chapter 11 of the standard course.

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Step Functions. Evaluate a greatest-integer, ceiling or per-started-unit rate rule, or read a step graph.

Made by the game’s own question engine. Try each one, then open its steps.

The

number

of

boxes

needed

to

pack

n

muffins

is

B (n) = ⌈ \frac{n}{6} ⌉ .

Find

B (13) .

Show the worked steps

$\frac{13}{6}$ $is$ $about$ $2.17 .$
$The$ $ceiling$ $rounds$ $it$ $up:$ $B (13) = 3 .$ $A$ $part-filled$ $box$ $is$ $still$ $a$ $box.$

Answer: $3$

The

number

of

full

teams

of

9

that

n

players

can

make

is

T (n) = ⌊ \frac{n}{9} ⌋ .

Find

T (43) .

Show the worked steps

$\frac{43}{9}$ $is$ $about$ $4.78 .$
$The$ $greatest$ $integer$ $rounds$ $it$ $down:$ $T (43) = 4 .$ $The$ $players$ $left$ $over$ $do$ $not$ $make$ $a$ $team.$

Answer: $4$

The

greatest

integer

function

⌊ x ⌋

gives

the

greatest

integer

less

than

or

equal

to

x .

What

is

⌊ - 0.2 ⌋ ?

Show the worked steps

$On$ $a$ $number$ $line$ $- 0.2$ $lies$ $between$ $- 1$ $and$ $0 .$
$The$ $greatest$ $integer$ $not$ $more$ $than$ $- 0.2$ $is$ $- 1 :$ $further$ $left,$ $not$ $nearer$ $zero.$

Answer: $- 1$

Textbook	Lessons
Standard course	11.5
Big Ideas Math Algebra 1	4.7
Big Ideas Math Algebra 1 (2022)	4.7
Carnegie Learning Algebra I	M2 4.4
enVision Algebra 1	5-3
enVision Algebra 1 (2024)	5-3
Eureka Math Algebra I (EngageNY)	3.15-3.16, 3.21-3.24
Glencoe Algebra 1	9-7
HMH Into Algebra 1	8.1
Illustrative Mathematics Algebra 1	4.12
Illustrative Mathematics Algebra 1 (v.360)	5.12
Reveal Algebra 1	4-6