Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
Calculus Applications Puzzle Lab
Critical Points, Motion, Optimization, Related Rates and Curve
Analysis
CALCULUS | GRADES 10-12
Page 1 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
WHAT YOU WILL LEARN
▸ Recognize and define core vocabulary related to applications of derivatives, including
critical point, extremum, concavity, and inflection point.
▸ Explain how the first and second derivatives relate to a function's increasing/decreasing
behavior and concavity.
▸ Define vocabulary related to motion and optimization applications, including velocity,
acceleration, constraint, and objective.
▸ Classify a real-world scenario as an optimization problem, a related rates problem, a
motion analysis problem, or a curve sketching problem.
▸ Use elimination reasoning to determine which function's critical point analysis matches
which classification from indirect clues.
▸ Apply the relationship between position and velocity across a repeated pattern, and
correctly sequence the steps for solving an optimization or related rates problem.
▸ Evaluate derivatives to solve real-world motion and optimization problems, revealing a
hidden word.
Page 2 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
HOW TO PLAY - YOUR PUZZLE JOURNEY
This template takes you through seven learning puzzles built around the same topic, each
one built around a different way of thinking, plus a dedicated Bonus Challenge Section with
ten tiered challenges, and a Player Progress Tracker at the end. Every puzzle also
includes its own Concept Check.
Every answer is collected together near the end so you (or a parent or teacher) can check
the work.
1 WORD SEARCH - Recognize: Find every key term hidden in the grid.
2 CONCEPT MAP - Connect: Fill in how key terms relate to one another.
3 CROSSWORD - Retrieve: Use the clues to spell out each key term correctly.
4 SORT & CLASSIFY - Distinguish: Place each item into its correct category.
5 LOGIC GRID - Deduce: Use the clues to match each entity correctly.
SEQUENCE & PATTERN - Organize: Fill in several missing items, then
6
reorder a scrambled sequence, and explain the rule.
CODEBREAKER - Apply: Use the Code Key to answer each question and
7
reveal the hidden message.
BONUS CHALLENGE SECTION - Transfer: Complete ten tiered challenges
8
of increasing depth.
Page 3 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
APPLICATIONS VOCABULARY UNLOCK -
PUZZLE 1 OF 7: WORD SEARCH
Puzzle Focus: This warm-up reinforces the core vocabulary of applications of
derivatives - critical point, concavity, optimization, and more - before you apply these
ideas in the puzzles ahead. Find every item from the bank below - it may run across,
down, or diagonally.
R F N Y T Z Z T J K H I J
Y N K O F E A A F T N A L
C S O K I N X M T C W A E
S O T I O T W T R I C M M
H F N I T X C E R I B U Q
V A T C U A A E T E M J I
W O U F A S Z I L I M L U
M K O B I V R I X F A U M
D F K N F C I A M T N I M
H X G P Z Z M T L I P I N
B M Z H H H F Y Y P T R D
D E C R E A S I N G Z P I
G K M I N I M U M O T T O
Page 4 Protymera
Calculus Applications Puzzle Lab
Critical Points, Motion, Optimization, Related Rates and Curve
Analysis
CALCULUS | GRADES 10-12
Page 1 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
WHAT YOU WILL LEARN
▸ Recognize and define core vocabulary related to applications of derivatives, including
critical point, extremum, concavity, and inflection point.
▸ Explain how the first and second derivatives relate to a function's increasing/decreasing
behavior and concavity.
▸ Define vocabulary related to motion and optimization applications, including velocity,
acceleration, constraint, and objective.
▸ Classify a real-world scenario as an optimization problem, a related rates problem, a
motion analysis problem, or a curve sketching problem.
▸ Use elimination reasoning to determine which function's critical point analysis matches
which classification from indirect clues.
▸ Apply the relationship between position and velocity across a repeated pattern, and
correctly sequence the steps for solving an optimization or related rates problem.
▸ Evaluate derivatives to solve real-world motion and optimization problems, revealing a
hidden word.
Page 2 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
HOW TO PLAY - YOUR PUZZLE JOURNEY
This template takes you through seven learning puzzles built around the same topic, each
one built around a different way of thinking, plus a dedicated Bonus Challenge Section with
ten tiered challenges, and a Player Progress Tracker at the end. Every puzzle also
includes its own Concept Check.
Every answer is collected together near the end so you (or a parent or teacher) can check
the work.
1 WORD SEARCH - Recognize: Find every key term hidden in the grid.
2 CONCEPT MAP - Connect: Fill in how key terms relate to one another.
3 CROSSWORD - Retrieve: Use the clues to spell out each key term correctly.
4 SORT & CLASSIFY - Distinguish: Place each item into its correct category.
5 LOGIC GRID - Deduce: Use the clues to match each entity correctly.
SEQUENCE & PATTERN - Organize: Fill in several missing items, then
6
reorder a scrambled sequence, and explain the rule.
CODEBREAKER - Apply: Use the Code Key to answer each question and
7
reveal the hidden message.
BONUS CHALLENGE SECTION - Transfer: Complete ten tiered challenges
8
of increasing depth.
Page 3 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
APPLICATIONS VOCABULARY UNLOCK -
PUZZLE 1 OF 7: WORD SEARCH
Puzzle Focus: This warm-up reinforces the core vocabulary of applications of
derivatives - critical point, concavity, optimization, and more - before you apply these
ideas in the puzzles ahead. Find every item from the bank below - it may run across,
down, or diagonally.
R F N Y T Z Z T J K H I J
Y N K O F E A A F T N A L
C S O K I N X M T C W A E
S O T I O T W T R I C M M
H F N I T X C E R I B U Q
V A T C U A A E T E M J I
W O U F A S Z I L I M L U
M K O B I V R I X F A U M
D F K N F C I A M T N I M
H X G P Z Z M T L I P I N
B M Z H H H F Y Y P T R D
D E C R E A S I N G Z P I
G K M I N I M U M O T T O
Page 4 Protymera
