Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
The Integrals Challenge - Calculus
Puzzle Workbook
Antiderivatives, Definite Integrals, Integration
Techniques & the Fundamental Theorem of Calculus
ADVANCED HIGH SCHOOL & INTRODUCTORY COLLEGE
CALCULUS | GRADES 11-12
Page 1 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
WHAT YOU WILL LEARN
▸ Recognize and define core integral vocabulary, including antiderivative, indefinite
integral, definite integral, and integration.
▸ Explain how differentiation and integration are inverse operations of one another through
the Fundamental Theorem of Calculus.
▸ Define vocabulary related to integration techniques, including u-substitution, integration
by parts, upper and lower bounds, and Riemann sum.
▸ Classify an integral by the technique required to evaluate it - the power rule, substitution,
a basic formula, or integration by parts.
▸ Use elimination reasoning to determine which definite integral corresponds to which
numerical value from indirect clues.
▸ Apply the power rule for integration across a repeated pattern, and correctly sequence
the steps for evaluating a definite integral using the Fundamental Theorem of Calculus.
▸ Evaluate definite integrals to solve problems and reveal a hidden word.
▸ Understand the role of the constant of integration, C, in every indefinite integral.
▸ Apply the Fundamental Theorem of Calculus to compute the net change of a function
over an interval.
▸ Recognize basic antiderivative formulas for power functions, exponential functions, and
trigonometric functions.
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 Challenge Section with twelve
tiered challenges, and a Player Progress Tracker at the end. Every puzzle also includes
its own Concept Check with three questions. 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.
CHALLENGE SECTION - Transfer: Complete twelve tiered challenges of
8
increasing depth.
Page 3 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
INTEGRAL VOCABULARY UNLOCK - PUZZLE 1
OF 7: WORD SEARCH
Puzzle Focus: This warm-up reinforces the core vocabulary of integrals - antiderivative,
indefinite, definite, 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.
C A Z T A M R E R X M J R V J
D M F B N V B T D E G Y K J G
I J Z Y T X O I U G Q S V Y U
K N H A I E U N Y N X B N Y X
G O T C D V N I E A V D N S U
P T I C E A D F Z H I G P J B
A A L U R L S E T C N T Q L C
R T J M I U R D U T D F M A B
E I M U V A N H M E E A W V T
A O B L A T S T N N F Y Z R L
A N U A T E Q F Y Q I H P E U
B H I T I W H N D H N Z W T Y
L Z Q I V L R K J R I C Y N S
C T L O E W R B V C T I K I A
H V Z N I F M B F P E O G T W
Page 4 Protymera
The Integrals Challenge - Calculus
Puzzle Workbook
Antiderivatives, Definite Integrals, Integration
Techniques & the Fundamental Theorem of Calculus
ADVANCED HIGH SCHOOL & INTRODUCTORY COLLEGE
CALCULUS | GRADES 11-12
Page 1 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
WHAT YOU WILL LEARN
▸ Recognize and define core integral vocabulary, including antiderivative, indefinite
integral, definite integral, and integration.
▸ Explain how differentiation and integration are inverse operations of one another through
the Fundamental Theorem of Calculus.
▸ Define vocabulary related to integration techniques, including u-substitution, integration
by parts, upper and lower bounds, and Riemann sum.
▸ Classify an integral by the technique required to evaluate it - the power rule, substitution,
a basic formula, or integration by parts.
▸ Use elimination reasoning to determine which definite integral corresponds to which
numerical value from indirect clues.
▸ Apply the power rule for integration across a repeated pattern, and correctly sequence
the steps for evaluating a definite integral using the Fundamental Theorem of Calculus.
▸ Evaluate definite integrals to solve problems and reveal a hidden word.
▸ Understand the role of the constant of integration, C, in every indefinite integral.
▸ Apply the Fundamental Theorem of Calculus to compute the net change of a function
over an interval.
▸ Recognize basic antiderivative formulas for power functions, exponential functions, and
trigonometric functions.
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 Challenge Section with twelve
tiered challenges, and a Player Progress Tracker at the end. Every puzzle also includes
its own Concept Check with three questions. 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.
CHALLENGE SECTION - Transfer: Complete twelve tiered challenges of
8
increasing depth.
Page 3 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
INTEGRAL VOCABULARY UNLOCK - PUZZLE 1
OF 7: WORD SEARCH
Puzzle Focus: This warm-up reinforces the core vocabulary of integrals - antiderivative,
indefinite, definite, 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.
C A Z T A M R E R X M J R V J
D M F B N V B T D E G Y K J G
I J Z Y T X O I U G Q S V Y U
K N H A I E U N Y N X B N Y X
G O T C D V N I E A V D N S U
P T I C E A D F Z H I G P J B
A A L U R L S E T C N T Q L C
R T J M I U R D U T D F M A B
E I M U V A N H M E E A W V T
A O B L A T S T N N F Y Z R L
A N U A T E Q F Y Q I H P E U
B H I T I W H N D H N Z W T Y
L Z Q I V L R K J R I C Y N S
C T L O E W R B V C T I K I A
H V Z N I F M B F P E O G T W
Page 4 Protymera
