Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
Division Concepts & Fact Fluency
Equal Groups, Remainders, Division Vocabulary, Fact Fluency
& Multiplication Connections
GRADES 3-5 | BASIC DIVISION & FACT FLUENCY
Page 1 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
WHAT YOU WILL LEARN
▸ Recognize and define core division vocabulary, including dividend, divisor, quotient, and
remainder.
▸ Explain how the dividend, divisor, quotient, and remainder relate to one another,
including how a related multiplication fact can check a division answer, with the remainder
included when necessary.
▸ Define vocabulary related to division models and strategies, including partition division,
measurement division, and repeated subtraction.
▸ Classify division facts by whether they produce a remainder, and by special cases such
as dividing by 1 or dividing a number by itself.
▸ Use elimination reasoning to determine unknown division facts from indirect clues about
quotients and divisors.
▸ Recognize and extend a division pattern with a constant divisor.
▸ Understand that multiplication and division are inverse operations and use this
relationship to check division answers.
▸ Apply the rule that, in valid whole-number division by a nonzero divisor, the remainder
is always less than the divisor.
▸ Solve division facts and use the results to reveal a hidden word.
▸ Apply division reasoning to real-world sharing and grouping situations.
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 that
8
apply and extend the skills from the seven puzzles.
Page 3 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
DIVISION VOCABULARY UNLOCK - PUZZLE 1 OF
7: WORD SEARCH
Puzzle Focus: This warm-up reinforces the core vocabulary of division - dividend,
divisor, quotient, 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.
M D V A E E F P Z M V E
I O I I V B Q J F J B Y
Q B K V J A D U R N J E
I U S G I N Z E A L O A
P D O H O D D K Y L N W
S R I T A N E N K M I B
F O C V I R R N R E D S
A D U A I E E N D C P F
C R M T F S N R B U B G
T E R Z D X O T O P K O
R Y Z A H F G R O G K R
L L T H Y W G F C G F D
Page 4 Protymera
Division Concepts & Fact Fluency
Equal Groups, Remainders, Division Vocabulary, Fact Fluency
& Multiplication Connections
GRADES 3-5 | BASIC DIVISION & FACT FLUENCY
Page 1 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
WHAT YOU WILL LEARN
▸ Recognize and define core division vocabulary, including dividend, divisor, quotient, and
remainder.
▸ Explain how the dividend, divisor, quotient, and remainder relate to one another,
including how a related multiplication fact can check a division answer, with the remainder
included when necessary.
▸ Define vocabulary related to division models and strategies, including partition division,
measurement division, and repeated subtraction.
▸ Classify division facts by whether they produce a remainder, and by special cases such
as dividing by 1 or dividing a number by itself.
▸ Use elimination reasoning to determine unknown division facts from indirect clues about
quotients and divisors.
▸ Recognize and extend a division pattern with a constant divisor.
▸ Understand that multiplication and division are inverse operations and use this
relationship to check division answers.
▸ Apply the rule that, in valid whole-number division by a nonzero divisor, the remainder
is always less than the divisor.
▸ Solve division facts and use the results to reveal a hidden word.
▸ Apply division reasoning to real-world sharing and grouping situations.
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 that
8
apply and extend the skills from the seven puzzles.
Page 3 Protymera
, Grid Learning System (GLS) - Puzzle Based Mathematical Reasoning
DIVISION VOCABULARY UNLOCK - PUZZLE 1 OF
7: WORD SEARCH
Puzzle Focus: This warm-up reinforces the core vocabulary of division - dividend,
divisor, quotient, 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.
M D V A E E F P Z M V E
I O I I V B Q J F J B Y
Q B K V J A D U R N J E
I U S G I N Z E A L O A
P D O H O D D K Y L N W
S R I T A N E N K M I B
F O C V I R R N R E D S
A D U A I E E N D C P F
C R M T F S N R B U B G
T E R Z D X O T O P K O
R Y Z A H F G R O G K R
L L T H Y W G F C G F D
Page 4 Protymera
