Array Detective Game
Array Detective
AVMR II Multiplication Game • Grade 3
2–4 Players Goal: 5 Clue Badges
How to Play: Say: “I see ___ rows of ___ dots, so the total is ___!”
1. Roll & Move Roll 1 die and jump your game piece that many spaces.
2. Pick Your Card Land on green? Draw Green. Land on gold? Draw Gold!
3. Crack the Array Tell your partner the total dots without counting by 1s!
4. Earn a Badge Write it on your Case File. First to 5 Badges wins!
Start Here
HQ GATE
Ready Agent
#1
Unscreened All Dots Visible
Draw Green
#2
Mystery Under Screen
Draw Gold
#3
Lens Boost Secret Clue
+1 Free Badge
#4
Mystery Under Screen
Draw Gold
#15
Mystery Under Screen
Draw Gold
Headquarters Station
Bureau of Secret Arrays
Keep decks face down here while playing!
UNSCREENED CARDS Place Green Deck Here
MYSTERY SCREEN CARDS Place Gold Deck Here
Detective Secret Tip:
Count equal rows: “3, 6, 9, 12!” • Don't count dots one by one!
#5
Unscreened All Dots Visible
Draw Green
#14
Turn-Around Switch Factors
e.g. 3×4 = 4×3
#6
Double Mystery Big Challenge
Earn 2 Badges!
#13
Unscreened All Dots Visible
Draw Green
#7
Safe House Agent Rest
Take a Breather
Finish Vault
THE VAULT
Crack the Case!
#11
Mystery Under Screen
Draw Gold
#10
Sneak Peek Uncover 1 Row
Bonus Help!
#9
Unscreened All Dots Visible
Draw Green
#8
Mystery Under Screen
Draw Gold
Array Detective • Math Recovery (AVMR II) Station Game Page 1 of 8 • Game Board
Unscreened Cards • Set A
Green Deck • Cut along dashed lines • Cards U1–U8
Task: Name rows, columns & total
CARD U1 Unscreened
How many dots in all?
CARD U2 Unscreened
How many dots in all?
CARD U3 Unscreened
How many dots in all?
CARD U4 Unscreened
How many dots in all?
CARD U5 Unscreened
How many dots in all?
CARD U6 Unscreened
How many dots in all?
CARD U7 Unscreened
How many dots in all?
CARD U8 Unscreened
How many dots in all?
Cut along dashed lines • Fully visible arrays Page 2 of 8 • Cards (Set A)
Unscreened Cards • Set B
Green Deck • Extra Practice • Cards U9–U16
Task: Name rows, columns & total
CARD U9 Unscreened
How many dots in all?
CARD U10 Unscreened
How many dots in all?
CARD U11 Unscreened
How many dots in all?
CARD U12 Unscreened
How many dots in all?
CARD U13 Unscreened
How many dots in all?
CARD U14 Unscreened
How many dots in all?
CARD U15 Unscreened
How many dots in all?
CARD U16 Unscreened
How many dots in all?
Cut along dashed lines • Fully visible arrays Page 3 of 8 • Cards (Set B)
Mystery Screen Cards • Set A
Gold Deck • Row & Column Peeks + Single Reveals • Cards S1–S8
AVMR II Covered Arrays
CARD S1 Row & Column Peek
SCREEN
How many dots under the screen and in all?
CARD S2 Row & Column Peek
SCREEN
How many dots altogether?
CARD S3 Row & Column Peek
SCREEN
How many dots altogether?
CARD S4 Row & Column Peek
SCREEN
How many dots altogether?
CARD S5 Row Screen
SCREEN
3 rows in all
How many dots in all?
CARD S6 Row Screen
SCREEN
4 rows in all
How many dots in all?
CARD S7 Row Screen
SCREEN
6 rows in all
How many dots in all?
CARD S8 Column Screen
SCREEN
5 columns in all
How many dots in all?
Partially screened arrays • AVMR II Level 3 Figurative Multiplication Page 4 of 8 • Cards (Set A)
Mystery Screen Cards • Set B
Gold Deck • Extra Challenge • Cards S9–S16
AVMR II Covered Arrays
CARD S9 Row & Column Peek
SCREEN
How many dots altogether?
CARD S10 Row & Column Peek
SCREEN
How many dots altogether?
CARD S11 Row & Column Peek
SCREEN
How many dots altogether?
CARD S12 Row & Column Peek
SCREEN
How many dots altogether?
CARD S13 Row Screen
SCREEN
3 rows in all
How many dots in all?
CARD S14 Row Screen
SCREEN
3 rows in all
How many dots in all?
CARD S15 Column Screen
SCREEN
7 columns in all
How many dots in all?
CARD S16 Column Screen
SCREEN
6 columns in all
How many dots in all?
Partially screened arrays • AVMR II Level 3 Figurative Multiplication Page 5 of 8 • Cards (Set B)
Detective Case File
My Array Evidence & Strategy Log
Dossier #3-ARRAY
Detective Name:
Partner:
Date:
Detective Speak: “I see ___ rows with ___ dots in each row, so there are ___ dots altogether!”
| Card | Array Type | Rows × Dots in Each Row | My Equation & Total | How I Solved It | Badge |
|---|
| #1 | [ ] Unscreened [ ] Screened | | | | |
| | | | | |
| [ ] Skip-counted [ ] Known fact [ ] Counted dots |
|
| #2 | [ ] Unscreened [ ] Screened |
|
| [ ] Skip-counted [ ] Known fact [ ] Counted dots |
|
| #3 | [ ] Unscreened [ ] Screened |
|
| [ ] Skip-counted [ ] Known fact [ ] Counted dots |
|
| #4 | [ ] Unscreened [ ] Screened |
|
| [ ] Skip-counted [ ] Known fact [ ] Counted dots |
|
| #5 | [ ] Unscreened [ ] Screened |
|
| [ ] Skip-counted [ ] Known fact [ ] Counted dots |
|
| #6 | [ ] Unscreened [ ] Screened |
|
| [ ] Skip-counted [ ] Known fact [ ] Counted dots |
|
Detective Brain Work
When a card had a screen covering dots, how did you picture the hidden dots in your mind?
Student Case Log • Array Detective Page 6 of 8 • Student Sheet
Teacher Observation Chart
AVMR II Diagnostic Edition • Multiplication & Division Construct Levels
AVMR Level Tracking
Date / Session:
Station / Group Name:
Observer / Teacher:
AVMR II Multiplication Construct Levels:
Level 1: Unitary Counts individual dots by ones on visible rows. Cannot keep track of hidden dots.
Level 2: Perceptual Skip-counts when all rows are visible. Struggles when part of the array is screened.
Level 3: Figurative Visualizes composite units under screen. Skip-counts or adds equal hidden groups!
Level 4: Abstract Instantly uses known multiplication facts and derives (e.g. \(4 \times 6 = 24\)).
| Student Name | Card | Array Type Observed | Strategy Observed | AVMR Level | Notes / Instructional Next Steps |
|---|
| | | | | |
| [ ] Full Unscreened | | | | |
| [ ] Row & Col Peek | | | | | |
| [ ] Row/Col Screen | [ ] Counted by 1s (Unitary) | | | | |
| [ ] Skip-counted visible groups | | | | | |
| [ ] Visualized hidden rows/cols | | | | | |
| [ ] Used known fact / derived | 1 2 3 4 | | | | |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen | [ ] Counted by 1s (Unitary)
[ ] Skip-counted visible groups
[ ] Visualized hidden rows/cols
[ ] Used known fact / derived | 1 2 3 4 |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen | [ ] Counted by 1s (Unitary)
[ ] Skip-counted visible groups
[ ] Visualized hidden rows/cols
[ ] Used known fact / derived | 1 2 3 4 |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen | [ ] Counted by 1s (Unitary)
[ ] Skip-counted visible groups
[ ] Visualized hidden rows/cols
[ ] Used known fact / derived | 1 2 3 4 |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen | [ ] Counted by 1s (Unitary)
[ ] Skip-counted visible groups
[ ] Visualized hidden rows/cols
[ ] Used known fact / derived | 1 2 3 4 |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen | [ ] Counted by 1s (Unitary)
[ ] Skip-counted visible groups
[ ] Visualized hidden rows/cols
[ ] Used known fact / derived | 1 2 3 4 |
|
Formative Probing Questions:
To prompt visualization: “Close your eyes—can you picture the next hidden row under the screen? How many dots are in it?”
To prompt composite units: “Instead of counting 1 by 1, how can we count by the rows? (e.g. 4... 8... 12!)”
To prompt derived facts: “What easy fact do you know that is close to this? Can you double it or add 1 more group?”
Math Recovery Assessment • Add+Vantage Math Recovery (AVMR II) Page 7 of 8 • Diagnostic Chart (with Levels)
Teacher Observation Chart
Classroom Workshop Edition • Multiplication & Array Reasoning Notes
General Observation
Date / Session:
Station / Small Group:
Teacher / Observer:
Multiplication Reasoning Behaviors to Look For:
Equal Groups / Skip-Counting Counts by groups (e.g., 5, 10, 15, 20) instead of counting individual dots.
Mental Visualization (Screens) Can explain what rows look like underneath the cover without needing to uncover.
Fact Fluency & Deriving Uses known multiplication facts, doubles (e.g. 2 × 6 = 12, so 4 × 6 = 24), or commutative property.
| Student Name | Card | Array Type | Equation & Total | Strategy & Student Explanation | Teacher Notes & Next Steps |
|---|
| | | | | |
| [ ] Full Unscreened | | | | |
| [ ] Row & Col Peek | | | | | |
| [ ] Row/Col Screen | | | | | |
| [ ] Skip-counted rows
[ ] Visualized hidden screen
[ ] Used known fact / doubled |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen |
| [ ] Skip-counted rows
[ ] Visualized hidden screen
[ ] Used known fact / doubled |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen |
| [ ] Skip-counted rows
[ ] Visualized hidden screen
[ ] Used known fact / doubled |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen |
| [ ] Skip-counted rows
[ ] Visualized hidden screen
[ ] Used known fact / doubled |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen |
| [ ] Skip-counted rows
[ ] Visualized hidden screen
[ ] Used known fact / doubled |
|
|
| | [ ] Full Unscreened
[ ] Row & Col Peek
[ ] Row/Col Screen |
| [ ] Skip-counted rows
[ ] Visualized hidden screen
[ ] Used known fact / doubled |
|
Math Talk Conferencing Prompts:
“How did you know?” Prompt students to articulate whether they saw equal rows or groups, or used repeated addition.
“What if we turned it?” Rotate the array card to explore the commutative property: e.g. 3 rows of 5 vs 5 rows of 3.
“Can you prove it?” Have the student sketch their mental array on scrap paper or build it with counters to verify.
Classroom Math Workshop • Array Detective Station Page 8 of 8 • General Observation Chart
