Frame Facts Teacher Guide Fact Detective Academy
Frame the Facts Teacher Guide
DAYS 1-4
The Core Concept
Standard 1.OA.4 requires students to view subtraction (e.g., \(10 - 7 = \square\)) not simply as "taking away," but as finding the missing partner that makes the whole (e.g., \(7 + \square = 10\)). For remedial students, this shift is achieved by filling ten-frames with two colors of physical counters.
Daily warm-up: The 3-Minute Case Briefing
Before lessons, flash a ten-frame showing 5 yellow counters for 3 seconds. Ask: "How many did you see? How many more to make 10?" Repeat with various quantities to build visual fluency of missing partners.
Day 1: Ten-Frame Partners (Sums to 10)
15-20 Min
Objective: Solve subtraction within 10 by finding how many more to fill a single ten-frame.
Instructional Script
"Detectives, look at 10 - 7 = ?. We know the whole number is 10. Let's place 7 yellow counters first. How many empty boxes are left? We need red counters to fill them up. Let's count: 1, 2, 3! So, 7 and 3 make 10, meaning 10 - 7 = 3!"
Concrete Step: Place part counters of Color A. Fill remaining spaces with Color B to find the missing partner.
Prompt Question: "If we already have 7, how many more do we need to reach our total of 10?"
Day 2: Double Ten-Frame Cases (Sums 11 to 15)
15-20 Min
Objective: Use two ten-frames to solve subtraction problems with teenage numbers.
Instructional Script
"Our whole is 13, and one partner is 8. Let's put 8 yellow counters on our double ten-frame. How do we reach 13? Let's count ON using red counters: 9, 10, 11, 12, 13. Stop! How many red counters did we add? 5! So, 8 + 5 = 13, which tells us 13 - 8 = 5!"
Concrete Step: Place part counters. Count on by adding the second color to fill the first ten-frame and move to the second, stopping at the whole.
Critical Concept: Making ten is an intermediate step: "How many to make 10? How many more to get to 13?"
Fact Detective Academy Guide
PAGE 1 OF 2
Fact Detective Academy
Frame the Facts Teacher Guide
DAYS 1-4
Day 3: Transition to Representative Drawing
15-20 Min
Objective: Draw missing counters on ten-frames to represent subtraction as addition.
On Day 3, we transition students from placing physical counters to drawing them. Students draw solid circles for the known part and hollow circles (or circles with an "X") for the unknown part on printed ten-frames.
Visual Drawing Strategy:
"We draw 3 dark circles for our known part. We draw empty circles until we fill our total of 5. The empty circles are our missing partner!"
Day 4: Independent Practice with Math Talk
15-20 Min
Objective: Complete subtraction equations independently and explain the addition connection.
Students complete Day 4 of the Student Workbook. Focus on verbalization during independent work. Pair students up or meet in small groups to explain their math.
Partner Talk Frame:
"To solve 11 - 9 = ?, I thought 9 + [ ] = 11. I filled the ten-frame with 9 counters. I needed 2 more. So 11 minus 9 is 2!"
Misconceptions & Interventions
1. Subtracting from the Part
Symptom: Student starts with 7 counters (for \(10 - 7\)) and removes some.
Intervention: "This frame is our Whole. It holds 10. Our yellow partner is 7. We need to find how many more to fill the whole!"
2. Counting All vs. Counting On
Symptom: Student recounts all counters from 1 instead of starting from the known part.
Intervention: Cover the known part with a card written with "8". Tap the card and say "8," then tap empty boxes: "9, 10, 11."
Differentiated Pacing Guidelines:
Support (Tier 3) Stick with single ten-frame totals (within 10) for all 4 days. Do not move to double ten-frames until the "make ten" connection is fluent.
On-Track (Tier 2) Proceed as scheduled. Provide pre-colored red and yellow double-sided counters to support manual switching.
Extension Introduce equations with blank totals and parts, e.g., \([ ] - 6 = 8\), using the double ten-frames to reconstruct the whole.
Fact Detective Academy Guide
PAGE 2 OF 2
Frame Facts Workbook Fact Detective Academy
Frame the Facts Workbook
Day 1: Solve subtraction by finding the missing partner.
Name:
Date:
STRATEGY #1: Single Ten-Frame Partners
To solve subtraction like 10 - 7 = [ ], ask: "7 plus how many more makes 10?" Start with 7 yellow counters, then find how many red counters you need to fill the frame!
1 Case of the Missing Ten-Frame Partner (10 - 7 = ?) Total: 10
TEN-FRAME MODELER
Think Addition: 7 + ______ = 10
Solve Subtraction: 10 - 7 = ______
2 Case of the Missing Ten-Frame Partner (10 - 6 = ?) Total: 10
TEN-FRAME MODELER
Think Addition: 6 + ______ = 10
Solve Subtraction: 10 - 6 = ______
Fact Detective Academy
PAGE 1
Fact Detective Academy
Frame the Facts Workbook
Day 2: Solve double ten-frame mysteries by counting on.
DAY 2
STRATEGY #2: Double Ten-Frame Count On
To solve subtraction with teen numbers like 13 - 8 = [ ], start with 8 yellow counters. Add red counters and count on: "9, 10, 11, 12, 13." How many did you add to reach the total?
3 Case of the Missing Partner (13 - 8 = ?) Total: 13
Think: 8 + ______ = 13
Solve: 13 - 8 = ______
4 Case of the Missing Partner (12 - 7 = ?) Total: 12
Think: 7 + ______ = 12
Solve: 12 - 7 = ______
Fact Detective Academy
PAGE 2
Fact Detective Academy
Frame the Facts Workbook
Day 3: Draw missing partner circles to solve the mystery.
DAY 3
STRATEGY #3: Representative Draw-On
Now, let's draw! Solid circles ● are the part you know. Draw empty circles ○ in the white boxes until you reach your total.
5 Draw & Solve: 10 - 8 = ? Total: 10
Draw empty circles ○ to reach 10
Think: 8 + ______ = 10
Answer: 10 - 8 = ______
6 Draw & Solve: 14 - 9 = ? Total: 14
Draw empty circles ○ to reach 14
Think: 9 + ______ = 14
Answer: 14 - 9 = ______
Fact Detective Academy
PAGE 3
Fact Detective Academy
Frame the Facts Workbook
Day 4: Case Closed! Connect addition and subtraction sentences.
DAY 4
STRATEGY #4: Fact Family Connections
The Mystery of the Missing Footprints
Detective Max found 11 muddy footprints in the hallway. 8 of the footprints belonged to a dog. The rest belonged to a cat. How many cat footprints did Detective Max find?
Part Whole Mats Fact Detective Academy
Part-Part-Whole Evidence Mat
MATH MAT A
How to Investigate: Place the Whole number of counters in the top box. Place your known Part on the left. Find the missing Part to solve the subtraction mystery!
Whole (Total)
PLACE WHOLE COUNTERS HERE
Part 1 (Known Partner)
PLACE KNOWN
PART HERE
Part 2 (Missing Partner)
FIND THIS
PART TO SOLVE!
Equation Investigator
[ Whole ] − [ Part 1 ] = ______
&
[ Part 1 ] + ______ = [ Whole ]
Fact Detective Academy Materials
MAT 1
Fact Detective Academy
Printable Clue Tokens
HANDS-ON PACK
Instructions for Teacher: Print this sheet on heavy paper or cardstock. Cut along the dotted lines. Give a baggie of Yellow Magnifier Counters and Teal Footprint Counters along with the Number Tokens to students for active modeling.
Yellow Magnifier Counters (Color A)
Teal Footprint Counters (Color B)
Number & Symbol Tokens
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
−
=
?
Clue
Fact Detective Academy Materials
MAT 2
Part Whole Workbook Fact Detective Academy
Part Whole Workbook
Day 5: Solve subtraction by breaking wholes into parts.
Name:
Date:
STRATEGY #5: The Bar Model Partition
The Whole is the long top bar. The Parts are the smaller bottom boxes. Subtracting a part from the whole leaves the other part: Whole − Part = Missing Part.
1 Case of the Missing Bar Partner (11 - 7 = ?)
Whole: 11
Part: 7
Part: ?
Think: 7 + ______ = 11
Solve: 11 − 7 = ______
2 Case of the Missing Bar Partner (14 - 9 = ?)
Whole: 14
Part: 9
Part: ?
Think: 9 + ______ = 14
Solve: 14 − 9 = ______
3 Case of the Missing Bar Partner (12 - 4 = ?)
Whole: 12
Part: 4
Part: ?
Think: 4 + ______ = 12
Solve: 12 − 4 = ______
Fact Detective Academy
PAGE 1
Fact Detective Academy
Part Whole Workbook
Day 6 & 7: Case File Sort. Match related addition & subtraction keys.
DAYS 6-7
STRATEGY #6: Related Fact Sort Cut out the formula cards from Page 3. Match each subtraction card to its correct addition partner based on their shared numbers, and glue them into the Case Files below!
CASE FILE #101: The Whole is 11 ID: PPW-11
GLUE ADDITION KEY
GLUE SUBTRACTION CLUE
CASE FILE #102: The Whole is 14 ID: PPW-14
GLUE ADDITION KEY
GLUE SUBTRACTION CLUE
CASE FILE #103: The Whole is 15 ID: PPW-15
GLUE ADDITION KEY
GLUE SUBTRACTION CLUE
Fact Detective Academy
PAGE 2
Cut-Out Sheet
Detective Clue Cards
NO BACK CONTENT
Cut along the dotted lines below. Paste these clues into the matching Case Files on Page 2.
SUBTRACTION CLUES
11 − 4 = 7 SUB
14 − 9 = 5 SUB
15 − 6 = 9 SUB
ADDITION KEYS
4 + 7 = 11 ADD
9 + 5 = 14 ADD
6 + 9 = 15 ADD
DECOY CLUES (DO NOT BELONG TO ANY CASE FILE!)
10 − 2 = 8 DECOY
2 + 8 = 10 DECOY
Fact Detective Academy
PAGE 3
Fact Detective Task Cards Independent Station
Fact Detective Center Task Cards (Set A)
Days 8-10 • Cards 1-4
Card 1
1
The Cookie Caper
Detective Lily has 10 cookies in total. 6 are chocolate chip. The rest are sugar cookies. How many are sugar cookies?
Investigate: Count on from 6 to find the missing partner to make 10. Write the equations on your record sheet!
Card 2
2
Gold & Silver Badges
Detective Jack has 12 badges in total. 8 are gold. The rest are silver. How many silver badges does he have?
Investigate: Count on from 8 to 12. How many empty boxes do you fill? Fill out Card 2 on your recording sheet.
Card 3
3
Magnifying Glass Mix
The agency has 11 magnifying glasses. 5 are large and the rest are small. How many small ones are there?
WHOLE: 11
Part: 5
Part: ?
Investigate: Think of the parts of 11. If 5 is one part, what is the missing partner? Find it and write the match!
Card 4
4
Muddy Trails
There were 10 footprints in the garden. 3 washed away in the rain. How many footprints are still left?
Investigate: Start with the part you know: 3 footprints. How many more make the total of 10 footprints? Record your answer.
Cut on dotted lines to separate cards PAGE 1 OF 2
Independent Station
Fact Detective Center Task Cards (Set B)
Days 8-10 • Cards 5-8
Card 5
5
The Mystery Keys
There are 13 metal keys on a ring. 7 keys are bronze. The rest are copper. How many copper keys are there?
Investigate: Think: 7 + how many more = 13? Place 7 yellow counters, and count on to 13. Record your work.
Card 6
6
Locked Files
There are 15 folders in the filing cabinet. 9 are open and the rest are locked. How many locked folders are there?
WHOLE: 15
Part: 9
Part: ?
Investigate: Think of the addition connection: 9 + [ ] = 15. Count up from 9. What is the missing partner?
Card 7
7
Pencil Clues
A box has 14 yellow pencils. 8 pencils have sharp tips. The rest are dull. How many pencils are dull?
Investigate: Count on from 8 to 14 to find the dull pencils. Write the matching fact family on your recording sheet.
Card 8
8
Locked Boxes
Fact Detective Recording Sheets Fact Detective Academy
Center Recording Sheet
Record your findings for Task Cards 1, 2, 3, and 4.
Name:
Date:
DETECTIVE STRATEGY PATHS: 1 Ten-Frames 2 Counting On 3 Drawing Circles 4 Bar Model
Card 1: The Cookie Caper TOTAL: 10
MY PROOF DRAWING (DRAW CIRCLES OR TEN-FRAMES)
Think Addition: 6 + ______ = 10
Solve Subtraction: 10 − 6 = ______
Strategy: Ten-Frame Count On Draw
Card 2: Gold & Silver Badges TOTAL: 12
MY PROOF DRAWING (DRAW CIRCLES OR TEN-FRAMES)
Think Addition: 8 + ______ = 12
Solve Subtraction: 12 − 8 = ______
Strategy: Ten-Frame Count On Draw
Card 3: Magnifying Glasses TOTAL: 11
MY PROOF DRAWING (DRAW CIRCLES OR BAR MODELS)
Think Addition: 5 + ______ = 11
Solve Subtraction: 11 − 5 = ______
Strategy: Ten-Frame Bar Model Draw
Card 4: Muddy Trails TOTAL: 10
MY PROOF DRAWING (DRAW CIRCLES OR TEN-FRAMES)
Think Addition: 3 + ______ = 10
Solve Subtraction: 10 − 3 = ______
Strategy: Ten-Frame Count On Draw
Fact Detective Academy
RECORDS PAGE 1
Fact Detective Academy
Center Recording Sheet
Record your findings for Task Cards 5, 6, 7, and 8.
DAYS 8-10
DETECTIVE STRATEGY PATHS: 1 Ten-Frames 2 Counting On 3 Drawing Circles 4 Bar Model
Card 5: The Mystery Keys TOTAL: 13
MY PROOF DRAWING (DRAW CIRCLES OR TEN-FRAMES)
Think Addition: 7 + ______ = 13
Solve Subtraction: 13 − 7 = ______
Strategy: Ten-Frame Count On Draw
Card 6: Locked Files TOTAL: 15
MY PROOF DRAWING (DRAW CIRCLES OR BAR MODELS)
Think Addition: 9 + ______ = 15
Solve Subtraction: 15 − 9 = ______
Strategy: Ten-Frame Bar Model Draw
Card 7: Pencil Clues TOTAL: 14
MY PROOF DRAWING (DRAW CIRCLES OR TEN-FRAMES)
Think Addition: 8 + ______ = 14
Solve Subtraction: 14 − 8 = ______
Strategy: Ten-Frame Count On Draw
Card 8: Locked Boxes TOTAL: 12
MY PROOF DRAWING (DRAW CIRCLES OR BAR MODELS)
Think Addition: 9 + ______ = 12
Solve Subtraction: 12 − 9 = ______
Strategy: Ten-Frame Bar Model Draw
Fact Detective Academy
RECORDS PAGE 2