Concrete Division Reference Sheet Level 1 • Concrete Support 5th Grade Math • Unit 2
Sharing Into Fractions Reference Sheet
Visual step-by-step guide: Cut the wholes, count your pieces!
C-R-A Stage Concrete & Model
The Two Big Questions to Ask First:
1 What is being CUT? (Total objects)
2 WHO shares it? (Equal shares)
Worked Example: 4 Brownies Shared by 6 Friends Problem: \(4 \div 6\)
1 DRAW wholes
Draw the items being shared (4 brownies).
4 Whole Items
2 CUT each
Cut each whole into 6 equal parts for 6 kids.
Cut into 6ths
3 TAKE 1 share
Take 1 slice from each brownie for 1 person.
Shade 1 per item
4 COUNT pieces
Count the shaded pieces you collected.
1 + 1 + 1 + 1 = 4
4 slices of \(\frac{1}{6}\)
Answer: \(\frac{4}{6}\)
SPED Memory Anchor
TOP (Numerator): What you cut into pieces
BOTTOM (Denominator): How many people share
\(\text{Items Shared} \div \text{People Sharing} = \frac{\text{Items}}{\text{People}}\)
Watch Out Trap!
Do NOT just put the bigger number first!
6 friends \(\div\) 4 brownies WRONG!
You cannot cut up 6 friends!
4 brownies \(\div\) 6 friends CORRECT!
Cut the food, share with friends.
Fill-in Sentence Frames (Say it loud!)
• ______ whole items are shared equally among ______ people.
• Each person gets 1 piece from each item, which is \(\frac{1}{\text{people}}\) .
• In all, each person receives \(\frac{\text{items}}{\text{people}}\) of an item.
Visual Math Bridges • 20-Year SPED Practice Veteran Resource Keep this reference sheet on your desk during practice
Supported Division Reference Sheet Level 2 • Supported Guide 5th Grade Math • Unit 2 Lesson 4
Division Situations & GST Reference Sheet
Connecting situations, fraction bar tape diagrams, and equations.
Core Strategy GST Key & Tape Model
The GST Problem Solver Key Use this before writing your equation
G Groups
The number of equal shares or people sharing.
= Divisor = Denominator
S Size
The amount each group gets (fractional part).
= Quotient = Fraction \(\frac{T}{G}\)
T Total
The total amount of items being shared .
= Dividend = Numerator
The Three Representations: Moving Between Forms
1. Situation
5 children (G) share 4 cups of milk (T) equally. How much milk does each child receive?
2. Diagram
Draw 4 whole bars (Total). Split each into 5 equal parts (Groups). Shade 1 piece per bar.
1/5
1/5
1/5
1/5
Combined shaded pieces: \(\frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{4}{5}\) cup
3. Equation
\(4\) (Total)
\(\div\)
\(5\) (Groups)
\(=\)
\(\frac{4}{5}\) (Size of Share)
Universal Division Formula \(a \div b = \frac{a}{b}\)
First Number = Numerator (Total shared)
Second Number = Denominator (Number of equal shares)
Step 1: Label
Find what is being split (T) and who gets a share (G).
Step 2: Set Up
Write \(T \div G\). Never flip just to put big number first!
Step 3: Fraction
Write quotient directly as \(\frac{T}{G}\) and add units.
Visual Math Bridges • 20-Year SPED Practice Veteran Resource Grade 5 • Standard 5.NF.B.3 Support
Grade Level Division Reference Sheet Level 3 • Grade-Level Core 5th Grade Math • 5.NF.B.3
Division as Fractions Reference Sheet
Representing division with equations, diagrams, and fractional quotients.
Key Relationship \(a \div b = \frac{a}{b}\)
The Mathematical Principle
Division of whole numbers always yields a fraction quotient:
\(\text{Dividend} \div \text{Divisor} = \frac{\text{Dividend (Numerator)}}{\text{Divisor (Denominator)}}\)
Reading the Diagram
• Number of full bars = Total objects shared (\(a\))
• Equal pieces per bar = Number of shares (\(b\))
• One shaded piece per bar = Single share size (\(\frac{a}{b}\))
Two Types of Division Quotients Notice numerator vs. denominator size
Case A: Proper Fraction (\( < 1 \)) Items < People
Example: 4 pounds of blueberries shared by 6 students
Equation: \(4 \div 6 = \frac{4}{6}\text{ lb}\)
Each student gets less than 1 whole pound because there are more people than pounds.
Case B: Mixed Number (\( > 1 \)) Items > People
Example: 11 cookies shared equally by 3 siblings
Equation: \(11 \div 3 = \frac{11}{3} = 3\frac{2}{3}\text{ cookies}\)
Each sibling gets more than 1 whole cookie (3 wholes and \(\frac{2}{3}\) leftover).
Solving for Any Unknown in \(a \div b = \frac{a}{b}\) From Lesson Mini-Stamp
Unknown Quotient (\(S\))
\(2 \text{ pizzas} \div 5 \text{ people} = \text{?}\)
Write directly as fraction: \(\frac{2}{5}\) pizza .
Unknown Divisor (\(G\))
\(2 \text{ lbs clay} \div \text{?} = \frac{2}{5}\text{ lb}\)
The denominator reveals the shares: 5 friends .
Unknown Dividend (\(T\))
\(\text{?} \div 4 \text{ athletes} = \frac{7}{4}\text{ L}\)
The numerator reveals total: 7 liters shared.
30-Second Verification Checklist Did I put what is being SHARED in the numerator?
1. Items = Top 2. Shares = Bottom 3. Add Units
Visual Math Bridges • 20-Year SPED Practice Veteran Resource Grade 5 • Fluency across representations (MP1, MP2)
Concrete Ratio Reference Sheet Level 1 • Concrete Support 6th Grade Math • Unit 2 Lesson 1
Ratio Sorting & Matching Reference Sheet
Sort by categories, group items together, and match words to numbers!
C-R-A Stage Concrete Sorting
What is a Ratio?
A RATIO compares two or more groups. It answers: "How many of THIS do we have compared to THAT?"
Step 1: Ways We Can Sort Objects Into Categories
By Color
Blue vs. Orange
By Shape
Squares vs. Circles
By Pattern
Solid vs. Patterned
By Size
Small vs. Big
Step 2: The "Buddy Grouping" Model (6 Squares and 3 Circles) 6 Squares : 3 Circles
Group 1
2 sq : 1 cir
Group 2
2 sq : 1 cir
Group 3
2 sq : 1 cir
Big Discovery: In each equal group, there are 2 squares for every 1 circle ! 2 for every 1
The #1 Rule of Ratios: Order Matters!
Always write the numbers in the EXACT SAME ORDER as the words!
Ratio of Squares to Circles
6 to 3 (or 6 : 3)
Ratio of Circles to Squares
3 to 6 (or 3 : 6)
Step 3: Touch & Read Sentence Starters
"The ratio of [First Group] to [Second Group] is [#] to [#] ."
"For every [# of Group 1] , there are [# of Group 2] ."
Visual Math Bridges • 20-Year SPED Practice Veteran Resource Grade 6 • Ratios & Proportional Relationships (6.RP.A.1)
Supported Ratio Reference Sheet Level 2 • Supported Guide 6th Grade Math • Unit 2 Lessons 1 & 2
Ratio Language & Row Diagrams Reference Sheet
The 3 ways to write ratios, drawing row diagrams, and avoiding order traps.
Visual Model Row Diagrams
The 3 Ways to Write Any Ratio Example: 2 cups white paint and 6 tbsp blue paint
Format 1: With Word "TO"
2 to 6
"The ratio of white paint to blue paint is 2 to 6 ."
Format 2: With a COLON ( : )
2 : 6
Read the colon as the word "to" : 2 to 6 .
Format 3: "FOR EVERY"
For every 2... there are 6...
Can also simplify: "For every 1 cup white, there are 3 tbsp blue."
How to Draw a Row Diagram Stamp: Organizing by row reveals patterns!
White paint (cups):
1
1
2 cups
Blue paint (tbsp):
1
1
1
1
1
1
6 tablespoons
Look at the matching sets: Pair 1 white cup with 3 blue tablespoons! Simplified: 1 to 3
Critical Distinction: Part-to-Part vs. Part-to-Whole
Scenario: A dog park has 17 adult dogs and 8 puppies . (Total = 25 dogs)
Part-to-Part Comparison
Compares one group directly to another group:
Adult dogs to Puppies = 17 : 8
Part-to-Whole Comparison
Compares one group to the TOTAL of all groups:
Puppies to ALL dogs = 8 : 25 (17+8)
4-Step Ratio Solving Routine 1. Circle words → 2. Count items → 3. Draw row → 4. Match order
Order Never Flips!
Visual Math Bridges • 20-Year SPED Practice Veteran Resource Grade 6 • Ratio Language & Diagrams (IM 2.1 & 2.2)
Grade Level Ratio Reference Sheet Level 3 • Grade-Level Core 6th Grade Math • 6.RP.A.1 & 6.RP.A.3
Ratio Concepts & Multi-Term Models Reference Sheet
Representing two-term and multi-term ratios, scaling batches, and diagram reasoning.
Core Standard 6.RP.A.1 Mastery
1. Multiplicative
Ratios describe multiplication relationships , not addition. We scale up or down by multiplying or dividing.
2. Strict Ordering
The order of terms is sacred: \(A : B \neq B : A\). Term 1 always represents Quantity 1; Term 2 represents Quantity 2.
3. Consistent Units
In real-world objects (rulers, cats, erasers), quantities must scale by whole numbers because you cannot have a fraction of a discrete item.
Multi-Term Ratios (Comparing 3 Quantities) Andre's Desk Drawer Problem
Context: "There are 2 markers for every ruler . There are 3 pens for every marker ."
Rulers:
1
(1 unit)
Markers:
1
1
(2 per ruler)
Pens:
1
1
1
1
1
1
(3 per marker × 2 = 6 pens)
Ratio of Pens : Markers : Rulers
6 : 2 : 1
Stationery Sets (Pencils : Notepads : Erasers)
4 : 1 : 2
Reasonableness Check: Discrete Items
Question from Lesson: "Could there be 9 pens in Andre's drawer while keeping the same ratio?"
NO!
Since the ratio is 6 pens for every 1 ruler , having 9 pens would mean \(9 \div 6 = 1.5\) rulers. Because rulers are physical items that cannot be split into halves, 9 pens is impossible in this situation!
Independent Practice Self-Audit Did I verify word order, total counts, and reasonable whole units?
1. Words match Numbers 2. Parts vs Whole
Visual Math Bridges • 20-Year SPED Practice Veteran Resource Grade 6 • Ratios & Proportional Reasoning (MP1, MP2)
