Fraction Division Placement Test Diagnostic Placement Form A • Grade 6/7 Mathematics
Fraction Division Placement Test
Target Competency
Concepts, Fluency & Models
Student Name:
Date:
Class/Period:
Directions: Complete each problem carefully. For visual modeling tasks, label and partition clearly. For numerical equations, show all intermediate steps and express final answers in simplest form.
1 Visual Model Interpretation: Whole Divided by Unit Fraction
3 pts
Consider the division expression: \( 3 \div \frac{1}{4} \).
a. Partition each whole bar below into fourths and count the total number of parts to find the quotient.
Whole 1
Whole 2
Whole 3
Quotient: \( 3 \div \frac{1}{4} = \)
Meaning in words: "How many are in 3 wholes?"
2 Partitioning Area: Unit Fraction Divided by Whole
3 pts
Mia has \( \frac{1}{3} \) of a pan of cornbread. She shares it equally between \( 2 \) friends. What fraction of the original pan does each friend receive?
\( \frac{1}{3} \)
Partition the shaded third horizontally into 2 equal parts
Division Equation:
\( \frac{1}{3} \div 2 = \)
Multiplication Equivalent:
\( \frac{1}{3} \times \) =
3 Reciprocals & Inversion Strategy
4 pts
State the reciprocal (multiplicative inverse) for each value below and verify that their product equals 1:
a. \( \frac{4}{7} \)
Reciprocal:
Check: \( \frac{4}{7} \times \) ___ = 1
b. \( 6 \)
Reciprocal:
Check: \( 6 \times \) ___ = 1
c. \( 1\frac{2}{5} \)
Reciprocal:
Improper:
Placement Assessment • Page 1 of 2 Diagnostic Baseline Assessment
Placement Part II
Fraction by Fraction & Mixed Numbers
Continue showing all steps
4 Number Line Measurement Model
3 pts
Find the quotient using the number line below: \( \frac{3}{4} \div \frac{1}{8} \)
0
\( \frac{1}{4} \)
\( \frac{1}{2} \)
\( \frac{3}{4} \)
1
Each tick interval represents \( \frac{1}{8} \). Draw jumps of \( \frac{1}{8} \) from 0 to \( \frac{3}{4} \).
Number of jumps of \( \frac{1}{8} \) needed to reach \( \frac{3}{4} \): \( \frac{3}{4} \div \frac{1}{8} = \)
5 Standard Algorithm Fluency
4 pts
Calculate the quotient using the inverse multiplication strategy. Show all cross-cancellation and reduction steps:
\( \frac{5}{6} \div \frac{2}{3} \)
Step 1: Multiply by Reciprocal
Step 2: Simplify / Final Answer
6 Mixed Number Division
4 pts
Divide: \( 2\frac{1}{4} \div 1\frac{1}{2} \). Convert to improper fractions before computing.
Calculations & Reduction:
Final Simplified Quotient:
7 Contextual Application & Remainder Analysis
4 pts
A landscape gardener has \( 5\frac{1}{3} \) yards of edging border. Each miniature flower bed requires \( \frac{2}{3} \) of a yard. How many complete flower beds can be edged?
Mathematical Representation:
Total beds:
beds
Edging leftover:
yd
Part I: ___ / 10 Part II: ___ / 15 Total Score: ___ / 25
Placement Assessment • Page 2 of 2
Placement Diagnostic Guide Teacher Resource Diagnostic • Scoring • Placement
Placement Diagnostic Guide
Assessment Total
25 Points Total
This guide provides the complete solution criteria, rubric guidelines, and student placement thresholds to map diagnostic results directly to intervention pathways.
Part I: Conceptual Foundations & Inversion Logic (10 Points) Items 1 – 3
Item Target Skill Correct Response & Work Pts 1 Whole ÷ Unit Fraction (Bar Model) Each whole divided into 4 equal segments (\( 3 \times 4 = 12 \)). Quotient: 12 . Verbal: "How many fourths are in 3 wholes?" 3 pts 2 Unit Fraction ÷ Whole (Area Model) Shaded third split horizontally into 2 equal halves. Each sub-part represents \( \frac{1}{6} \). Equation: \( \frac{1}{6} \) ; Multiplicative: \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \) . 3 pts 3 Reciprocals & Multiplicative Inverses a: \( \frac{7}{4} \) (check: \( \frac{4}{7} \times \frac{7}{4} = 1 \))b: \( \frac{1}{6} \) (check: \( 6 \times \frac{1}{6} = 1 \))c: \( 1\frac{2}{5} = \frac{7}{5} \rightarrow \) Reciprocal is \( \frac{5}{7} \) 4 pts
Part II: Procedural Fluency & Contextual Applications (15 Points) Items 4 – 7
Item Target Skill Correct Response & Work Pts 4 Fraction ÷ Fraction (Number Line) Draw 6 jumps of size \( \frac{1}{8} \) from 0 to \( \frac{6}{8} \) (\( \frac{3}{4} \)). Quotient: 6 jumps. 3 pts 5 Inversion & Simplification Algorithm \( \frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} \) or \( 1\frac{1}{4} \) (accept 1 pt for reciprocal setup, 2 pts for simplification, 1 pt final). 4 pts 6 Mixed Number Division Convert: \( 2\frac{1}{4} = \frac{9}{4} \) and \( 1\frac{1}{2} = \frac{3}{2} \). Multiply: \( \frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2} \) or
Progress Monitoring Probe Pack Formative Monitoring Tiered Assessment Probes
Progress Monitoring Probe Pack
Probes 1 & 2
10 Pts Each • 10 Mins
PROBE 1 Target: Visual Models & Division Meaning
Name: Date: Score: ___ / 10
1. Tape Diagram Interpretation 2 pts
What division equation does this model represent?
\( \frac{1}{4} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)
Equation:
2. Number Line Jumps 3 pts
Show \( 2 \div \frac{2}{3} \) using jumps on the line below:
0 \( \frac{2}{3} \) 1 2
Quotient:
3. Area Division Model 2 pts
Divide \( \frac{1}{2} \) into 3 equal pieces:
\( \frac{1}{2} \div 3 = \)
4. Conceptual Reasoning 3 pts
Why is \( 4 \div \frac{1}{5} \) greater than 4?
Formative Check Divider
PROBE 2 Target: Procedural Fluency & Reciprocals
Name: Date: Score: ___ / 10
1. Reciprocal Matching 2 pts
Reciprocal of \( \frac{5}{9} \):
Reciprocal of \( 8 \):
2. Standard Algorithm 2 pts
Solve: \( \frac{2}{3} \div \frac{4}{9} \)
3. Cross Simplification 3 pts
Solve & simplify: \( \frac{7}{10} \div \frac{14}{15} \)
4. Whole by Fraction 3 pts
Solve: \( 6 \div \frac{3}{5} \)
Progress Monitoring Pack • Page 1 of 2 Probes 1 & 2 (Conceptual & Procedural)
Formative Monitoring
Probe 3 & Rapid Scoring Key
10 Pts • 10 Mins
PROBE 3 Target: Mixed Numbers & Scenarios
Name: Date: Score: ___ / 10
1. Mixed by Fraction 2 pts
Convert and solve: \( 3\frac{1}{3} \div \frac{5}{6} \)
2. Mixed by Mixed 3 pts
Solve in simplest form: \( 2\frac{2}{5} \div 1\frac{1}{5} \)
3. Word Problem with Meaningful Remainder Interpretation 5 pts
A ribbon designer has \( 7\frac{1}{2} \) feet of satin ribbon. Each gift bow requires \( 1\frac{1}{4} \) feet of ribbon.
Show division equation & steps:
How many bows can be made?
How much ribbon is left over?
Teacher Key Rapid Scoring & Intervention Thresholds
Probe 1 Key
1. \( 1 \div \frac{1}{4} = 4 \)
2. 3 jumps of size \( \frac{2}{3} \); Quotient = 3
3. \( \frac{1}{6} \)
4. Divisor is smaller than 1; there are 5 fifths in each whole (total 20).
Student Growth Tracker Sheet Student Dashboard Personal Growth Tracker
My Fraction Division Growth Journey
Goal Focus
Mastery & Independence
Student Name:
Grade/Period:
Teacher:
1. Progress Tracking Chart (Color Your Score)
Shade bars upward to your percentage score
Score: ___%
Baseline Test Placement
Score: ___%
Probe 1 Visual Models
Score: ___%
Probe 2 Procedural Fluency
Score: ___%
Probe 3 Mixed Numbers
Score: ___%
Exit Exam Mastery
0% 25% 50% 75% 100% Mastery
2. My Fraction Division Skills Checklist
Visual Models & Real Meaning
I can draw bar models and number line jumps to find how many parts fit into a whole.
Practicing Got It! Can Teach It
Procedural Fluency & Inversion
I can find reciprocals and multiply by the inverse, simplifying before multiplying.
Practicing Got It! Can Teach It
Mixed Numbers & Word Scenarios
I can rewrite mixed numbers as improper fractions and interpret remainders in story problems.
Practicing Got It! Can Teach It
3. Reflection & Target Goal
One strategy that helps me most:
One mistake I am watching out for:
Student Growth Tracker • Page 1 of 2 Student Progress Dashboard
Teacher Tool
Cohort Progress Monitoring Record
Classroom Data Log
Class Period: _______________ Total Students: _______ Target Date for Exit: _______________
| # | Student Name | Baseline
Targeted Intervention Log & Re-Test Plan
Group A: Visual Models
Students needing tape & number line re-teaching
Group B: Procedural Inversion
Students needing cross-reduction & reciprocal fluency
Fraction Division Exit Assessment Summative Mastery Exit Assessment • CCSS 6.NS.A.1
Fraction Division Exit Assessment
Assessment Total
30 Points Total
Student Name:
Date:
Class/Period:
Instructions: Demonstrate mastery across visual models, standard reciprocal algorithms, and applied word scenarios. Express all numerical answers in simplest terms.
Part I: Visual Models & Conceptual Reasoning (12 Points) Items 1 – 3
1 Tape Diagram Modeling: Whole Divided by Fraction
4 pts
Model the expression \( 4 \div \frac{2}{3} \) using the 4 wholes below. Partition each whole into thirds, group segments by \( \frac{2}{3} \), and determine how many groups of \( \frac{2}{3} \) are formed.
Whole 1
Whole 2
Whole 3
Whole 4
Total groups of size \( \frac{2}{3} \):
\( 4 \div \frac{2}{3} = \)
2 Double Number Line: Measurement Interpretation
4 pts
A science experiment requires \( \frac{3}{5} \) liter of solution per trial. Dr. Ellis has \( \frac{9}{10} \) liter available. Use the double number line below to find how many trials she can complete.
Liters:
0 \( \frac{3}{5} \) (1 trial) \( \frac{9}{10} \) (Total) 1
Trials:
0 1 ?
Division Equation: \( \frac{9}{10} \div \frac{3}{5} = \)
Number of trials:
3 Conceptual Mathematical Reasoning
4 pts
A classmate says: "Dividing by a fraction always makes the answer smaller, just like dividing whole numbers." Explain why this claim is incorrect using an example with \( \frac{1}{2} \).
Exit Assessment • Page 1 of 2 Part I: Visual Models & Concepts
Summative Mastery
Fluency & Mixed Number Scenarios
18 Points Remaining
Part II: Procedural Fluency & Inversion (8 Points) Items 4 – 5
4. Fraction ÷ Fraction 4 pts
Compute and simplify: \( \frac{8}{15} \div \frac{4}{5} \)
Multiply by reciprocal & cross-cancel:
Answer:
5. Whole Number ÷ Fraction 4 pts
Compute and simplify: \( 12 \div \frac{8}{9} \)
Show steps with improper form:
Answer:
Part III: Mixed Numbers & Applied Contexts (10 Points) Items 6 – 7
6 Mixed Number Inversion Operation
4 pts
Convert both values to improper fractions, multiply by the reciprocal, and state the quotient in simplest mixed or whole form:
Fraction Division Mastery Key Teacher Master Key Summative Scoring • Solutions
Fraction Division Mastery Key
Assessment Total
30 Points Total
Comprehensive worked solutions, step-by-step scoring criteria, and visual model benchmarks for evaluating the Fraction Division Exit Assessment.
Part I: Visual Models & Conceptual Reasoning (12 Points) Items 1 – 3
Item Target Skill Exemplar Solution & Work Pts 1 Tape Diagram Model (\( 4 \div \frac{2}{3} \)) Each of the 4 whole bars is partitioned into 3 equal pieces (total 12 thirds). Grouping pairs of thirds (\( \frac{2}{3} \)) yields exactly 6 full groups . Quotient = 6 . 4 pts 2 Double Number Line (\( \frac{9}{10} \div \frac{3}{5} \)) Common denominator: \( \frac{3}{5} = \frac{6}{10} \). \( 1 \) trial = \( \frac{6}{10} \) L. Therefore, \( \frac{9}{10} \) L equals \( 1 \) full trial plus \( \frac{3}{10} \) L (which is half of a trial). Quotient = \( \frac{9}{6} = \frac{3}{2} \) or \( 1\frac{1}{2} \) trials . 4 pts 3 Conceptual Explanation Dividing by a fraction between 0 and 1 asks how many fractional pieces fit into the dividend. Since pieces are smaller than 1, there are more pieces than whole units (e.g. \( 4 \div \frac{1}{2} = 8 \), because each whole contains 2 halves). 4 pts
Part II & III: Procedural Fluency & Mixed Scenarios (18 Points) Items 4 – 7
Item Target Skill Exemplar Solution & Work Pts 4 Fraction ÷ Fraction (\( \frac{8}{15} \div \frac{4}{5} \)) \( \frac{8}{15} \times \frac{5}{4} = \frac{2 \times 1}{3 \times 1} = \) \( \frac{2}{3} \) . (Award 2 pts for correct reciprocal multiplication, 2 pts for simplification). 4 pts 5 Whole ÷ Fraction (\( 12 \div \frac{8}{9} \)) \( \frac{12}{1} \times \frac{9}{8} = \frac{3 \times 9}{2} = \frac{27}{2} = \) \( 13\frac{1}{2} \) . 4 pts 6 Mixed Number Division (\( 3\frac{3}{4} \div 1\frac{7}{8} \)) Convert: \( \frac{15}{4} \div \frac{15}{8} = \frac{15}{4} \times \frac{8}{15} = \frac{1 \times 2}{1 \times 1} = \) 2 . 4 pts
