A 4-lesson Indiana Academic Standards ratio sequence preparing 6th graders for ILEARN. Covers ratio representations, equivalent ratio tables and graphs, unit rates, and mixed test-prep items with authentic item formats.
A school garden has 15 tomato plants, 10 pepper plants, and 5 cucumber plants. Which statements accurately describe the ratios within the garden?
Select THREE that apply:
A. The ratio of cucumber plants to tomato plants is \( 1 : 3 \).
B. The ratio of pepper plants to total plants in the garden is \( \frac{1}{3} \).
C. For every 2 pepper plants, there are 3 tomato plants.
D. The ratio of total plants to cucumber plants is 5 to 30.
E. The ratio of tomato plants to pepper plants is \( 2 : 3 \).
Indiana Academic Standards • 6th Grade Math Page 2 of 2
Mix 2 Ratio Table (Target: 12 cups black)
Conclusion & Justification:
Indiana Academic Standards • 6th Grade Math Page 1 of 2
Ratio Table Challenge • Page 2
IAS 6.AF.9 | Tables to Coordinate Graphs
3 Plotting Equivalent Ratios on the Coordinate Plane
Marcus earns $15 for every 2 hours he works assisting at the community garden.
Step A: Fill Table & Coordinates
Hours (\(x\))
Earnings (\(y\))
Ordered Pair \((x,y)\)
2
$15
(2, 15)
4
_____
(_, _)
6
_____
(_, _)
8
_____
(_, _)
Step C: Graph Observation
What pattern do you notice when you connect the points? Does the line pass through \((0, 0)\)?
Step B: Plot the Points 2 4 6 8 Hours Worked (x) 15 30 45 60 Earnings ($) (y) 0
A printer prints 35 pages every 2 minutes. The relationship is graphed on a coordinate plane with time in minutes on the \(x\)-axis and pages printed on the \(y\)-axis. Which of the following ordered pairs lie on the graph of this ratio relationship?
Select ALL that apply:
A. \( (4, 70) \)
B. \( (1, 17.5) \)
C. \( (6, 100) \)
D. \( (10, 175) \)
E. \( (70, 4) \)
Indiana Academic Standards • 6th Grade Math Page 2 of 2
2 Part 2 Solutions: Comparing Paint Mixtures
Mix 1 (Target 12 black) 16 White : 12 Black
Multiplied original ratio \(4:3\) by 4.
Mix 2 (Target 12 black) 15 White : 12 Black
Multiplied original ratio \(5:4\) by 3.
Exemplar Student Justification: "Mix 1 is lighter. When both mixtures have 12 cups of black paint, Mix 1 has 16 cups of white paint while Mix 2 has only 15 cups of white paint. Since Mix 1 has more white paint for the same amount of black paint (\( \frac{16}{12} > \frac{15}{12} \)), Mix 1 produces the lighter shade."
Indiana Academic Standards • Teacher Guide Page 1 of 2
Ratio Tables Teacher Guide • Page 2
Coordinate Graphs & ILEARN Item Rationales
3 Part 3 Solutions: Coordinate Graphing
Ordered Pairs Solution:
• \( (2, \$15) \) — given
• \( (4, \$30) \) — \(15 \times 2\)
• \( (6, \$45) \) — \(15 \times 3\)
• \( (8, \$60) \) — \(15 \times 4\)
Key Conceptual Takeaway:
The graphed points form a straight line that extends through the origin \( (0, 0) \). This confirms a proportional relationship where 0 hours worked yields $0 earned.
4 ILEARN Item 8: Distractor Analysis
Correct Answers: A, B, and D
Option A (4, 70) [CORRECT]: Multiplying 2 minutes by 2 yields 4 minutes; 35 pages × 2 = 70 pages.
Option B (1, 17.5) [CORRECT]: Unit rate of printing is \( 35 \div 2 = 17.5 \) pages per 1 minute.
Option C (6, 100) [INCORRECT]: Common error: student added 30 instead of multiplying by 3 (\(35 \times 3 = 105\), not 100).
Option D (10, 175) [CORRECT]: Multiplying 2 minutes by 5 yields 10 minutes; 35 pages × 5 = 175 pages.
Option E (70, 4) [INCORRECT]: Classic coordinate reversal trap! The question specifies \(x\) as time (minutes) and \(y\) as pages, making \((4, 70)\) correct and \((70, 4)\) inverted.
Remediation & Common Student Traps
Additive Thinking Trap
If a student sees \(2:5\) and thinks the next entry is \(4:7\) (adding 2 to each), show them with concrete fraction models that \( \frac{2}{5} \neq \frac{4}{7} \).
Small Group Scaffold
For struggling learners, always guide them to find the unit rate (value for 1) first. Once the unit rate is found, finding any column simply requires multiplying by that value.
Indiana Academic Standards • Teacher Guide Page 2 of 2
Solving two-step rate problems on ILEARN is simple when you find 1 unit first! Slide 4 of 5
Whiteboard Challenge: ILEARN Warmup
SOLVE & HOLD UP
Farmer Eli harvests 180 ears of Indiana sweet corn in 15 minutes.
TASK A: Unit Rate How many ears of corn does he harvest per minute?
\( 180 \div 15 = 12 \) ears/min
TASK B: Extension At this rate, how many ears will he harvest in 25 minutes?
\( 12 \times 25 = 300 \) ears
Get ready to reveal your whiteboards! Slide 5 of 5
Part A:
What is the crew’s unit seeding rate in square feet per hour?
Rate: ________ sq ft/hr
Part B:
The entire park soccer field has an area of 12,000 square feet. If the crew continues to work at this exact same rate, how many total hours will it take to seed the entire field?
Total Time Needed: ________ hours Show all division steps above
Indiana Academic Standards • 6th Grade Math Page 2 of 2
12 fencing boards for $75.00
Unit Cost: $_______ / board
Which store offers the better buy per fencing board? Justify your choice:
At the Indiana State Fair, an embroidery machine produces award ribbons. The machine creates 45 ribbons in 18 minutes at an unvarying, constant speed.
Part A (4 Points): Unit Rate & Tape Diagram
Find the unit production rate in ribbons per minute. Then draw or complete a diagram showing how many ribbons are made in 1 minute.
Tape Diagram / Visual Model:
Unit Rate: ________ ribbons/min
Part B (4 Points): Application & Explanation
The state fair coordinators place an order for 360 prize ribbons. How many minutes will it take the machine to fulfill this entire order? Write an explanation of how you used the unit rate to find the answer.
Final Answer: ________ minutes
Indiana ILEARN Math Assessment Simulation • Grade 6 Page 2 of 2
Item 5 Performance Task Rubric & Exemplars
IAS 6.AF.10 • 8 Total Constructed Response Points
Part A Rubric: Unit Rate & Visual Model (4 Points) 45 ribbons / 18 min = 2.5 ribbons/min
Score
Performance Criteria
4 Pts
Correct unit rate of 2.5 ribbons per minute (or \( \frac{5}{2} \) ribbons/min) with accurate division shown, AND a clearly drawn tape diagram/bar model showing the 45:18 ratio or unit scale.
3 Pts
Correct unit rate (2.5) with minor computational flaw in diagram, OR correct diagram with inverted rate (\(18/45 = 0.4\)).
2 Pts
Recognizes division is required (\(45 \div 18\)) but computational error made; incomplete diagram.
0-1 Pt
Incorrect arithmetic and no conceptual visual model.
Part B Rubric: Application & Explanation (4 Points) 360 ribbons ÷ 2.5 = 144 minutes
Score
Performance Criteria
4 Pts
Correct answer of 144 minutes (or 2 hours 24 minutes) with clear written justification explaining that dividing 360 ribbons by the unit rate of 2.5 ribbons per minute gives 144 minutes.
3 Pts
Correct answer of 144 minutes with minimal written justification, OR correct method (\(360 \div \text{Part A rate}\)) carried out correctly following an incorrect Part A.
2 Pts
Correct mathematical setup (\(360 \div 2.5\)) with division arithmetic error.
0-1 Pt
Incorrect operation (e.g. \(360 \times 2.5\) or \(360 - 45\)) with flawed reasoning.
Exemplar Full-Credit Written Response (8/8 Pts):
“For Part A, I divided 45 ribbons by 18 minutes to get 2.5 ribbons per minute. In my diagram, 1 minute corresponds to 2 and a half ribbons. For Part B, since the machine produces 2.5 ribbons every single minute, I divided the target 360 ribbons by 2.5 ribbons per minute: \( 360 \div 2.5 = 144 \). It will take exactly 144 minutes (or 2 hours and 24 minutes) to complete the 360 ribbons.”
