245
× 38
1960 (245 × 8)
+ 7350 (245 × 30)
9,310 parts
Rubric: 1 pt for accurate answer; 0.5 pt if single calculation slip with correct method.
7. Division (IAS 5.C.2) — 1 pt Quotient: 156
\(3,744 \div 24\):
• 24 goes into 37: 1 time (rem. 13)
• Bring down 4 \(\rightarrow\) 134: 24 goes in 5 times (\(5 \times 24 = 120\), rem. 14)
• Bring down 4 \(\rightarrow\) 144: 24 goes in 6 times (\(6 \times 24 = 144\), rem. 0)
Quotient = 156 (R 0)
8. Decimal Operations (IAS 5.C.8) — 2 pts (1 pt each) Addition & Multiplication
a) 42.85 + 7.6 = 50.45
Must align decimals: \(42.85 + 07.60 = 50.45\).
Watch for: Students adding 5 + 6 without aligning tenths to tenths.
b) 8.4 × 0.35 = 2.940 (or 2.94)
\(84 \times 35 = 2,940\). Three total decimal places (\(1 + 2 = 3\)).
Placing decimal gives 2.940 = 2.94.
9. Fractions with Unlike Denominators (IAS 5.C.4) — 2 pts (1 pt each) Mixed Number Operations
a) \(2\frac{1}{3} + 1\frac{3}{4} = 4\frac{1}{12}\)
Common denominator is 12:
\(2\frac{4}{12} + 1\frac{9}{12} = 3\frac{13}{12} = 4\frac{1}{12}\) (or \(\frac{49}{12}\)).
b) \(5\frac{1}{2} - 2\frac{5}{6} = 2\frac{2}{3}\)
Common denominator is 6:
\(5\frac{3}{6} - 2\frac{5}{6} = 4\frac{9}{6} - 2\frac{5}{6} = 2\frac{4}{6} = 2\frac{2}{3}\) (or \(\frac{8}{3}\)).
10. Fraction Multiplication & Division (IAS 5.C.5 & 5.C.7) — 2 pts Word Problem & Computations
Recipe: \(\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}\) cup
Multiply numerators \(1 \times 3 = 3\); multiply denominators \(2 \times 4 = 8\).
Answer: 3/8 cup of sugar.
Division: i) 12 ii) 1/12
• i) \(4 \div \frac{1}{3} = 4 \times 3 = \mathbf{12}\) (How many thirds in 4 wholes?)
• ii) \(\frac{1}{4} \div 3 = \frac{1}{4} \times \frac{1}{3} = \mathbf{\frac{1}{12}}\) (Dividing 1/4 into 3 parts)
Domain 2 Subtotal: 8 Points Crossroads Math Challenge • Teacher Key Page 2 of 4
KEY
Crossroads Math Challenge • Solutions
Teacher Scoring Guide
Domain 3 Key Algebraic Thinking & Coordinate Graphing Solutions
Total: 7 Points
11. Order of Operations (IAS 5.AT.1) 1 pt • Value: 43
\([(18 - 6) \times 3] + (28 \div 4)\)
\(= [12 \times 3] + 7\)
\(= 36 + 7 = \mathbf{43}\)
Common error: Performing operations from left to right without respecting brackets/parentheses.
12. Writing Expressions (IAS 5.AT.2) 1 pt • Option A
Correct: A. \(6 \times (9 + 4) - 15\)
"Sum of 9 and 4" requires parentheses \((9 + 4)\) so it is evaluated before multiplying by 6. Then 15 is subtracted.
Option C and D fail to group the addition first.
13. Patterns & Function Tables (IAS 5.AT.3) — 2 pts Completed Table & Rule
Relationship Analysis:
The y-value is always 3 times the x-value (\(y = 3x\)). Alternatively: for every increase of 2 in x, y increases by 6.
1 pt for table cells; 1 pt for stating relationship.
14. Coordinate Graphing (IAS 5.AT.4) 2 pts
Check for accurately plotted points:
• (0, 0) at origin
• (2, 6) right 2, up 6
• (4, 12) right 4, up 12
• (6, 18) right 6, up 18
Points form a straight line passing through origin.
15. Directional Coordinates (IAS 5.AT.5) 1 pt
"Start at the origin (0, 0). Move 7 units right along the horizontal x-axis, then move 4 units up along the vertical y-axis."
Common error: Reversing coordinates (moving 4 right, then 7 up). Reinforce (x, y) = (horizontal, vertical).
Domain 3 Subtotal: 7 Points Crossroads Math Challenge • Teacher Key Page 3 of 4
KEY
Crossroads Math Challenge • Solutions
Teacher Scoring Guide
Domains 4 & 5 Key Measurement, Geometry & Data Solutions
Total: 8 Points
16. Unit Conversions (IAS 5.M.1) — 2 pts
4 yards:144 inches (\(4 \times 36\))
3.5 liters:3,500 mL (\(3.5 \times 1,000\))
48 ounces:3 pounds (\(48 \div 16\))
All 3 correct = 2 pts; 2 correct = 1 pt; 1 correct = 0.5 pt.
17. Volume of Prisms (IAS 5.M.2 & 3) — 1 pt
\(V = l \times w \times h\)
\(V = 8 \times 5 \times 4\)
\(V = 40 \times 4 = \mathbf{160\text{ cm}^3}\)
Students may also calculate base area \(B = 8 \times 5 = 40\) then \(V = B \times h = 40 \times 4 = 160\).
18. 2D Figure Classification (IAS 5.G.1 & 5.G.2) — 2 pts
a) Rectangle / Parallelogram:
ALWAYS
Rectangles have 2 pairs of parallel sides.
b) Rhombus / Square:
SOMETIMES
Only when all 4 angles are 90°.
c) Trapezoid / Quadrilateral:
ALWAYS
Trapezoids have exactly 4 sides.
19. Line Plot with Fractional Data (IAS 5.DS.1) — 3 pts
Plot Frequencies: 2 1/4: 3 ✕'s | 2 1/2: 2 ✕'s | 2 3/4: 1 ✕ | 3: 1 ✕ | 3 1/4: 1 ✕
Part a: Shorter than 2 1/2 in = 3 caterpillars (those at 2 1/4 in). (1 pt)
Part b: \(3\frac{1}{4} - 2\frac{1}{4} = \mathbf{1\text{ inch}}\) difference. (1 pt)
Indiana Academic Standards (IAS) Remediation Guide
| Domain / IAS Standard | Questions | Targeted Intervention Strategy |
|---|---|---|
| 5.NS: Number Sense | Q1 - Q5 | Use base-ten blocks and place value charts to visualize 10x shifts. Emphasize adding trailing zeros for decimal comparison. |
| 5.C: Computation | Q6 - Q10 | Use fraction bars/area models for unlike denominators. Practice unit fraction division word problems with bar models. |
| 5.AT: Algebraic Thinking | Q11 - Q15 | Color-code grouping symbols in order of operations. Use physical floor grid or "over then up" mnemonic for (x, y) coordinates. |
| 5.M / 5.G / 5.DS: Geom & Data | Q16 - Q19 | Build 3D prisms with unit cubes to link layer area to volume formula (\(V = B \times h\)). Use Venn diagrams for 2D shape hierarchy. |
Domains 4 & 5 Subtotal: 8 Points | Total Packet Points: 30 Points
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