1,081
Two-Digit Breakdown: • Row 1 (ones): 3 × 47 = 141.
• Row 2 (tens): 20 × 47 = 940.
• Check: Zero placeholder must be present in ones place of second line.
10 Ans: 11,250 (10 pts)
625
×18
5000
+ 6250
11,250
Multi-Step carrying: • Row 1: 8 × 625 = 5,000.
• Row 2: 10 × 625 = 6,250.
• Total product = 11,250.
• Watch for carry-over addition errors.
Answer Key: Multiplication
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Teacher Answer Key Assessment Tool
Grades 4-5 Diagnostic • Phase 4 Word Problems
EVALUATOR
11
Carabiners: 1,220 • Difference: 230
Part A (Addition): Calculate total safety carabiners.
895 (ordered) + 325 (in stock) = 1,220 total carabiners
Part B (Subtraction): Difference between ropes and carabiners.
1,450 (climbing ropes) - 1,220 (total carabiners) = 230 more ropes
Common Error: Students might subtract the 325 directly from ropes or fail to compute the intermediate total first.
12
630 Crates
Multiplication Setup: 18 sleds × 35 crates per sled.
35 × 18 = 35 × (10 + 8)
• 35 × 8 = 280 (partial product)
• 35 × 10 = 350 (partial product)
• 280 + 350 = 630 total crates
Key Focus: Ensuring standard vertical multi-digit layout. Points awarded for correct carrying (40 + 240) and zero placement.
13
$810 remaining
Step 1: Calculate Adult Permit Cost: 12 × $145 = $1,740.
Step 2: Calculate Youth Helper Permit Cost: 6 × $75 = $450.
Step 3: Sum total expenditure: $1,740 + $450 = $2,190.
Step 4: Subtract from budget: $3,000 - $2,190 = $810 remaining.
Common Error: Multiplying only one set or subtracting passes from budget before calculating total youth helper expenses.
Answer Key: Applied Trails
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Teacher Resources Diagnostic Insights
Scoring Breakdown, Error Guides, and Standard-Aligned Checklists
| Skill Category | Full Credit (100%) | Partial Credit (50%) | No Credit (0%) |
|---|---|---|---|
| Phase 1: Addition | Correct sums with aligned carrying numbers shown. | One calculation slip but correct place alignment and carried digits. | Incorrect place alignment or missing carried values. |
| Phase 2: Subtraction | Correct differences showing regrouped values above zeros. | Correct borrowing process but minor fact errors (e.g., 14-8=5). | Subtracted smaller digit from larger digit (e.g., 0-3=3). |
| Phase 3: Multiplication | Both partial products correct, with carrying and 0 placeholder visible. | Forgot zero placeholder OR made an arithmetic carrying mistake. | Single line multiplication or failed to write partial products. |
| Phase 4: Word Problems | Correct multi-step calculations with workspaces filled; appropriate labels. | Correct setup but calculation mistake; or correct values with no work shown. | Wrong operational choices (e.g. adding instead of multiplying). |
4.NBT.B.4 (Addition & Subtraction) Fluently add and subtract multi-digit whole numbers using standard algorithms. (Problems 1-6)
4.NBT.B.5 / 5.NBT.B.5 (Multiplication) Multiply multi-digit whole numbers (up to 2-digit by 2-digit) using equations or partial products. (Problems 7-10)
4.OA.A.3 / 5.NBT.B.5 (Word Problems) Solve multi-step word problems posed with whole numbers using the four operations. (Problems 11-13)
90 - 100% Summit Mastery Ready for advanced grade-level work.
75 - 89% Basecamp On-Track Target specific operations with minor mistakes.
50 - 74% Developing Climber Struggling with regrouping steps or placeholders.
Below 50% Intensive Guide Needs conceptual intervention on place value.
Evaluation Guides & Standards Tracking
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