Climber's 2 Numbers & Sum:
Why this combination works best:
Summit Sums • Triple-Digit Strategy Game Mathematical Practices: MP1 (Make sense of problems) • MP3 (Construct viable arguments) Page 2 of 2
• Greedy Hundreds: Placing the highest rolled digits in the hundreds place (e.g., 600 + 500), immediately exceeding 1,000. Prompt: "What is 600 + 500? Can you reach the summit if you start above 1,000?"
• Compensation Direction: Adding instead of subtracting the borrowed amount in step 3 (e.g., 498 + 325 → 500 + 325 = 825, then doing 825 + 2 = 827). Prompt: "Did you make the original number bigger or smaller when you rounded? How do you balance it?"
• Place Value Slip in Partial Sums: Treating tens like single units (e.g., in 50 + 70 writing 12 instead of 120). Prompt: "Are those 5 ones or 5 tens? What is 5 tens plus 7 tens?"
Summit Sums • Teacher Facilitation Guide Page 1 of 2
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Strategic Placement: "Look at your 6 dice. Before writing, what hundreds digits will guarantee your sum stays in the 800s or 900s?"
Method Comparison: "You solved this with standard algorithm. If you had to explain this mentally to someone without paper, what strategy would you choose?"
Efficiency Check: "Why is Friendly Numbers faster for 396 + 428 than for 342 + 423? What digit makes the difference?"
Partner Verification: "Partner 2, did Partner 1's second strategy prove the first answer was correct? Did they arrive at the same total?"
Sample Round: Climber rolls [ 5, 2, 8, 4, 3, 1 ] Optimal Target: 979 or 965
Digit Arrangement: 548 + 431 = 979 (or 531 + 428 = 959)
Route 1 (Partial Sums): 500+400=900; 40+30=70; 8+1=9 → 979
Route 2 (Friendly Numbers): 548+2=550; 550+431=981; 981-2=979
Expedition Log Key (Page 2 Prompts):
Prompt 1 (Digit Placement):
Exemplar Answer: The Hundreds place has a place value 100 times larger than the Ones place. If I put high digits (like 5 and 6) in the Hundreds, the sum is already 1,100, which busts. I put digits that add to 8 or 9 (like 5 and 4, or 6 and 3) in the Hundreds place to get as close to 1,000 as possible.
Prompt 2 (Strategy Comparison):
Exemplar Answer: Compensation was much faster when an addend ended in 8 or 9 (e.g., 498) because adding 2 makes an exact hundred (500), eliminating the need for regrouping. Partial sums was better when numbers were scattered (like 342 + 235) with no digits near a friendly hundred.
Prompt 3 (Guide Challenge: 6, 5, 4, 3, 2, 1):
Optimal Solution: 641 + 352 = 993 (Difference of only 7 from 1,000!) or 642 + 351 = 993, or 651 + 342 = 993. Hundreds must be 6 and 3 (600+300=900). Tens must be 5 and 4 (50+40=90). Ones must be 2 and 1 (2+1=3). Total = 993. Any pair with hundreds 6 and 4 gives 1,000+ which immediately busts.
Support (Tier 1/2)
Provide base-ten value mats. Allow students to roll 4 dice first (two 2-digit numbers targeting 100) before transitioning to 3-digit addends.
On-Level (Tier 1)
Standard 6-sided dice targeting 1,000. Require one mental-focused strategy (Partial Sums or Compensation) and written verification.
Extension (Enrichment)
The Subtraction Avalanche: Start at 1,000 and subtract two 3-digit rolled numbers to get closest to exactly 0 without negative altitude!
Calculation Fluency (4 pts) Accurately computes 3-digit sums using at least two distinct mathematical strategies.
Strategic Reasoning (4 pts) Places rolled digits strategically into place values to optimize proximity to 1,000.
Mathematical Discourse (4 pts) Clearly articulates why a specific strategy was chosen using place value vocabulary.
Summit Sums • Teacher Facilitation Guide & Answer Key Page 2 of 2
