Mia is baking two batches. Batch 1 uses 3/4 cup of sugar. Batch 2 uses 2/3 cup. She started with 2 cups of sugar. How much is left? Estimate first: batch 1 is close to 1 cup, batch 2 is close to 1/2 to 2/3 of a cup — total used ≈ 1 1/2 cups, so about 1/2 cup should be left. Step 1 — total used: 3/4 + 2/3. Product method, denominator 12: 9/12 + 8/12 = 17/12 = 1 5/12 cups. Step 2 — left over: 2 − 1 5/12 = 7/12 cup. Reasonableness check: 7/12 is a bit more than 1/2 — close to the estimate of about 1/2 ✓. Model: bars in twelfths for the two batches, then a 2-cup bar with 1 5/12 crossed out, beside a 0–2 number line in twelfths: jump 9/12, then 8/12 to 17/12, then the gap from 17/12 up to 2 is 7/12.

Tom walks 5/6 km to the park, then 1/2 km more to the store. How far does he walk in total? → in sixths: 5/6 + 3/6 = 8/6 = 1 1/3 km