F7 · Mixed Numbers: Two Ways to Add and Subtract
“I can add and subtract mixed numbers in two ways — by converting to fractions greater than 1, and by working with wholes and parts separately — and I estimate first so I can tell whether my answer is reasonable.”
1 3/4 + 2 1/2. Estimate first: 1 3/4 is close to 2, and 2 1/2 is between 2 and 3, so the sum should land between 4 and 5. Method 1 — wholes and parts separately: wholes 1 + 2 = 3; parts 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4; total 3 + 1 1/4 = 4 1/4. Method 2 — convert to fractions greater than 1: 1 3/4 = 7/4 and 2 1/2 = 5/2 = 10/4; 7/4 + 10/4 = 17/4 = 4 1/4. Same answer both ways — they must agree, because both count the same total amount. Model: bars showing 1 whole + 3 quarters beside 2 wholes + 2 quarters (renamed), beside a number line in quarters: start at 1 3/4, jump 2 wholes, then jump 2/4 more, land on 4 1/4.
Why must Method 1 and Method 2 give the same answer?
1 1/3 + 1 1/6. Parts way: wholes 2; parts 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 → 2 1/2. Check by converting: 4/3 + 7/6 = 8/6 + 7/6 = 15/6 = 5/2 = 2 1/2 ✓
“2 3/5 + 1 1/5: convert first — 2 3/5 = 13/5 and 1 1/5 = 6/5. So 13/5 + 6/5 = 19/5 = ___ as a mixed number” → 3 4/5
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.