Success criteria
- I can explain why unlike fractional units must be renamed.
- I can add or subtract and simplify.
- I can estimate the size of the answer before calculating.
Explain
Adding thirds directly to fourths is like adding metres directly to centimetres without choosing a common unit. Draw fraction bars to show why twelfths work for 2/3 + 3/4, then explain the renaming in words.
Independent practice
For 2/3 + 3/4, enter the numerator of the simplified answer.
The full answer is 17/12. Which estimate makes sense?
2/3 and 3/4 together are more than one whole but far below two.
For 5/6 − 1/4, enter the numerator of the simplified answer.
Check the denominator after solving: the simplified difference is 7/12.
Transfer
A board is 5/6 m long. A damaged 1/4 m section is removed. Draw and calculate the usable length, then explain why subtracting denominators would describe the wrong-sized pieces.
Delayed check
Four days later, solve 3/5 + 7/10 and 7/8 − 1/3 with estimates and no model unless you choose one.
Evidence and next step
Save one model-to-equation explanation at jeremy/portfolio/math/unit-3/unlike-fractions.md.
- Efficient and explained on two days → continue.
- Method correct but estimate absent → estimate two new sums without calculating.
- Denominators added/subtracted → rebuild with equal-size fraction strips.