Adding Fractions by Matching Units

Create the complete core lesson for Section 7.8-A. Use Arin only. Follow this sequence and include every equation and learning pause. 1. Open with 1/2 + 1/4 = ?. Ask what happens when one-half and one-fourth are combined. 2. VISUALISE UNITS: show halves and fourths as differently sized fractional pieces. Explain why they cannot be combined directly as if they were identical units. 3. MAKE UNITS MATCH: subdivide one-half into fourths and show 1/2 = 2/4. 4. COMBINE VISUALLY: show 2/4 + 1/4 = 3/4; animate three equal fourth-pieces joining. 5. SAME DENOMINATOR: show 2/5 + 1/5 = 3/5. Add the number of fifths and retain the denominator. Also show 3/7 + 2/7 = 5/7. 6. EXPLAIN THE RULE: same denominator → add numerators → keep the denominator. Explain that the denominator names the size/type of fractional unit, so denominators are not added. 7. QUICK PRACTICE with thinking pauses: 3/8 + 2/8 → reveal 5/8; 1/3 + 1/6 → show 1/3 = 2/6, then 2/6 + 1/6 = 3/6 = 1/2. 8. MEMORY CARD: Check units → make them the same if needed → combine. Tease that the next lesson will focus on addition with different denominators. Core equations to display accurately: 1/2 = 2/4 2/4 + 1/4 = 3/4 2/5 + 1/5 = 3/5 3/7 + 2/7 = 5/7 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 Use fraction strips or circles divided into equal parts. Every partition must be equal. Pause before practice answers. Do not teach the full common-denominator method for unrelated examples beyond what is needed to illustrate 1/3 + 1/6.