tlh teacher’s little helper
Lesson plan

Adding and subtracting fractions

Teacher-facing plan: I do · We do · You do.

Anchor the whole lesson on one big idea and say it often: you can only add or subtract parts that are the same size. The denominator is the name of the part; adding fractions is just counting parts, so the parts must share a name first.

1. Same denominators — counting parts (3 min)

Model 2/5 + 1/5 with fraction strips: "Two fifths and one more fifth is three fifths. I am counting fifths, the same way I count apples. The name of the part — fifths — does not change."

2. Related denominators — rename, then count (8 min)

Pose 1/3 + 1/6. Think aloud: "These parts have different names — thirds and sixths — so I can't count them together yet. But 6 is a multiple of 3, so these are related denominators. I only need to rename ONE fraction."

1/3 + 1/6 → rename 1/3 as 2/6 thirds 1/3 sixths 1/6 1/6 1/6 1/3 covers exactly two sixths → 1/3 = 2/6 2/6 + 1/6 = 3/6 = 1/2 ×2 on top and bottom: 1/3 = (1×2)/(3×2) = 2/6
The fraction wall shows why 1/3 and 2/6 are the same amount — then the addition is just counting sixths.

Show the written strategy beside the wall: multiply numerator and denominator of 1/3 by 2 to get 2/6, then 2/6 + 1/6 = 3/6 = 1/2. Always finish by asking "Is my answer in simplest form?"

3. Subtraction works the same way (4 min)

Model 7/8 - 1/4: "8 is a multiple of 4, so I rename 1/4 as 2/8. Now 7/8 - 2/8 = 5/8." Reinforce: we renamed the quarter, we never touched the eighths — always rename the fraction with the smaller denominator.

Guided practice on mini whiteboards. Work through each problem as a class using the three-step routine — students chant it back before each question:

  1. SAME? Are the denominators the same? If yes, just count the parts.
  2. RENAME. If not, find the related denominator (the bigger one) and rename the other fraction using equivalence.
  3. COUNT & SIMPLIFY. Add or subtract the numerators, keep the denominator, then simplify or write as a mixed number.

Whiteboard sequence (reveal one at a time, students hold up answers, discuss errors immediately):

  1. 3/8 + 2/8 — same denominators (answer 5/8)
  2. 1/2 + 1/4 — rename 1/2 as 2/4 (answer 3/4)
  3. 2/3 + 1/6 — rename 2/3 as 4/6 (answer 5/6)
  4. 9/10 - 2/5 — rename 2/5 as 4/10 (answer 5/10 = 1/2 — insist on simplest form)
  5. 3/4 + 1/2 — answer goes past one whole: 3/4 + 2/4 = 5/4 = 1 1/4

Students complete the Adding and Subtracting Fractions worksheet independently. It ramps through five sections: same denominators → equivalence warm-up → related denominators → mixed numbers and beyond one whole → worded problems, plus an optional challenge.

  • Everyone: Sections 1–3.
  • Most: Sections 1–4 and the worded problems in Section 5.
  • Challenge: Section 6 (three related fractions, missing-number puzzles).

Fraction walls and fraction strips stay on desks throughout — using the model is a strategy, not a crutch. Require the renaming step to be written for every related-denominator question; a bare answer does not show the mathematics.

Teacher table: run the reteach group (identified by the hinge question) with fraction strips, staying on physically-modelled same-denominator and halves/quarters questions until students can verbalise why the parts must match.