| Objectives | Students will be able to: (1) generate equivalent fractions and simplify to lowest terms fluently; (2) convert between mixed numbers and improper fractions. |
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| Materials | Fraction walls (support); equivalence chains; conversion strips. |
| Key vocabulary | equivalent, lowest terms, mixed, improper |
| Engage (starter) | (10 min) The toolkit inspection: before fractions can be added, compared or conquered, three tools must be sharp — equivalence, simplifying, conversion. Today: the sharpening. |
| Develop (main) | (35 min) 1. Equivalence engine re-proved (×1 in disguise) then drilled: three names each for four fractions. 2. Simplifying with the biggest-common-divider hunt: 12/18 → 2/3 in one cut. 3. Conversion sprints both ways (17/5 ↔ 3 2/5, the division-remainder link recited). 4. Tracker-honest speed check: ten mixed toolkit items. |
| Plenary (close) | (10 min) Toolkit verdicts: which tool is each student's sharpest, which needs the stone? |
| Assessment | Speed check 8 of 10; one-cut simplification achieved at least once; conversions fluent. |
| Teacher notes | Toolkit speed is what separates fraction success from fraction suffering in Weeks 2-4 — an hour invested here repays itself every day until the exam. |
| Objectives | Students will be able to: (1) add and subtract fractions with different denominators using common denominators; (2) explain why same-size pieces are required. |
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| Materials | Fraction strips; common-denominator frames; the "same pieces" anchor chart. |
| Key vocabulary | common denominator, unlike, rename |
| Engage (starter) | (10 min) The impossible addition: 1/2 + 1/3 — "halves and thirds are DIFFERENT-SIZED pieces; you cannot count them together any more than you can add 2 goats and 3 chickens and get 5 goats!" Rename both in SIXTHS: 3/6 + 2/6 = 5/6. |
| Develop (main) | (35 min) 1. The common-ground hunt: smallest number both denominators divide into (6 for 2 and 3; 12 for 3 and 4). 2. Rename-then-operate modelled twice with strips as proof. 3. Six-pack rising: unlike pairs, one subtraction, one answer needing simplifying. 4. The goat-and-chicken explanation retold by two students in their own words. |
| Plenary (close) | (10 min) One full solution performed: hunt, rename, operate, simplify — the four-beat rhythm chanted. |
| Assessment | 4 of 6 correct with renaming shown; the same-pieces reasoning retold; one simplified answer. |
| Teacher notes | The four-beat rhythm (hunt, rename, operate, simplify) is the procedure — but the goats-and-chickens WHY is what survives exam pressure. Test the why, not just the how. |
| Objectives | Students will be able to: (1) add and subtract mixed numbers including regrouping cases (3 1/4 - 1 3/4); (2) choose between whole-and-parts and improper-conversion methods. |
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| Materials | Fraction circles; two-roads frames; problem strips. |
| Key vocabulary | mixed number, regroup, convert |
| Engage (starter) | (10 min) The carpenter's cut: a board of 3 1/4 metres, cut 1 3/4 m for a shelf — "take 3/4 from 1/4?! Not enough!" The regrouping ghost returns wearing fraction clothes: break one whole into 4/4. |
| Develop (main) | (35 min) 1. Road one: whole-and-parts (wholes together, parts together, regroup when short). 2. Road two: convert both to improper, operate, convert back. 3. Same problem down both roads — same answer, different journey. 4. Six-pack with road of choice; one addition crossing a whole (2 3/4 + 1 1/2). |
| Plenary (close) | (10 min) Roads census with reasons: improper is safer under pressure; whole-and-parts is faster when clean. Wisdom is matching road to problem. |
| Assessment | 4 of 6 correct by chosen road; the regrouping case survived; road choice justified once. |
| Teacher notes | The G3 break-a-ten and today's break-a-whole are the SAME move — say so explicitly; students who see mathematics rhyming across years trust it more. |
| Objectives | Students will be able to: (1) compute fractions of quantities fluently (3/5 of 45); (2) solve reverse problems (2/3 of a number is 24 — find the number). |
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| Materials | Bar-model frames; quantity problem packs (catch shares, land plots, savings). |
| Key vocabulary | of, reverse, whole, bar model |
| Engage (starter) | (10 min) The savings reveal: "Marcia saved 3/4 of her market earnings — $600 saved. What did she EARN?" The reverse gear: if 3 parts are 600, one part is 200, four parts are $800. The bar model draws the logic. |
| Develop (main) | (35 min) 1. Forward drills: divide-by-bottom-times-by-top on six quantities. 2. The bar model formalised: whole bar, parts shaded, known value labelled. 3. Reverse problems via the bar: find one part, rebuild the whole — four cases. 4. Mixed forward/reverse pack where students must first DIAGNOSE the direction. |
| Plenary (close) | (10 min) Direction diagnosis drill: five problems read aloud; class calls "forward" or "reverse" with the tell ("of a known whole" vs "is a known part"). |
| Assessment | Forward 5 of 6; reverse 3 of 4 with bar drawn; diagnosis 4 of 5. |
| Teacher notes | Reverse fraction problems are prime exam discriminators — and the bar model is the great equaliser, turning abstract reversal into a picture any student can rebuild. |
| Objectives | Students will be able to: (1) consolidate the week's fraction operations; (2) complete the week checkpoint. |
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| Materials | All kits; checklist; trackers. |
| Key vocabulary | All week vocabulary |
| Engage (starter) | (10 min) Medley: one toolkit sprint, the four-beat rhythm chanted, one direction diagnosis. |
| Develop (main) | (35 min) Checkpoint circuit: T1 toolkit strip (equivalence, simplify, convert); T2 two unlike-denominator operations; T3 one mixed-number subtraction with regrouping; T4 one forward and one reverse quantity problem with bar model. Trackers updated. |
| Plenary (close) | (10 min) Preview: "Next week the DECIMAL — fractions' ten-based cousin — takes the stage, with money as its home ground." |
| Assessment | Checkpoint across four stations; regrouping case and reverse problem are the discriminators. |
| Teacher notes | Fractions return in Wave 2 for multiplication and division — this week's flag is planted on add/subtract ground. Tracker gaps here get homework packs before the topic compounds. |