Skill: course-build → write-mcqs @ b0fa825
Topic 15 — question types in the PP100 bank, one exemplar each (2 October 2026, v2 — the blind read, guidance and figure reviews applied; ids are the v2 positions, PP-1 … PP-51; v3 polish: the fourth option on the four type-7 items is a mass-based distractor, and PP-46\* stirs protein powder)
James reviews a bank as its question TYPES first, one exemplar each (vault: 50 Decisions/A bank is reviewed as its question types first, one exemplar each.md). This sheet lists the ten types the Grade 4 Topic 15 bank runs on and prints one exemplar per type in full as it ships in content/G4T15_pp100_bank.py. Item ids are the bank's positions (PP-1 … PP-51; v1's PP-9, the loaf, is cut, so every v1 id from PP-9 on is one lower here). Every bank item carries type_, its number below. Typed items are marked \*.
One cluster. The topic is one PP100 cluster of three atoms (MAT4-040 → 041 → 042, capstone 042). Items per atom: 16 · 18 · 18. Tiers: 17 easy · 19 medium · 16 hard (11 typed numeric, 5 four-option MCQs). No term is coined in this topic, so the hard tier recalls none; it produces numbers.
The bar list (things a generated bank must never use because they break the taught claim): nothing that fizzes or makes a gas (baking soda and vinegar, a fizzing tablet — stuff leaves as gas; that is Topic 16's and Grade 5's); nothing hot or melting (ice, a steaming drink — water leaves as vapour); nothing eaten, peeled or thrown away unless the item is ABOUT stuff taken away (types 2 and 4); soil in water is a mixture, never called a solution; no "weigh / weight" anywhere; "lighter" only inside a quoted belief; the chocolate bar, the cracker, the clay, the rice and beans, the sugar and water are the lessons' own things and never appear as a bank scene; no headache character (Miss Vance, Finley, Fiona, Frances) appears in a bank item — claim-makers are "a girl" / "a boy".
⟂ draw constraints (never in one PP100 draw; v2): PP-6 ⟂ PP-7 (the same true-sentence set); PP-12 ⟂ PP-13 (a pan balance, two pieces stated); PP-26 ⟂ PP-27 ⟂ PP-41\ (the reverse move three times) and PP-40\ ⟂ PP-41\ (the reverse move typed, from a drawing and from the stem); PP-39\ ⟂ PP-40\ (the two drawn-reading typed items of MAT4-041); PP-12 ⟂ PP-29 (level pans, whole against pieces); PP-20 ⟂ PP-21 (which-case pair, the same four kinds); PP-37 ⟂ PP-51 (a reading 2 / 5 grams short); PP-14 ⟂ PP-33 (two cups mixed, the number asked); PP-46\ ⟂ PP-17 (a dissolved powder's mass added to one reading).
Freshness (v2 correction). v1 claimed every bank item was a fresh instance. The blind readers found lesson scenes renamed (v1 ids, with the v2 id in brackets): PP-8 / PP-9 (L01 q9's reason set; PP-9 cut), PP-13 (L02 q8; now PP-12), PP-17 / PP-37 (L03 q3; now PP-16 / PP-36), PP-40 / PP-41 (L02 q5; now PP-39\ / PP-40\), PP-46 (L03 q9; now PP-45\), PP-47 (L03 q11; now PP-46\), and clone pairs PP-6 / 7, PP-13 / 14 (now 12 / 13), PP-27 / 28 (now 26 / 27), PP-40 / 41 (now 39 / 40). v2 cuts the loaf, re-scenes or re-moves the rest (a different MOVE, not only a different noun: three pieces instead of two; the whole and one piece drawn; three cups; one reading drawn and the other stated) and marks the pairs ⟂ above. The reviewer's three Topic 14 scenes (oats and nuts, bath salts, birdseed) are re-scened too.
The ten types
| # | Question type | Exemplar | Items | Count | Hard end |
|---|---|---|---|---|---|
| 1 | Predict the reading after a thing is broken into pieces, every piece on the pan; the whole's reading drawn or stated; four numbers (half, a little less, the same, a little more). | PP-1 | PP-1–5 | 5 | none — easy |
| 2 | Pick the true sentence about the pieces' reading, including the boundary where some stuff left the pan. | PP-6 | PP-6, PP-7, PP-18, PP-19 | 4 | none — easy and medium |
| 3 | Why the reading stays the same: four reasons, one the rule's reason. | PP-8 | PP-8, PP-16, PP-36 | 3 | none — easy and medium |
| 4 | Which case keeps the mass (or loses it): four cases, one with every piece back on the pan. | PP-20 | PP-20, PP-21, PP-34 | 3 | none — medium |
| 5 | A claim fixed as wrong (or right) in the stem — or a reading that breaks the pattern: which sentence shows it. | PP-22 | PP-22, PP-23, PP-28, PP-31, PP-32, PP-37, PP-38, PP-51 | 8 | PP-37, PP-38, PP-51 |
| 6 | Add the pieces to find the whole (or run it backwards): four numbers, or four lines of working. | PP-9 | PP-9–12, PP-24, PP-26, PP-27, PP-30, PP-44 | 8 | PP-44 (two steps chained) |
| 7 | Pan-balance prediction: a whole against the pieces of a second one; four outcomes. | PP-12 | PP-12, PP-13, PP-25, PP-29 | 4 | none — easy and medium |
| 8 | Type the mass of the whole from two drawn readings, three stated masses, a level balance, or the whole take away one piece. | PP-39\* | PP-39\–44\ | 5 | all hard, all typed |
| 9 | Predict the mixture's reading or how it compares: four numbers or four comparisons. | PP-14 | PP-14, PP-15, PP-17, PP-33, PP-35, PP-50 | 6 | PP-50 (breaking then mixing) |
| 10 | Type the mass of the mixture from two drawn readings or two stated masses, with the containers tracked back onto the pan, or the mixture take away one part. | PP-45\* | PP-45\–50\, PP-52\* | 6 | all hard, all typed |
The exemplars, in full
Type 1 — PP-1 (easy, MAT4-040, figure pp_muffin_52). A girl breaks the muffin on the scale into pieces and puts every piece back on the pan. What does the scale read now?
Options: 26 grams · 48 grams · 52 grams · 56 grams.
Why: When you break a thing into pieces, the mass stays the same. Every piece of the muffin is on the pan. No stuff was added, and no stuff was taken away. So the scale reads 52 grams.
Nearest lesson-side instance: L01 q2 (the cookie crumbled, less / the same / more). Here the four options are numbers around the drawn reading. Fresh scene kind: a muffin broken up.
Type 2 — PP-6 (easy, MAT4-040). A whole pear on a scale reads 150 grams, then it is cut into slices and every slice goes back on the pan. Which sentence is true?
Options: The slices read 75 grams. · The slices read 150 grams. · The slices read less than 150 grams. · The slices read more than 150 grams.
Why: The slices are the same stuff as the whole pear, just cut up. Every slice is on the pan. No stuff was added, and no stuff was taken away. So the slices read 150 grams.
Nearest lesson-side instance: L01 q5 (paper torn into strips, the reading stated). PP-18 and PP-19 are this type's boundary (the peel in the bin; the bark dust brushed off).
Type 3 — PP-8 (easy, MAT4-040). A pizza on a scale reads 400 grams, then it is cut into eight slices and all eight slices go back on the pan. Why does the scale read 400 grams again?
Options: The slices are lighter, but the scale adds a gram for each slice. · Every slice of the pizza is on the pan. · Slices press harder on the pan than a whole pizza. · The scale shows its last reading again.
Why: The slices are the same stuff as the whole pizza, just cut up. Every slice is on the pan. No stuff was added, and no stuff was taken away. So the scale reads 400 grams again.
Nearest lesson-side instance: L01 q9 (the waffle, three reasons). The distractors are the induced beliefs the lesson never states as true; v2 puts the "lighter" belief in the first distractor as a false mechanism (the reviewer's bare "The slices are lighter, but there are more of them." is a compensation argument a careful child could defend, so it is not used as written).
Type 4 — PP-20 (medium, MAT4-040). In which case does the scale read the same as it did before?
Options: A pancake is torn up, and every piece goes on the pan. · A banana is peeled, and only the fruit goes on the pan. · A sandwich is cut in half, and one half is eaten. · An egg is cracked, and only the inside goes on the pan.
Why: The mass stays the same when every piece is on the pan. Only the pancake has every piece on the pan. The peel, the eaten half and the shell are stuff taken away. So the pancake's scale reads the same.
Nearest lesson-side instance: L01 q4 and q6 (one slice on the floor; powder on the fingers), asked one case at a time. Here four cases are sorted at once.
Type 5 — PP-22 (medium, MAT4-040). A boy says a crumbled cheese puff has less mass than the whole cheese puff because the crumbs are tiny, but he is wrong. Which sentence shows why?
Options: Tiny crumbs have more mass than big pieces. · The scale cannot see tiny crumbs. · Crumbs take up more room on the pan. · The crumbs are the same stuff as the whole cheese puff.
Why: The crumbs are the same stuff as the whole cheese puff, just broken up. No stuff was added, and no stuff was taken away. So the crumbs have the same mass as the whole cheese puff.
Nearest lesson-side instance: L01 q7 (Frances's toast crumbs, bare yes / no — Driver et al. 1994; Stavy 1990). The bank form fixes the verdict and asks for the reason (James, 28 Sep 2026: no verdict and reason in one option). The hard end of this type (PP-37, PP-51) gives a reading that breaks the pattern (2 grams short; 5 grams short) and asks which sentence explains it.
Type 6 — PP-9 (easy, MAT4-041). A stick of butter is cut into two pieces with masses of 40 grams and 65 grams. What was the mass of the whole stick?
Options: 25 grams · 65 grams · 105 grams · 130 grams.
Why: The mass of the whole is the masses of the pieces added together. 40 + 65 = 105. So the whole stick had a mass of 105 grams.
Nearest lesson-side instance: L02 q6 (the bagel, typed). Here the sum is chosen among the difference, one piece and a double. PP-24 asks for the line of working; PP-26 and PP-27 run the rule backwards; PP-44 (hard) chains a take-away with a further cut.
Type 7 — PP-12 (easy, MAT4-041). A whole sausage, 90 grams, goes on the left pan of a pan balance, and two pieces of a second sausage, 50 grams and 40 grams, go on the right pan. What happens?
Options: The left pan hangs lower. · The right pan hangs lower. · The pans hang level. · The pan with more pieces hangs lower.
Why: The two pieces together have 50 + 40 = 90 grams. The whole sausage has 90 grams. The masses are the same. So the pans hang level. There are more pieces on the right pan, but together they have the same mass as the whole sausage.
Nearest lesson-side instance: L02 q8 (the roll, the pieces' total stated). Here and in PP-13, PP-25 and PP-29 the student adds first (90 against 50 + 40; 28 against 14 + 10; 55 against 30 + 30; 50 against 20 + 20 + 10).
Type 8 — PP-39\* (hard, MAT4-041, typed, figure pp_soap_pieces). A bar of soap is in three pieces, one on each scale. How many grams will the scale read with all three pieces on one pan? Type the number.
Accept: 84 · 84 grams · 84 g · 84 gram · eighty-four · eighty-four grams · eighty four · eighty four grams.
Why: The mass of the whole is the masses of the pieces added together. Piece 1 reads 40 grams, piece 2 reads 24 grams, and piece 3 reads 20 grams. 40 + 24 + 20 = 84. So the scale will read 84 grams.
Hard because: three readings are taken from the drawing and added; the number is produced. PP-40\ draws the whole brownie (28 grams) and one piece (11 grams) and asks for the other piece (17); PP-41\ runs the rule backwards from the stem (53 − 29); PP-43\* reads a level balance as "the same mass" before adding.
Type 9 — PP-14 (easy, MAT4-042). A girl mixes a cup of popcorn, 38 grams, and a cup of peanuts, 110 grams, in one cup, then puts both cups back on the pan. What does the scale read?
Options: 72 grams · 110 grams · 148 grams · 296 grams.
Why: The mass of a mixture is the masses of its parts added together. 38 + 110 = 148. So the scale reads 148 grams.
Nearest lesson-side instance: L03 q10 (two kinds of pasta, typed). PP-15 asks the comparison in words (apple juice and grape juice); PP-17 the dissolved powder on one reading (a mug of water, 215 grams, and 10 grams of powdered milk stirred in); PP-50 (hard) breaks the dried fruit first and then mixes.
Type 10 — PP-45\* (hard, MAT4-042, typed, figure pp_cereal_raisins). A cup of cereal, a cup of raisins and a cup of banana chips sit on three scales. The raisins and the banana chips are poured into the cereal and stirred, and all three cups go back on one pan. How many grams will the scale read? Type the number.
Accept: 275 · 275 grams · 275 g · 275 gram · two hundred seventy-five · two hundred seventy-five grams · two hundred seventy five · two hundred seventy five grams · two hundred and seventy-five · two hundred and seventy-five grams.
Why: The mass of a mixture is the masses of its parts added together. The cup of cereal reads 135 grams, the cup of raisins reads 85 grams, and the cup of banana chips reads 55 grams. 135 + 85 + 55 = 275. So the scale will read 275 grams.
Hard because: three readings are taken from the drawing and added, with all three cups tracked back onto the pan; the number is produced. PP-46\ dissolves the powder out of sight, the glass's reading drawn (230 grams) and the powder's 25 grams stated; PP-47\ is the atom's own soil-in-water; PP-48\ tracks three containers and adds the jar's own 100 grams (315); PP-49\ runs the rule backwards with no container (360 − 185).
Design-move inventory (one line per bank item: the MOVE · the SCENE KIND · the nearest earlier item)
| Id | d | Atom | Type | Move · scene kind · nearest earlier |
|---|---|---|---|---|
| PP-1 | easy | 040 | 1 | predict pieces' reading from drawn whole · a muffin broken · L01 q2 |
| PP-2 | easy | 040 | 1 | same move · an eraser cut in three · PP-1 (different thing, cut not broken) |
| PP-3 | easy | 040 | 1 | same move, whole stated · cheese cut into cubes · L01 q5 |
| PP-4 | easy | 040 | 1 | same move, whole stated · a dog biscuit snapped · L01 q3 |
| PP-5 | easy | 040 | 1 | predict from a drawn whole / "?" pair card · a crayon in three · L01 headache card form |
| PP-6 | easy | 040 | 2 | pick the true sentence · a pear sliced · L01 q5 |
| PP-7 | easy | 040 | 2 | pick the true sentence · cardboard cut into squares · PP-6 |
| PP-8 | easy | 040 | 3 | the reason, the "lighter" belief as a false mechanism among the distractors (v2) · a pizza in eight · L01 q9 |
| PP-9 | easy | 041 | 6 | add two stated masses · a stick of butter · L02 q6 |
| PP-10 | easy | 041 | 6 | add two stated masses · a rope · PP-9 |
| PP-11 | easy | 041 | 6 | add three stated masses · a string · L02 q7 |
| PP-12 | easy | 041 | 7 | balance, two pieces stated, equal sums (v2) · a sausage · PP-13 (⟂) |
| PP-13 | easy | 041 | 7 | balance, pieces sum less · a cheese stick · L02 q9 |
| PP-14 | easy | 042 | 9 | add two cups, both back on pan · popcorn and peanuts · L03 q10 |
| PP-15 | easy | 042 | 9 | compare in words · apple juice and grape juice (liquids; v2) · L03 q2 |
| PP-16 | easy | 042 | 3 | the reason for a mixture · orange juice and water (v2) · L03 q3 FRQ |
| PP-17 | easy | 042 | 9 | dissolved powder, one reading on the scale (v2) · powdered milk in a mug of water · L03 q11 |
| PP-18 | medium | 040 | 2 | boundary: peel binned (v2: option D plainer) · an orange · L01 q4 |
| PP-19 | medium | 040 | 2 | boundary: dust brushed off · a dry stick · L01 q6 |
| PP-20 | medium | 040 | 4 | which case keeps the mass · four foods · new |
| PP-21 | medium | 040 | 4 | which case loses mass · four things · PP-20 (⟂) |
| PP-22 | medium | 040 | 5 | claim fixed wrong, reason · a cheese puff crumbled · L01 q7 |
| PP-23 | medium | 040 | 5 | claim fixed right, reason (v2: the key one clause) · a twig snapped · L01 q8 |
| PP-24 | medium | 041 | 6 | pick the line of working · a wooden ruler · new |
| PP-25 | medium | 041 | 7 | balance, pieces sum more · a hamburger bun · PP-13 |
| PP-26 | medium | 041 | 6 | reverse: whole take away a piece · a cinnamon stick · new |
| PP-27 | medium | 041 | 6 | reverse · a stick of taffy · PP-26 (⟂) |
| PP-28 | medium | 041 | 5 | judge a prediction against the reading · a wafer · new |
| PP-29 | medium | 041 | 7 | balance, three pieces (v2: option D carries no reason) · a snack bar · PP-12 (⟂) |
| PP-30 | medium | 041 | 6 | add two three-digit masses · a pound cake · PP-9 |
| PP-31 | medium | 042 | 5 | claim fixed wrong ("packing") · sawdust and wood chips · L03 q4 |
| PP-32 | medium | 042 | 5 | claim fixed wrong (dissolved = gone) · instant coffee in cold water (v2) · L03 q5 |
| PP-33 | medium | 042 | 9 | add with containers tracked · corn flakes and blueberries · PP-14 (⟂) |
| PP-34 | medium | 042 | 4 | which case keeps the mass (bookkeeping) · cornmeal and cinnamon · PP-20 |
| PP-35 | medium | 042 | 9 | reverse: mixture take away a part · dried apple and banana · PP-26 |
| PP-36 | medium | 042 | 3 | the reason · chocolate chips in cookie dough (v2) · PP-16 |
| PP-37 | hard | 040 | 5 | a reading 2 grams short: explain · a taco shell · PP-19 |
| PP-38 | hard | 040 | 5 | arrangement belief (spread vs piled) · a dry leaf · new |
| PP-39\* | hard | 041 | 8 | THREE drawn readings added, typed (v2) · soap in three pieces · L02 q5 |
| PP-40\* | hard | 041 | 8 | reverse from a drawing: the whole and one piece drawn, typed (v2) · a brownie · PP-41 (⟂) |
| PP-41\* | hard | 041 | 8 | reverse, typed · a candy cane · PP-26 (⟂) |
| PP-42\* | hard | 041 | 8 | three stated masses, typed · licorice · PP-11 |
| PP-43\* | hard | 041 | 8 | level balance then add, typed · a cheese block · PP-12 |
| PP-44 | hard | 041 | 6 | chain: take away, then cut further · a pie · new |
| PP-45\* | hard | 042 | 10 | three drawn cups added, typed (v2) · cereal, raisins and banana chips · L03 q9 |
| PP-46\* | hard | 042 | 10 | dissolved; the glass's reading drawn, the powder stated, typed (v2; v3: protein powder) · protein powder in a glass of water · PP-17 (⟂) |
| PP-47\* | hard | 042 | 10 | the atom's example, typed · soil in a jar of water · new |
| PP-48\* | hard | 042 | 10 | three containers tracked, the jar's own 100 grams added, typed (v2: 315) · vinegar and oil · PP-33 |
| PP-49\* | hard | 042 | 10 | reverse, no container, typed (v2) · fruit salad · PP-35 |
| PP-50 | hard | 042 | 9 | chain: break then mix · seeds and dried fruit · new |
| PP-51 | hard | 042 | 5 | a reading 5 grams short: explain · sprinkles and frosting · PP-37 (⟂) |
| PP-52\* | hard | 042 | 10 | two stated masses, typed · flour and baking powder · PP-17 |