Study Plan D

Chapter 4 looks like four topics. It is really one skill used four ways: break a number into primes, then read the answer off.

Step 1 — prime factorisation (Monday). Split until every branch is prime.

72 → 8 × 9 → (2 × 4) × (3 × 3) → 2 × 2 × 2 × 3 × 3 = 2³ × 3².
60 → 6 × 10 → (2 × 3) × (2 × 5) = 2² × 3 × 5.

Step 2 — GCF (Monday). Take the primes they share, each at the lower power. 72 and 60 share 2² and 3¹ → GCF = 4 × 3 = 12.

Step 3 — simplifying fractions (Tuesday). Dividing top and bottom by the GCF finishes the job in one move. 60/72: divide both by 12 → 5/6. Done, and guaranteed fully simplified.

Step 4 — LCM (Wednesday). Take every prime that appears, each at the higher power. For 72 = 2³ × 3² and 60 = 2² × 3 × 5 → 2³ × 3² × 5 = 8 × 9 × 5 = 360.

The one-line check: GCF × LCM = the product of the two numbers. 12 × 360 = 4,320, and 72 × 60 = 4,320. ✔ If that check fails, one of your two answers is wrong.

Oops! The classic mix-up is taking the higher power for the GCF. Think about what the words mean: the greatest common factor has to divide into both numbers, so it can only use what both actually have — the lower power. The LCM is a multiple of both, so it needs the higher.

If the GCF is not obvious, chip away — the answer is the same, it just takes more steps.

Worked example. 84/126. Both even → 42/63. Both divide by 3 → 14/21. Both divide by 7 → 2/3.

Quick divisibility checks: 2 if it ends even · 3 if the digits add to a multiple of 3 (8+4 = 12 ✔) · 5 if it ends in 0 or 5 · 9 if the digits add to a multiple of 9.

Oops! You may only divide top and bottom by the same number, and only by dividing — not subtracting. 84/126 is not 82/124.

The name just means “divine reading”. It is a slow re-reading of a short passage, four times, each time doing something different:

1. Read — what does it actually say?
2. Reflect — which word or phrase stands out?
3. Respond — say something back about that word.
4. Rest — stop and be quiet with it.

Wednesday asks you to design your own plan. A plan that survives contact with a real week has three parts: when (a time already in your day), what (a specific book, not “the Bible”) and how much (small enough to finish on a bad day).

Oops! The obstacle Tuesday asks you to name is usually not “no time” — it is having no decided time. “Whenever I can” is the plan that quietly fails.

Two to three minutes is roughly 300–400 words. That is five beats, about 30 seconds each:

1. The constraint — what were you required to do, and what were you not allowed to use?
2. The design — what you built, in one sentence a stranger would understand.
3. The test — what actually happened on Wednesday. Numbers if you have them.
4. The change — what failed and what you did about it. This is the part judges care about most.
5. The next iteration — what you would change with one more day.

Your posted storyline is “design with empathy, take risks with faith over fear.” Beat 4 is where that shows up honestly.

Oops! Hiding the failure is the most common mistake in a design presentation. “It worked perfectly” is both less interesting and less believable than “the first arm snapped, so we shortened the lever and it held.”

Tuesday’s gallery walk is about connection, not lists. The short version:

• Skeletal gives the frame; muscular pulls on it to move.
• Respiratory takes oxygen in; circulatory delivers it everywhere.
• Digestive turns food into fuel; circulatory carries that fuel too.
• Nervous is the control system telling the others what to do and how fast.

Worked example — a sprint. Nervous system fires → muscles pull on bones → the muscles burn fuel and oxygen → breathing speeds up (respiratory) → heart rate rises to deliver more (circulatory). One action, five systems.

Oops! “Physical wellness” is not just exercise. Sleep, food and rest are part of the same unit — which is exactly why the driving question asks what wellness is before asking how to get it.