Study Plan B

The one rule that makes every comparison easy: compare place by place from the left, and stop at the first place where they differ.

Worked example. Which is bigger, 0.4 or 0.25?

Tenths place first: 4 vs 2. Four tenths beats two tenths, so 0.4 > 0.25 — even though 25 looks like a bigger number than 4.

The trick that removes the confusion: pad with zeros so both have the same number of places. 0.4 becomes 0.400, and 0.25 becomes 0.250. Now 400 > 250, plainly. Adding zeros on the end of a decimal never changes its value.

Worked example — ordering. Put 0.7, 0.68, 0.702, 0.6 in order. Pad: 0.700, 0.680, 0.702, 0.600. Read as whole numbers: 600 < 680 < 700 < 702. So 0.6 < 0.68 < 0.7 < 0.702.

Oops! The most common decimal mistake is “longer means bigger”. 0.25 has more digits than 0.4 but is smaller. Length is not value.

Rounding asks: which of the two nearest values is this closer to? Three steps, every time:

1. Underline the place you are rounding to.
2. Look at the one digit immediately to its right — only that one.
3. 0–4, the underlined digit stays. 5–9, it goes up by one. Then drop everything after it.

Worked example. Round 3.472 to the tenths. Underline 4; the digit to its right is 7; 7 ≥ 5 so round up → 3.5.

Worked example. Round 3.472 to the hundredths. Underline 7; the digit to its right is 2; 2 < 5 so stay → 3.47.

Worked example with a carry. Round 2.196 to the hundredths. Underline 9; to its right is 6, so round up: 9 becomes 10, which carries → 2.20. Keep the final zero — it shows the place you rounded to.

Oops! Look at one digit only. Rounding 3.449 to tenths is 3.4, not 3.5 — the 9 at the end does not get to push the 4 up through the 4.

Thursday adds “represent the value of the digit”, which is asking for the digit’s worth, not its name.

In 5.638: the 6 is in the tenths place and is worth 0.6 (six tenths). The 3 is hundredths, worth 0.03. The 8 is thousandths, worth 0.008.

Say it as a fraction to check: thousandths means /1000, so 8 thousandths = 8/1000 = 0.008. ✔

Monday’s target lists three functions. They are easy to remember because each one answers a different question:

• Support and protection — what holds you up and shields the organs. (Skull, ribs.)
• Storing minerals — bone is the body’s calcium bank. It lends calcium out and takes it back.
• Making new blood cells — red marrow inside the bone produces red and white blood cells.

Why the chicken bone goes in vinegar. Vinegar is a weak acid, and acid dissolves calcium salts. Leave a bone in it and the mineral is stripped out, leaving the flexible protein (collagen) behind — so the bone goes rubbery and bendy.

That is the point of the demo: it separates the two ingredients. Mineral gives hardness; collagen gives flexibility. Real bone needs both — all mineral and it would shatter, all collagen and it would flop. And it explains the diet link: without dietary calcium, the bank runs low.

Oops! The vinegar does not make the bone “rot” or “soften with water”. It removes the calcium specifically. If you are asked what is left, the answer is the protein framework.

Thursday’s comparison is an engineering idea. A solid rod and a hollow tube of the same mass — the tube is stiffer, because the material sits far from the centre where bending stress is highest. Material in the middle of a beam does very little work.

Inside the ends of a long bone, spongy bone forms a lattice of tiny struts laid out along the lines the load actually travels — exactly what a truss bridge does with steel. You get strength where force goes and empty space everywhere else.

The result: a femur can carry many times your body weight while staying light enough to swing when you run. And the leftover space is not wasted — it holds the marrow that does Monday’s third job.

Tuesday and Wednesday build one skill. Read a label in this order:

1. Serving size first. Every other number on the label is per serving. A small bag that is “2.5 servings” multiplies everything by 2.5.
2. Servings per container — the trap that follows from step 1.
3. The %DV column. Rule of thumb: 5% or less is low, 20% or more is high.
4. The ingredients list, which is ordered by weight — first ingredient = most of what is in there.

Worked example. A label says 150 calories, servings per container 3. Eating the whole container is 450 calories, not 150.

Oops! “0 g trans fat” and similar claims on the front are allowed to round down. The ingredients list is the more honest source.

Thursday’s target asks for geographic and economic factors, which is a cause-and-effect question with a tidy answer.

Geography pushed them out. The Phoenician homeland was a narrow coastal strip with mountains at its back — very little farmland, no room to expand inland. What it did have: excellent natural harbours and the cedar forests of Lebanon, which are superb shipbuilding timber.

So the economy went outward. If you cannot grow wealth, you carry it. They became the carriers and middlemen of the Mediterranean, trading cedar, glass, and above all purple dye.

Tyrian purple is why Friday is Wear Purple Day. The dye was extracted from murex sea snails — thousands of them for a small amount of dye — so it cost more than its weight in precious metal and became the colour only royalty could afford. The colour stayed imperial for centuries afterwards. The Greek word phoinix, the likely root of “Phoenician”, means purple-red.

The export that outlasted the dye: the Phoenician alphabet. A trading people needed fast record-keeping, so they used about 22 characters for sounds instead of hundreds of pictures. The Greeks adopted it, the Romans adapted it, and you are reading its descendant now.

Three cities to keep straight: Tyre (the great island fortress-port, the dye), Sidon (the older city, glass), Byblos (the papyrus trade — the Greek word for book, biblion, comes from it, and so does “Bible”).

Tuesday’s list looks long until you sort it. Go around the region rather than down the list:

• The two rivers of Mesopotamia: Tigris (east) and Euphrates (west). They run roughly parallel to each other and empty into the Persian Gulf. Between them is the land the name means — “between the rivers”.
• The Fertile Crescent is the arc that curves from the Persian Gulf up along those rivers and back down the Mediterranean coast. Draw it as one sweeping arc, not a blob.
• Seas, working round the region: Mediterranean and Black Sea to the north-west, Caspian and Aral to the north-east, then south-east to the Persian Gulf, out into the Arabian Sea and the Indian Ocean, and back up the Red Sea on the western side.
• Land features: Zagros Mountains to the east (they wall off the plain), Arabian Desert to the south.

Friday’s smaller map zooms into Israel: Mediterranean on the coast, Sea of Galilee in the north, Jordan River running south from it into the Dead Sea. The cities follow the water — Tyre, Sidon and Byblos on the coast going north, Jerusalem and Jericho inland.

Oops! The Dead Sea is a lake, and the lowest point on land. The Jordan flows into it and nothing flows out — which is exactly why it is so salty.

Wednesday asks you to discuss why each item was used, so tie every feature to the environment:

• Goat-hair tents — portable for herders following pasture. Black goat hair is coarse and swells when wet, so the weave tightens and sheds rain, while loose weave lets hot air out in the dry season.
• Flat roofs — in a dry climate you do not need a pitch to shed snow, so the roof becomes another room: sleeping in the heat, drying grain, working.
• Winnowing — toss threshed grain into the breeze; heavy kernels fall straight down, light chaff blows aside. It is a free sorting machine, which is why the image turns up so often as a metaphor.

Three days, three movements of one story. The quiz targets are listed right on the posted rows, so use them as the revision list:

1. Joseph rises (6-A). Pharaoh dreams of seven fat cows and seven thin ones, and seven full ears and seven withered. Joseph says the dream is one message given twice: seven years of plenty, then seven of famine — and then does the thing that gets him promoted, which is to propose a plan (store a fifth of every harvest) rather than only an interpretation.
2. Joseph tests and forgives (6-B). The brothers come to buy grain and do not recognise him. He accuses them of spying, keeps Simeon, demands Benjamin, hides the silver cup in Benjamin’s sack. The tests are not revenge — they are designed to find out whether these men would abandon a favoured younger brother a second time. When Judah offers himself in Benjamin’s place, the answer is no, and Joseph reveals himself.
3. Joseph provides (6-C). The family settles in Goshen. Joseph’s summary line is the theological centre of the whole lesson: “You meant evil against me, but God meant it for good.”

The tribes connection (Wednesday): Jacob’s twelve sons become the twelve tribes of Israel — so the family Joseph saves from famine is the nation the rest of the Old Testament is about. That is why this story sits where it does.

Posted on the Monday, Tuesday, Wednesday and Thursday Bible rows; Friday has no Bible class. It opens “Praise the LORD! I will give thanks to the LORD with my whole heart…” and moves through God’s works being great, studied, remembered, and ends at verse 5 with God providing food for those who fear him and remembering his covenant.

Why it may have been paired with Joseph (our reading, not a note from the teacher): verse 5 is about provision and a remembered covenant — which is exactly the famine, the grain, and the family preserved. Memorise it with that link and both stick.

A way to learn five verses: learn the first word of each verse in order first, then fill each one in. The skeleton holds the rest up.

The brief says “a 3D model that can be printed”, and that second half is a real constraint, not decoration. Four things decide it:

• It must be solid, not a shell of loose faces. Every surface has to join up into one watertight object — a printer needs to know what is inside and what is outside.
• Overhangs. Plastic cannot be laid down on thin air. Anything leaning out more than about 45° from vertical needs support underneath, so a design that stands up on its own base prints far better.
• Thin parts break. Very fine spikes, lettering or blades come out fragile or fail to print at all. Thicken anything delicate.
• A flat bottom. A wide, flat face on the build plate stops the print peeling up as it cools.

The design brief also asks the model to represent a way to enhance God’s creation — so leave yourself a sentence explaining what the object is for. That sentence is usually what the mark is really on.