Printing: use your browser's print (Ctrl+P / ⌘P). It comes out as exactly 4 A4 sheets (2 pieces of paper double-sided). No answers in here.

time yourself (optional)

Stretch (not recorded)From Sun 27 September, any time1 / 4

Stretch — three stories

Not recorded — this is the slot where getting it wrong is fine. September's multiples, factors and fractions, in science and social studies

Name Date

The stretch slot

A step or two above usual: 3–4 questions per story, getting harder. You need not finish. Some numbers are not needed. After each answer, one line on why.

1 · Science × common multiples — the weather club station

Source 1

The weather club at a school (made up) uses a playground station to record temperature every 20 minutes, rainfall every 30, and a sky photo (for cloud cover) every 45. All three started together at 9:00. The thermometer is 1.5 m above the ground.

Source 2 · The times each thing was recorded, 9:00 to 11:00 (a made-up club)

1At what time do all three next record at the same moment?

time yourself (optional)

Stretch (not recorded)From Sun 27 September, any time2 / 4

Stretch — three stories

Name Date

2From 9:00 to 17:00 (counting 9:00 and 17:00), how many times are temperature and rainfall recorded at the same moment?

3The club wants all three to line up exactly once an hour. Temperature (20) and rainfall (30) stay; only the photo interval changes. Choose every interval that works.
10 min　·　12 min　·　15 min　·　25 min　·　40 min

You need 60 to be the lowest common multiple of the three intervals.

4A typhoon is coming, so only rainfall is changed to every 10 minutes (temperature 20, photo 45). A club member says:
"We measure the rain more often now, so all three will line up sooner than before."
Is this right? Circle right or not right and give the reason in one sentence.

time yourself (optional)

Stretch (not recorded)From Sun 27 September, any time3 / 4

Stretch — three stories

Name Date

2 · Social studies × fractions — how two islands use their land

Source 3

Islands A and B are both made up. Island A: 48 km², 3,600 people. Island B: 72 km², 5,400 people.

Source 4 · Land use, taking each whole island as 1. 'Other' is left as ?

5What fraction of Island A is 'other'? Give it in lowest terms.

6Someone says: "The share of farmland is bigger on Island A (¹⁄₆) than on Island B (¹⁄₈), so Island A also has more farmland area."
Is this right? Show your working and give the reason in one sentence.

¹⁄₆ of 48 km² is one part when 48 is split into 6 equal parts.

7Island A plans to turn some forest into farmland so that farmland is ¹⁄₄ of the island. Homes & factories and 'other' stay the same. What fraction will be forest?

time yourself (optional)

Stretch (not recorded)From Sun 27 September, any time4 / 4

Stretch — three stories

Name Date

3 · Social studies × common factors, odd & even — releasing farmed young fish

Source 5

A port's fishing co-operative (made up) takes 3 boats out to release young flounder and red sea bream it has raised. The fish come in bags of 100.
Rule: every point gets the same number of flounder bags as every other point, and the same number of sea bream bags as every other point. No bag of either kind is left over.

Source 6 · young fish	Bags	Length of one (about)
flounder	84	5 cm
red sea bream	60	4 cm

8What is the largest possible number of points? How many bags of each fish go to one point?

9The co-operative wants an even number of points. Write every number of points that keeps the rule.

10Next year there may be 65 bags of sea bream (flounder stays at 84).
(1) Keeping the rule, can the number of points be even? Circle yes or no; one sentence why.
(2) At least how many sea bream bags must be added so that 6 or more points are possible?