Printing: use your browser's print (Ctrl+P / ⌘P). The whole week is 20 A4 sheets (10 pieces of paper double-sided) — the same content as the single days.
20 minutes, then stop
Maths A (practice)Tue 13 October1 / 4
Long division by two digits
Estimate, multiply, subtract. What the remainder means depends on the story
NameDate
How to make the estimate
Round the divisor to a multiple of ten and ask "how many of those fit into the number?"
Then multiply, subtract. The remainder you are left with is always smaller than the divisor.
Question 1 is already done for you
Work out 236 ÷ 38.
① Round 38 to 40. 236 is about six 40s → estimate 6
② 38 x 6 = 228
③ 236 − 228 = 8 (smaller than 38, so OK)
④ Answer 6 remainder 8 Check 38 x 6 + 8 = 236
Your turn from here
2Work out 365 ÷ 52 in long division. First round 52 to a multiple of ten and make your estimate.
52 → 50. 365 is about seven 50s.
3Work out 782 ÷ 31 in long division. The answer has two digits.
4Work out 645 ÷ 27 in long division, then check it: divisor x quotient + remainder.
If the check is not 645, go back and redo it.
20 minutes, then stop
Maths A (practice)Tue 13 October2 / 4
Long division by two digits
NameDate
When the estimate is off
The product is bigger than the number being divided → the quotient is too big. Take 1 off. The remainder is the divisor or more → the quotient is too small. Raise it. An estimate may miss. Fix it and the answer still comes out right.
5In 170 ÷ 28 you round 28 to 30 and guess 5. Take 28 x 5 away from 170: what is left? Is 5 right? Write the correct quotient and remainder.
If the remainder is 28 or more, the quotient is too small.
6In 150 ÷ 22 you round 22 to 20 and guess 7. What is 22 x 7? Is it bigger than 150? Write the correct quotient and remainder.
If you cannot take it away from 150, the quotient is too big.
What to do with the remainder
7135 pupils go out by bus. One bus holds 42. How many buses are needed?
With 3 buses, some people are left behind.
20 minutes, then stop
Maths A (practice)Tue 13 October3 / 4
Long division by two digits
NameDate
8There are 300 mandarins. 18 go into each box. How many full boxes of 18 can you make, and how many mandarins are left over?
Count only the boxes that hold exactly 18.
9Someone answered 143 ÷ 26 as "4 remainder 39". 26 x 4 + 39 does make 143. It is still wrong. Say what is wrong and write the correct answer.
Remember: the remainder is smaller than the divisor.
10150 ÷ 24 = 6 remainder 6. Write the answer to each of A to C.
A A car seats 24; 150 people ride. How many cars?
B Boxes of 24 are made from 150 sweets. How many boxes can you make?
C A 150 cm string is cut into 24 cm pieces. How many pieces, and how many cm are left?
Same sum, different answer — the story decides.
20 minutes, then stop
Maths A (practice)Tue 13 October4 / 4
Long division by two digits
NameDate
11A 4 m 50 cm tape is cut into 35 cm pieces. How many pieces, and how many cm are left?
Use cm first: 4 m 50 cm = 450 cm.
12Find the number in the box: □ ÷ 23 = 15 remainder 8.
□ = divisor x quotient + remainder (the check, used backwards)
13When you divide by 27, the remainder can be anything from 0 up to what? And which number gives quotient 12 with the largest possible remainder when divided by 27?
The largest remainder = divisor − 1
20 minutes, then stop
Costume 1Wed 14 October1 / 4
Choose one of these two
1 Pokémon 2 everyday life — do sheet 1 or sheet 2, then everyone does 3 and 4
NameDate
1 · Pokémon — how many hits?
How many more hits? = HP left ÷ damage per hit. The game numbers are made up.
If there is a remainder, you need one more hit (round up).
Example · already worked
HP left 150. Each hit does about 40. How many more hits?
① Estimate: 40 x 3 = 120 (still left), 40 x 4 = 160 (over 150)
② 150 ÷ 40 = 3 remainder 30
③ 30 HP is still left, so one more hit → 4 hits
1HP left 215. Each hit does 35. How many more hits? Use long division.
How much HP do 6 hits take off? Is that enough?
2HP left 312. Each hit does about 48. Say your estimate out loud first (48 ≈ 50, 312 ≈ 300), then work it out properly in long division. How many more hits?
3HP left 360. Each hit does a whole number from 40 up to (but not including) 50. How many hits in the luckiest case, and in the unluckiest?
The biggest damage is 49 (it must be less than 50).
20 minutes, then stop
Costume 1Wed 14 October2 / 4
Choose one of these two
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2 · Everyday life — petrol for the car
Km per litre = distance driven ÷ litres used. The numbers are made up.
Before you divide, say the rough answer out loud first.
Example · already worked
A full 50 L tank took the car 650 km. How many km per litre?
① Estimate: 50 x 10 = 500 km. 650 is more → more than 10 km per litre
② 650 ÷ 50 = 13 → 13 km
1A full 45 L tank took the car 540 km. How many km per litre?
Estimate first: 45 L x 10 km = 450 km. 540 is more than that.
2A full 38 L tank took the car 456 km. First say "more or less than 10 km per litre?", then work out the km per litre in long division.
3A car goes 13 km on 1 litre and has to drive 200 km. What is the least number of whole litres that is enough?
How far do 15 litres go?
20 minutes, then stop
Costume 1Wed 14 October3 / 4
Choose one of these two
NameDate
3 · From here, everyone
4Work out 678 ÷ 32 in long division.
Round 32 to 30 and make your estimate.
5You work out 208 ÷ 26 by rounding 26 to 30 and guessing 6. Take 26 x 6 away from 208: what is left? Then fix the quotient and give the correct answer.
See how many times the divisor fits into the remainder and you can fix it in one go.
6You buy sweets at 38 yen each with 1,500 yen.
A Round 38 to 40 and say roughly how many you can buy.
B Use long division to find how many you can buy and how many yen are left.
38 yen is cheaper than 40, so the real number is a little more than the estimate.
20 minutes, then stop
Costume 1Wed 14 October4 / 4
Choose one of these two
NameDate
4 · Rounding and estimating
7Round 6,451 to the nearest hundred.
The tens digit is 5. Which way does exactly 5 go?
8Whole numbers that round to 4,300 (nearest hundred): write their range using "at least" and "less than".
Just below 4,300 is 4,200 and just above is 4,400. Where are the midpoints?
9You have 1,500 yen and buy things at 398, 249 and 505 yen. Round each up to the hundred, estimate the total, and say whether the money is enough.
Rounding up makes it bigger than the real total. If that is still enough, you are safe.
20 minutes, then stop
Maths B (word problems)Fri 16 October1 / 4
Putting rounding to work
Say "about how many?" out loud first, then calculate
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Three ways to round
Ordinary rounding … "about how many?" Round up … "is it enough?" "how many buses?" (when too little is a problem) Round down … "how many can I buy?" "how many boxes can I fill?" (leftovers do not count) Each time, say "about how many?" out loud before you calculate.
Question 1 is already done for you
The snack limit for the trip is 800 yen. You buy things at 278, 196 and 152 yen. Is it enough?
① Round each up to the hundred: 300 + 200 + 200 = 700
② 700 is less than 800 → enough (the real total is 626 yen)
Your turn from here
2You have 1,500 yen and buy things at 468, 735 and 249 yen.
A Round each up to the hundred: what is the estimated total? Can you say "enough"?
B Estimate again, rounding each up to the ten. Is it enough?
If A goes over 1,500, the estimate may simply be too generous.
3There are 87 cookies and each box holds 12.
A Say first "about how many boxes?" (87 ≈ 90, 12 ≈ 10)
B Use long division: how many boxes are needed?
The leftover cookies need a box too.
20 minutes, then stop
Maths B (word problems)Fri 16 October2 / 4
Putting rounding to work
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4Chairs are set out 32 to a row, in 48 rows. Round both numbers to their first digit and estimate the total, then work it out exactly in long multiplication.
5The attendance at an event, rounded to the nearest hundred, was 3,600 (made up). The real number is at least what and less than what?
Around 3,600 are 3,500 and 3,700. Where are the midpoints?
6Of the whole numbers that round to 25,000 (nearest thousand), write the smallest and the largest.
The midpoint is at 500. 25,500 rounds to 26,000.
7Town A has 12,480 people and town B has 12,520, a difference of only 40. Round each to the nearest thousand. Why do the rounded numbers differ by 1,000 when the real difference is only 40?
12,500 is the border between rounding down and rounding up.
20 minutes, then stop
Maths B (word problems)Fri 16 October3 / 4
Putting rounding to work
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8You have 1,000 yen and sweets cost 48 yen each. How many can you buy, and how many yen are left? Say your estimate first (48 ≈ 50).
Money that is not enough for one more sweet buys nothing (round down).
9316 pupils ride buses. A bus holds up to 45.
A Round 45 to 50 and make an estimate.
B Use long division: how many buses are needed?
C Why do A and B differ?
One person left over still needs one more bus.
10You buy 29 cakes at 78 yen each. Round both numbers to their first digit and estimate the cost. Then work out the real cost and say whether the estimate is bigger or smaller.
20 minutes, then stop
Maths B (word problems)Fri 16 October4 / 4
Putting rounding to work
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11You buy 7 pencils at 58 yen and 3 notebooks at 147 yen. Round every price to the nearest ten and estimate the total.
Say first: "more or less than 1,000 yen?"
12The number of fourth-graders, rounded to the nearest ten, is 120. Split them into groups of 4. What is the fewest and the most groups there could be? (Leftover pupils form one more group.)
First the range: at least 115 and less than 125.
13Doing 528 x 19 in long multiplication you got 100,032. Use an estimate to check it, and if it is wrong give the right answer.
If the size is different from the estimate, doubt the digits first.
20 minutes, then stop
Costume 2 + correctionsSun 18 October1 / 4
Choose one of these two
1 Food 2 Pokémon — do sheet 1 or sheet 2, then everyone does 3 and 4
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1 · Food — the price of one
Price of one = total price ÷ number of pieces. When packs hold different numbers, compare the price of one to see which is the better buy.
Example · already worked
A pack of 15 sweets costs 735 yen. How much is one?
① Estimate: 15 x 50 = 750 yen → about 50 yen each
② 735 ÷ 15 = 49 → 49 yen
1Doughnuts: 12 for 636 yen. How much is one?
12 x 50 = 600. 636 is a little more than that.
2Cookies: pack A is 14 for 658 yen, pack B is 25 for 1,150 yen. First say "both are about 50 yen each", then work out the price of one in long division and say which is cheaper and by how many yen.
When the estimate cannot decide it (the gap is small), calculate properly.
3Juice costs 38 yen a bottle. With 1,000 yen, how many bottles can you buy, and how much change is left?
Money too little for another bottle is the change.
20 minutes, then stop
Costume 2 + correctionsSun 18 October2 / 4
Choose one of these two
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2 · Pokémon — a move that does double
If a move does double damage, how does the number of hits change? The numbers are made up.
A remainder means one more hit.
Example · already worked
HP left 180. A normal move does 30 per hit; a super-effective move does double. How many hits with the super-effective move?
① Double → 30 x 2 = 60
② 180 ÷ 60 = 3 → 3 hits (a normal move would need 180 ÷ 30 = 6 hits)
1HP left 372. A normal move does 24 per hit. Round 24 to 20 and say your estimate first, then work out in long division how many more hits are needed.
Rounding 24 down to 20 makes each hit look weaker, so the estimate runs high.
2The super-effective move does 48 per hit (double the normal move). HP left is 372. How many more hits? Is it exactly half the number of hits for the normal move?
3HP left 250. Each hit does a whole number from 21 up to (but not including) 30. Find the fewest and the most hits it could take.
The biggest damage is 29 (less than 30).
20 minutes, then stop
Costume 2 + correctionsSun 18 October3 / 4
Choose one of these two
NameDate
3 · From here, everyone
4Work out 905 ÷ 37 in long division.
37 → 40. Two 40s fit into 90.
5Round 38,527 to the nearest thousand.
The hundreds digit is 5. Which way does exactly 5 go?
6There are 100 pencils. They go in boxes of one dozen (12). How many full boxes can you make, and how many pencils are left? And how many boxes are needed to hold all 100?
"Boxes you can fill" and "boxes to hold everything" treat the remainder differently.
20 minutes, then stop
Costume 2 + correctionsSun 18 October4 / 4
Choose one of these two
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4 · Corrections, and one puzzle problem
7Pick one question you got wrong this week from your notebook and do it again.
- Which question (day and number)
- Why you got it wrong (estimate / multiplying / subtracting / remainder / other)
Once you can do it the second time, that question is finished.
8Sum and difference — Two children have 58 sweets between them. A has 12 more than B. How many does each have?
Draw bars. A's bar is 12 longer than B's. Take off the 12 and the two bars are equal: 58 − 12 = 46, split in two.
9Someone answered 200 ÷ 32 as "5 remainder 40". What is wrong? Write the correct answer.
The same mistake as Tuesday's remainder that was bigger than the divisor.
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 18 October, any time1 / 4
Stretch — level up
Not recorded. Getting it wrong is fine.
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1 · Buses for the trip [social studies: school trip]
Source 1
The fourth graders (made-up) go on a school trip. A bus holds 45 people. One bus costs 52,000 yen.
class
Class 1
Class 2
Class 3
Class 4
students
36
35
37
33
Source 2 — number of students (made up)
Question 1 is already done for you
Classes 1 and 2, 71 students, ride the buses. How many buses?
71 ÷ 45 = 1 remainder 26 (45 × 1 = 45, 71 − 45 = 26)
The 26 left over must ride too → 1 + 1 = 2 buses
2Round each class to the nearest ten and estimate how many students there are in all. Then work out the exact total too.
Look at the ones: 5 to 9 goes up, 0 to 4 stays.
3Someone says: "The estimate is 150. The real number, 141, is less than that, so 3 buses are enough." Is that right? Say why.
Work out 141 ÷ 45. What happens to the ones left over?
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 18 October, any time2 / 4
Stretch — level up
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2 · Moon shapes and time in the sky [science: the moon]
Source 1
In one place (made-up) the times when the moon rises and sets were recorded. The moon's shape goes through a whole cycle in about 30 days.
shape
new moon (not seen)
half moon
full moon
days since new moon
day 0
day 7
day 14
moonrise
6:10 am
noon
5:50 pm
moonset
5:50 pm
11:40 pm
6:20 am next day
Source 2 — moonrise and moonset (made-up numbers)
Question 4 is already done for you
On the new-moon day, how long is the moon in the sky?
6:10 am → noon is 5 h 50 min, noon → 5:50 pm is also 5 h 50 min.
5 h 50 min + 5 h 50 min = 11 h 40 min
5On the night of the full moon, how long is the moon in the sky?
Split it: 5:50 pm → midnight → 6:20 am.
6Someone says: "The moon rises about 30 minutes later each day." Use the sources to decide whether that is right.
Compare moonrise on day 0 and day 14. Change it to minutes and divide by 14.
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 18 October, any time3 / 4
Stretch — level up
NameDate
3 · The gym's electricity bill [social studies: electricity]
Source 1
The electricity bill of a school gym (made-up), month by month. The gym has 48 lights.
Source 2 — the gym's electricity bill. Brackets show the days in the month. The numbers are made up.
Question 7 is already done for you
How many yen per day in June?
June has 30 days → 37,800 ÷ 30
To divide by 30, divide by 10 and then by 3: 3,780 ÷ 3 = 1,260 yen
8How many yen per day in July? First treat 52,700 as 50,000 and 31 as 30 and write "about how much". Then work out the answer in long division.
Check that the answer is close to your guess.
9Someone says: "Even if you triple August's cost per day, it does not reach July's cost per day." Is that right? Explain with numbers.
Divide August by 31, multiply by 3, and compare with July.
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 18 October, any time4 / 4
Stretch — level up
NameDate
4 · How often the heart beats [science: the human body]
Source 1
A wrist device counted the pulse of a 10-year-old (made-up). The pulse count is the same as the number of heartbeats.
when
resting
after walking
after running
time measured
15 min
3 min
2 min
pulse count
1,080
270
324
Source 2 — pulse counts (made-up numbers)
Question 10 is already done for you
While resting, how many beats per minute?
1,080 ÷ 15 = 72 (15 × 70 = 1,050, the other 30 is 15 × 2)
Answer: 72 beats a minute
11Suppose the resting rate lasted a whole day (24 hours). How many heartbeats in a day? Then round it to the nearest ten thousand.
1 hour is 60 minutes. Find the beats in 1 hour, then times 24. Look at the thousands to round.
12Someone says: "After running, the pulse per minute is more than twice the resting pulse." Is that right? Explain with numbers.
Divide the running figure by 2 minutes. Double the resting figure.
kids/learn — weekly worksheet. The answers have a page of their own.