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 (new unit)Tue 6 October1 / 4
Long division by two digits
Estimate → guess → multiply → subtract → bring down
It is the same four moves as one-digit division. Only "guess" is harder.
1 Treat the divisor as a round ten 2 Find a nearby times-table fact 3 Try it 83 ÷ 21 21 → 20. 80 ÷ 20 = 4 … the estimate is 4
21 × 4 = 84 is bigger than 83! → change to 3. 21 × 3 = 63, 83 − 63 = 20
Answer 3 remainder 20 (20 is smaller than 21, so it is fine)
2Write the estimate of each quotient as a sum, like 80 ÷ 20 = 4.
(1) 58 ÷ 19 (2) 47 ÷ 16
Round both numbers to something neat: 16 → 20, 47 → 40.
3Work out 97 ÷ 31 with long division. Write the estimate too.
4Work out 86 ÷ 29 with long division.
29 → 30. Multiply the guess back: does it go over 86?
20 minutes, then stop
Maths A (new unit)Tue 6 October2 / 4
Long division by two digits
NameDate
When the estimate misses
If the product is bigger than the number being divided → the quotient is too big. Take 1 off.
If the remainder is the same as the divisor or bigger → the quotient is too small. Add 1.
A remainder is always smaller than the divisor. 64 ÷ 16 16 → 20, 60 ÷ 20 = 3 … estimate 3
16 × 3 = 48, 64 − 48 = 16 … same as the divisor! → change to 4. 16 × 4 = 64, remainder 0
5A child guessed a digit for each division. Is it right? If not, fix it and write the correct quotient and remainder.
(1) 85 ÷ 17, guessed 4 (2) 55 ÷ 18, guessed 4
Multiply and subtract, then look at the remainder.
6Work out 69 ÷ 17 with long division.
17 → 20, 60 ÷ 20 = 3. After multiplying and subtracting, is the remainder smaller than 17?
7Work out 458 ÷ 52 with long division.
52 → 50. Try 450 ÷ 50 = 9 first.
20 minutes, then stop
Maths A (new unit)Tue 6 October3 / 4
Long division by two digits
NameDate
When you get stuck
156 ÷ 26
1 ÷ 26 is too small, and so is 15 ÷ 26. "It does not go in" and you stop
→ Look at all three digits, 156, as one lump. The quotient starts in the ones.
26 → 30, 150 ÷ 30 = 5 … estimate 5. 26 × 5 = 130, 156 − 130 = 26 … same as the divisor!
→ change to 6. 26 × 6 = 156, remainder 0. (No 0 is written in the tens.)
8Work out 138 ÷ 23 with long division.
1 and 13 are both smaller than 23. Take 138 as one lump.
9Work out 756 ÷ 21 with long division. (The quotient has two digits.)
First 75 ÷ 21. 21 → 20, 80 ÷ 20 = 4 goes over 75 when multiplied back.
10A child answered "247 ÷ 32 = 6 remainder 55". The check (32 × 6 + 55) works out. The answer is still wrong. Why? Write the correct answer too.
20 minutes, then stop
Maths A (new unit)Tue 6 October4 / 4
Long division by two digits
NameDate
What a remainder means depends on the story
Take 134 ÷ 24 = 5 remainder 14 and three stories:
- 134 people ride 24-seat buses → the other 14 ride too. 5 + 1 = 6 buses (round up)
- 134 pencils go in bags of 24 → 5 bags, 14 pencils left (round down)
- 134 stickers to 24 people, the same number each → 5 each, 14 left over
The sum and the quotient are the same. Only "what to do with the remainder" differs.
11134 people will ride in buses that hold 24 each. How many buses are needed?
What happens to the people left over?
12There are 100 cookies, packed 14 to a box.
(1) How many full boxes of 14 are there, and how many cookies are left?
(2) If the leftover cookies go in a box too, how many boxes are needed in all?
13A ribbon is 230 cm long. Pieces of 35 cm are cut from it.
(1) How many pieces, and how many cm are left?
(2) How many more cm would give one more piece?
(2) How far is the leftover from 35?
20 minutes, then stop
Costume 1Wed 7 October1 / 4
Choose one of these two
1 Basketball 2 Shopping — do sheet 1 or sheet 2, then everyone does 3 and 4
NameDate
1 · Basketball — shooting, roughly
Success rate is really said in percent. Here we ask one in how many goes in: shots taken ÷ shots made. When the numbers are awkward, estimate first.
Example 60 shots, 20 made → 60 ÷ 20 = 3 → one in 3
1A player took 84 shots and made 28. One in how many goes in?
28 → 30. Estimate first, then divide.
2Player A made 22 of 88 shots, player B made 30 of 90. For each, one in how many goes in? Who shoots better?
3A player took 58 shots and made 19. Say "about one in ...?" from an estimate first, then work out 58 ÷ 19 by long division.
What does the remainder stand for?
20 minutes, then stop
Costume 1Wed 7 October2 / 4
Choose one of these two
NameDate
2 · Shopping — the total before the till
Work out a rough total before you reach the till. Round, then add (an estimate). How many you can buy at one price is a division.
Example 188 yen and 304 yen → 200 + 300 → about 500 yen
1You buy three things at 298 yen, 412 yen and 199 yen. Round each to the nearest hundred and estimate the total.
2Gum costs 47 yen each. You buy as many as you can with 300 yen. How many, and how much change?
47 → 50. Try 300 ÷ 50 = 6.
3You buy things at 698 yen, 405 yen and 296 yen, and have 1,600 yen. Round each up to the hundred. Is it enough?
Rounding up gives an estimate bigger than the real total.
20 minutes, then stop
Costume 1Wed 7 October3 / 4
Choose one of these two
NameDate
3 · From here, everyone
4Work out 275 ÷ 34 with long division.
34 → 30. Try 270 ÷ 30 = 9 and multiply back.
5Estimate 4,829 + 3,174 by rounding each to the nearest hundred. Say "about ..." out loud before you write.
687 people ride in boats that hold 12 each. How many boats are needed?
20 minutes, then stop
Costume 1Wed 7 October4 / 4
Choose one of these two
NameDate
7You pay 3,210 yen using only 1,000-yen notes. How many notes are needed?
8Work out 412 ÷ 57 with long division.
57 → 60. 60 × 7 = 420 is close to 412.
9Work out 252 ÷ 36 with long division.
After subtracting, is the remainder smaller than 36?
20 minutes, then stop
Maths B (practice)Fri 9 October1 / 4
Rounding and estimating
Before you calculate: "about how many?"
NameDate
Say "about ..." out loud first. Then calculate, and check they are close.Loud enough for a parent to hear. An estimate you did not say is not an estimate.
Question 1 is already done for you
Round 4,268 to the nearest hundred. (three ways)
Round down zero out the tens and ones → 4,200 Round up if the tens and ones are not 0, add 1 to the hundreds → 4,300 Ordinary rounding the tens digit is 6, which is 5 or more, so up → 4,300
Your turn from here
2Round 7,218 to the nearest thousand three ways: round down, round up, and ordinary rounding.
To the nearest thousand, look at the hundreds.
3You buy a 489-yen book and a 302-yen notebook. Say "about ..." out loud first, then round each to the nearest hundred and estimate the total.
4You spend 2,896 yen out of 5,203 yen. Round each to the nearest hundred and estimate what is left.
20 minutes, then stop
Maths B (practice)Fri 9 October2 / 4
Rounding and estimating
NameDate
"At least", "at most" and "less than"
110 or more (at least) … includes 110 and goes up 110 or less (at most) … includes 110 and goes down less than 110 … does not include 110 and goes down
The 5 in the middle
Does 4,550 round to 4,500 (nearest hundred)? Treating the tens digit 5 as "round down" and saying 4,500 → 5 rounds up. 4,550 → 4,600. So 4,550 is not in the range for 4,500 (at least 4,450 and less than 4,550).
5The whole numbers that round to 300 (nearest ten): write their range two ways.
(1) using "at least" and "less than" (2) using "at least" and "at most"
Draw a number line and look either side of 300.
6Whole numbers that round to 4,500 (nearest hundred): write the range using "at least" and "less than". Also write the largest whole number.
7A ride lets in people who are "at least 110 cm and less than 140 cm" tall. Can each of these ride? Write yes or no.
(1) 109 cm (2) 110 cm (3) 140 cm (4) 139 cm
20 minutes, then stop
Maths B (practice)Fri 9 October3 / 4
Rounding and estimating
NameDate
Pick the method from the story
Making sure there is enough → round up How many you can buy, how many fit → round down
Wanting a rough comparison → ordinary rounding
8235 people ride in buses that hold 40 each. How many buses are needed? Also write which rounding method you used.
When you need to be sure there is enough…
9Sweets cost 85 yen each. You buy as many as you can with 700 yen. How many?
10A town has 27,418 people.
(1) Round to the nearest thousand.
(2) Round keeping only the first digit.
20 minutes, then stop
Maths B (practice)Fri 9 October4 / 4
Rounding and estimating
NameDate
11You buy 31 items at 78 yen each. Round both numbers, keeping only the first digit, and estimate the cost.
12You buy things at 305, 198, 287 and 156 yen, and have 1,000 yen. Round each up to the hundred. Can you say it is enough? Then add them exactly to check whether it really is.
13About how much is 4,187 + 3,912? Say it out loud before calculating, then choose.
A 800 B 8,000 C 80,000
Write why you chose it.
20 minutes, then stop
Costume 2 + correctionsSun 11 October1 / 4
Choose one of these two
1 Geography 2 Basketball — do sheet 1 or sheet 2, then everyone does 3 and 4
NameDate
1 · Geography — comparing populations
Big populations are easier to compare as rounded numbers. Made up. The prefectures and their populations are all invented.
Prefecture
Population
Sunnyside
312,486
Bluesky
1,873,540
Moonfield
905,718
Seabreeze
1,246,093
Four made-up prefectures
1Round the population of Sunnyside, keeping the first 2 digits.
Look at the 3rd digit from the left.
2Round Bluesky and Seabreeze, keeping the first 2 digits each. Which is bigger, and by about how many?
3About how many times bigger is Bluesky than Sunnyside? Round both keeping 2 digits, treat 10,000 as one unit, and divide.
1,900,000 is 190 ten-thousands, 310,000 is 31. So 190 ÷ 31.
20 minutes, then stop
Costume 2 + correctionsSun 11 October2 / 4
Choose one of these two
NameDate
2 · Basketball — per game
Per game = total ÷ number of games. A free throw is 1 point, a three-pointer is 3 points.
On Wednesday it was "one in how many". Today it is "how many per game".
1A team made 108 free throws in 12 games. How many per game?
12 → 10. Will the answer be a bit under 10?
2A team made 252 three-pointers in 28 games. How many per game?
28 → 30. Try 240 ÷ 30 = 8, multiply and subtract.
3Making 252 three-pointers is how many points in all? First treat 252 as 250 to estimate, then work out the exact points.
20 minutes, then stop
Costume 2 + correctionsSun 11 October3 / 4
Choose one of these two
NameDate
3 · From here, everyone
4Work out 345 ÷ 48 with long division.
48 → 50. Start from 350 ÷ 50 = 7.
5Of the whole numbers that round to 8,000 (nearest thousand), write the smallest and the largest.
On a number line, left and right of 8,000.
6A book has 215 pages. You read 32 pages a day. In how many days do you finish it?
20 minutes, then stop
Costume 2 + correctionsSun 11 October4 / 4
Choose one of these two
NameDate
4 · Corrections, and one puzzle problem
7Pick one question you got wrong this week from your notebook and do it again.
1 Which day and number? 2 Your answer and the right one 3 Where did it go wrong? 4 Redo it
Once you can do it the second time, that question is finished.
8Sum and difference — Two people have 70 stickers together. A has 12 more than B. How many does each have?
Draw a bar diagram first. How do you make A's bar the same length as B's?
9A "the first digits will not go" problem, like Tuesday's. Work out 288 ÷ 36 with long division.
28 is smaller than 36. Take 288 as one lump.
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 11 October, any time1 / 4
Stretch — level up
Not recorded. Getting it wrong is fine. Some numbers in the sources are not needed.
NameDate
1 · Waste and recycling [social studies: rubbish]
A (made-up) town put recycling boxes for plastic bottles in three places. Here is how many bottles were collected in 14 days. One bottle weighs about 25 g.
place
station
school
community hall
bottles in 14 days
658
504
392
Source — bottles collected in 14 days (made up)
Question 1 is already done for you
How many bottles a day were collected at the community hall?
Per day = 392 ÷ 14. Treat 14 as 10: 39 ÷ 10 → 3?
14 × 3 = 42 is bigger than 39 → 2. 14 × 2 = 28, 39 − 28 = 11, bring down the 2 → 112. 14 × 8 = 112.
Answer: 28 bottles
2How many bottles a day were collected at the station, and at the school?
Estimate first, then write the digit. Treat 14 as 10.
3Someone says: "The three places together collect more than 100 bottles a day, so in 30 days they will collect more than 3,000." Is that right? Explain, using your answers to questions 1 and 2.
First add the three amounts a day.
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 11 October, any time2 / 4
Stretch — level up
NameDate
2 · Pulse [science: body and exercise]
You can count your pulse at your wrist. A whole minute is long, so count for only 15 seconds and convert to one minute (made-up numbers). The classroom was 24 °C that day.
Source — pulse beats counted in 15 seconds (made-up numbers)
Question 1 is already done for you
Resting: how many beats in one minute?
18 beats in 15 seconds. One minute = 60 seconds = 4 lots of 15 seconds.
18 × 4 = 72 → 72 beats
2At the resting pulse, in which minute does the count reach 1000? (Use the beats in one minute from question 1.)
Treat 72 as 70: about how much is 1000 ÷ 70? Then divide by the real 72 and think about what the remainder means.
3Someone says: "Just after running, the pulse is more than twice the resting pulse." Is that right? Explain, using the numbers converted to one minute.
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 11 October, any time3 / 4
Stretch — level up
NameDate
3 · Ways to connect batteries [science: electricity]
A motor car (weight 120 g) was run on a 6 m (= 600 cm) course with the batteries connected in different ways (made up). In series the batteries are in one line; in parallel they are side by side.
connection
time for 6 m
1 battery
24 s
2 in series
15 s
2 in parallel
24 s
Source — running times (made up)
Question 1 is already done for you
With 1 battery, how many cm per second?
Per second = 600 ÷ 24. Treat 24 as 20: 60 ÷ 20 → 3?
24 × 3 = 72 is bigger than 60 → 2. 24 × 2 = 48, 60 − 48 = 12, bring down the 0 → 120. 24 × 5 = 120.
Answer: 25 cm
2With 2 batteries in series, how many cm per second?
First think of 60 ÷ 15. Which multiple of 15 makes 60?
3Someone says: "With 2 batteries in series, the car goes exactly twice as fast as with 1." Is that right? Explain, using your answers to questions 1 and 2.
What is 2 times 25?
10 minutes a sheet, then stop
Stretch (not recorded)From Sun 11 October, any time4 / 4
Stretch — level up
NameDate
4 · The trip bus [social studies: transport]
Fourth graders are going on a trip by bus (made up). One bus holds 40 people at most. Hiring one bus costs 12,000 yen. The place is 28 km away.
who
class 1
class 2
class 3
teachers
people
29
30
28
3
Source — who is going (made up)
Question 1 is already done for you
How many people are going in all, teachers included?
29 + 30 + 28 + 3 = 59 + 31 = 90
Answer: 90 people
2(1) How many buses are needed for 90 people?
(2) If 90 people share the hire cost of that many buses equally, how much is it each?
What does the remainder of 90 ÷ 40 mean? Can those people just be left?
3Someone says: "Even if the 3 teachers did not ride, the number of buses would be the same." Is that right? Explain with numbers.
kids/learn — weekly worksheet. The answers have a page of their own.