01
Big numbers up to 1,000,000
· Big numbers in the place value chart Solution
| Th | H | T | O |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
= 1234
| Th | H | T | O |
|---|---|---|---|
| 5 | 6 | 7 | 8 |
= 5678
| Th | H | T | O |
|---|---|---|---|
| 9 | 0 | 8 | 1 |
= 9081
| Th | H | T | O |
|---|---|---|---|
| 2 | 4 | 5 | 6 |
= 2456
| Th | H | T | O |
|---|---|---|---|
| 7 | 3 | 9 | 2 |
= 7392
| Th | H | T | O |
|---|---|---|---|
| 6 | 0 | 1 | 5 |
= 6015
| Th | H | T | O |
|---|---|---|---|
| 8 | 3 | 4 | 7 |
= 8347
| Th | H | T | O |
|---|---|---|---|
| 3 | 7 | 2 | 9 |
= 3729
| Th | H | T | O |
|---|---|---|---|
| 4 | 5 | 8 | 6 |
= 4586
| Th | H | T | O |
|---|---|---|---|
| 9 | 0 | 5 | 2 |
= 9052
| Th | H | T | O |
|---|---|---|---|
| 1 | 6 | 7 | 3 |
= 1673
| Th | H | T | O |
|---|---|---|---|
| 2 | 9 | 4 | 8 |
= 2948
· Sort from small to large! Solution
· Number line up to a million Solution
· Compare the big numbers Solution
623,456<891,234
567,890=567,890
734,567>725,134
454,321>445,321
998,765>989,765
236,541<263,541
45,678<87,654
71,823=71,823
565,432<656,432
88,453>87,921
385,213<835,213
192,340<921,340
· Rounding to thousands Solution
234,617≈235,000
41,850≈42,000
128,390≈128,000
563,472≈563,000
617,845≈618,000
748,163≈748,000
825,609≈826,000
936,284≈936,000
· Splitting even bigger numbers Solution
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 1 | 8 | 3 | 9 | 4 | 7 |
= 183,947
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 5 | 0 | 2 | 6 | 7 | 1 |
= 502,671
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 7 | 6 | 4 | 3 | 2 | 8 |
= 764,328
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 9 | 1 | 8 | 2 | 5 | 4 |
= 918,254
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 3 | 0 | 6 | 5 | 9 | 2 |
= 306,592
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 6 | 4 | 7 | 1 | 8 | 3 |
= 647,183
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 8 | 2 | 9 | 4 | 1 | 0 |
= 829,410
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 5 | 7 | 3 | 9 | 2 | 6 |
= 573,926
· Neighbor numbers up to 1,000,000 Solution
· Ten thousand less and ten thousand more Solution
· Thousand steps on the number line Solution
· Sort from big to small! Solution
· Steps of one hundred on the number line Solution
· In steps of 10,000 and 100,000 Solution
· Building the number from the place values Solution
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 2 | 9 | 4 | 6 | 1 | 7 |
= 294,617
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 5 | 3 | 8 | 0 | 2 | 4 |
= 538,024
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 7 | 1 | 6 | 4 | 9 | 3 |
= 716,493
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 4 | 8 | 2 | 7 | 5 | 6 |
= 482,756
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 9 | 0 | 3 | 5 | 8 | 1 |
= 903,581
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 6 | 4 | 7 | 2 | 9 | 0 |
= 647,290
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 3 | 7 | 5 | 9 | 4 | 2 |
= 375,942
| HTh | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| 8 | 2 | 6 | 1 | 7 | 5 |
= 826,175
· Even or odd? Big numbers Solution
· Neighbor numbers that change place value Solution
A hundred thousand and a thousand less and more Solution
· Who am I? Solution
- I have 3 hundred thousands.
- My ten thousands and thousands digits are 8 and 4.
- My hundreds, tens and ones digits are 5, 1 and 9.
Solution: 384,519
- I am greater than 500,000 and smaller than 600,000.
- My ten thousands and thousands digits are 2 and 6.
- My hundreds, tens and ones digits are all 0.
Solution: 526,000
- I am a round number of hundred thousands.
- I am greater than 700,000.
- If you halve me, you get 400,000.
Solution: 800,000
- My hundred thousands digit is 6.
- My ten thousands digit is half as big.
- My thousands, hundreds and tens digits are all 0.
- My ones digit is twice as big as my ten thousands digit.
Solution: 630,006
· Almost the same numbers Solution
890,234>809,234
512,345<521,345
398,765>389,765
945,123<954,123
734,512<734,521
198,765>189,765
456,789<465,789
682,345<682,435
623,456<623,465
745,123=745,123
267,890<276,890
87,654>87,645
· Rounding to ten thousands Solution
34,617≈30,000
128,463≈130,000
262,918≈260,000
547,236≈550,000
615,472≈620,000
733,891≈730,000
856,104≈860,000
924,785≈920,000
· Comparing different numbers of digits Solution
812,345>98,765
654,321>645,321
87,654<587,654
736,428<736,482
99,999<999,998
654,321>65,432
520,481>520,418
90,959<599,091
718,239>71,823
845,671=845,671
783,924>738,924
921,387>219,387
· Writing big numbers Solution
· Even more number secrets Solution
- I am greater than 240,000 and smaller than 250,000.
- My thousands and hundreds digits are 3 and 7.
- My tens and ones digits are 8 and 4.
Solution: 243,784
- I have 6 hundred thousands and 1 ten thousand.
- My thousands and hundreds digits are 9 and 0.
- My tens and ones digits are 5 and 2.
Solution: 619,052
- I have 8 hundred thousands.
- My ten thousands digit is half as big as my hundred thousands digit.
- My thousands, hundreds and tens digits are all 0.
- My ones digit is the biggest single digit.
Solution: 840,009
- I am greater than 900,000.
- I am an even number.
- My ten thousands, thousands, hundreds and tens digits are all 0.
- My ones digit is 6.
Solution: 900,006
· Writing numbers with zeros Solution
· In steps of 25,000 and 50,000 Solution
· Rounding to hundred thousands Solution
148,372≈100,000
152,941≈200,000
347,128≈300,000
353,862≈400,000
646,295≈600,000
654,713≈700,000
847,356≈800,000
853,194≈900,000
· Counting back in big steps Solution
02
Written arithmetic
· Big numbers semi-written Solution
341 + 256 =
= 340 + 250 + 1 + 6
= 590 + 7
= 597
524 + 173 =
= 520 + 170 + 4 + 3
= 690 + 7
= 697
617 + 251 =
= 610 + 250 + 7 + 1
= 860 + 8
= 868
438 + 351 =
= 430 + 350 + 8 + 1
= 780 + 9
= 789
762 + 125 =
= 760 + 120 + 2 + 5
= 880 + 7
= 887
926 + 143 =
= 920 + 140 + 6 + 3
= 1060 + 9
= 1069
· Number walls up to 1,000,000 Solution
· Written addition without a carry Solution
· Written subtraction without regrouping Solution
· Written multiplication with two digits Solution
· Inverse problems up to 1,000,000 Solution
357,177 + 354,134 = 711,311
711,311 − 354,134 = 357,177
711,311 − 357,177 = 354,134
356,890 + 376,255 = 733,145
733,145 − 376,255 = 356,890
733,145 − 356,890 = 376,255
568,290 + 209,563 = 777,853
777,853 − 209,563 = 568,290
777,853 − 568,290 = 209,563
216,815 + 378,387 = 595,202
595,202 − 378,387 = 216,815
595,202 − 216,815 = 378,387
169,347 + 344,143 = 513,490
513,490 − 344,143 = 169,347
513,490 − 169,347 = 344,143
279,069 + 184,341 = 463,410
463,410 − 184,341 = 279,069
463,410 − 279,069 = 184,341
· Written addition with a carry Solution
· Subtracting with regrouping Solution
· Written division without a remainder Solution
· Mental arithmetic with numbers up to 10,000 Solution
1234+2143=3377
3421+4233=7654
3165+2317=5482
6789−1234=5555
8765−5344=3421
6455−2134=4321
4567+1234=5801
2314+4475=6789
· Estimating with hundreds Solution
4238 + 3891 ≈8100
6790 - 2940 ≈3900
3170 + 4620 ≈7800
8340 - 3810 ≈4500
5260 + 2730 ≈8000
7480 - 4390 ≈3100
· Written addition: big numbers Solution
· Swap problems when adding big numbers Solution
327,145+245,318=572,463↔245,318+327,145=572,463
456,283+318,472=774,755↔318,472+456,283=774,755
178,562+483,619=662,181↔483,619+178,562=662,181
534,217+296,384=830,601↔296,384+534,217=830,601
· Written subtraction: big numbers Solution
· Dividing by bigger divisors Solution
· Mental arithmetic with numbers up to 100,000 Solution
12,345+21,433=33,778
23,451+44,435=67,886
37,112+21,374=58,486
67,894−21,343=46,551
87,654−53,133=34,521
64,567−21,345=43,222
45,678+12,311=57,989
23,145+44,742=67,887
· Estimating with thousands Solution
412,300 + 297,600 ≈710,000
689,400 - 295,100 ≈394,000
234,800 + 349,200 ≈584,000
718,600 - 382,300 ≈337,000
523,400 + 264,900 ≈788,000
846,200 - 479,800 ≈366,000
· Crossing the ten Solution
346,285 + 258,749 =
= 346,280 + 258,740 + 5 + 9
= 605,020 + 14
= 605,034
512,367 + 184,528 =
= 512,360 + 184,520 + 7 + 8
= 696,880 + 15
= 696,895
273,916 + 381,457 =
= 273,910 + 381,450 + 6 + 7
= 655,360 + 13
= 655,373
428,634 + 297,189 =
= 428,630 + 297,180 + 4 + 9
= 725,810 + 13
= 725,823
165,797 + 439,628 =
= 165,790 + 439,620 + 7 + 8
= 605,410 + 15
= 605,425
637,458 + 195,366 =
= 637,450 + 195,360 + 8 + 6
= 832,810 + 14
= 832,824
· Even more number walls Solution
· With bigger numbers Solution
· More inverse problems Solution
136,437 + 361,194 = 497,631
497,631 − 361,194 = 136,437
497,631 − 136,437 = 361,194
188,929 + 320,959 = 509,888
509,888 − 320,959 = 188,929
509,888 − 188,929 = 320,959
203,848 + 137,685 = 341,533
341,533 − 137,685 = 203,848
341,533 − 203,848 = 137,685
202,713 + 173,952 = 376,665
376,665 − 173,952 = 202,713
376,665 − 202,713 = 173,952
410,605 + 236,531 = 647,136
647,136 − 236,531 = 410,605
647,136 − 410,605 = 236,531
503,036 + 188,186 = 691,222
691,222 − 188,186 = 503,036
691,222 − 503,036 = 188,186
· Written division with a remainder Solution
· Mental arithmetic with numbers up to 1,000,000 Solution
241,352+125,413=366,765
541,623+234,152=775,775
876,543−342,132=534,411
789,654−234,123=555,531
· Euli has miscalculated again Solution
528,620+261,999=790,619
387,609−58,953=328,756→328,656
397,918+297,736=695,654
436,632−150,661=286,971→285,971
· Subtracting with several regroupings Solution
· Five-digit times two-digit Solution
· Addition with several addends Solution
· Dividing by two-digit numbers Solution
· Estimating with ten thousands Solution
384,700 + 271,500 ≈650,000
716,200 - 293,800 ≈430,000
458,300 + 326,900 ≈790,000
893,600 - 447,200 ≈440,000
265,400 + 538,100 ≈810,000
947,300 - 562,600 ≈390,000
· Checking multiplication and division Solution
86,457 × 8 = 691,656
691,656 + 8 = 86,457
8 + 691,656 = 86,457
945,216 : 6 = 157,536
157,536 + 6 = 945,216
6 + 157,536 = 945,216
72,318 × 9 = 650,862
650,862 + 9 = 72,318
9 + 650,862 = 72,318
834,568 : 4 = 208,642
208,642 + 4 = 834,568
4 + 208,642 = 834,568
125,409 × 5 = 627,045
627,045 + 5 = 125,409
5 + 627,045 = 125,409
736,281 : 7 = 105,183
105,183 + 7 = 736,281
7 + 105,183 = 736,281
· Multiplying numbers with zeros inside Solution
· Euli checks the sums again Solution
463,815+274,906=738,721
812,340−96,475=725,865→715,865
259,438+168,295=427,633→427,733
694,027−385,119=308,908
03
Multiplication and division
· Calculating with key facts Solution
5 × 7 = 35
1 × 7 = 7
6 × 7 = 42
5 × 9 = 45
2 × 9 = 18
7 × 9 = 63
5 × 8 = 40
3 × 8 = 24
8 × 8 = 64
5 × 8 = 40
2 × 8 = 16
7 × 8 = 56
5 × 7 = 35
3 × 7 = 21
8 × 7 = 56
5 × 9 = 45
1 × 9 = 9
6 × 9 = 54
5 × 9 = 45
3 × 9 = 27
8 × 9 = 72
5 × 8 = 40
1 × 8 = 8
6 × 8 = 48
5 × 7 = 35
2 × 7 = 14
7 × 7 = 49
· Dividing without a remainder Solution
14 : 2 =7
24 : 3 =8
20 : 4 =5
30 : 5 =6
54 : 6 =9
28 : 7 =4
80 : 8 =10
27 : 9 =3
26 : 2 =13
36 : 3 =12
44 : 4 =11
70 : 5 =14
· Dividing with a remainder Solution
25 : 4 =6 R 1
34 : 5 =6 R 4
47 : 6 =7 R 5
29 : 3 =9 R 2
53 : 7 =7 R 4
38 : 4 =9 R 2
45 : 8 =5 R 5
59 : 9 =6 R 5
· Times and divided stories Solution
- 1. 7500
- 2. 600
- 3. 3600
- 4. 800
- 5. 1008
· Times before plus Solution
3 + 4 × 5 =23
6 × 2 + 5 =17
20 − 3 × 4 =8
7 × 3 − 9 =12
4 × 5 + 6 =26
30 − 4 × 6 =6
8 + 5 × 2 =18
9 × 2 + 7 =25
5 + 6 × 4 =29
8 × 4 + 9 =41
40 − 5 × 6 =10
9 × 3 − 8 =19
2 × 9 + 15 =33
25 − 3 × 7 =4
12 + 4 × 6 =36
6 × 8 − 20 =28
· Times tables Solution
· Semi-written multiplying Solution
32 × 4 =
= 30 × 4 + 2 × 4
= 120 + 8
= 128
26 × 7 =
= 20 × 7 + 6 × 7
= 140 + 42
= 182
24 × 6 =
= 20 × 6 + 4 × 6
= 120 + 24
= 144
35 × 4 =
= 30 × 4 + 5 × 4
= 120 + 20
= 140
45 × 3 =
= 40 × 3 + 5 × 3
= 120 + 15
= 135
37 × 5 =
= 30 × 5 + 7 × 5
= 150 + 35
= 185
· Dividing, also with tens Solution
18 : 3 =6
32 : 4 =8
54 : 9 =6
180 : 3 =60
320 : 4 =80
540 : 9 =60
48 : 6 =8
35 : 5 =7
64 : 8 =8
480 : 6 =80
350 : 5 =70
640 : 8 =80
· Multiply the big times tables Solution
6 + 6 + 6 + 6 + 6 + 6 + 6 + 6=48→6fits into 488times
7 + 7 + 7 + 7 + 7 + 7=42→7fits into 426times
8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8=72→8fits into 729times
9 + 9 + 9 + 9 + 9 + 9 + 9=63→9fits into 637times
· Big times and divided tasks Solution
- 1. 25,200
- 2. 12,000
- 3. 38,250
- 4. 14,000
- 5. 36,000
· Times before plus with parentheses Solution
( 8 + 4 ) × 3 =36
( 20 − 5 ) : 3 =5
40 − ( 6 + 4 ) × 2 =20
( 12 − 3 ) × 5 =45
( 30 : 6 ) + 8 =13
6 × ( 7 − 2 ) =30
( 9 + 6 ) : 5 =3
50 − ( 8 × 4 ) =18
3 × ( 9 + 4 ) =39
60 − ( 7 + 5 ) × 4 =12
( 4 + 7 ) × 6 =66
( 56 : 8 ) − 3 =4
· Times tables with tens Solution
· Multiplying across the ten Solution
48 × 6 =
= 40 × 6 + 8 × 6
= 240 + 48
= 288
56 × 7 =
= 50 × 7 + 6 × 7
= 350 + 42
= 392
67 × 5 =
= 60 × 5 + 7 × 5
= 300 + 35
= 335
43 × 8 =
= 40 × 8 + 3 × 8
= 320 + 24
= 344
58 × 6 =
= 50 × 6 + 8 × 6
= 300 + 48
= 348
74 × 5 =
= 70 × 5 + 4 × 5
= 350 + 20
= 370
· Semi-written dividing Solution
1284 : 4 =
= 1280 : 4 + 4 : 4
= 320 + 1
= 321
2478 : 6 =
= 2460 : 6 + 18 : 6
= 410 + 3
= 413
3654 : 7 =
= 3640 : 7 + 14 : 7
= 520 + 2
= 522
4872 : 8 =
= 4800 : 8 + 72 : 8
= 600 + 9
= 609
5628 : 7 =
= 5600 : 7 + 28 : 7
= 800 + 4
= 804
6345 : 9 =
= 6300 : 9 + 45 : 9
= 700 + 5
= 705
· Dividing with bigger numbers Solution
45 : 5 =9
56 : 7 =8
63 : 9 =7
72 : 8 =9
84 : 7 =12
88 : 8 =11
91 : 7 =13
95 : 5 =19
98 : 7 =14
99 : 9 =11
76 : 4 =19
78 : 6 =13
· Dividing with a remainder up to 100 Solution
31 : 7 =4 R 3
46 : 9 =5 R 1
17 : 5 =3 R 2
61 : 7 =8 R 5
53 : 8 =6 R 5
85 : 9 =9 R 4
44 : 6 =7 R 2
69 : 6 =11 R 3
· Dividing with a zero in the answer Solution
· Multiples of tens Solution
20 + 20 + 20 + 20 + 20 + 20 + 20=140→20fits into 1407times
30 + 30 + 30 + 30 + 30 + 30 + 30=210→30fits into 2107times
40 + 40 + 40 + 40 + 40 + 40 + 40 + 40=320→40fits into 3208times
50 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50=450→50fits into 4509times
· Swap problems when multiplying Solution
16×125=2000↔125×16=2000
35×24=840↔24×35=840
250×8=2000↔8×250=2000
48×15=720↔15×48=720
125×32=4000↔32×125=4000
64×25=1600↔25×64=1600
75×12=900↔12×75=900
18×150=2700↔150×18=2700
· Times with tens Solution
3×40=120
4×50=200
5×60=300
6×70=420
7×80=560
8×90=720
9×30=270
4×90=360
12×40=480
13×20=260
14×50=700
16×40=640
5×70=350
6×30=180
9×50=450
8×40=320
· Euli checks times and divided by Solution
96,845×8=774,760
742,836:6=123,860→123,806
78,256×7=547,972→547,792
735,462:6=122,577
· Times before plus, with division Solution
72 : 8 + 15 =24
( 45 : 5 ) × 4 =36
6 × 9 − 54 : 6 =45
90 − 7 × 8 =34
81 : 9 + 6 × 7 =51
( 60 − 12 ) : 6 =8
3 × ( 24 : 4 ) =18
96 : 8 × 5 =60
56 : 7 + 9 × 4 =44
100 − 48 : 6 =92
( 48 : 6 ) × 7 =56
7 × 8 − 63 : 9 =49
· Times tables with hundreds Solution
· First multiply or divide, then keep going Solution
- 1. 216 → 69
- 2. 144 → 125
- 3. 40 → 27
- 4. 245 → 46
- 5. 360 → 387
· Dividing with hundreds and thousands Solution
2400 : 6 =400
4800 : 8 =600
6300 : 9 =700
6400 : 2 =3200
3600 : 4 =900
5600 : 7 =800
1500 : 5 =300
3500 : 7 =500
5400 : 3 =1800
7200 : 6 =1200
4200 : 2 =2100
1600 : 8 =200
· Dividing with a remainder up to 1000 Solution
125 : 6 =20 R 5
143 : 8 =17 R 7
217 : 9 =24 R 1
184 : 7 =26 R 2
251 : 4 =62 R 3
309 : 7 =44 R 1
425 : 9 =47 R 2
166 : 7 =23 R 5
· Word problems about packing and sharing Solution
- 1. 52,000
- 2. 49,000
- 3. 45,500
- 4. 51,890
- 5. 68,600
· Multiples of two-digit numbers Solution
24 + 24 + 24 + 24 + 24 + 24 + 24=168→24fits into 1687times
35 + 35 + 35 + 35 + 35 + 35 + 35 + 35=280→35fits into 2808times
45 + 45 + 45 + 45 + 45 + 45 + 45 + 45 + 45=405→45fits into 4059times
16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16=192→16fits into 19212times
· Times with hundreds Solution
3×200=600
4×300=1200
5×400=2000
6×500=3000
7×600=4200
8×700=5600
9×800=7200
6×900=5400
· Dividing by two-digit numbers with a remainder Solution
· Smart math: make the numbers fit Solution
25 × 17 × 4 =1700
4 × 38 × 25 =3800
6 × ( 100 − 1 ) =594
( 40 + 3 ) × 7 =301
125 × 9 × 8 =9000
50 × 23 × 2 =2300
7 × ( 200 − 3 ) =1379
( 300 + 8 ) × 6 =1848
8 × 19 × 125 =19,000
2 × 45 × 50 =4500
9 × ( 100 − 2 ) =882
( 500 + 4 ) × 2 =1008
· Times tables with two-digit numbers Solution
04
Quantities and scale
· Reading lengths Solution
· Kilometers, metric tons and grams Solution
3 km =3000m
4 t =4000kg
6000 m =6km
7000 kg =7t
5 kg =5000g
9 t =9000kg
2000 m =2km
8000 g =8kg
8 km =8000m
3000 kg =3t
6 kg =6000g
9000 m =9km
· From the model to reality Solution
Scale 1 : 100
3 cm →300cm
6 cm →600cm
11 cm →1100cm
25 cm →2500cm
9 cm →900cm
40 cm →4000cm
17 cm →1700cm
30 cm →3000cm
7 cm →700cm
14 cm →1400cm
22 cm →2200cm
35 cm →3500cm
· Measuring bars Solution
· Estimating everyday measures Solution
Hamburg to Munich is about ≈800 km
An empty truck weighs about ≈8 t
A full bathtub holds about ≈150 l
· Comparing weights Solution
2 kg>1950 g
3000 g=3 kg
5 kg>4800 g
750 g<1 kg
6 kg<6250 g
8000 g=8 kg
4 kg>3900 g
9500 g<10 kg
· Days and weeks in the calendar Solution
1. May 19
2. 21
3. June 6
4. March 23
· Converting meters and centimeters Solution
2 m =200cm
500 cm =5m
1 m 50 cm =150cm
375 cm =3 m 75 cm
4 m =400cm
800 cm =8m
2 m 25 cm =225cm
640 cm =6 m 40 cm
3 m =300cm
600 cm =6m
1 m 75 cm =175cm
425 cm =4 m 25 cm
6 m =600cm
900 cm =9m
3 m 40 cm =340cm
560 cm =5 m 60 cm
· Hours, minutes and seconds Solution
2 h =120min
3 min =180s
180 min =3h
240 s =4min
5 h =300min
4 min =240s
360 min =6h
120 s =2min
7 h =420min
8 min =480s
540 min =9h
300 s =5min
· From the map to reality Solution
Scale 1 : 1000
12 cm →12,000cm
15 cm →15,000cm
23 cm →23,000cm
34 cm →34,000cm
27 cm →27,000cm
46 cm →46,000cm
18 cm →18,000cm
35 cm →35,000cm
21 cm →21,000cm
38 cm →38,000cm
29 cm →29,000cm
42 cm →42,000cm
· Which scale fits? Solution
2 kg1 kg + 1 kg
Balanced500 g + 500 g2 kg
right heavier3 kg1 kg + 500 g
left heavier1 kg + 500 g2 kg
right heavier200 g + 300 g1 kg
right heavier2 kg + 1 kg3 kg
Balanced4 kg2 kg + 1 kg
left heavier1 kg500 g + 200 g
left heavier· Which scale fits? With tons and kilograms Solution
1 t500 kg + 500 kg
Balanced2 t1 t + 500 kg
left heavier1 t + 500 kg2 t
right heavier250 kg + 250 kg1 t
right heavier3 t2 t + 1 t
Balanced500 kg + 500 kg + 1 t2 t
Balanced4 t2 t + 1 t
left heavier1 t500 kg + 200 kg
left heavier· Comparing liters and milliliters Solution
2 l>1950 ml
3000 ml=3 l
1500 ml<2 l
5 l>4800 ml
250 ml<1 l
6000 ml=6 l
4 l<4300 ml
7 l>6500 ml
· Beyond the year in the calendar Solution
1. January 15
2. 9
3. December 17
4. December 3
· From reality to the map Solution
Scale 1 : 250
750 cm →3cm
1250 cm →5cm
2750 cm →11cm
3250 cm →13cm
4750 cm →19cm
5250 cm →21cm
6750 cm →27cm
8250 cm →33cm
· Estimating more measures Solution
A blue whale weighs about ≈150 t
A fully loaded freight train weighs about ≈4000 t
A city bus weighs about ≈10 t
· Full, half and quarter hours Solution
O 'clock and half-past times Solution
8:00 a.m. → 9:00 a.m. :60min
7:00 a.m. → 7:30 a.m. :30min
10:30 a.m. → 12:00 p.m. :90min
2:00 p.m. → 4:00 p.m. :120min
9:30 a.m. → 10:00 a.m. :30min
6:00 a.m. → 8:30 a.m. :150min
· Converting decimal measures Solution
2.35 m =235cm
1.75 kg =1750g
3.45 € =345ct
0.8 l =800ml
4.7 cm =47mm
1.25 l =1250ml
12.99 € =1299ct
2.5 t =2500kg
0.6 kg =600g
6.25 m =625cm
0.35 l =350ml
7.5 cm =75mm
· Comparing weights and liters Solution
4 kg<4010 g
2500 ml>2 l
9000 g=9 kg
1 l>999 ml
6 kg<6200 g
8 l=8000 ml
3750 g<4 kg
5 l>4990 ml
· Comparing lengths and times Solution
3 m>295 cm
4 km<4100 m
2 h<125 min
1 m=1000 mm
5 km>4900 m
195 min>3 h
250 cm>2 m
7500 m<8 km
· Adding dollars and cents Solution
1. $37 and 44¢
2. $25 and 25¢
3. $38 and 44¢
4. $63 and 95¢
· Counting big amounts Solution
· To the nearest five minutes Solution
· Clock times to the exact minute Solution
· Quarter hours and minutes Solution
8:15 a.m. → 9:00 a.m. :45min
10:45 a.m. → 11:30 a.m. :45min
1:20 p.m. → 2:00 p.m. :40min
3:50 p.m. → 5:00 p.m. :70min
7:35 a.m. → 8:15 a.m. :40min
9:10 a.m. → 11:25 a.m. :135min
· Time spans over several hours Solution
7:50 a.m. → 10:35 a.m. :165min
8:40 a.m. → 12:05 p.m. :205min
6:25 a.m. → 9:50 a.m. :205min
11:55 a.m. → 2:20 p.m. :145min
9:20 a.m. → 1:45 p.m. :265min
1:35 p.m. → 5:10 p.m. :215min
· Adding up bigger amounts Solution
1. $224 and 40¢
2. $138 and 33¢
3. $269 and 94¢
4. $82 and 14¢
· What does the class trip cost? Solution
1. $486 and 25¢
2. $443 and 15¢
3. $506 and 70¢
4. $390 and 40¢
· Mixed units Solution
3 l =3000ml
5000 ml =5l
1.5 l =1500ml
0.75 l =750ml
2.5 km =2500m
8000 m =8km
3.2 kg =3200g
7000 g =7kg
9000 ml =9l
0.5 km =500m
1.2 kg =1200g
4000 g =4kg
· Putting routes on the city map Solution
Scale 1 : 20,000
4600 m →23cm
7200 m →36cm
9400 m →47cm
5800 m →29cm
8600 m →43cm
6200 m →31cm
9800 m →49cm
3400 m →17cm
05
Geometry
· Complete the mirror images Solution
· Counting shapes Solution
· Continue the pattern Solution
· Finding right angles Solution
· Drawing parallel lines Solution
· Adding blocks up Solution
· Covering areas Solution
· Drawing perpendicular lines Solution
· Perimeter and area Solution
A = 15 cm²
U = 16 cm
A = 24 cm²
U = 20 cm
A = 16 cm²
U = 20 cm
A = 35 cm²
U = 24 cm
A = 18 cm²
U = 22 cm
A = 49 cm²
U = 4 cm
· Mirroring at the horizontal axis Solution
· Difficult patterns Solution
· Points in the coordinate system Solution
A: (2 | 3)
B: (5 | 1)
C: (1 | 5)
D: (4 | 4)
· Sliding shapes diagonally Solution
· Reading coordinates Solution
A: (3 | 2)
B: (6 | 5)
C: (1 | 4)
D: (5 | 6)
· Counting shapes exactly Solution
· Mirroring slanted lines Solution
· Which one is a cube net? Solution
· Right angles on slopes Solution
· Calculating perimeter and area Solution
A = 54 cm²
U = 30 cm
A = 48 cm²
U = 32 cm
A = 70 cm²
U = 34 cm
A = 64 cm²
U = 32 cm
A = 70 cm²
U = 38 cm
A = 99 cm²
U = 40 cm
· Drawing shapes exactly Solution
· Tricky areas Solution
· Turning shapes around a point Solution
· Counting shapes safely Solution
· Reading points safely Solution
A: (4 | 1)
B: (2 | 6)
C: (6 | 3)
D: (3 | 5)
· Spotting and continuing patterns Solution
· Look down at the tower from above Solution
· Finding right angles in shapes Solution
· Corners, edges and faces Solution
How many faces does a cube have?6
How many corners does a cube have?8
How many edges does a cube have?12
How many corners does a box (rectangular prism) have?8
How many edges does a box (rectangular prism) have?12
How many corners does a pyramid with a square base have?5
· Which one is a box net? Solution
· Look down at the tower from above Solution
· Which faces do you need? Solution
Cube
Circle 0
Triangle 0
Square 6
Rectangle 0
Box
Circle 0
Triangle 0
Square 0
Rectangle 6
Pyramid
Circle 0
Triangle 4
Square 1
Rectangle 0
Cylinder
Circle 2
Triangle 0
Square 0
Rectangle 0
Cone
Circle 1
Triangle 0
Square 0
Rectangle 0
Sphere
Circle 0
Triangle 0
Square 0
Rectangle 0
· Covering big areas Solution
· Bigger rectangles and squares Solution
A = 384 cm²
U = 80 cm
A = 225 cm²
U = 4 cm
A = 576 cm²
U = 100 cm
A = 378 cm²
U = 82 cm
A = 540 cm²
U = 114 cm
A = 625 cm²
U = 4 cm
· Mirroring a house and a heart Solution
· Prism and pyramid with a hexagon Solution
How many faces does a prism with a hexagonal base have?8
How many corners does a prism with a hexagonal base have?12
How many edges does a prism with a hexagonal base have?18
How many corners does a pyramid with a hexagonal base have?7
How many edges does a pyramid with a hexagonal base have?12
How many edges does a prism with an octagonal base have?24
· Points near the edge and in the middle Solution
A: (5 | 2)
B: (1 | 1)
C: (6 | 6)
D: (2 | 4)
· More cube nets Solution
· Perimeter and area in meters Solution
A = 7140 m²
U = 346 m
A = 2116 m²
U = 4 m
A = 1404 m²
U = 158 m
A = 2240 m²
U = 198 m
A = 1369 m²
U = 4 m
A = 2407 m²
U = 224 m
06
Word problems, data and chance
· Word problems with two steps Solution
- 1. 14,100
- 2. 2350
- 3. 3650
- 4. 2500
- 5. 550
· Certain, possible or impossible? Solution
I draw a filled marble.possible
I draw a dotted marble.impossible
I draw a filled or empty marble.certain
I draw an empty marble.possible
· Car colors in front of the school Solution
· Finding combinations Solution
· Smart adding: friendly numbers first Solution
235 + 478 + 165 =878
349 + 276 + 51 =676
186 + 395 + 14 =595
527 + 168 + 273 =968
418 + 355 + 82 =855
263 + 599 + 137 =999
746 + 109 + 54 =909
382 + 447 + 118 =947
695 + 318 + 305 =1318
154 + 289 + 46 =489
473 + 226 + 27 =726
838 + 172 + 99 =1109
· Visitors at the theme park Solution
On which day did the most visitors come?Saturday
How many visitors came on Thursday and Friday together?8000
How many more visitors came on Saturday than on Thursday?3300
How many visitors came per day on average?4900
· From the table to the chart Solution
BookNumber
Mystery8
Comic12
Non-fiction6
Fairy tale9
What was borrowed the most?Comic
· From the chart to the table Solution
· Which bar is wrong? Solution
· Word problems with three steps Solution
- 1. 30,100
- 2. 1100
- 3. 16,200
- 4. 19,400
- 5. 385
· Double big numbers Solution
| 15,000 | 42,000 | 130,000 | 240,000 | 315,000 | 480,000 |
| 30,000 | 84,000 | 260,000 | 480,000 | 630,000 | 960,000 |
| 25,000 | 70,000 | 160,000 | 250,000 | 305,000 | 460,000 |
| 50,000 | 140,000 | 320,000 | 500,000 | 610,000 | 920,000 |
· Drawing marbles Solution
· Again: certain, possible, impossible Solution
I draw a striped marble.impossible
I do not draw a dotted marble.certain
My first marble is empty.possible
I draw two filled marbles one after the other.possible
· Always half Solution
| 40,000 | 86,000 | 124,000 | 264,000 | 470,000 | 620,000 |
| 20,000 | 43,000 | 62,000 | 132,000 | 235,000 | 310,000 |
| 68,000 | 92,000 | 180,000 | 340,000 | 540,000 | 900,000 |
| 34,000 | 46,000 | 90,000 | 170,000 | 270,000 | 450,000 |
· Combining in order Solution
· Which is more likely? Solution
Which is more likely: a striped marble or a filled one?the striped one
How many marbles are in the bag altogether?15
Which is less likely: an empty marble or a filled one?the empty one
How many more striped marbles than filled marbles are in the bag?5
· Word problems with big numbers Solution
- 1. 212,000
- 2. 100,000
- 3. 55,000
- 4. 155,000
- 5. 585,000
· Do you need all the numbers? Solution
- 80 (you don't need 85)
- Missing: how many books are ordered
- Missing: how many seats one row has
- 555 (you don't need 9)
· Converting decimals with zeros Solution
4.05 € =405ct
2.04 kg =2040g
3.08 m =308cm
0.65 m =65cm
6.4 km =6400m
1.06 l =1060ml
0.25 t =250kg
5.09 € =509ct
0.9 km =900m
7.03 m =703cm
0.45 kg =450g
3.5 t =3500kg
· Tickets sold Solution
How many tickets were sold in total?74,000
How many more tickets were sold for the train than for the ferry?25,000
How many tickets were sold for bus and tram together?31,000
How many more tickets were sold for the bus than for the ferry?3500
· Times before plus with big numbers Solution
( 126 + 74 ) × 5 =1000
940 − 15 × 36 =400
3672 : 9 + 258 =666
50 × ( 307 − 143 ) =8200
( 4836 − 1236 ) : 6 =600
750 + 24 × 25 =1350
1536 − ( 36 + 64 ) × 12 =336
8 × 125 + 4864 : 8 =1608
· Find the wrong bar Solution
· Counting all possibilities Solution
· Two-step word problems with measures Solution
- 1. 20,400 → 15,900
- 2. 44,460 → 5540
- 3. 1920 → 720
- 4. 28,300 → 7700
- 5. 360 → 280
· Residents of the districts Solution
How many residents does the city have in total?102,200
How many more residents does the south have than the east?13,200
How many residents do north and west have together?51,800
By how much must the east grow to be as big as the west?8700
07
Fractions and parts
· Which fraction is colored? Solution
· Half and a quarter Solution
1/2 of 40 m =20m
1/2 of 26 kg =13kg
1/2 of 500 g =250g
1/2 of 18 l =9l
1/4 of 40 m =10m
1/4 of 24 kg =6kg
1/4 of 200 g =50g
1/4 of 36 l =9l
· Which fraction is bigger? Solution
· Fractions on rectangles and bars Solution
· Thirds and fifths Solution
1/3 of 90 cm =30cm
1/3 of 27 kg =9kg
1/3 of 600 m =200m
1/3 of 150 ml =50ml
1/5 of 45 l =9l
1/5 of 250 g =50g
1/5 of 100 cm =20cm
1/5 of 80 m =16m
· Same number of colored parts Solution
· Fifths and sixths Solution
· Several parts at once Solution
3/4 of 400 m =300m
2/3 of 600 kg =400kg
3/4 of 200 g =150g
2/5 of 450 l =180l
3/5 of 500 cm =300cm
2/3 of 120 ml =80ml
3/4 of 480 kg =360kg
4/5 of 250 m =200m
· Equal or not? Solution
· Eighths and tenths Solution
· Sixths and eighths Solution
1/8 of 400 m =50m
3/8 of 240 kg =90kg
5/8 of 160 l =100l
7/8 of 320 m =280m
1/6 of 300 g =50g
5/6 of 180 cm =150cm
1/6 of 900 ml =150ml
5/6 of 600 m =500m
A close call Solution
08
Puzzles and games
· Magic square: sums 60, 90, 120 Solution
· Magic triangles with the numbers 21 to 26 Solution
· Big math square Solution
· Spider wheel: times tables Solution
· Arrow arithmetic up to 1,000,000 Solution
· Calculate with the cards Solution
· Find the secret ingredient! Solution
· Find the way out of the dungeon! Solution
· Find the right path! Solution
· Color in the magic picture Solution
· Magic square: sums 210, 240, 270 Solution
· Magic triangles with big numbers Solution
· Boss level: Grade 4 Solution
- 3731,4955,8686
- 3681,5880,9561
- 5901,6209,12110
- 2383,2367,4750,5900,8150
- 3090,2575,5665,6900,10400
- 3707,3893,7600,9050,13550