Milestones in Mathematics for NSW
Student Portfolio Year 5: Answers
Note: For SPs not listed below there are either no specific answers or answers will depend on the
responses of individual students.
SP 2
Student to record heights of fellow students and graph the information.
SP 3
Ogerville cricket team
season statistics
Player
Total
ML Hadden
598
DR Martyn
640
SP Shore
651
RT Pointing
713
MG Shore
662
DM Leanin
656
AC Gilcross
795
SK Storm
81
GW Marr
131
JP Gillett
64
B Free
28
1. Gilcross by 82 runs.
2. 97
3. Zoomtown by 139 runs.
4. They scored 69 less runs.
5. Ogerville won by 1596 runs.
Zoomtown cricket team
season statistics
Player
Total
ME Tresthick
435
NV Kight
305
RC Crane
472
MP Lawn
675
N Huss
578
AJ Sturt
511
PD Colling
187
A Flint
106
ID Black
35
AR Cradd
46
JM Anders
73
SP 4A
1.
472
460
1 008
696
894
458
511
476
657
678
976
1 068
514
2 915
5 184
734
2 616
610
1 476
656
2.
a.
b.
SP 4B
1.
628
$ 7.50 x
5
$37.50
$50.00 $37.50
$12.50
432 x
9
3 888
Yes
3 888 (greater than 3 000)
1 004
489
834
456
672
429
852
1 233
666
904
999
530
3 305
4 518
1 170
3 052
1 875
2 325
1 098
$ 4.50 x
4
$18.00
$30.00 $18.00
$12.00 change
132 x
8
1 056
Yes
2.
a.
b.
56 more seats than 1000
SP 5A
1.
1 302
2 605
3 438
3 496
2 303
968
1 124
3 588
729
2 605
4 039
5 376
5 706
598
1 776
2.
a.
434 x
8
3 472
b.
248 x
5
1 240
c.
Student to make up their own problem.
SP 5B
1.
1 625
2 055
4 086
4 232
3 143
1 344
1 226
4 062
1 173
3 320
2 716
6 112
6 678
1 198
3 108
2.
a.
b.
c.
327 x
9
2 943
136 x
7
952
Student to make up their own problem.
SP 6
(Not drawn to scale in answers)
A=
120 x 68 =
8 160 m2
Rugby League field
= 450m2
91 x 55 =
5 005 m2
Netball courts
Hockey complex
45 x 9 =
4 095 m2
50 x 25 =
1 250 m2
Aquatic Centre
Total area: 18 960 m2
Soccer Arena
SP 7
1.
15/5
=
15 ÷ 5
=
_____
5) 15
40/8
=
40 ÷ 8
=
_____
8) 40
36/12 =
36 ÷ 12
=
_____
12) 36
27/3
=
27 ÷ 3
=
_____
3) 27
24/6
=
24 ÷ 6
=
_____
6) 24
30/6
=
30÷ 6
=
_____
6) 30
2.
16/4
_____
4) 16
18 ÷ 6
18/6
_____
6) 18
36 ÷ 4
36/4
_____
4) 36
14 ÷ 2
14/2
_____
2) 14
15 ÷ 3
15/3
_____
3) 15
9÷3
9/3
_____
3) 9
12 ÷ 4
12/4
_____
4) 12
24 ÷ 8
24/8
_____
8) 24
25 ÷ 5
25/5
_____
5) 25
40 ÷ 4
40/42
_____
4) 40
16 ÷ 4
SP 7 Cont.
3.
a.
18 ÷ 2
b.
18/2
_____
2) 18
= 9 pairs
20 x 4
= 80 legs
SP 7B
1.
20/4
20 ÷ 4
_____
4) 20
32/8
32 ÷ 8
_____
8) 32
48/12
48 ÷ 12
_____
12) 48
30/3
30 ÷ 3
_____
3) 30
18/6
18 ÷ 6
_____
6) 18
36/6
36 ÷ 6
_____
6) 36
2.
24 ÷ 12
24/4
12 ÷ 6
12/6
45 ÷ 5
45/5
20 ÷ 2
20/2
24 ÷ 3
24/3
18 ÷ 3
18/3
27 ÷ 3
27/3
24 ÷ 8
24/8
36 ÷ 6
36/6
60 ÷ 6
60/6
____
4) 24
____
6) 12
____
5) 45
____
2) 20
____
3) 24
____
3) 18
____
3) 27
____
8) 24
____
6) 36
____
6) 60
SP 7B cont.
3.
a.
____
2) 32
b.
32/2
32 ÷ 2
= 16 pairs
40 x 4 = 160 pairs
(This is a multiplication question in a division exercise. Changed in next edition)
SP 8
Student to complete pictorial timetable.
SP 9A
2.
42 ÷ 4 = 10 2/4
23 ÷ 2 = 11 1/2
19 ÷ 4 = 4 3/4
13 ÷ 2 = 6 1/2
29 ÷ 4 = 7 1/4
3.
11 1/2 pairs because 23 ÷ 2 = 11 1/2
SP 9B
1.
28 ÷ 3 = 9 1/3
46 ÷ 4 = 11 1/2
9 1/3
3) 28
____
4) 46
Remainder
27 ÷ 3 = 9
28 - 27 = 1
= 1/3
31 ÷ 2 = 15 1/2
____
2) 31
Remainder
Remainder
=
1/2
17 ÷ 2 = 8 1/2
____
2) 17
Remainder
16 ÷ 2 = 8
17 - 16 = 1
22 ÷ 4 = 5 1/2
____
4) 22
Remainder
37 ÷ 4= 9 1/4
____
4) 37
Remainder
=
=
2/4
1/2
36 ÷ 4 = 9
37 - 36 = 1
2.
Number of glasses ÷ number of glasses is each box = number of boxes.
25 ÷ 2 = number of boxes.
24 ÷ 2 = 12
25 - 24 = 1
Remainder = 1/2
2/4
1/2
=
1/2
=
1/4
44 ÷ 4 = 11
46 - 44 = 2
30 ÷ 2 = 15
31 - 30 = 1
20 ÷ 4 = 5
22 - 20 = 1
=
=
25 ÷ 2 = 12 1/2
I will need 12 1/2 boxes.
SP 10A
1.
Thirds
Sixths
Twelfths
0
1
0
1
0
1
2.
5/6 = larger fraction.
3.
2/6
4/12
1/3
10/12
3/6
2/3
4.
Oger = 10/12
8/12
Sister = 9/12
Oger’s class got the best result, because it is the larger fraction.
Brainteaser
6 extra cuts of the pizza.
SP 10B
1.
2/3
4/6
8/12
2/6
4/12
SP 11
3/6
2.
4/6
8/12
2/3
6/12
2/6
1/3
4/12
Brainteaser
2 pieces.
SP 11
1.
2.
Hexagonal Pyramid
Triangular Pyramid
Correction: Should be 5 faces with a square based pyramid – not 8.
3.
Pentagonal Pyramid
Hexagonal Pyramid
Triangular Pyramid
SP 12
1.
246
848
2 446
9 936
8 246
2.
12 963
16 888
12 884
17 324
12 684
3.
28 856
25 002
17 335
6 425
13 512
Brainteasers
7 704
50 706
45 703
28 736
274 068
SP 13A
1.
Student to complete.
2.
ten
thousands
thousands
hundreds
tens
ones
a.
2
6
2
3
5
b.
4
2
9
8
0
c.
7
2
4
5
0
d.
3
8
1
6
4
e.
6
3
7
9
0
3.
a.
23 237
b.
75 824
c.
64 619
d.
81 582
e.
48 375
f.
52 941
4.
a.
12 456, 21 465, 24 681, 26 481, 34 567
b.
23 568, 34 579, 86 420, 87 643, 97 531
c.
21 548, 31 759, 35 721, 42 860, 87 531
d.
45 623, 45 632, 46 532, 78 934, 78 943
SP 13B
1.
Student to complete.
2.
ten
thousands
thousands
hundreds
tens
ones
a.
4
3
4
2
5
b.
5
1
6
7
0
c.
9
9
1
2
0
d.
2
7
3
5
3
e.
8
4
6
7
0
3.
a.
45 471
b.
97 666
c.
97 932
d.
72 471
e.
84 719
f.
32 671
4.
a.
b.
c.
d.
24 678, 43 787, 46 801, 48 401, 56 797
12 457, 23 468, 75310, 76 532, 86 421
32 659, 42 869, 46 832, 53 970, 98 642
56 734, 56 742, 57 643, 89 944, 89 954
SP 14
Timeline
The following times should be drawn onto the timeline:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
9:20
9:30
9: 40
9:45
9:50
10:23
11:01
12:30
1:00
2:30
3:00
Shuttle manouvers
Shuttle burns off fuel
Final check
Descent
Touch down
Towed back
Crew driven back
Crew welcomed back
Debriefing
Return to living quarters
Rest
SP 15
1.
Student alternatives possible.
SP 16
.710
Seven hundred and ten thousandths
.625
Six hundred and twenty five thousandths
.250
Two hundred and fifty thousandths
.750
Seven hundred and fifty thousandths
.410
Four hundred and ten thousandths
.215
Two hundred and fifteen thousandths
.513
Five hundred and thirteen thousandths
.295
Two hundred and ninety five thousandths
.8
Eight hundred thousandths
SP 17
1.
1
2
3
4
2
20 cm
2
3
4
2.
1
2
3
2
20 cm
3
4
5
4
2
5
SP 17 cont.
3.
1
2
3
4
2
36 cm
5
6
5
6
2
3
4
5
6
4.
1
2
3
4
2
56 cm
7
2
3
4
5
6
7
8
5.
Multiplied the number of blocks across the top, by the number of blocks down the left hand side to give
area in cm2
SP 18
1.
a. 16 20
24
28
b. There are 4 tiles in each row, as you add a row you add 4 more tiles to the total number of tiles.
c. Add 4.
2.
a. 12
15
18
21
b. There are 3 tiles in each row, as you add a row you add 3 more tiles to the total number of tiles.
c. Add 3.
SP 19
a.
13
8
6
8
10
5
8
10
b.
7 - 8 am
c.
Noon - 1 pm
d.
8 - 9, 10 - 11, 1 - 2
e.
Lunch traffic.
f.
Getting to work.
g.
People at work or finished lunch and walking.
h.
13 the same number as the morning peak.
SP 20
1.
a.
b.
c.
d.
e.
f.
g.
8
8
Swimming
Rugby
12
Swimming
25 if they did one sport each.
2.
a.
b.
c.
d.
e.
150
35
15
20
Depends on time of day teacher does this.
SP 21
1.
a.
12
18
21
b.
Multiply the number of triangles by 3 to get the number of sides.
c.
Number of triangles x 3 = number of sides.
2.
a.
16
b.
Multiply the number of squares by 4 to get the number of sides.
c.
Number of squares x 4 = number of sides.
3.
a.
24
b.
Multiply the number of hexagons by 6 to get the number of sides.
c.
Number of hexagons x 6 = number of sides.
4.
a.
24
b.
Multiply the number of octagons by 8 to get the number of sides.
c.
Number of octagons x 8 = number of sides.
20
30
32
24
28
36
48
SP 22
1.
a.
30
b.
Saturday
c.
Friday
d.
40
e.
Multiple possibilities
f.
135
2.
a.
250
b.
50
c.
Holden
d.
Mazda
e.
80
SP 23A
1.
Student generated answers.
2.
a.
b.
c.
d.
e.
Thirty two thousand and ninety eight.
Twenty three thousand five hundred and six.
Sixty four thousand eight hundred and seventy eight.
Fourteen thousand and three.
Ninety thousand three hundred and fifty.
3.
a.
b.
c.
d.
10 231
22 400
87 025
43 110
4.
a.
b.
43 768
23 789
5.
23 567
45 678
32 789
20 567
45 768
36 789
18 567
45 876
36 879
17 567
46 578
89 763
SP 23B
1.
a.
forty-five thousand and seventy six.
b.
forty-seven thousand, nine hundred and one.
c.
eighty-six thousand and ninety-five.
d.
twenty-two thousand and four.
e.
eighty-thousand, nine hundred and seventy.
2.
a.
b.
c.
d.
26 456
44 590
68 024
39 200
3.
a.
b.
65 980
45 901
65 998
54 901
68 790
58 901
4.
45 778
42 778
40 778
SP 24
Station 1
2.61 kg
1.345 kg
2.8 kg
67 890
58 990
39 778
Station 2
7
6
5
4
3
2
1
John
Jill
LiMei
Kim
Sue
Station 3
81, 243, 729
108, 324, 972
250, 1 250, 6 250
Station 4
375
1 840
5 912
Station 5
43 562, 45 632, 46 352, 46 532, 54 632
45 839, 83 459, 83 549, 84 359, 93 458
Final Station - Brainteaser
Multiples possible.
David
67 980
77 985
SP 25
1.
10 000
1 000
100
10
1
a.
3
5
7
9
2
b.
9
0
1
4
6
c.
4
0
7
8
2
d.
1
3
7
9
5
e.
5
0
2
4
6
f.
6
7
8
3
4
Challenge
2.
a.
b.
c.
59
90
120
SP 26A
1.
60
60
231
2.
1 951
4 831
3.
413
30
106
460
2 560
4 910
62 033
19 680
512 789
82 669
21 090
725 680
25 833
Individual answers
SP 26B
1.
80
60
720
2.
1 950
3 640
3.
578
30
36 024
105
650
4 909
2 550
SP 27A
1.
7
32
18
11
15
10
27
7
18
2.
a.
Multiple answers possible.
b.
Worked out answers each side of = and must be the same to be correct.
3.
a.
7+9=z+5
z = 11 pears
b.
SP 27B
1.
9
29
16
8
17
12
23
7
31
21 + 31 = 4 + z
z = 48 runs
2.
a.
Multiple answers possible.
b.
Worked out answers each side of = and must be the same to be correct.
3.
a.
8 + 6 = 3 + --14 = 3 + 11
= 11 red pens
b.
SP 28
2.
Ogerville Sports Complex
590 m
.59 km
29 + 47 + 22 = 15 + --98 = 5 + 83
The rest of the team shot 83 goals
Ogerville Shopping Plaza
1 120 m
1.12 km
Km is a more appropriate measure for very large areas like the shopping centre.
SP 29
a.
845 seats
b.
850 spaces
c.
225
605
202
1032
They sold 32 more seats
than were available IF 1000
seats is the maximum number
of seats.
d.
$1585
e.
$70 - $68
= $2 change
f.
120 - 114
= 6 kg under max. weight.
SP 30
1.
6
5
7
1
10
3
4
25
2.
0.5
0.5
0.1
0.1
0.5
0.5
0.5
0.1
3.
20
20
3
10
6
10
6
18
4.
13
6
3
7
53
11
SP 31A
a.
62 trees
b.
308 barrels
c.
209 kms
d.
71 boxes
e.
300 words
f.
204 newspapers
g.
409 spaces
h.
6 x 145 = 870
His 865 cattle
will fit
i.
$5
1 046 ÷ 7 = 149.4
c.
3 524 ÷ 4 = 881
f.
i.
2 429 ÷ 7 = 347
3 132 ÷ 3 = 1044
(assumes all 3 are
the same length)
SP 31B
a.
236 = 29.5
b.
8
(Correct book to 232
and answer = 29)
(Correct book to 1050
and answer = 150)
232 ÷ 8 = 29
d.
g.
865 ÷ 5 = 173
1 224 ÷ 4 = 43
e.
h.
8 850 ÷ 5 = 1 770
10 328 ÷ 8 = 1291
SP 32
40o
50o
90o
25o
45o
75o
55o
20o
105
133
135
115
55
20
35
SP 33
It bounces away from the wall at the same angle.
SP 34
1.
Teachers to draw diagrams.
Improper Fractions
11/2 = 3/2
13/4 = 7/4
11/3 = 4/3
12/4 = 6/4
12/3 = 5/3
16/8 = 14/8
2.
Teachers to draw diagrams.
8
/6 = 12/6 = 11/3
4
/3 = 11/3
6
/2 = 3/1 = 3
5
/4 = 11/4
12
/10 = 12/10 = 11/5
7
/4 = 13/4
SP 35
1.
6 000
8 000
4 000
2.
Students to draw picture graphs.
SP 36
Multiple answers possible.
7 000
6 000
SP 37
1.
a.
.3
.45
0.5
.65
.7
1
0
b.
.2
.55
.35
.8
.9
1
0
2.
a.
.2
.5
.6
.8
b.
0.0
.1
.3
.5
c.
0.0
.15
.25
.3
.5
.9
d.
0.0
.05
.1
.35
.55
.65
3.
a.
.04
.34
.43
.435
.44
b.
.075
.077
(.7 & .70)
.75
SP 38
Student generated answers.
SP 39
1.
13.86
8.26
29.95
4.53
37.95
9.17
10.83
9.88
31.84
75.85
53.06
71.92
19.52
127.15
480.25
1 165.85
2.
23.59 +
5.60
29.19
4.67 +
34.80
39.47
85.90 +
32.56
118.46
65.09 +
3.88
68.97
3.
3.45
67.54
2.30 +
73.29
60.89
3.25
15.10 +
79.24
43.67
7.50
12.45 +
63.62
7.80
98.54
16.09 +
122.43
SP 40
1.
22.33
42.64
86.12
44.58
86.30
11.20
545.13
892.22
27.45
35.10
35.36
27.85
9.07
87.44
433.52
968.94
231.228
22.082
952.787
33.516
344.122
34.556
2.
356.78 4.67
352.11
46.78 14.80
31.98
454.70 34.56
420.14
987.50 65.71
921.79
578.45 36.70
541.75
123.79 3.50
120.29
23.456 4 635
18.821
876.50 90.45
786.05
SP 41
1.
Lake Ogerville
Ogerville Business Park
Station
Ogerville Orchards (on boundary)
-
1 km
2 km
50 metres
2 km
SP 42
1.
2.
a.
b.
c.
d.
$4.25
$5.30
$3.55
$5.25
$4.30
$4.20
3.35 metres
3.275 metres
5.05 metres
4.896 metres
SP 43
1.
a.
20 c
b.
$1
$1.50
2.
a.
b.
6.8 cm
21.2 cm
.025 m
or 2.5 cm
SP 45A
1.
a.
4 thousands
9 tens
9 hundreds
0 hundreds
b.
6 ten thousands
8 thousands
8 tens
0 thousands
2.
a.
b.
c.
30 000 + 5 000 + 700 + 20
40 000 + 8 000 + 900 6
30 000 + 80 + 6
3.
a.
b.
34 789
57 890
34 879
57 980
34 978
58 097
34 987
58 790
37 849
59 087
4.
a.
b.
65 847
13 452
65 748
12 543
65 487
12 453
65 478
12 354
37 849
12 345
b. ________
9 tens
6 hundreds
2 hundreds
5.
Student generated answer.
SP 45B
1.
a. 9 ones
9 thousands
5 tens
3 hundreds
2.
a. 60 000 + 8 000 + 50 + 3
b. 70 000 + 2 000 + 200 + 9
c. 60 000 + 3 000 + 300 + 10 + 9
3.
66 801
60 019
66 810
60 219
66 811
61 209
66 901
62 209
69 272
62 219
4.
a. 77 665
b. 13 351
77 627
13 346
77 625
13 343
77 526
13 342
77 265
13 332
SP 45B
1. & 2. Cobar
Tumut
Muswellbrook
Broken Hill
Coffs Harbour
Bathurst
Dubbo
Orange
Wagga Wagga
Albury
5 300
6 300
10 541
19 834
26 083
27 036
30 937
31 970
44 451
69 880
3.
Newcastle 279 975
Sydney 3 502 301
4.
12 times
5.
15 times
Woollongong 228 846
SP 47A
1.
a.
.2572
1.4565
3.1246
77.2573
.0221
.23615
.1589
.005621
.1823
1.1111
.00351
.0121212
6.5265
.2167
.01555
3.3257
b.
The numbers do not change only decimal point moves 2 places to the left.
c.
Move decimal point 2 places to left.
2.
a.
.0675
.089
.2456
.00575
.6666
1.5025
SP 47B
1.
a.
.3165
.0341
.1941
6.6375
b.
2.
a.
2.6525
.24735
2.2222
.3178
49.6195
.1699
.00431
.07666
88.3595
.007834
.0271717
4.44563
You move the decimal point two places to the left.
.0985
.099
.3749
.00685
.7777
3.5045
SP 49
1.
$31 839
2.
$33 630
3.
Yes, cost is $33 379
4.
$90 970
5.
$37 702
6.
$1 000
SP 50
Student to draw graphs.
Corrections
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