Operations and Number Patterns Upper Primary - Blake Education

8678_cover.qxd.qxd:TM UP Operations Cover.qxd

5/2/08

3:17 PM

Page 1

Targeting Maths Upper Primary

Ove 90 B r LMs

Graded activities that target all Maths topics

Operations and Number Patterns

MULTIPLICATION

Formal setting out of multiplication algorithms is practised with both vertical and horizontal forms. Algorithms extend to multiplying by three-digit numbers. Estimation is encouraged. Patterns are discovered and extended. Multiplication facts are practised through completion of speed grids and finding missing digits. Problem solving uses multiplication in varied ways. Areas are calculated, money spent, a wedding and the school concert organised and the school doors all repaired. Students are also required to write their own problems to fit given information. The activity page explores products in a fun way and there are two assessment pages.

41

UPPER PRIMARY

BLM Content *

MULTIPLICATION Prisms UNIT 1 Pyramids Extended form Contracted Building 3Dform Solids Patterns Drawing 3D Solids Problem solving

Materials needed for each BLM.

1 Look and see – patterns; codes. * calculator

2 Extended form – calculating the extended 2-digit ¥ 1-digit algorithm; using columns; horizontal and vertical calculations.

3 Contracted form – calculating the contracted algorithm; estimating; calculator usage. * calculator

Estimation

4 Patterns – multiplying by 1, 10, 100; multiplying decimals; the movement of the decimal point. * calculator

Assessment outcomes A student: uses multiplication involving whole numbers to solve problems.

5 Concert problems – estimating; identifying

•

recalls and uses multiplication facts up to 10 ¥ 10.

6 Calculated effort – finding the path taken;

•

models and explains patterns related to number facts for multiplication.

•

selects appropriate strategies to approximate and calculate solutions to problems involving whole numbers, money and decimal fractions.

•

appreciates how mathematics is used in a range of aspects of society.

•

uses understood written methods to multiply whole numbers to two-digit numbers.

•

uses a calculator efficiently for operating on numbers.

•

estimates and calculates mentally.

•

number sentences; calculation of problems.

calculator usage; identifying number sentences when problem solving. * calculator, coloured pencils

7 Assessment

Language estimate, calculate, units, ones, tens, hundreds, thousands, columns, decimals, decimal point, trade, contracted form, extended form, multiply, multiplication

Materials/resources Base 10 materials, calculator, coloured pencils, Times Table Poster

42

8 Activity – Finding products.

*

Remember

Encourage students to:

* * * *

seek help when unsure. explain their understandings. use Times Table Poster if needed. use concrete materials if necessary.

*

Additional Activities

I Using supermarket catalogues, explore how multiplication is used.

I Play board games using 3 dice and calculators. To move forward multiply the 3 dice and add the numbers in the total, e.g. 3 x 6 x 4 = 72 7 + 2 = 9, move forward 9 spaces. If the total was 184, add 1, 8 and 4 to get 13 then add 1 and 3 to move forward 4 spaces.

I Students design a simple multiplication board game for lower grades using 2, 3, 4, 5 or 10 times tables.

I Daily multiplication grid – students beat their own time if using the same grid outline, developing accuracy and confidence.

ANSWERS CONT… BLM 3 1 a f 2 a e 3 a d 4 a 5 a 6 a

156 b 234 c 512 d 455 e 108 144 27 x 6 b 32 x 5 c 81 x 8 d 15 x 9 47 x 7 f 13 x 1 $217.20 b $239.85 c $198.10 $333.60 e 105.42 5 382 b 3 765 c 2 013 d 3 720 e 364 F b T c T d F e T f F 3 b 6 c 7 d 6, 1 e 3, 1

BLM 4 1 Student to check using a calculator. 2 a 300 b 950 c 90 d 820 e 4 400 f 6 300 g 580 h 9 900 i 670 j 7 500 k 180 l 260 3 Student to check using a calculator. 4 3.25 32.5 325 . 62 06 620.6 6 206 97.34 973.4 9 734 . 582 11 5 821.1 58 211 5 a it didn’t move b one place to the right c two places to the right 6 Student to check using a calculator.

BLM 5 1 72 2 170 3 32 4 352 5 $216 6 1 650 7 1 pair

BLM 6 1 Teacher to check. 2 a 87 b 696 c no, 174 e hinges $29.58 f 4 days

ANSWERS BLM 1 1 Teacher to check.

BLM 2 1 a 98 b 86 c 88 d 96 e 648 f 448 g 963 h 627 2 a F b T c F d F e T f T g T h F i F 3 a 260 b 48 c 568 d 168 e 189 f 108 g 170 h 474 4 Teacher to check.

d $31.32

BLM 7 1 a 186 b 128 c 468 d 0 2 a 170 b 26 700 c 9 840 d 410 e 82.5 f 376 3 a correct b incorrect - 665 c correct d incorrect - 1746 4 a 945 b 1 968 c 2 208 d 1 516 e 2 538 f 1 440 g 1 904 h 5 490 5 a 152 b $119.70 c 13.5 metres 6 a 2 b 4 c 2, 7 d 9

BLM 8 Answers will vary. One solution is: highest – 63 ¥ 9, 52 ¥ 8, 41 ¥ 7, 1270 lowest – 14 ¥ 9, 25 ¥ 8, 36 ¥ 7, 578

43

BLM 1 Name 0000000000000000000000000000000000 Date 00000000

LOOK AND SEE 1

a Complete the grid. 8

10

3

4

1

5

0

9

7

2

6

x5 x 10

b What is the pattern?00000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000

2

a Multiply the calculations from A to Z then check using a calculator. A 2 x 2 = 0000

B 4 x 3 = 0000

C 8 x 5 = 0000

D 7 x 3 = 0000

E 3 x 2 = 0000

F 6 x 9 = 0000

G 9 x 4 = 0000

H 5 x 3 = 0000

I

J 3 x 9 = 0000

K 9 x 9 = 0000

L 5 x 4 = 0000

M 10 x 5 = 0000

N 7 x 5 = 0000

O 5 x 2 = 0000

P 4 x 6 = 0000

Q 6 x 7 = 0000

R 7 x 8 = 0000

S 3 x 3 = 0000

T 4 x 8 = 0000

U 6 x 2 = 0000

V 9 x 7 = 0000

W 4 x 4 = 0000

X 10 x 10 = 000

Y 8 x 8 = 0000

Z 9 x 8 = 0000

4 x 2 = 0000

b Calculate the value of your name. 000000000000000000000000 c Compare this to three friends’ names and rank the four in order from least to most. 0000000000000000 0000000000000000 0000000000000000 0000000000000000

d Repeat with your surnames. 0000000000000000 0000000000000000 0000000000000000 0000000000000000

e With a partner try other comparisons such as: teachers’ names, street names, football teams, Olympic sports, TV shows etc.

f Represent your findings using as many mathematical explanations as you can (e.g. graphs, chance and data, numerical comparisons).

44

Outcomes • Recalls multiplication facts up to 10 x 10. • Models and explains patterns related to number facts for multiplication. • Uses multiplication involving whole numbers to solve problems. © Blake Education Targeting Maths. This page may be reproduced for classroom use.

BLM 2 Name 0000000000000000000000000000000000 Date 00000000

EXTENDED FORM 1

Multiply. Remember to keep numbers in the correct columns. a T U b T U c T U 9

8

¥

4

3

¥

1

2 ¥

2

d

2

T

U

3

2

¥

4

3

(8 ¥ 1) (90 ¥ 1)

e

H

T

U

3

2

4

¥

2

f

True or false? a 13 ¥ 3 = 19 0000

U

1

1

2

g

H

T

U

3

2

1

¥

4

h

T

U

6

2

7

¥

3

b 34 ¥ 2 = 68 0000 e 349 ¥ 0 = 0 0000 h 444 ¥ 2 = 666 0000

H

1

c 24 ¥ 4 = 86 0000 f 863 ¥ 1 = 863 0000 i 245 ¥ 3 = 645 0000

Complete these algorithms using the extended form.

a

65 x

4

T

¥

2

d 123 ¥ 3 = 126 0000 g 403 ¥ 2 = 806 0000

3

H

b

4

16 x

3

c

d

71 x

8

e

84 x

2

27 x

f

7

12 x

g

h

34

9

x

8

10

5

79 x

6

Complete.

¥

7

2

5

9

6

0

4

3

1

3 6 9 Outcomes • Uses understood written methods to multiply whole numbers to two-digit numbers. • Explains patterns related to number facts for multiplication. © Blake Education Targeting Maths. This page may be reproduced for classroom use.

45

BLM 3 Name 0000000000000000000000000000000000 Date 00000000

CONTRACTED FORM 18 x 34 72

1

a

2

b

x

897

18 x 5

or

81 x 8

or

101 x 2

b 32 x 5 d 15 x 9 f 13 x 1

f

or

62 x 2

or

96 x 1

or

73 x 0

b $79.95 x

c $39.62

3

x

d $83.40

5

x

b

6

c

753 x

5

d

671

e $15.06

4

x

x

3

e

465 x

True or false? Use a calculator. a 0.36 x 4 = 144 0000 b 6.27 x 5 = 31.35 0000 d 18.03 x 6 = 108.08 0000 e 20.02 x 7 = 140.14 0000

7

8

182 x

b

2 x

2 46

15 x 90

c

34 x

5

1

0

2

c 101.00 x 0 = 0 0000 f 42.15 x 10 = 4.215 0000

Write the missing digits.

a

46

or

8

x

6

e

Try these!

a

5

d

Calculate, then check with a calculator.

a $27.15

4

c

Circle the larger answer.

a 27 x 6 c 56 x 4 e 47 x 7

3

Estimate answers first. Then set each one out vertically to solve it. a 52 x 3 Est. 00000000 b 39 x 6 Est. 00000000 c 64 x 8 Est. 00000000 d 91 x 5 Est. 00000000 e 27 x 4 Est. 00000000 f 18 x 8 Est. 00000000

d

69 x

9 2

Outcome • Selects appropriate strategies to calculate solutions to problems involving whole numbers, money and decimal fractions. © Blake Education Targeting Maths. This page may be reproduced for classroom use.

e

57 x 1 07

3

BLM 4 Name 0000000000000000000000000000000000 Date 00000000

PATTERNS 1

2

3

4

Use a calculator. Look for the patterns. a 6 x 1 = 0000 b 17 x 1 = 0000 c 6 x 10 = 0000 17 x 10 = 0000 6 x 100 = 0000 17 x 100 = 0000 On the back of this page continue this pattern Now calculate without using a calculator. a 3 x 100 = 0000 b 95 x 10 = 0000

22 x 1 = 0000 22 x 10 = 0000 22 x 100 = 0000 for 43, 85, 103.

d 39 x 1 =

0000 39 x 10 = 0000 39 x 100 = 0000

e 44 x 100 = 0000 f 63 x 100 = 0000 i 67 x 10 = 0000 j 75 x 100 = 0000

c 10 x 9 = 0000 g 58 x 10 = 0000 k 10 x 18 = 0000

d 10 x 82 = 0000 h 99 x 100 = 0000 l 10 x 26 = 0000

Now try these. a 56 x 1 000 = 0000 b 381 x 100 = 0000 e 47 x 1 000 = 0000 f 272 x 0 = 0000

c 198 x 100 = 0000 d 80 x 100 = 0000 g 9 x 1 = 000 h 65 x 100 = 0000

Use a calculator and watch the answers carefully. x1

x 10

x 100

3.25 62.06 97.34 582.11

5

Where did the decimal point move to when you: a multiplied by 1? 00000000000000000000000000000000

Check using a calculator.

b multiplied by 10? 0000000000000000000000000000000 c multiplied by 100? 000000000000000000000000000000

6

Complete these. NO CALCULATORS! x1 14.49 30.82 23.71 6.432 10.549 76.58 322.44 587.90

x 10

x 100

x 1000 ONIC ELECTR TOR LA CALCU 0N 7

A/C

MR

8

9

5

4

2

1

M−

M+

√

%

×

6

÷ −

3 .

+

=

1

Outcomes • Models and explains patterns related to number facts for multiplication. • Uses a calculator efficiently for operating on numbers. © Blake Education Targeting Maths. This page may be reproduced for classroom use.

47

BLM 5 Name 0000000000000000000000000000000000 Date 00000000

CONCERT PROBLEMS Miss Major-Mayhem is organising the School Concert. Help her finalise the arrangements. Estimate first, then calculate to see if your estimate makes sense.

1

Three rows of VIP seats are to be set out with 24 seats in each row. How many VIP reserved signs need to be made? Estimation 000000000000

2

Calculation 000000000000

With over 1 000 people expected to fill the Concert Hall, each wearing one pair of shoes, how many pairs of shoes will Miss Major-Mayhem wear on the night? Estimation 000000000000

48


Three A4 pages are used per program. How many pages are needed for 550 programs? Estimation 000000000000

7


Hall hiring costs $72 per hour. The concert will take 3 hours. What is the amount written on the cheque Miss MajorMayhem sends, prior to the night of the concert? Estimation 000000000000

6


Miss Major-Mayhem said that eight rows of 44 seats would be needed for the school students. How many students attend the school? Estimation 000000000000

5


The Consistent Effort Awards are being made. Kindergarten, Year 1 and Year 2 need four each. Years 3 – 6 need five each. How many need to be printed? Estimation 000000000000

4


Nathan’s mum will make seventeen flower arrangements required on the night. Each arrangement consists of 10 roses. How many roses must she order? Estimation 000000000000

3

Working Out


Outcomes • Uses understood written methods to multiply whole numbers to two-digit numbers. • Appreciates how mathematics is used in a range of aspects of society. © Blake Education Targeting Maths. This page may be reproduced for classroom use.

BLM 6 Name 0000000000000000000000000000000000 Date 00000000

CALCULATED EFFORT

1

Secure the loose pavers by colouring in those which have answers that are even. Write the largest answer on the glue bucket. Start

2

789 x 4

224 x 5

251 x 3

753 x 100

39 x 9

59 x 5

17 x 1

120 x 3

369 x 7

46 x 9

717 x 2

99 x 3

103 x 5

854 x 5

35 x 5

258 x 7

410 x 10

33 x 5

83 x 3

615 x 10

98 x 6

139 x 2

68 x 1

101 x 7

459 x 7

13 x 9

45 x 9

29 x 3

8x4

77 x 9

170 x 9

22 x 8

47 x 2

86 x 8

10 x 9

678 x 1

60 x 5

1 x 53

783 x 3

155 x 9

963 x 7

345 x 5

37 x 10

914 x 5

88 x 4

66 x 8

14 x 7

9x6

Read the problems carefully before calculating.

a How many doors are there? 00000000 b Darrel has attached 174 door handles to the doors of a new school. How many screws does he need if he uses 8 screws per door? (Hint: Remember that a door has two handles.) 00000000

c Each door has two hinges. He has 164. Is this enough? 00000000 How many does he need in total? 00000000

d Every hinge requires 6 screws. What will the total cost be if the screws are three cents each? 00000000

e Hinges cost $0.35 each. Which costs more – the hinges or the screws? 00000000 By how much? 00000000

f Darrel and Stan need roughly 20 minutes to complete each door. How many days will it take them if they work from 9 am to 6 pm with an hour lunch break? 00000000 Outcomes • Uses understood written methods to multiply whole numbers to two-digit numbers. • Appreciates how mathematics is used in a range of aspects of society. © Blake Education Targeting Maths. This page may be reproduced for classroom use.

49

ASSESSMENT

BLM 7

Name 0000000000000000000000000000000000 Date 00000000

MULTIPLICATION 1

a ¥

2 3

b

62

¥

3

a 17 ¥ 10 =

¥

4

¥

2

b 267 ¥ 100 = 0 0 00

c 984 ¥ 10 = 00

00

d 4.1 ¥ 100 = 00

00

e 8.25 ¥ 10 = 00

f 3.76 ¥ 100 = 00

00

00

0

Find and correct the errors by rewriting each one below.

b

72

c

95 ¥

6

4 32

d 5 82

916 ¥

7

1 02

a

¥

4

3 664

b

3

2 45

c

d

Multiply to solve these algorithms. Show your working.

a 189 ¥ 5 a

b 246 ¥ 8 b

c 552 ¥ 4 c

d 379 ¥ 4 d

e 4 23

f 7 20

g 2 72

h 6 10

¥

¥

¥

¥

6

2

7

9

a At a local neighbourhood meeting 4 rows of chairs were set up with 38 in each row. How many people could be seated? 00000000

b Nicole sold six pairs of shoes on sale at $19.95 each. What was the total amount of her sales? 00000000

c Silvana received an order to cut and sew nine tablecloths 1.5 metres in length. How much material is needed to complete the order? 00000000

6

567

00

¥

5

d

234

00

a

4

c

32

Fill in the missing digits.

a

b

7 ¥

5

3 60

360 ¥ 1 440

c

159

d

4

¥

8

¥

1

2

2 82

50 © Blake Education Targeting Maths. This page may be reproduced for classroom use.

3

BLM 8

ACTIVITY PAGE Name Date

PRODUCTS Your aim is to make the highest or lowest total possible. • Place the digits 1–6 in the six boxes. Each digit may only be used once. • Work out the products. • Find the sum of the products. • Try this several times until you have the highest/lowest total you can find. HIGHEST TOTAL Product ¥ 9

00000000

¥ 8

00000000

¥ 7

00000000

¥ 9

00000000 Total

LOWEST TOTAL Product ¥ 9

00000000

¥ 8

00000000

¥ 7

00000000

¥ 9

00000000 Total

Variation: Make the task more interesting by having 9 boxes and using the digits 1–9.

51

8678_cover.qxd.qxd:TM UP Operations Cover.qxd

5/2/08

3:17 PM

Page 2

Targeting Maths The Targeting Maths Series is a comprehensive resource for primary schools. It has been designed to provide busy teachers with all the additional material they need when teaching mathematics. All aspects of the primary mathematics curriculum are covered in this twelve book series. With Targeting Maths, teachers can easily find student activities, reproducible pages and assessment ideas for every mathematical topic or concept. Each topic is covered by one or more units of work which are progressive in level. Each unit starts with two teaching pages that include outcomes, language and materials needed. This is followed by a description of the six blackline masters and all their answers. There are activities and exercises for extension as well as reinforcement and practice, plus high interest activities and games. Each unit ends with an assessment page, which is a valuable teaching resource in itself. They can be used to assess specific outcomes or as a pre-test to discover levels of student understanding. There are four books at each level—Lower, Middle and Upper Primary.

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Measurement

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Middle Primary

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Middle Primary

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Middle Primary

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ISBN 978-1-86509-867-8

Measurement

9

781865 098678