Let's Do Mathematics 6 – Worktext B by Regal_Education

n ca t Wo r k t e xt x

for le arner arners 11 - 12 yea r s o l d

Aligned to the US Common Core State Standards

n ca t Wo r k t e xt x

for le arne arners 11 - 12 yea r s o l d

Let’s Do Mathematics

Re ga le du ca tio n

Let’s Do Mathematics is a series covering levels K-6 and is fully aligned to o the United States Common Core State Standards (USCCSS). Each level consists of two books boo (Book A and Book B) and combines textbook-style presentation of concepts oncepts pts as well as workbook practice.

Central to the USCCSS is the promotion of problem-solving skills ls and reasoning. Let’s Do Mathematics achieves this by teaching and presenting ng g concepts through throu a problem-solving based pedagogy and using the concrete-pictorial-abstract pictorial-abstract torial-abstract ((CPA) approach. Learners acquire knowledge and understanding a ng off concepts through thr th guided progression beginning with concrete examples and experiences which then w flow into pictorial representations and finally mastery at the and symbolic level. e abstract an a This approach ensures that learners develop a fundamental understanding of concepts damental ental understa underst rather than answering questions by learned procedures edures es and algorithms. algorit

Key features of the series include:

Anchor Task

Integers Inte

Anchorr Task

Open-ended activities serve as the starting point for understanding new vities concepts. Learners engage in activities e and discussions to form concrete experiences before the conceptt is formalized.

Fractions

Anchor Task

ChicFinae g

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14 Graham Crackers

1 cup pecans 2

4 tbsp butter

1 cup sugar 4 1 tsp cinnamon 2

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2 egg yolks

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Let’s Learn n

Crust

2 1 lbs cream cheese 2 3 cup sour cream 4 1 tsp salt 2 3 1 cups sugar 4

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Concepts are presented sented in a clear and a colorful manner.. Worked rked problems problem provide learners step-by-step ers with ith guided step-by ste progression through Series gh examples. Ser mascots provide rovide de guidance through throug throu helpful comments observations omments ments and observa when new concepts oncepts are introduced. intro

30 minutes 1 hour 15 minutes

Ingredients

98 9 8

Let’s ’ L Learn

When findi ng the area of triangles, height. we first

need to find

Lets find the

the base and

base and heig

(a)

hts of som

e more trian

gles.

The height must be perpendic ular to the base.

In this triangle, the height is not a side length.

height

We can choo se any side of the trian let's take the gle to be the base to be base. For the BC. triangle ABC, The height of the trian gle is chosen base . This is a right given by the perpendi cular heig height. -angled trian ht to our gle, so AB is the perpendi cular BC is the base and AB is the height.

(b)

base

If we choose the base to be MO, the is perpendi cular to the height is given base. by the line NP

which

height

base

For a base SU, the perp endicular heig triangle at line TV. ht is

located outs ide

the

Let’s Practice

(d)

Let’s Practice 1.

Identify the base and

height of the triangles

base =

height =

(a)

Learners demonstrate their understanding of concepts through a range of exercises and problems to be completed in a classroom environment. Questions provide a varying degree of guidance and scaffolding as learners progress to mastery of the concepts.

base = height = F

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(e)

(b)

base =

ight = height

height =

(f)

(c)

base =

height =

base =

height =

At Home

Complete the followin g. Show your working in its simplest form. and write your answer

(a)

4 x 7 5

At Home

Further practice designed to be completed without the guidance of a teacher. Exercises and problems in this section follow on from those completed under Let’s Practice.

(c)

Multiply the mixed numbers. Show your yo working and answer in its simples write your t form. orm.

(a) 3 2 x 5 5

(b) 6 x 2 3

5 x 8 12

(d) 10 x 5 6

(b) 2 x 3 5 8

(c)

(e) 6 x 3 7

(f)

4x22 3

(d) 7 x 3 3 5

7 x 9 5

(e) 12 x 4 1 8

(f)

8x53 12

1 12

1 13

Hands On

Learners are encouraged to ‘learn by doing’ through the use of group activities and the use of mathematical manipulatives.

ngle with the Hands On area of a recta is half the of a triangle ao the area Show that height. and he 12 cm. same base a height of 16 cm and of h widt has a gle below The rectangle of 192 cm2 . height of 12 area cm and a It has an ar base of 16 a has te page the opposite tri gle on The trian th so the dotted lines the m. g cm. up alon to neatly fill . Then cut grid below m the page triangle from nge pieces in the Cut out the rrange the 3 pieces. Arra triangle is in rectangle. half of the

Solve It!

The figures are made up of semicircles (half circles) and straight lines. Can you find the area of each figure? Take π = 3.14 and round off your answer to 1 decimal place.

(a)

Solve It!

(b)

Activities that require learners earners ers to apply logical reasoning problem-solving. oning g and problem-so problem n posed ed which do not have h Problems are often a olving them. Learners Learn L routine strategy for solving are encouraged to think a range k creatively and an apply ap of problem-solving solving g heuristics.

2 cm

5 cm

The figure below is made from a square of side length 6 cm. The circular hole in the middle has a diamete r that is 2 the side length of the square. Find the 3 area of the figure. Take π = 3.14 and round off your answer to 1 decima l place.

as a decimal p the percentage Express Exp

Looking Back

(a) 12%

What percentage of each square is

colored?

(a)

(b)

(c)

Consolidated solidated practice where whe learners demonstrate on a emonstrate their understanding under u range ange of concepts taught taug within a unit.

(c)

(e) 70%

(d)

Color 14% of the square.

42%

and fraction in its simplest form. (b) 28%

(d) 86%

(f)

50%

percentage. Express the fraction as a decimal and 4 17 (b) 20 (a) 100

Color 45% of the square.

(c)

15 60

(d)

66 88

235

234

iii

Contents 2 2 16 24 46

Re ga le du ca tio n 7

Geometry Properties of Circles Area of Circles Area of Triangles Area of Composite Figures

8 Time Expressing 12-hour and 24-hour -hour ur Time Duration of Time Word Problems

66 68 69 74 85

9 Speed ance e Speed and Distance Average Speed ed ems ms Word Problems

94 94 109 120

10 Pie Chartss ding g and Interp Int Reading Interpreting Pie Charts ord Problems Word

138 138 160

174 174 180 18 186 192 197 201 206 210 216 221

12 End-of-year Exam Section A Section B Section C

226 226 234 241

ed uc ati on

11 Problem Solving Act It Out Draw a Model Guess-and-Check Make a List Look for Patterns Work Backwards Simplify the Problem Solve Part of the Problem Before-After Concept Make Suppositions

Geometry

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Properties of Circles Anchor Task

Diameter D

Green circle reen circ Blue circle ue circ Red circle

Circumference

Let’s Learn

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Let's look at the different parts of a circle.

O is a point at the center enter er of the circle. circ AB is a straight line e that passes through th the center pointt O.

eter of the circle. AB is a diameter

OC is a straight ht line from the center of the circle cle to its perimeter. perime

OC is a radius of the circle.

DE is a straight line that does not pass through the center of the circle. c DE is a chord of the circle.

OA and OB are also radii of the al circle. Radii is plural of radius.

The diameter of a circle is 2 x the radius.

ati on

Recall that the path around a shape such as a rectangle or triangle is called the perimeter. The perimeter of a circle has a special name me – circumference. The circumference of a circle is its perimeter.

Re ga le

Dominic placed a piece of string so that it fits around a circle. He then measured the length of the string to find the circumference mference erence of the circle. c

Dominic used string to find the circumference of different sized circles. circumfe He recorded his findings ngs gs in a ttable.

Circle 1 Circle 2 Circle 3

Diameter meter (cm) 5 10 20

Circumference (cm) 15.7 31.4 62.8

Doubling the diameter also doubles the circumference!

uc ati on

Dominic uses a calculator to divide the circumference by the diameter for each circle. He notices that the quotient is the same for every circle. rcle. Diameter Circumference Circumference ÷ (cm) (cm) Diameter Circle 1 5 15.7 3.14 Circle 2 10 31.4 3.14 Circle 3 20 62.8 3.14

The circumference of any circle divided by its diameter always the same meter is alwa alw value. This value is represented by the symbol of the ol π, which hich is a letter le Greek alphabet. We say this symbol as 'pie'. approximate π as the e'. We e can appro decimal 3.14 or the fraction

22 . 7

πd means π x d.

Circumference = π x d = πd

Re ga l

The diameter of a circle its radius. So we can also write: rcle is 2 times tim t

Circumference = 2 x π x r = 2πr

2xπxr means 2πr.

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Find the circumference of each circle. Take π = 3.14 and round off your answer to 1 decimal place. The diameter of the circle is 10 cm.

Circumference = πd = 3.14 x 10 cm = 31.4 cm

10 cm

Make sure you rite the correc write correct unit of lengt length.

The radius of the circle is 4 in.

4 in

ference nce = 2πr Circumference = 2 x 3.14 3 x 4 in = 8 x 3.14 in 25.1 in =2

The diameter of the he circle is 5 m.

Circumference = πd C Circu = 3.14 x 5 m = 15.7 m

Find the circumference of each circle. Take π =

22 . 7

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The diameter of the circle is 7 cm.

Circumference = πd

22 x 7 cm 7 = 22 cm

7 cm

e = πd Circumference =

4 cm 5

= = = =

4 22 x2 5 7 1 22 14 x 5 7 22 x 14 7x5 22 x 2 5 44 4 =8 5 5

The ci circumference is 8 circum

14 =2 7

4 cm. 5

Can you express the circumference as a decimal?

Let’s Practice The center of each circle is point O. Labeled lines are straight ght lines. nes. Identify the radius of each circle.

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(a)

(b)

radius =

(c)

radius =

(d)

M Q

R N

radius dius =

radius =

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2. O is a point on the center of each circle. Labeled lines are straight lines. Identify the diameter of each circle. (a)

(b)

W U

diameter =

(c)

(d)

diameter ameter er =

diameter =

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3. The grid below is made up of 1 cm by 1 cm squares. Find the diameter and circumference of each circle. Take π = 3.14 and round off ff your answer to 1 decimal place. Circle A

Circle B

Circle C

Circle E

Circle D

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4. A mini pizza has a diameter of 8 cm. Find the circumference. Take π = 3.14 and round off your answer to 1 decimal place.

5. The radius of a round hot tub is 2 meters. Find nd the he circumference. circumfe o 1 decimal cimal plac place. Take π = 3.14 and round off your answer to

6. The diameter of a sports arena na is 70 meters. me met Find the circumference. Take π =

22 . 7

7. A round nd place ace mat has a radius of 14 cm. Find the circumference. Take ke π =

22 2 . 7

Solve It!

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The figures are made up of semicircles (half circles) and straight ght lines. nes. Can you find the perimeter of each figure? Take π = 3.14 and round und off ff your yo answer to 1 decimal place. (a)

(b)

4 cm

(c)

4 cm m

4 cm

10 cm

At Home The center of each circle is point O. Labeled lines are straight ght lines. nes. Identify the radius of each circle.

Re ga le du ca tio n

(a)

(b)

radius =

radius radiu =

(c)

(d)

Q R

T O

radius ius =

radius =

Re ga le du ca tio n

2. O is a point on the center of each circle. Labeled lines are straight lines. Identify the diameter of each circle. (a)

(b)

diameter =

(c)

(d)

diameter ameter er =

diameter =

Re ga le du ca tio n

3. A discus has a diameter of 22 cm. Find the circumference. Take π = 3.14 and round off your answer to 1 decimal place.

4. A round table has a radius of 50 cm. Find the e circumference circumferenc rcumferenc in meters. o 1 decimal cimal plac place. Take π = 3.14 and round off your answer to

5. A round swimming pool has a diameter of o 14 ft. Find the circumference. Take π =

22 . 7

6. A round nd place ace mat has a radius of 14 cm. Find the circumference. Take ke π =

22 2 . 7

Area of Circles

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Anchor Task

Let’s Learn

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Let's find the area of a circle. Dominic divides a circle into 4 equal qual parts. He cuts the parts and arranges them as shown below.

πr

He continues to divide circles into more equal arranges them qual parts and a as shown.

πr

πr π

More divisions results in the arrangement looking more like a rectangle!

πr

As we continue to divid divide the circle, the arrangement of the parts forms a rectangle ectangle of height heig r and width πr. The area of the rectangle is π x r x r. Area of circle = π x radius x radius =πxrxr

Let’s Practice Find the area of each circle. Take π = 3.14 and round off your answer to 1 decimal place. ace.

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(a)

2 cm

(b)

(c)

5 ft

(d))

14 in O

2. Find the area of each circle. Take π =

22 . 7

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(a)

7 cm

(b)

28 in

(c)

21 m

(d)

56 6 cm c

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3. A round swimming pool has a radius of 15 m. Find its area. Take π = 3.14 and round off your answer to 1 decimal place.

4. A circular sports field has a diameter of 100 m. Find its area. area o 1 decimal cimal plac place. Take π = 3.14 and round off your answer to

5. A coin has a diameter off 14 mm. Find the area. Take π =

22 . 7

6. A round d place ce mat has a diameter d of 35 cm. Find the area. Take π =

22 . 7

Solve It! The figures are made up of semicircles (half circles) and straight ght lines lines. Can you find the area of each figure? Take π = 3.14 and d round nd off your answer to 1 decimal place. (a)

le du ca tio n

(b) 2 cm

2 cm

5 cm

The figure below a square of side length 6 cm. elow w is made from f 2 The circular has a diameter that is the side length ar hole e in the middle m 3 of the square. area of the figure. Take π = 3.14 and round off quare. re. Find the a your answer place. wer to 1 decimal dec

Re g

At Home Find the area of each circle. Take π = 3.14 and round off your answer to 1 decimal place. ace.

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(a)

12 cm

(b)

18 m

2. Find the area of each circle. e.. Take π = (a)

28 in

(b))

70 cm O

22 . 7

Re ga le du ca tio n

3. A wall clock has a diameter of 32 cm. Find the area. Take π = 3.14 and round off your answer to 1 decimal place.

4. A pizza has a radius of 8 in. Find the area. o 1 decimal cimal plac place. Take π = 3.14 and round off your answer to

5. A coat button has a diameter meter er of 21 mm. Find the area. Take π =

6. An archery chery target arget has a radius ra 49 cm. Find the area. Take π =

22 . 7

Anchor Task

Area of Triangles

Let’s Learn

Re ga le du ca to n

When finding the area of triangles, we first need to find the base ase and height. A

The height must be perpendicular to the base.

We can choose any side of the triangle iangle gle to be the base. For the triangle ABC, let's take the base to be BC.

The height of the triangle is given height to our en by the perpendicular pe chosen base. This is a right-angled triangle, so AB is the perpendicular -angled gled trian triangl height. BC is the base and AB is the height. heig he

height

base

Let's find the base and height of some more triangles. (a)

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In this triangle, the height is not th. a side length.

height

base

If we choose the base to be MO, the height is giv g given by the line NP which is perpendicular to the base.

(b)

height

base

For height is located outside the For a base SU, the th perpendicular p triangle at line lin TV.

Find the area of triangle ABC. 1 cm

1 cm

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The triangle is inside a rectangular grid square is ular grid where each e 1 cm by 1 cm.

To find the area of the triangle, ngle, we need to choose a base and find the height. Let's choose BC as the he base. ase. The height of the triangle to the base. riangle gle is perpendicular perpend perpe This is a right-angled gled triangle, so the height is AB.

This triangle has a base of 10 cm and a height of 5 cm.

height 5 cm

base 10 cm

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The area of a triangle is given by:

Area of a triangle =

1 x base x height 2

rea of the The area gle is half the triangle area of rectang rectangle ABCD.

For our triangle:

Area of triangle =

1 x 10 cm x 5 cm 2 1 x 50 cm2 2

= 25 cm2

Our triangle is enclosed in a rectangle tangle gle ABCD. To find the area of a rectangle we multiply the length by the width.

Area of rectangle = length x width = 10 cm cm x 5 cm m 2 = 50 cm

Visually, we can see that divides the rectangle into halves. So, hat the triangle trian the area of the triangle gle is half of o the th area of the rectangle. A

1 area of rectangle 2

1 area a of rectangle ctang 2

Each square in the grid is 1 cm by 1 cm. Find the area of the triangle.

6 cm

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7 cm

Area of triangle = = =

1 x base x height 2 1 x 7 cm x 6 cm 2 1 x 42 2 cm2 2

= 21 cm c 2

Find the area ea of the triangles. triangl

(a)

Area of triangle =

= =

1 x base x height 2 1 x7mx8m 2 1 x 56 m2 2

= 28 m2

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(b)

Area of triangle = =

10 in

1 x base se x heigh height h 2 1 x 8 in x 10 in 2 1 x 80 in2 2

= 40 in i 2

8 in

(c)

30 cm

15 cm

Area of triangle = = =

1 x base x height 2

1 x 15 cm x 30 cm 2 1 x 450 cm2 2

= 225 cm2

Let’s Practice Identify the base and height of the triangles.

Re ga le du ca tio n

(a)

base =

height =

(b)

base se =

height =

(c)

base se =

height =

(d)

Re ga le du ca tio n

base =

height =

(e)

base =

height =

(f)

base =

height =

Each square in the grids is 1 cm by 1 cm. Find the area of the triangles.

Re ga le du ca tio n

(a)

1 x base x heigh height he 2 1 = x x 2 1 = x 2

Area of triangle =

(b)

1 x base x height 2 1 = x x 2 1 = x 2

Area of triangle tria =

(c)

1 x base x height 2 1 x x = 2 1 = x 2

Area of triangle =

1 x base se x height 2 1 = x x 2 1 = x 2

Area of triangle =

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(d)

(e)

1 x base x height 2 1 x x = 2 1 = x 2

Area rea off triangle =

(f)

1 x base x height 2 1 = x x 2 1 = x 2

Area of triangle =

Find the area of each triangle. Show your working in the space provided.

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(a)

12 cm

5 cm

Area rea =

cm2

Area =

in2

(b)

10 m

(c)

8 in

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(d)

6 cm

4 cm

Area =

cm2

Area =

ft2

(e)

12 ft

7 ft

(f)

2 cm

14 cm 14

Area a=

cm2

Hands On

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Show that the area of a triangle is half the area of a rectangle e with h the same base and height. The rectangle below has a width of 16 cm and a height of 12 cm. cm 2 It has an area of 192 cm .

6 cm m and a height heig of The triangle on the opposite page has a base of 16 12 cm.

Cut out the triangle from the page. Then cut along the dotte dotted lines so the n the e grid below to neatly fill up triangle is in 3 pieces. Arrange the pieces in half of the rectangle.

Re ga le du ca tio n

Re ga le du ca tio n This page is blank to allow llow for or a cut-ou cut-out on the previous page.

At Home Identify the base and height of the triangles.

Re ga le du ca tio n

(a)

base se =

height =

(b)

base =

height =

(c)

base =

height =

(d)

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base =

height eight =

(e)

base =

height =

(f)

base =

height =

Each square in the grids is 1 cm by 1 cm. Find the area of the triangles. Show your working in the space provided.

Re ga le du ca tio n

(a)

Area =

(b)

Area =

(c)

Area =

Re ga le du ca tio n

(d)

Area rea =

(e)

Area =

(f)

Area =

Solve It!

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Ethan is designing a mask for a dress-up party. The mask is made from a piece of square cardboard of side de length 20 cm h. He cut a 12 cm by 3 cm rectangular hole for the mouth. For the eyes, he cut 2 right-angled triangles of the same ame me size. They each had a base and height of 8 cm. Find the area of Ethan's mask.

Ethan's mask k has an area of

cm2.

Anchor Task

Area of Composite Figures

Let’s Learn

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The figure below is inside a 1 cm by 1 cm grid. Let's find its area.

We can divide the figure into a triangle tr and a square. sq

Find the area of the composite osite shapes and add to find fi d the h totall area of the figure.

4 cm

3 cm

1 x 3 cm x 4 cm 2 1 x 12 cm2 = 2

Area B =

3 cm

Area C = 3 cm x 3 cm = 9 cm2

= 6 cm cm2

Area A = Area Area B + Area C A = 6 cm cm2 + 9 cm2 = 15 cm2

Re ga le du ca tio n

Find the area of the figure.

6 cm

3 cm

4 cm

We can break the figure into 2 triangless and d a rectangle. rectangl rectang

6 cm

c 6 cm

6 cm

3 cm

4 cm

Area of figure = Area P + Area Are Q + Area R

Area P =

1 x 3 cm x 6 cm 2

= 9 cm2

Area Q = 4 cm m x 6 cm = 24 4 cm cm2 Area aR=

Is there another way to break up the figure to find the area?

1 x 4 cm x 6 cm c 2

= 12 cm cm2

Area of figure figu = 9 cm2 + 24 cm2 + 12 cm2 = 45 cm2

Find the area of figure ABCD.

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Area of figure ABCD = Area of triangle ABD triangle CBD BD – Area of tr tria 1 x7mx5m 2 1 x 35 m2 = 2

Area of triangle ABD =

= 17.5 m2

1 x7mx2m 2 1 x 14 m2 = 2

Area of triangle CBD =

= 7 m2

Area off figure ure ABCD = 17.5 m2 – 7 m2 = 10.5 m2

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Find the area of the yellow figure.

2 in

8 in

4 in

12 in

Area of yellow figure = Area of triangle angle gle – Area of rectangular hole 1 x 12 in x 8 in n 2 1 = x 96 in2 2

Area of triangle =

= 48 in2

Area of rectangle gle = 2 in x 4 in = 8 in2

Area of yellow ow figure = 48 in2 – 8 in2 = 40 in2

Let’s Practice The pink figure is drawn with straight lines inside a rectangle. ngle. Find the area of the pink figure.

Re ga le du ca tio n

6 cm

2 cm

4 cm

The area of the pink figure =

11 cm

cm2.

Find the area of the figure.

Re ga le du ca tio n

20 cm

6 cm

5 cm

Area =

cm2

The side of a factory wall needs to be painted. The dimensions of the wall are shown in the grid below. Each square on the grid represents 1 square meter. Find the total area of the wall.

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The area of the wall =

Find the area of the colored part of figure LMNOP.

Re ga le du ca tio n

M 2 cm

2 cm

5 cm

7 cm

Area of colored figure =

12 cm

Solve It! ABCDE is composed of the triangles ABE, BCD and BDE. Triangle BDE is twice the area of triangle BCD. Find the area of the figure ABCDE.

Re ga le du ca tio n

3 cm

5 cm

4 cm m

Area ABCDE C =

Figure PQRST is composed of triangle PQR and square PRST. The area of the colored part of PQRST is 38 cm2. Find the side length of the square PRST.

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2 cm

The side length of the square PRST =

At Home The figure below is a triangle with a 1 cm by 1 cm square hole.. Find the area of the figure.

Re ga le du ca tio n

25 cm

7 cm

18 cm

6 cm

Area =

Find the area of the blue figure.

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5 ft

2 ft

Area =

5 ft

4 ft

Each square in the grid has a side length of 1 inch. Find the area of the figure.

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Area =

The green figure below is drawn inside a rectangle. Find the area of the figure.

Re ga le du ca tio n

Area =

Looking Back O is a point on the center of each circle. Labeled lines are e straight aight lines lines. Identify the diameter of each circle.

Re ga le du ca tio n

(a)

(b)

diameter =

diameter diam diame =

O is a point on the centerr of each ch circle. Labeled lines are straight lines. Identify the radius of each ach circle.

(a)

(b)

radius =

Find the area of each circle. Take π = 3.14 and round off your answer to 1 decimal place.

Re ga le du ca tio n

(a)

20 cm

(b)

9 in

Find the area of each circle. rcle.. Take π =

(a)

7 ft

(b)

63 mm O

22 . 7

Re ga le du ca tio n

5. A pie has a diameter of 11 cm. Find the area. Take π = 3.14 and round off your answer to 1 decimal place.

6. A round sticker has a radius of 16 mm. Find the area. o 1 decimal cimal plac place. Take π = 3.14 and round off your answer to

7. A plate has a diameter of 28 8 cm. Find area. ar Take π =

22 . 7

8. A dart board d has a radi radius 14 in. Find the area. Take π =

22 . 7

Identify the base and height of the triangles. (a)

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base =

height =

(b)

base = bas

height = heig

(c)

base =

height =

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10. Each square in the grids is 1 in by 1 in. Find the area of the triangles. Show your working in the space provided. (a)

Area =

(b)

Area =

(c)

Area =

11.

Find the area of the figure.

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4 cm

2 cm

14 cm

Area =

12.

Find the area of the figure.

Area =

Find the area of the figure.

Re ga le du ca tio n

13.

2 cm

3 cm

3 cm m

4 cm

2 cm

Area =

Time

Anchor Task

globalair.ae

Global Airlines rlines nes Departures

13 15

09 10

14 00

21 55

23 40

Dubai (DXB)

ed u

08 25

Frankfurt (FRA)

San Francisco (SFO)

Cairo (CAI)

Arrivals ivals

15 20 Amsterdam terdam (AMS)

23 59

21 15 Melbourne (MEL)

05 15+1

23 00

19 45+1

New York (JFK) (JFK

Dubai (DXB)

Expressing 12-hour and 24-hour Tim Time

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Let’s Learn

The times on the departure board are shown in 24-hour time. e. When we use 24-hour time, we do not need to use a.m. m. or p.m. p.m

When using 24-hour is expressed as 00 00. ur time, me, midnight midnigh midni 12:00 a.m.

0 a.m. 6:00

00 00

06 00

In 24-hour time time, you normally do don’t say o’clock. o’cloc

12: 12:00 noon 12 00

6:00 p.m. 18 00

12:00 a.m.

00 00

For 18 00, we say eighteen hundred hours.

Re ga le du ca tio n

To convert times between noon and midnight into 24-hour time, you add om 24-hour 24 12 to the hours. To convert times between noon and midnight from time to 12-hour time, you subtract 12 from the hours and add p.m. Ethan goes fishing at 3:20 p.m. Express the time Ethan goes fishing in 24-hour time.

3 + 12 = 15

12-ho time: 12-hour 3:20 p.m. 3 tthree twenty p.m. 24-hour time: 15 20 fifteen twenty

Ethan goes to bed at 21 45. Express the time Ethan goes to bed n go goe ed in 12-hour time.

21 – 12 = 9

24-hour time: 21 45 twenty-one forty-five 12-hour time: 9:45 p.m. nine forty-five p.m.

Let’s Practice Write the times in 24-hour time.

Re ga le du ca tio n

(a)

(b)

Morning:

Morning: ning:

Afternoon:

Evening:

(c)

(d))

Morning:

Night:

(e)

(f)

Morning:

Night: h

Afternoon:

(a)

(b)

(c)

(d)

ion

Write the times in 12-hour time using a.m. or p.m.

Re ga le du c

(f)

(e)

Complete the table.

Flight Departures es – Sa San Francisco International Airport (SFO) City

Denver ve

Departure

(12-hour)

(24-hour time)

11:45 a.m.

Chicago

New Y York

San Diego S

00 05

10:20 a.m.

20 10

At Home

eg al ed uc ati on

Complete the table.

School Athletics Day Program

Activity

12-hour Time

Headmaster’s opening speech.

9:15 a.m.

High jump Discus

24-hour -hour Time

09 94 45

10:50 a.m.

Shot put

12 30

Javelin

1:35 5 p.m.

4 x 100 m relay

2:25 :25 p.m.

100 m sprint

18 45

Awards ceremony ony

20 05

Duration of Time

Let’s Learn

le du c

Halle and Sophie went for a picnic in the park at 11 30. They y leftt at 13 55. How long were Halle and Sophie in the park?

11 30

25 min 13 30

13 55

2 h + 25 min = 2 h 25 min Halle and Sophie were in the park for or 2 h 25 min. m

Re g

Dominic and Jordan rode their the lake. They arrived at 14 40 and heir bikes to th hiked around the lake until 16 25. 5. How long lon lo was their hike?

20 min m

14 40 4

15 00

1 h + 20 min + 25 min = 1 h 45 min Dominic and Jordan hiked for 1 h 45 min. nd J

25 min 16 00

16 25

ed uc a

Blake and his family are taking the train to the beach. The train departs at 11 30. They arrive at the beach 3 hours 35 minutes later. Whatt time did they arrive at the beach?

11 30

35 5 min m

14 1 30

15 05

3 hours after 11 30 is 14 30. 35 min after 14 30 is 15 05. Blake and his family arrived at the 05. e beach each at 15 05

Re g

minute She finished playing at 13 30. Riley played ice hockey for 2 hours 45 minutes. aying g ice hockey? hockey What time did Riley start playing

15 min n

10 45

30 min

11 00

11 30 3

2h 13 30

2 hours before 13 30 is 11 30. 30 minutes before 11 30 is 11 00. minu 15 minutes utes before befor 11 00 is 10 45. b Riley started ice hockey at 10 45. ed playing pl

Complete the word problems. Use a timeline to show your working. Keira started doing her homework at 16 25. She stopped d for dinner at 18 35. How long did Keira spend doing her homework? omework? work?

A train left Boston at 09 15. It arrived d in New York C City at 13 22. How long was the train ride?

Blake visited his uncle at 11 38. 38 He left his uncle’s house at 13 55. How long did Blake ke spend visiting visiti his uncle?

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Ethan and Dominic started playing chess at 13 26. They played for 2 hours 34 minutes. What time did they finish playing chess? s?

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Sophie arrived at school at 08 25. Her English class started 2 hours 43 minutes es after she sh arrived. What time did Sophie’s English class ss start? art?

Wyatt washed d the e car with his h father f for 1 hour 47 minutes. They started d washing shing the car c at 11 30. e did they they finish was What time washing the car?

Riley chatted with her aunt on the phone for 1 hour 16 minutes. She finished the conversation at 13 05. At what time did she start chatting with her aunt?

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A tennis match lasted 3 hours 28 minutes. nutes.. The matc ma match finished at 21 25. What time did the tennis match start? art?

On Sunday, Sophie ophie ie did housework house housewo for 2 hours 45 minutes. She finished the housework housewor at 115 15. e did Sophie Sophie start sta doing do What time housework?

Solve It! On Saturday, Halle had singing lessons at 10 15. Her lesson n went nt for 1 hour 25 minutes. After her lesson, she walked home. The e walk alk took to 38 minutes. When she arrived home, she had lunch. Itt took ok her 45 minutes to finish lunch. She then read a book for 2 hourss 10 minutes. minutes At what time did Halle finish reading her book?

Re ga le du ca tio n

Wyatt went on a holiday to Resort Island with his family. The map on the opposite page shows the nearby islands and the travel time b by boat. Use the map to answer the questions. Show your working. orking. ng.

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(a) Wyatt took the boat from Resort Island to Jungle Island nd at 10 50. 50 He went sightseeing for 1 hour 15 minutes. He then en took ook the boat boa to Desert Island for lunch. What time did he arrive ve at Desert Island? Islan Isla

(b) Wyatt took the boat from Resort sort Island sland to Icy Island and took photographs for 45 minutes. s. He then took tthe boat to Volcano Island and went hiking forr 1 hour 15 minutes. Finally, Wyatt took the minut minu boat to Jungle Island and 05 in time for dinner with his nd arrived rrived at 18 0 family. What time did Wyatt Island? tt leave Resort Res Re

(c)

Wyatt att was on Volcano Volca Island and wanted to return to Resort Island. To o do this, his, he had to sstop at some islands to change boats. Each change nge of boat too took 5 minutes. It took Wyatt 2 hours 7 minutes to return turn to Resort Island. Is Which islands did Wyatt stop at on his return turn trip?

Rocky Island

a Resort Island 29 min

34 min

du ca

16 min 25 min

Icy Island

Jungle Island

5m 25 min

19 min 28 min 42 min

Vo V olcano IIsland sland Volcano Desert Island 48 min

At Home

Re ga le du ca tio n

Complete the word problems. Use a timeline to show your working. 1.

Ms. Kang started playing golf at 08 35. She finished playing ying golf at 111 55. How long did Ms. Kang spend playing golf?

Jessica works at the ice-creamery mery on Saturd Saturda Saturday. She started her shift at 11 30 and worked for 5 hours urs 50 minutes. What time did Jessica finish her shift?

A school ool play ay goes for 2 hours h 45 minutes. The play finishes at 21 15. What at time me did the school scho schoo play start?

Mr. Pritchard ran a marathon in 3 hours 18 minutes. He started running at 13 52. At what time did Mr. Pritchard finish the marathon??

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Fabio opened his barber shop at 10 45. 5. He e closed the shop at 20 30. How long was Fabio’s barber shop open? n

Mr. Whyte raced ed hiss car for 2 hours 55 minutes. He finished the race at 16 45. What time me did the car race rac start?

Hands On

Work in pairs. Use the map below to create a story problem for or your our partner. Pick a start time and list the places your hiked. Have e your ur partner work out the time you arrived at the final destination. When en they hey answer answe correctly, rrectly, switch roles.

42 min

60 min

28 min

30 min

25 min

29 min

1 h 15 min

Let’s Learn Sophie is going on vacation with her family to an n island resort. To get there, they spend 3 hours 18 8 minutes on a train. They then take the ferry to the island. The ferry trip is 2 hours 37 minutes. How long did it take to get to the resort? 2 h 37 min

Re ga le du ca

3 h 18 min

Word Problems

train ride

ferry ride

3 h 18 min + 2 h 37 min = 5 h + 18 min + 37 min in = 5 h 55 min

It took 5 hours 55 minutes to gett to the resort resort.

The flight from Las Vegas to o Phoenix hoenix takes tak 1 hour 28 minutes. It takes 4 hours 5 minutes to drive. How much faster is it to fly from rom Las Vegas egas to Phoenix than to drive? ?

1 h 28 min fly

drive

R Regroup 1 h hour into 60 minutes. Then subtract.

4 h 5 min m

4 h 5 min – 1 h 28 min m = 3 h + 65 min – 1 h – 28 min n = 2 h 37 min

It is 2 hours faster to fly from Las Vegas to Phoenix than to drive. ours 37 minutes m

Wyatt reads for 47 minutes every day. How long does Wyatt spend reading in 1 week?? 47 min

Re ga le du ca t

329 min = 5 h 29 min

In 1 week, Wyatt spends 5 hours 29 minutes reading. reading

Mr. Gil walks to work everyday. In n 5 days ays he walks walk wal w alks for a total of 3 hours 10 minutes. If he walks ks forr the th he same ame me duration each day, how long does it take ake him to o walk k to work?

First, st, convert con thee hours into minutes.

190 min

190 min ÷ 5 = 38 min m

Each day, Mr. Mr Gil spends 38 minutes walking to work.

Let’s Practice

Re ga le du ca tio n

Complete the word problems. Show your working. 1.

Michelle ran for 1 hour 28 minutes. She then cycled forr 2 hours ours 43 minutes. How long did Michelle spend exercising in all?

It took Jordan 3 hours 17 minutess to reach the top to of a mountain. Blake reached the mountain top 1 hour our ur 45 minutes ffaster than Jordan. How long did it take Blake to reach h the he mountain top?

Sophie spent pent nt 1 hour 48 minutes m minu cleaning her bedroom. Chelsea spent 2 hours 12 minutes her bedroom. How much longer did Chelsea nutes cleaning clean spend bedroom than Sophie? nd cleaning eaning her bedr bed

Ethan takes 5 minutes 42 seconds to walk around his neighborhood block. How long will it take Ethan to walk around the block 7 times? times

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It takes Mrs. Siew 17 minutes to fold a tray ay of dumplings. dumplings How long will it take Mrs. Siew to fold 12 trays ays of dumplings? dump

On a hike, Halle and nd Sophie Soph Sop stopped pp for a break 7 times. Each break wass the same of minutes. The total break ame number nu time was 3 hours ourss 23 minutes. minutes How Ho long was each break?

At Home

Re ga le du ca tio n

Complete the word problems. Show your working. 1.

Blake took 2 hours 25 minutes to revise for his history test. He took 3 hours 12 minutes to revise for his mathematics test. How w much longer long did he take to revise for his mathematics test than n his history test? test

Keira made a series of 8 video o clips for a school scho presentation. Each clip ran for the same length of time. me. The whole who series ran for 1 hour 12 minutes. How long was each ch video deo clip?

Halle swims wimss one lap of o a swimming sw pool in 3 minutes 26 seconds. How long ong does oes it take for f her to swim 12 laps of the swimming pool?

Solve It!

Re ga le du ca tio n

Complete the word problems. Show your working. 1.

Jordan took 42 minutes to walk from his house to the e library. rary. He read rea in the library for 2 hours 38 minutes and left at 16 50. 0. What hat time did Jordan leave his house?

A baker takes 12 minutes to o prepare a cake mix, 25 minutes to bake the cake and 15 minutes to add minute inu dd the th icing. She needs to bake 12 cakes by 13 15. What is the e latest test time tim the baker should start making the cakes?

Looking Back Write the times in 24-hour time.

Re ga le du ca tio n

(a)

(b)

Morning:

Morning: ning:

Afternoon:

(c)

(d))

Morning:

Night:

Afternoon:

Write the he times mes in 12-hour 12-h time t using a.m. or p.m.

(a)

(b)

(e)

(f)

tio n

(d)

Re ga le du ca

(c)

Complete the table.

Departures – Midtown B Bus Terminal

City

The Bronx

Departure Depar

Departure

(12-hour) (12-ho

(24-hour time)

6:45 a.m.

Newark

Yonkers ke

Staten aten Island Isla

17 25

3:40 p.m.

23 20

After school, Halle plays chess with her friend for 1 hour 34 minutes. She then walks 46 minutes back to her home. She arrives home e at 18 00. What time did Halle start playing chess with her friend?

Re ga le du ca tio n

A teacher takes 18 minutes to mark k an exam. How long will it take her to mark 13 such exams?

It took Riley 2 hours urs 51 minutes minu to t jog around the lake 9 times. How long doess Riley take to jog jo 1 time around the lake?

Speed

Speed and Distance Anchor Task

100 meters Ethan Blake Michelle Riley

15.4 s 14.2 2s 15.1 s 16.0 .0 s

Sophie Dominic ominicc Halle Wyatt Wya yatt

14. 41 s 15.5 5s

Let’s Learn

Re ga le du c

A truck and a car are traveling in the same direction. They are traveling at different speeds. Speed is how fast something is moving. It is the distance something so omething ething hing moves mov move moves per unit of time.

truck The speed of the tr ck is 60 kilometerss per hour. hour Traveling at this speed, the truck will cover er a distance distan of 60 kilometers in 1 hour. We write this as 60 km/h.

The speed of the car is 100 kilometers hour. lometers eters per ho Traveling at this speed, the car will cover a distance of 100 kilometers in 1 hour. We write this as 100 km/h. /h We can calculate speed distance by time. peed by dividing dividin divi speed = distance ÷ time

The greater the distance per pe unit un time, the faster the speed.

The speed ed of a brisk walk is about 6 km/h.

The speed of a galloping horse is about 45 km/h.

A caterpillar crawls 50 centimeters in 5 minutes. nutes. Find the speed of the caterpillar in cm/min..

Re ga le du ca tio

speed = distance ÷ time = 50 ÷ 5 = 10

The speed of the caterpillar is 10 cm/min.

rs in n 4 hours. A plane travels a distance of 3,200 kilometers Find the speed of the plane in km/h. 3,200 ÷ 4 = 800

The speed of the plane is 800 km/h.

An owl flies 99 meters in 9 seconds. nds. Find the speed of the owl in m/s. 99 ÷ 9 = 11

The speed of the owl iss 11 m/s. m

Wyatt jogged 750 0 meters eters in 3 minutes. minut m Find Wyatt's speed eed in m/min. 750 ÷ 3 = 250 0

Wyatt jogged ogged ed at a speed of 250 m/min.

When speed, we can calculate the distance it will cover en we know an object's obje forr a given amou amount of time. distance = speed x time stanc

Re ga le du ca ti n

Riley skates at a speed of 4 m/s for 20 seconds. ds. How far does Riley skate? distance = speed x time = 4 x 20 = 80 Riley skates 80 m. 1

akersfield sfield at a A car took 2 4 h to travel from Springfield to Bakersfield speed of 60 km/h. How far is Springfield from m Bakersfield? ersfield? 1

60 x 2 4 = 60 x 4 = 135

eld. Springfield is 135 km from Bakersfield.

A cyclist rides at a speed of 32 2 km/h. h 1 How far does he ride in 2 2 hours? urs? 1

32 x 2 2 = 32 x 2 = 80

The cyclist rides 80 km m in 2 2 h. h

A fighter jett flies at a speed of 400 4 m/s. How far can an the fighter jet ffly in 1 minute? 1 m = 60 s 400 x 60 = 2,400 2,400 400 m = 2.4 km

The e fighte fighter jet can fly 2.4 km in 1 minute.

ga le du ca tio n

When we know the speed an object is moving and the distance it needs to cover, we can calculate the time it will take to cover that distance. e. time = distance ÷ speed

A plane travels at a speed of 900 km/h. How long does it take for the plane to fly 2,700 km from Singapore to Hong Kong? time = distance ÷ speed = 2700 ÷ 900 =3

The plane takes 3 h to fly from Singapore re to Hong ong Kong. Kong A snail crawls at a speed of 8 cm/min. min. How long g does it take for the snail to cross a path n ath 2.4 m in length? 2.4 m = 240 cm 240 ÷ 8 = 30

It takes the snail 30 minutes nute to cross nutes oss the th path.

The distance between and Slicks Creek is 385 km. The top ween n Harbortown Harbortow a speed of Mr. Whyte's hyte's motorcyc motorcycle is 110 1 km/h. What is the shortest time he can ride from Harbortown bortown to Slicks Slick Creek?

385 5 ÷ 110 = 3.5 The shortest est time tim Mr. Whyte can ride from Harbortown to Slicks Creek is 3.5 h.

Let’s Practice The distance from a shoe factory to a warehouse is 240 km. Itt takes a truck 3 h to travel between the factory and the warehouse. ehou Find the speed of the truck.

A tortoise covered a distance off 600 0 m in 50 min. m Find the speed of the tortoise.

Sophie lives ives 8.5 km from he her school. To get from her home to school takes 10 min. does Sophie travel to school? n. At what speed spe s

Re ga le du ca tio n

Station A is 270 km from Station B. A train takes 3 h to travel from Station A to Station B. Find the speed of the train.

Re ga le du ca tio n

Traveling at top speed, it takes 3 hours rs forr a fighter jet je to cover a distance of 6,500 km. What is the top op speed peed of the fighter jet?

A bird flew 156 6 m in 12 s. What Wha w was the speed of the bird?

100

A cyclist rides for 4 hours at a speed of 27 km/h. How far did the cyclist ride?

Re ga le du ca tio n

Find the distance covered by a cheetah ah that hat runs at a speed of 20 m/s for 2 min.

Keira rolled a balll the width of o her he classroom at a speed of 75 cm/s. It took the ball all 10 s to roll from one on side to the other. What is the width of Keira's classroom? assroom? oom

1 01

Re ga le du ca tio n

10. 2 laps of the running track at Blake's school is 400 m in length. If Blake runs at a speed of 4 m/s, how long will it take him to complete of ete 7 laps l the running track?

11.

A car is traveling on a motorway at the e speed of 85 8 km/h. How long will it take the car to cover over a distance distanc of o 255 km?

12.

Sophie walks of 55 m/min. She leaves home at alks to school at a speed sp 7:45 a.m. school at 8:05 a.m. How far is Sophie's house m. and nd arrives at sch from her school? ho

1 02

Solve It!

Re ga le du ca tio n

The table below shows the speeds of different commercial plane ane models and the distances they can cover in a given time. Answer the following questions to complete the table. 1. 2. 3. 4.

What is the speed of a B707 plane? How long does it take a B777 plane to fly 4,320 0 km? m? How far does a B787 fly in 7 hours? What is the speed of the B950 plane? Model

Distance (km)

Time (min) in)

B707

6,300

540

B777

4,320

B787

B950

720 km/h

420

11,400

Speed Spe

825 km/h

720

1 03

Hands On

In small groups, go into your schoolyard and use a trundle wheel to measure and mark a distance of 100 m. Use a stopwatch to time how long it takes to complete each activity shown in the table. Calculate your speed to complete the table.

Re ga le du ca t

Activity

Distance (m)

walk

100

job

100

run

100

hop

100

Speed Sp

Use a trundle wheel to measure easure asure the length of the school cho basketball etba tb court. Use the stopwatch topwatch watch to t time how long it takes kes for a soccer socce ball to move from m one side of the basketball ball court to the th other oth when it iss pushed ushed in the different diffe ways shown n in the table. tab Activity ctivity

Roll slowly

Roll quickly quick Throw Kick

104

Time (s))

Dist Distance (m)

Time (s)

Speed of Ball

At Home To escape a predator, a gazelle ran 420 m in 70 s. What was the speed spee of the gazelle?

A truck takes 9 h to drive 720 km from Melbourne Melbourn to Sydney. Find the speed of the truck.

The swimming school is 25 m in length. Halle takes 7 2 mming ng pool pool at Halle's H

Re ga le du ca tio n

es to swim 9 lengths leng minutes of the pool. At what speed does Halle swim?

1 05

Ethan took 8 min to walk from his home to the local park. He walked at a speed of 42 m/min. How far is Ethan's house from the local al park? par

Re ga le du ca tio n

An albatross flies at the speed of 111 m/ss for 4 2 ho hours. What distance does the albatross cover?

Wyatt constructed nstructed ucted a dirt track trac for his remote-controlled car. One lap of the track at a speed of 35 km/h, how long will it take k is 75 m. Traveling Trave for the e car to o complete 7 laps?

106

A plane flies at a speed of 665 km/h. The plane leaves Los Angeles at 6:10 a.m. and flies 3,990 km to New York. What time doess the plane p arrive in New York?

Re ga le du ca tio n

A rabbit hops at a speed of 6 m/s. /s. How long will wi it take to cross a field 450 m wide?

A peregrine ne falcon alcon spots prey that is 175 m away. It dives towards the prey at 70 m/s. How long lon will w it take for the peregrine falcon to reach its prey? ey?

1 07

Solve It!

Re ga le du ca tio n

The students in Grade 6 are going on a school camp in two buses, uses, s, Bus A and Bus B. The distance from the school to the camp is 150 km. Bus A left for the camp at 8:00 a.m. Bus B left for the camp at 8:30 a.m. Both buses arrived at the camp at 10:30 a.m. Find the speed of the buses. es.

108

Average Speed

Re ga le du ca tio n

Let’s Learn

When an object is moving, its speed usually changes. A moving ing car may slow down to turn a corner, or speed up as it moves from om a road onto a motorway.

dividin the total We can calculate the average speed an object movess by dividing distance traveled by the total time taken. average speed = total distance traveled ÷ total tal time taken ta

During a bicycle race, riders must ride up and down p one side of a mountain m the other side. The distance up the mountain ountain in is 3,000 m. The distance down the mountain is 3,750 m. It takes es a cyclist 10 min m to cycle up the mountain and 5 min to cycle down was the average n the mountain. What W speed of the cyclist? Distance = 3,000 m Time = 10 min

Distance stance = 3,750 m Time = 5 min

Ascent

Descent

m/ m/m ? m/min

To find the average e speed, eed, we fir first need to find the total distance traveled and the total time e taken. ken. Total distance = 3,000 ,000 + 3,750 = 6,750 m Total time me = 10 + 5 = 15 min

average verage speed = total distance traveled ÷ total time taken = 6,750 6,7 ÷ 15 = 450 4

The average ge sspeed of the cyclist was 450 m/min.

1 09

Re ga le du ca tio n

Chelsea usually walks from her home to her school. On Monday, she n 8 min. m left home at 8:10 a.m. She walked the first 800 m to the market in Realizing she may be late, she ran the remaining 700 m and arrived ed at school at 8: 22 a.m. Find Chelsea's average speed from her er home ome to her school. Distance = 800 m Time = 8 min

Home

Distance = 700 m Time = 4 min

choo School

Market

? m/min

Total distance = 800 + 700 = 1,500 m Total time = 8 + 4 = 12 min

average speed = total distance traveled aveled eled ÷ total time tim taken = 1,500 ÷ 12 = 125

Chelsea's average speed from rom her home hom to her school was 125 m/min.

A bus traveled from Town wn A to Town D. The bus left Town A at 8:45 a.m. and arrived in Town D att 12:45 was the average speed of the bus 45 p.m. What Wha W own D? from Town A to Town Town A

Town C

Town wn B

64 4 km

90 9 km k

Total distance stance ce = 64 km + 90 km + 110 km = 264 64 km Total otal time taken = 4 h Average verage speed = 264 2 ÷ 4 = 66

The average speed of the bus was 66 km /h. age sp ag

110

Town D

110 km

Let’s Practice

Re ga le du ca tio n

Draw a diagram and show your working for each question. 1.

A salesman took 2 h to drive 108 km from Town A to Town n B. He took 3 h to drive 216 km from Town B to Town C. What was the average speed of the salesman forr the whole trip? trip

111

The school running track has a length of 480 m. Wyatt ran 2 laps of the school running track. He ran the first lap in 4 minutes. He ran n the second s lap in 6 minutes. Find Wyatt's average speed for the 2 laps. s.

Re ga le du ca tio n

112

A train left Station Y at 6:15 a.m. and traveled at an average speed of 1

eed tto 80 km/h for 1 2 hours. The train then increased its average speed

Re ga le du ca tio n

90 km/h and arrived at Station Z at 9:45 a.m. Find the distance stance ce from Station Y to Station Z.

1 13

Riley walked 480 meters at a speed of 120 m/min to get from her school to the park. She then took 6 minutes to walk from the e park to her home. The distance from the park to Riley's home is 520 m. Find Riley's average speed from her school to her home.

Re ga le du ca tio n

114

Hands On

Re ga le d

Use some cones to mark distances in your school as shown.

The distance between Cone e A and Cone B is 100 meters. The distance between Cone Co B to o Cone C is 20 meters. ne C to Cone D is i 120 meters. The distance from Cone Use a stopwatch to o time me how long lon it takes you to complete the activities shown in the table. to complete each activity, then ble. Calculate alculate your yo speed sp calculate your average erage speed from Cone A to Cone D. Activity ivit

Distance (m)

Walk from m Cone A to Cone Co B

100

Crawl awl from Cone B to Cone C

Run from Cone Con C to Cone D

120

Time (s)

Speed

Average Speed

1 15

At Home

Re ga le du ca tio n

Draw a diagram and show your working for each question. 1.

Ethan walked 440 meters at an average speed of 80 m/min. min. 1 Jordan took 1 2 minutes more to cover the same distance. stance. ce What was Jordan's average speed?

116

Chelsea took 8 minutes to kayak from the campsite to the lake at a speed of 48 m/min. She took 6 minutes to kayak back from lake to m the la the campsite.

Re ga le du ca tio n

(a) Find the distance from the campsite to the lake. (b) What was Chelsea's average speed for the whole ole journey? ourney?

1 17

A plane is flying at a height of 3,200 feet. A skydiver leaps from the plane and falls at an average speed of 320 ft/s for 8 seconds. ds. He then opens his parachute and lands 32 seconds later.

Re ga le du ca tio n

(a) What was the skydiver's average speed from when en he opened the th parachute to when he landed? (b) What was the skydiver's average speed from the plane to the ground?

118

Halle and Sophie competed in a 420 m race. Sophie ran at an average speed of 8 m/s. Halle ran at an average speed of 7 m/s.

Re ga le du ca tio n

(a) How long did it take for Sophie to finish the race? inish h line? (b) How far had Halle ran when Sophie crossed the finish

1 19

Word Problems

Re ga le du ca tio n

Let’s Practice Draw a diagram and show your working for each word problem. oblem. 1.

120

Mrs. Wong took 3 hours to drive from Town A to Town own B at an average aver av speed of 70 km/h. On her way back, she drove at an average speed sp of 60 km/h. How long did Mrs. Wong take to drive B to rive e back from Town T Town A?

Wyatt started cycling at 8:30 a.m. By 10:30 a.m. he had covered a distance of 15 km.

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(a) Find his average speed in km/h. me average (b) If he cycled a further distance of 7.5 km at the same speed, what would the time be? (c) The next day, Wyatt started cycling at the same me time. This time, tim his average speed was double that of the day before. What dis distance will he cover if he finishes cycling at 10:00 a.m.? m.?

121

Halle traveled from her home to her cousin's house. She covered er of 2 1 the trip in the 1st hour and 3 of the trip in the 2nd hour. It took ook 1 hour to

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travel the remaining 15 km. Find her average speed for the whole trip.

122

Mr. Robinson drove from his home to his beach house. He traveled the first 96 km at an average speed of 72 km/h. h. He traveled the remaining 36 km at an average speed of 54 km/h.

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(a) How far is Mr. Robinson's house to his beach house? e? (b) Find his average speed for the whole journey.

123

Halle took 3 hours to cover 3 of a journey to her grandmother's er house. She covered the remaining 90 km in 2 hours. Find her average speed for the whole journey.

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1 24

A motorist took 2.5 hours to travel from Town X to Town Y. His average 2 speed for the whole journey was 60 km/h. For the first 3 off the e journey, jo erage ge speed he traveled at an average speed of 50 km/h. Find his average for the remaining journey.

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125

Solve It! 3

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A motorist traveled from Town A to Town B. After traveling 4 of the journey at an average speed of 50 km/h, he continued to travel another nother er 90 km to reach Town B. 1.

Find the distance between the two towns.

If his average speed for the whole journey was 60 km/h, fin find his average speed for the last part of the journey. rney.

1 26

At Home

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Draw a diagram and show your working for each word problem. em. 1.

Keira and Blake took 2 hours to hike from the lake to the waterfall at a an average speed of 70 m/min. On their way back, they an y hiked at a average speed of 60 m/min. How long did it take Keira and Blake to hike from the waterfall back to the lake?

127

Wyatt took 5 minutes to walk from his house to the sports store at an average speed of 45 m/min. He then took another 10 minutes tes to walk to the restaurant at an average speed of 30 m/min.

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(a) How far did he walk altogether? (b) Wyatt rides the same distance on his bicycle at an average speed spe 3 times faster than the speed he walked. How w long will it take Wyatt to cover the same distance?

1 28

A motorcyclist took 3 hours to travel from Town X to Town Y at an average speed of 70 km/h. A truck took 4 hours for the same me journey. jou

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(a) Find the average speed of the truck. he truck ruck travel trave in (b) At the same average speed, what distance can the 6 hours?

129

Wyatt cycled from Town A to Town B. He covered 6 of the trip ip in the 1 first hour and 4 of the trip in the second hour. He took 2 hours ourss to cycle cy

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the remaining 35 km. Find his average speed for the whole hole trip. trip

130

Bus A and Bus B left Portsea College at midday for an interschool sports competition. Bus A traveled at an average speed of 60 km/h. /h. When Wh Bus A arrived at the stadium at 12 30, Bus B was 2 km from m the e stadium. stadiu Find the average speed of Bus B.

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1 31

Blake and Ethan started cycling from the same starting point in opposite directions. Ethan cycled at an average speed of 30 km/h. 0 km/ Blake cycled at an average speed that was 10 km/h slower er than han that of Ethan. They stopped cycling after 18 minutes. Find the distance stance ce between betwee them now.

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132

Solve It! John and Leon started driving from Town A to Town B at the same 3 time. After 2 hours, John reached Town B while Leon had ad completed ompleted 4

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of the journey.

(a) If John’s average speed for the whole journey ney ey was 70 km/h, km/h find 3 Leon’s average speed for the first 4 of the e journey. urney 1

(b) If Leon’s average speed for the last 4 wass increased b by 7.5 km/h, 1 he journey? how long did he take for the last 4 of the

1 33

Looking Back The distance from a toy factory to a toy shop is 260 km. Itt takes kes a truck 4 h to travel between the factory and the shop. Find the speed of the truck.

Riley took 9 min to walk from herr house house. e to her grandmother's gr g She walked at a speed of 63 m/min. How far is Riley's house from her grandmother's house?

A plane is traveling veling at a sspeed of 930 km/h. How long will it take for the plane to o cover ver a distance distanc of 2,325 km?

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1 34

Jordan took 3 hours to walk 12 km to his uncle's house. He took 2 hours to walk back to his house. What was Jordan's average speed ed for the return journey?

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The distance around a lake ke is 400 00 meters. meters Halle took 13 minutes to cycle 2 around the lake 6 3 times. es. (a) Find the total distance ce Halle cycled. cyc (b) What was Halle's le'ss average le a ge speed? spe

1 35

Ethan walked on a beach in 1 direction for 3 hours at an average speed of 75 m/min. He then turned around and walked back at an n average aver speed of 60 m/min.

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(a) How long did the return trip take? (b) What was Ethan's average speed for the whole e journey? rney?

1 36

Halle and Riley started jogging from the park in opposite directions. Halle jogged at an average speed of 80 m/min. After 10 minutes, nutes, they were 1,800 m apart. Find Riley's jogging speed.

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1 37

10 Pie Charts Reading and Interpreting Pie Charts

ed uc at

Anchor Task Favorite Sport running swimming tennis badminton football

3 8 5 2 6

What is your favorite sport, Jordan?

1 38

I love tennis!

Let’s Learn

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Mrs. Jones asked the students in her science class where they y would uld like to t go on a field trip. 60% of the students chose the aquarium. The remaining emaining 40% of the students chose the zoo. We can represent the data in a pie chart.

Zoo 40%

The size of o each portion in a pie chart is relative lative to its value.

Aquarium 60%

represent represen 100%, or 1 whole. The combined parts in the pie chartt represents

In 1 day, a greengrocer sold fruit. He sold 21 apples, 12 pears and d 60 pieces of fr 9 oranges. The rest of the fruit uit sold were mangoes. Fruit

Apples es

Pears

Oranges

Mangoes

Number Sold

Let's use a pie and interpret the data e chart art to represent repres Thee largest portion pie on in the p apples. chart is apple

Mangoes ? Oranges 9

Apples 21

Pears 12

1 39

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Which type of fruit did the greengrocer sell the most? We can see that the largest portion of the pie chart is apples. So, the greengrocer sold apples the most. Which type of fruit did the greengrocer sell the least? We can see that the smallest portion of the pie chart is oranges. ges. So, the greengrocer sold oranges the least. How many mangoes did the greengrocer sell?

uit in all. We know that the greengrocer sold 60 pieces of fruit 60 – 21 – 12 – 9 = 18 The greengrocer sold 18 mangoes.

tivitiess whilst on a holiday. The pie Mr. Whyte spent $700 on different activities chart shows the amount of money spent on each a activity.

1 1 1 + + =1 4 4 2

Fishing

Diving

Dining

ng the he data in the th pie pii chart, h By interpreting we can see that Mr. Whyte spent ey on diving. diving half of his money 1 = $350 2 Mr. Whyte spent $350 $35 on o diving.

$700 x

We can also see the other half of his money was spent equally on fishing d dinin dining. and $175 $350 ÷ 2 = $ Mr. Whyte spe spent $175 on fishing and $175 on dining.

140

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Jordan asked 40 students in Grade 6 how they get to school. He created a pie chart to represent the data he collected.

Walk

Ride 4 Car 6

Half of the students tudents walk or ride. The other ome to school in half come bus a car or bus.

Bus 14

How many students walk to school? 40 – 4 – 6 – 14 =16 16 students walk to school.

What fraction of the students ride de to o school? 1 4 = 40 10 1 of the students ride to school. hool. ol. 10

What fraction of the students a bus to school? udent take t 14 7 = 40 20 7 of the students dents ts take a bus to school. 20

rcent nt of students ri rid or come to school in a car? What percent ride 1 10 = = 25% 40 4

5% of students ride or come to school in a car. 25%

1 41

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A group of 60 students in Grade 6 were asked which sport they'd prefer to play in an interschool competition. The pie chart shows how many any students stu chose each sport.

Golf

Basketball

Wh fraction What on of the stud students prefer to pla play basketball? ketball?

Soccer 1 5

Tennis 2 5

What was the most preferred sport off the Grade 6 students? stu Tennis was the most preferred sport.t. What fraction of the students preferred eferred rred to play golf? g 1–

1 1 20 8 4 5 3 2 – – = – – – = 0 20 20 5 5 4 20 20 20

3 of the students preferred d to o play golf. go 20

How many students preferred eferre to play basketball? 1 1 of 60 = x 60 4 4 60 = 15 = 4

15 studentss preferred erred to play pla basketball. b

What percent ent of students preferred to play tennis? 2 4 = = 40% 5 10

stu p 40% of students preferred to play tennis.

142

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Blake and his friends put their money together to buy a gift for Ethan. The amount each friend contributed is shown in the pie chart below. elow.

Sophie

Wyatt (20%)

Blake (36%)

nt of the What percent money did Sophie an and lle contribute? Halle

Halle

What percent of the money did Halle contribute? ontribute? ibute? 50% – 36% = 14% Halle contributed 14% of the money.

What percent did Blake, Wyatt and Halle contribute altogether? contrib cont 36% + 20% + 14% = 70% Blake, Wyatt and Halle contributed the money altogether. ributed ted 70% of th

What percent of the money did d Sophie contribute? c 100% – 70% = 30% Sophie contributed 30% of the money. m Sophie contributed ed $90. 90. How much wass the e gift for Ethan? Etha 30% $90 0 1% $3 100% $300 The gift for Ethan cost $300 $300.

at is the ratio of the amount of money Blake contributed to the amount What off money Sophie con contributed? 36 6 : 30 = 6 : 5 o the amount am The ratio of of money Blake contributed to the amount of Sophie c money Sop contributed is 6 : 5.

1 43

Let’s Practice The pie chart below shows the number of animals at a pe petting etting g zoo.

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Sheep 9

Ducks 3

Rabbits 12

Goats 6

(a) How many ducks and goats are att the petting zoo?

(b) How many more rabbits than han ducks are at a the petting zoo? (c)

How many fewer ducks ks than an goats are ar a at the petting zoo?

(d) How many animals ls are re at the petting pett pet zoo altogether?

(e) What fraction of the animals nimals a at the petting zoo are goats? (f)

What fraction tion of the anim a animals at the petting zoo are either sheep

its? or rabbits?

(g) What at fraction raction of th the an animals at the petting zoo are not rabbits? bits?

1 44

Riley saved $900 in 4 months. The pie chart below shows how much she saved each month.

Feb Jan $105

Mar

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Apr

tio n

(a) In which month did Riley save the most money? money mone (b) How much did Riley save in n February? (c)

How much did Riley save ve in n April?

(d) How much did Riley y save ve in March?

(e) What fraction of the e money wa was saved in March and April? (f)

What fraction on of the m money was saved in January?

(g) What fraction action on of the mo money was saved in February and March gether? her? altogether?

1 45

On school camp, Chelsea took 450 photographs. She transferred them to her computer and put them into folders based on different ent themes. the er. The pie chart shows the number of photographs in each folder.

Beach Lake 125

Forest

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Friends 160

ion

(a) How many forest photographs aphs are there? (b) How many beach photograph tograph aph are there? th the (c)

What fraction of the he photographs hotographs are in the 'Lake' folder?

(d) What fraction of the photographs photograp hotogra are in the 'Friends' folder? (e) What percent ent of the photographs ph are in the 'Beach' folder?

(f)

What percent ercent nt of the photographs p photog are in the 'Forest' folder?

(g) What at is the ratio ratio of the number of beach photographs to photographs Chelsea's friends? hotographs raphs of Ch Chels

146

60 students were graded on their English essays. The pie chart shows the number of students that received each grade.

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A 5 12

C 1 5

(a) What was the most common received? on grade e students studen stude (b) What fraction of studentss received eceived a D? (c)

How many students received ed a B?

(d) How many students nts received eceived a g grade lower than a B? (e) What percentt of st studentss received rec a C?

(f)

What is the he ratio atio of the number nu n of students who received a B to the totall number students? mber of student stu

(g) What at is the ratio ratio of the number of students who received a C to the who received an A? e number mber of students studen stu

1 47

The pie chart shows the number of the different type of vehicles p parked in Sunshine College in an afternoon. Express the number mber of ction of the total number of vehicles ve cles in each type of vehicle as a fraction the car park. Buses (13) Cars (45)

Motorcycles (20)

Re ga le du c

Vans (22)

(a) Cars:

(b)) Vans: ans

(c)

(d)) Buses: Buses:

Motorcycles:

The pie chart shows the e amount mount of money mo Keira and her friends spent at the aquarium gift shop. hop. Express the t amount of money each child spent as a percentage off the they spent in all. he total amount a

Wyatt ($84)

Keira

148

Chelsea elsea ($56)

Halle Ha ($100) ($100

(a) Keira:

(b) Wyatt:

(c)

(d) Halle:

Chelsea: Chelse Ch

The pie chart shows the percentage of items sold in a clothes shop.

Hats Dresses Skirts

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Shirts (38%)

ere skirts? kir kirt (a) What percent of clothess sold wer were

(b) What percent of clothes sold d were ere dresses? dresse (c)

What percent of clothess sold d were hats? hats

(d) What fraction of clothes thes sold ld were sskirts or dresses? (e) What is the ratio off the e number numbe of hats sold to the total number of items sold?

(f)

60 hats were e sold. Find the t number of dresses, skirts and shirts sold. old.

Dresses sold: Dresse Dr

Skirts sold:

Shirts sold:

1 49

Hands On The table below shows the number of different snacks sold ld during a lunch break.

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Snack

Nuts

Chips

Chocolate e

Fruit

Number Sold

18 8

Use the Matholia chart tool to create a pie chart represent the data hartt to represen represe in the table. Print and paste your pie chart below. ow. Label the t pie chart and express the values as percentages.

150

The table below shows the number of students learning different languages at an international school.

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Language

English

Arabic

Chinese

Spanish

Number of Students

Use the Matholia chart tool to create a pie chart to represent the data in the table. Print and paste your pie chart below. ow. Label the pie p chart and express the values as fractions.

1 51

At Home The pie chart below shows the number of bunches of flowers werss a florist floris sold in 1 week. Daisies 27

Tulips 81

Lilies 45

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Roses 108

(a) How many bunches of roses were sold? ses and tulips we (b) How many more rosess than n daisies were we w sold? (c)

How many fewer lilies lies than roses w were sold?

(d) How many bunches off flowers were sold in all? (e) What fraction on off the bu bunches of flowers sold were daisies? (f)

What fraction action on of the flowers fl flower sold were either lilies or roses?

(g) What at fraction action of the flowers flo sold were not roses?

152

Mrs. Jenkins spent $1,000 on gifts for her children. The pie chart below shows how much she spent on each item. Bat $75 Guitar

Dollhouse $175

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Surfboard

tio n

(a) How much more was the dollhouse ouse e than the bat? b

(b) What percent of the money y spent was the guitar? (c)

What fraction of the money oney y spent was the surfboard?

(d) What was the total costt of the guita guitar and the surfboard? (e) What fraction of the e money wa was spent on the dollhouse? (f)

What is the ratio tio of the th cost of the surfboard to the cost of

ar? the guitar?

153

Riley kept a tally of the number of different colored butterflies in her garden. She spotted 50 butterflies in all. She created the pie chart e char below to represent her data. Yellow 6 Blue 8

Re ga le du c

Orange

Green 19

tio n

(a) How many orange butterfliess did Riley spot?

(b) What fraction of the butterflies erflies rflies Riley spo spotted spot were green? (c)

What fraction of the butterflies rflies Riley spotted s were yellow?

(d) What percentage of the he butterflies butterflie butter Riley spotted were blue? (e) What percentage ag of the age e butterflies butte spotted were not green? (f)

What was the ratio of blue blu b butterflies spotted to yellow butterflies

d? spotted?

154

The pie chart shows the amount of different dishes sold at a Thai restaurant in one day. There were 180 dishes sold in all. Curry 1 6

Soup 2 9

Rice

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Salad

(a) What fraction of the dishes sold salads? old were salads

(b) What fraction of the dishes ess sold were sou soups so or curries? (c)

What fraction of the dishess sold were curries or rice?

(d) How many rice dishes shess were sold? so

(e) How many curries rr and soups were sold? rries (f)

What was the ratio of curries cu c to salads sold?

(g) What was was the he ratio of rice dishes to soups sold?

155

The pie chart shows the number of different items sold in a bakery in 1 day. Express the number of each item as a fraction of the he total tota number of items sold.

Cakes (32) Pies

Donuts (38)

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Rolls (98)

(a) Cakes:

(b) Pies:

(c)

(d) R Rolls: olls olls:

Donuts:

The pie chart shows the mass of different differen meats sold by a butcher over the weekend. Express ress the mass of o each type of meat sold as a percentage of the total meat sold. al mass ass of me mea Fish (30kg)

Chicken

Beef

Lamb

(a) ( Fish: (c)

156

Lamb: a Lamb:

(b) Beef:

(d) Chicken:

The pie chart shows Mr. Woods' expenses for 1 month. Food

Utilities

Transport (15%)

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Rent (40%)

(a) What percent of Mr. Woods' expenses ensess are on food? fo foo (b) What percent of Mr. Woods' expenses nses are on o utilities? (c)

What fraction Mr. Woods' s' expenses are o on rent and utilities?

(d) What is the ratio of Mr. Woods' ods' expenses expen on rent and transport to his total expenses for 1 month?

(e) Mr. Woods spends en $2,200 ends 00 on rent. Calculate his other expenses.

Utilities:

Food:

Transport:

157

Solve It! On Saturday, 800 people visited the City Museum. The pie e chart art shows show the different countries of the visitors. The number of visitors itors from Canada was the same as the number of visitors from m Spain. ain.

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Thailand

Spain (15%)

United States

China

Australia

Canada

(a) Express the number off visitors from each country as a fraction.

(b) Ho How ow many visitors were from China or Thailand?

1 58

The pie chart shows the colors of candies in a jar.

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Purple 1 6

Yellow

Blue

Orange

Green 1 5

The total number of candies es in the jar is 1,2 11,200. How many candies of each ach color are there? th

159

Word Problems

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Let’s Practice

Students in Grade 6 were asked to name their favorite te type ype of movies. movie mov Their responses were recorded in a pie chart.

15%

30%

50%

Animation on Horrorr medy y Comedy rama Drama

(a) What fraction of the e students nts liked h horror movies? (b) A total of 120 students How many more ents gave their responses. r students liked animation mation on movies movie than dramas? (c) How many fewer wer students ents like horror movies than comedies?

160

The pie chart shows how pupils of Southport School travel to school.

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Walk

Cycle (10%)

Public Transport rt (35%)

School bus (50%)

(a) What percentage of the e pupils walk to school? (b) What fraction of the he pupils travel trav to school by public transport? (c) Given that there are who walk to school, how many e 60 0 pupils w pupils attend Sout Southport School? So Schoo

1 61

The pie chart shows how Ethan spends his weekly pocket money of $20.

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Stationery (5%)

Savings (15%)

Transport (20%)

Food and nd Drink Dri (60%) 0%

(a) (b) (c) (d)

1 62

How much money doess Ethan spend spen on food and drink? How much money y does es he spend spe on stationery? What fraction of the does he save? e money do How much more ore money m y does Ethan spend on food and drink than transport? ransport? nsport

The pie chart shows the number of different colored marbles that Riley has. She has 50 blue marbles.

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Orange

Gray 1 5

Blue

Red

(a) How many marbless does es Riley have altogether? (b) What is the ratio of the e number numbe of o orange marbles to the total number of marbles has? rbles les she ha h (c) What fraction of tthe marbles arbles are either gray or red?

1 63

The pie chart shows the different menu items that customers ordered at a restaurant one evening. Each customer ordered one menu item. it There were 6 customers who ordered pasta.

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Fish and Chips (15%)

Pasta (10%)

n Grilled Chicken (35%)

Seafood Platter (15%)

Salad (25%) 25%)

merss ordered the th seafood platter? (a) How many customers e number numbe of customers who ordered the (b) What is the ratio of the salad to the total number that evening? otal n ota er of customers c (c) What fraction menu is fish and chips? on of the m

1 64

The pie chart shows the types of fruits consumed by the students at ed was 4 High Ridge school in a day. The number of apples consumed times the number of oranges consumed.

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Oranges

Pears rs

Apples (60%)

Strawberries rawberries (10%)

(a) What fraction of the he fruits ruits consum consumed cons were oranges? (b) What percentage of the were pears? he fruits consumed c (c) 48 apples were re consumed. con c ed. How ed Ho many strawberries were consumed? H

1 65

At Home The pie chart shows the types of animals 40 pupils kept as pets. ets.

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Rabbits (10%)

Birds (30%)

Fish (40%)

Cats

(a) (b) (c) (d)

1 66

What fraction of the he pupils kept kep ffish? What fraction of the e pupils kept kep birds? What percentage ag of the age e pupils pupi keep cats? How many pupils pils kept ke rabbits? b

The pie chart shows how Sophie spent her money in a week. The ratio of the amount of money she spent on transport to the amount ount sshe spent on clothes was 1 : 2. She spent $60 more on food than an on shoes. shoes

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Food (45%)

Shoes (25%)

Transport sport (10%) 0%

Clothes

(a) How much did Sophie phie spend on transport? tra tr (b) How much did she e spend end on shoes? sho sh (c) What fraction of the money was w spent on clothes?

1 67

The pie chart shows the types of flavored ice cream sold at a shop last month. The shop sold 1,200 ice creams in all. Half of the e ice creams cr ored ice sold were chocolate. The shop sold 3% more strawberry flavored creams than banana flavored ice creams.

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Strawberry

Banana

Vanilla (17%)

Chocolate

vored ice creams cre (a) How many vanilla flavored did the shop sell? he ice cream cre (b) What percentage off the sold last week were strawberry flavored? avo avore (c) What fraction on of the fflavored ice cream is banana?

168

A survey was conducted in a food mall to find out the favorite food of a group of tourists in Singapore. The pie chart below shows ows the results of the survey.

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Satay

Chilli Crab (40%)

Claypot Rice e

Chicken Rice (30%) 0%)

he tourists tourist c (a) What percentage of the chose satay as their favorite local food? (b) The number of to tourists who chose chicken rice was 30 more c than the claypot was the total number of tourists who ypot ot rice rice. What W took part in this his survey?

1 69

Looking Back At Florida Gardens College, there are 720 students. Each student ent is required to choose one club to join. The pie chart shows ows the he percentage of students in each club.

Hiking (20%) Photography (35%) Yoga

Re ga le du

Reading (30%)

(a) What percentage of the e students udents are in i the yoga club? (b) How many studentss are in the hiking hikin club? (c)

How many studentss are re in the photography p club?

(d) How many more ore students stud st are a in the photography club than the reading club??

170

In 1 week, a fast food restaurant sold 450 items in total. The pie chart shows the number of each item sold.

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Drinks

Nuggets 1 5

Burgers 4 15 Fries 1 6

(a) What fraction of the items sold d were ere drinks?

(b) What percentage of the items tems ems sold were nuggets? (c)

How many burgers were ere sold old in 1 week? wee we

(d) How many more burgers ers than fries frie were sold in 1 week?

1 71

Wyatt has a jar containing 500 marbles. He sorted them by color into 5 containers. The pie chart shows the number of marbles in each jjar.

Purple (110)

Blue (45) Yellow (55)

Green (135)

Re ga le du ca

Orange

(a) How many marbles are orange? e?

(b) What percentage of the marbles are yellow yello or blue? (c)

What fraction of the marbles es are purple? purp pu

(d) What fraction of the e marbles are n not green?

(e) What is the ratio of green een marbles mar marb to purple marbles to yellow marbles?

172

The pie chart shows the number of pupils with and without glasses in a class. There are 24 boys in the class.

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Boys without glasses

Boys with glasses

(a) (b) (c) (d)

Girls with glasses (30%)

Girls without glasses (10%)

How many boys wear ar glasses? ses? What fraction of the glasses? e girls rls wear glas How many pupils are there in the t class? What percentage of the do not wear glasses? he boys d

1 73

Problem Solving

Re ga le du ca tio n

Act It Out

Example 14 cards, labeled from 1 to 14, are grouped in pairs. The e sums of the numbers nu n in each pair are 4, 6, 13, 14, 20, 21 and 27. What are the he e 7 number pairs? pa

10 11 12 1 13 14

Let's draw a table to keep track sums. rack k of the different diffe Sum

Possible ible Pairs Pair

(1, 3)

(2, 4)

(5, 5, 8) (6, 7)

8) (13, 1) (5, 9) (6, 8

(8, 12 12) (9, 11) (14, 6)

(9 112) (10, 11) (13, 8) (9,

(13, 14)

174

Re ga le du ca tio n

There is only 1 way to make a sum of 4, 6 and 27. We can remove them from the table. Sum

Possible Pairs

(5, 8) (6, 7)

(5, 9) (6, 8)

(8, 12) (9, 11)

(9, 12) (10, 11)

Every card must be used once only. The 10 card is only used use with 11 to make a sum of 21. So, we can remove the 11 card pairs. d from m other possible pos Sum

Possible Pairs

(5, 8) (6, 7)

(5, 9) (6, 8))

(8, 12)

(10, 11)

Similarly, the 9 card is only used us with ith 5 to make the sum of 14. So, we can remove the 5 card from pairs. rom other possible po We have found our 7 number pairs. p

1 3

2 4

6 7

13 14

5 9

8 12

10 11

17 5

Boats A, B, C, D and E went trawling for fish. Boat A and Boat D caught the least number of fish. Boat B caught more fish than Boat D but fewer fish than Boat C. Boat E caught fewer fish than Boat B. Which boat caught the most number of fish?

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176

Ethan has 24 poles that are each 1 meter in length. How many different rectangles can he make using all of the poles?

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17 7

In a classroom, there is a row of 5 chairs. The chair in the middle is empty. The boys and girls want to swap sides. To do this, the e boys can only move to the next chair to their left. Similarly, the girls can only umber er of moves move move to the next chair to their right. What is the least number needed for both the boys and girls to swap sides?

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ion

178

A BBQ shop has 7 full gas bottles, 7 half-full has bottles and 7 empty gas bottles. Each gas bottle is equal in size. 3 people are looking oking to buy some gas bottles for their BBQ. How can the shop distribute ute the he gas ets the he same bottles equally between the 3 people such that each gets amount of gas and the same number of bottles?

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179

Draw a Model Example

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2 n of the Ethan had some books to give to his friends. He gave 13 lesss than 5 3 books to Wyatt. He then gave 8 more than of the remaining aining ng books to 8 Halle and had 32 books left over. How many books did d Ethan have at first?

s. Let's t's draw a bar b model. Work backwards from when Ethan had 32 books. ng book remaining

books given to Halle

Ethan gave 8 more than

3 of his books ooks to Halle a an and was left with 32 books. 8

5 parts of the bar model is equal ual to 32 + 8 = 40 books. We can find the value of 1 part art by dividing by 5. 40 ÷ 5 = 8

To find the total number berr of books bo boo Ethan h had before he gave some to Halle, we need to find the So, we multiply 1 part by 8. e value ue of 8 parts. part pa 8 x 8 = 64

Ethan had 64 books some to Halle. ooks before he gave g

180

Let's draw another bar model to find how many books Ethan had at first. 13

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books given to Wyatt

Ethan gave 13 less than

2 of the books to Wyatt.t. 5

From our bar model, we can see that 8 green en parts make up u 3 blue parts plus 13. 3 blue parts = 8 green parts – 13. 8 green parts = 64 books. 64 - 13 = 51 3 blue parts = 51 books 1 blue part = 51 ÷ 3 = 17

5 blue parts = 17 x 5 = 85

So, Ethan had 85 books at first. firs

18 1

A goldsmith wants to sell a bracelet and make a profit of 50%. If the bracelet was sold at a discount of 10%, he would make a profit ofit of $25. If he sells it at a discount of 40%, he would make a loss of $35. 5. How much must the goldsmith sell the bracelet to gain a 50% % profit?

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182

Dominic, Jordan and Riley had $216 between them. Dominic gave g Jordan some money, and Jordan's amount tripled. Jordan then gave g some money to Riley and Riley's sum of money doubled. The 3 friends friend e money oney did now have an equal amount of money. How much more Dominic have than Riley at first?

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183

There are 120 students in Grade 6 at Burleigh Junior School. 70 students can speak German and 80 can speak French. 30 of them cannot speak German or French. How many students can speak both German h Germ and French?

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184

Mr. Enkel took 3 hours to drive from Singapore to Malacca at an average speed of 80 km/h. From Malacca, he took anotherr 2 hou hours to travel to Kuala Lumpur. His average speed for the whole le journey urney was 75 km/h. Find his average speed for the journey from om Malacca to Kuala Lumpur.

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185

Guess-and-Check

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Example ach Four classes A, B, C and D participated in a dance contest. Each udges. es. The class received a whole number score from 1 to 10 by the judges. re for average score of classes B, C and D was 6. The average score classes A, B and D was 5. Class D scored more than Class ass B. Cla Class C ch h of the classes received the highest score of 9. Find the score of each classes.

asses B The average score off classes B, C and D is 6. Multiply the average er of classes to ffind their combined score. score by the number 6 x 3 = 18.

ore of 9 so we can subtract. Class C has a score 18 - 9 = 9.

he combined score sc So, the of classes B and D is 9.

186

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The average score of classes A, B and D is 5. Multiply the average score by the number of classes to find their combined score. 5 x 3 = 15. d Class ass A's score sco The sum of classes B and D is 9. So, we can subtract to find score. 15 - 9 = 6.

Class A has a score of 6.

's use guess-and-check. guess To find the remaining scores of classes B and D, let's ater than han 10. 10 The score of Class B and class D can't be greater The sum of the scores of Class B, C and D iss 18. The sum of the scores of Class A, B and D is 15. 5. Guess of Class B's Score

Guess of Class D's score

Total tal of B, C and dD

Total of A, B and D

1 + 9 + 9 = 19

6 + 1 + 9 = 16

2 + 9 + 9 = 20

6 + 2 +9 = 17

2 + 9 + 8 = 19

6 + 2 + 8 = 16

2 + 9 + 7 = 18

6 + 2 + 7 = 15

The scores for each class ss are are: Class A = 6 Class B = 2 Class C = 9 Class D = 7

1 87

There are 629 students participating in the American Mathematics Competition at Palm Beach Junior School. Each class has the he same sam number of students. There must be at least 20 students in n a class. How many classes are there?

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188

Halle's math test had a total of 50 questions. For every question answered correctly, 2 marks were awarded. 5 marks were deducted deduc for each incorrect answer. If a question is not answered, no marks are ar empted pted by Halle Hall awarded or deducted. The number of questions not attempted estions. ons. How m ma was equal to the number of incorrectly answered questions. many questions did she get correct if she scored a total off 82 marks?

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18 9

Riley puts 2 coins in her money box each day. The value of each coin is either 10 cents or 20 cents. Her mother also puts a 50-cent coin in the box every 7 days. The total value of the coins after 84 days $34.20. ys was as $34.2

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(a) How many coins were there altogether? (b) How many of the coins were 20 cents coins?

190

A bicycle shop has a total of 37 bicycles and tricycles. Each bicycle sells for $189 while each tricycle sells for $99. There are a total of 90 wheels wh on the bicycles and tricycles. How much will the shopkeeper per earn if all a the bicycles and tricycles are sold?

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19 1

Make a List

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Example The diagram shows 2 types of squares. The 4 smaller squares res are re identical. identical The side length in centimeters of all the squares is a whole e number. umber. The 2 total area of 1 large square and 1 small square is 100 cm . What hat is the perimeter of the figure?

We need to find the 2 areas that at add to 100. Area of small square

Area Are of large square

Total area

check

4 x 4 = 16

5 x 5 = 25

25 + 16 = 41

5 x 5 = 25

6 x 6 = 36

25 + 36 = 61

6 6 x 6 = 36

7 x 7 = 49

36 + 49 = 85

6 x 6 = 36

8 x 8 = 64

36 + 64 = 100

yes

So, the have a side length of 6 cm and the larger square he smaller squa squares h hass a side length of o 8 cm. c To find the perimeter, we add. P =6+6+6+1+1+6+6+6+1+1+6+6+6+1+1+6+6+6+1+1 = 80 0 The figure has a perimeter of 80 cm.

192

3 pipes, A, B and C are connected to an empty container. Pipe A can fill 1 1 of the container in 1 hour. Pipe B can fill of the container er in n 1 hour. h 10 8 1 However Pipe C drains of the container in 1 hour. At first, rst, pipe A and 16 pipe B were turned on. After 1 hour, pipe C was turned d on for 2 hours hour before being turned off. How long did it take to fill up p the e container? contain

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193

Dominic has the same number of candies and chocolates. If he gave each of the 18 students in Class A an equal number of candies, dies, he would have 7 candies left. If he gave each of the 12 students nts in n Class B late left. What iis an equal number of chocolates, he would have 1 chocolate the total number of candies and chocolates Dominic has?

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194

Mr. Olsen put aside $1,533 to spend. Every day he spent twice the amount spent the day before. If he spent $3 on the first day, y, which whic was a Monday, on what day would he have spent all of his money? oney? y?

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19 5

Look for Patterns

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Example ern. There are 139 marbles of 3 colors arranged in the following pattern. How many more green than blue marbles are there in all??

There are 4 marbles in each repeating part of the pattern. To find the total number of sets, we divide. 139 ÷ 4 = 34 R 3

The remaining 3 marbles are red, blue and green.

Let's find the number of blue and nd green reen marbles marb marble in 34 sets. In one set, there is one blue and two green marbles. arbles. Total green = 34 x 2 = 68 Total blue

= 34 x 1 = 34

So, there are 68 green een marbles and a 34 blue marbles in a set of 34.

There are 1 of each h color remaining. rem remainin So we add 1 to both green and blue totals. There are e 69 green marbles marble and 35 blue marbles. 69 – 35 = 34 4

So, o, there are 34 more green marbles than blue marbles.

196

Mrs. Wong installed new tiles in her rectangular living room measuring 6 m by 3 m. She used triangular tiles as shown in the diagram am below. be e. The The contractor charged $3 to cement each tile or part of a tile. g room was cost of cutting a tile was $5. The labor cost for tiling the living he new tiles? $300. How much did Mrs. Wong pay in total to install the

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50 cm

60 cm

197

A dictionary has 1,348 pages. How many pages of the book have the digit(s) 1 in the page number?

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198

A ball is thrown off a building from a height of 30 m. Each time the 3 ball bounces, it reaches a new maximum height of its previous revious ous 5 maximum height. What is the total vertical distance the ball would have hav traveled when it touches the ground for the 5th time?

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199

Find the 62nd digit in the repeating digit pattern below.

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3 7 8 0 3 7 8 0 3 7 8 0 3 ...

200

Example

ed uc ati on

Work Backwards 1 e distance ance in the Ethan took a train from City A to City B. He covered of the 3 1 first hour. In the next hour, he covered of the total distance ance e of the journ journey. 4 He then took 1 h 12 min to travel the remaining 80 km. Calculate his average speed in km/h for the whole journey. ourney. urney. 1 3 1h

City A

Recall that average speed =

1 4

1 h 12 min

City B

total distance e traveled ve total time me taken aken

jjo Let's work backwards and find the fraction of the journey that was covered in the final stage. Last stage = 1 –

1 5 1 – = 3 4 12

5 = 80 km 12 1 = 80 ÷ 5 = 16 km 12 12 = 16 x 12 = 192 km 12

stance ce between City A and City B is 192 km. The total distance The total time e taken = 1 h + 1 h + 1 h 12 min = 3 h 12 min = 3.2 3 h average erage speed =

192 19 = 60 3.2

e speed s The average for the whole journey was 60 km/h. 201

1 Wyatt and Jordan had some pens. Wyatt gave of his penss to Jordan. 2 1 Jordan then gave of his pens back to Wyatt. In the end,, Wyatt yatt had 3 3x pens and Jordan had 2x pens.

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(a) How many pens did Wyatt have at first? Give your answer in terms of x. (b) What was the total number of pens they had d when x = 10?

202

5 Some water is held in 2 containers – A and B. of the water in A is 6 7 poured into B. of the new amount of water in B is then poured red back bac 9 into A. In the end, A contained 160 liters of water and B contained ained 40 liters of water. What was the volume of water in A initially? tially? y?

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20 3

Sophie, Halle and Riley had 180 hairpins. When Sophie gave some of her hairpins to Halle, the number of hairpins Halle had was doubl doubled. mberr of Halle then gave some of her hairpins to Riley and the number al number mber of hairpins Riley had was doubled. The 3 girls had an equal e at first? hairpins at the end. How many hairpins did each girl have

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204

Mrs. Farrugia gave 2 more than half of her pies to her daughter, Kathy. Mrs. Farrugia then gave 4 more than half of the remaining pies to her e given ven to he grandson, Luke. 3 more than half of the leftover pies were her granddaughter, Ella. In the end, Mrs. Farrugia had 2 piess for herself. How many pies did she have at first?

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20 5

Simplify the Problem

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Example Mr. Tan has some potted plants. He arranged the plants along perimeter ng the e perimete of 2 squares as shown in Diagram A. The distance between en each ach potted plant was 2 m. After arranging the plants, he placed a string tring of lights over ov he string of lights light was ligh the plants as shown in Diagram B. The total length of the 112 m. How many potted plants did Mr. Tan have?

Diagram A

Diagram B

For each potted plant, 4 meters of lights hts are needed. neede

The potted plants at the junctionss of the square are a connected to by the lights to 3 potted plants as shown. plants are connected by wn. Allll other potted pott po the lights to 2 potted plants.

The 2 plants at the e junction nction each use an additional 2 m of string light. Let's subtract 4 m from length of the lights. m the total tota len 112 m – 4 m = 108 8m

Divide by the string light required for 1 potted plant to find the total e length of strin number er of potted plants. 108 8 ÷ 4 = 27 potted plants. Mr. Tan has 27 p potte

206

What is the maximum number of triangles that can be cut from a rectangular sheet of wood as shown below?

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3 cm

4 cm

1.3 m

20 7

The figure in Diagram A is made from a single length of wire bent to form a square of area 81 cm2. The wire is then straightened ed an and bent again to form the shape in Diagram B. Each of the connectors onnectors ectors connecting the three identical circles measure 4 cm. 22 Find the radius of each of the circles. Take π as . Leave eave e your answer answ 7 as an improper fraction in cm.

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Diagram A

208

Diagram gram B

The price for a bento box meal at a restaurant was $21. During the Black Friday sale, the price for a bento box meal was reduced. ed. The number of bento box meals sold was tripled and the amount ount of money collected was doubled. How much was the bento to box ox meal m after the price reduction?

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20 9

Solve Part of the Problem

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Example The figure below shows 3 overlapping circles. The overlaps of 2 circles form the areas B and C. The ratio of area A to area B is 1 : 2. Area a C is 5% less than tth 2 area B. If the area of C is 20 cm , what is the area of the e green en circle?

area of C = 20 cm2 area of B = 105% of area C = 105% x 20 cm2 = 21 cm2 area A : area B = 1 : 2 2 units = 21 cm2 1 unit = 21 ÷ 2 = 10.5 cm m2 area A = 10.5 cm2

area of green n circle rcle = area A + area ar B = 10.5 + 21 = 31.5 cm c 2

210

The diagram shows 4 squares of side length 25 cm. The curved sections were formed from a semicircle and a quarter-circle. le. Find the area of the shaded portion. Take π as 3.14.

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21 1

The figure QRSTU shows a square B enclosed in a rectangle. Based on the diagram, the area A is 12 cm2 more than the sum of areas eas B and C. The area A is equal to that of C. The length RS is twice that at of ST. Find the length of square B.

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212

It takes 5 men, each working 4 hours per day to complete building a hut in 3 days. On the 1st day, all the men were present and worked worke as planned. However, on the 2nd day, only 3 men turned up to work and each of them only worked for 3 hours. On the 3rd day, only 4 men m turned up to work. How many hours does each worker er have ave to work wor on the 3rd day to complete building the hut?

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21 3

Tap A takes 3 minutes to fill a tank. Tap B takes 9 minutes to fill the same tank. If both taps are turned on at the same time, how w long will it take to fill up the tank?

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214

Mr. Craven wanted to buy a watch. The watch dealer told Mr. Craven that all of the watches available cost less than $1,000. The cheapest cheap watch available was $100. The prices of all the watches sold old had an even number digit in the ones place, and the digit in the tenss place was less than 8. Given that all of the watches were priced in n whole hole dollars, dolla how many watches did the watch dealer have if every ery watch was priced differently?

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215

Before-After Concept

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Example Riley has 20% more stickers than Dominic. If Riley gives 40 stickers tickers rs to Dominic, he will have 20% more stickers than Riley. How many stickers do they have in all? Before

Riley (120%) %)

% – 1 unit) nit Dominic (100%

After

Riley iley (100% – 1 unit)

Domin Domi Dominic (120%)

20% of 1 unit = 40 1 unit = 5 x 40 = 200

Total number of stickers kers = 220% 220 x 200 = 440 kers in all. They had 440 stickers

216

1 Jordan had 2 boxes of cards. He transferred of the cards from fro 3 1 Box 1 to Box 2. Then he transferred of the cards from Box ox 2 back 3 1 ck to Box to Box 1. Finally, he transferred of the cards from Box 1 back 3 ds in Box 2. How 2 again. There are now 68 cards in Box 1 and 90 cards many cards were in each box at the beginning?

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21 7

1 Sophie gave of her money to her sister, Chelsea. Chelsea then the gave 2 1 1 of her money back to Sophie. Sophie then gave of her er money to 4 3 d $1,325. 325. Chelsea again. Finally Sophie had $975 and Chelsea had

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How much money did Sophie have at first?

218

5 her brother’s age. Elaine is 28 years rs old o now. 7 an In how many years time will her brother be 27 years olderr than 1 Elaine’s age? 2 3 years ago, Elaine was

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219

Wyatt had some green beans and red beans in the ratio 8 : 5. He had 126 more green beans than red beans. After he sold d an equal e number of each type of bean, the ratio of the number of green en beans bean to red beans he had became 3 : 1. How many beans did d he sell in total?

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220

Make Suppositions

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Example A fruit seller bought a total of 286 apples and oranges from a farmer. rmer He bought each fruit at $0.85. Upon bringing the fruits back ck to o his shop, he h threw away 12 rotten fruits. He then sold the remaining oranges ges for $1.10 and each and the remaining apples for $1.30 each. If he made a profit of $87.10, how many apples did he e sell? First, let's find the initial cost price. 286 x $0.85 = $243.10

12 fruits were rotten and could not be sold. 286 – 12 = 274

Find the total amount of money he received sales. eceived d from ssa Income = expenses + profits = $243.10 + $87.10 = $330.20 He received $330.20 from sales. ales..

Assuming all the fruits sold were ere e apples: apples $1.30 x 274 = $356.20 $356.20 - $330.20 = $26

This is $26 more than the money received from sales. rec $1.30 - $1.10 = $0.20 20 The price difference ence in apples app and a oranges is $0.20 $26 ÷ $0.20 0.20 = 130

He sold 130 oranges 274 74 – 130 = 144

He sold 144 44 apples. app

221

Ethan has a total of 35 $5 and $2 notes. If he has a total of $115, how many $5 notes does Ethan have?

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22 2

In a mathematics competition, each pupil has to answer 10 questions. 5 points were given for each correct answer and 2 points poin d all the were deducted from each wrong answer. Halle answered uestions ons did questions and scored a total of 36 points. How many questions she answered correctly?

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223

Andy paid $4.40 for 2 pens and 1 marker pen. The marker pen cost 20 cents more than a pen. How much is the cost of 1 pen?

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22 4

Blake bought 50 pens and rulers altogether. Each pen costs $1.20 and each ruler costs $2.40. The difference between the total al cost of the pens and the total cost of the rulers is $12. How many ny pens and rulers did Blake buy?

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225

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End-of-year Exam

Section A – Multiple Choice Questions Questions 1 – 20 carry 1 mark each. There are 4 options given en in each a question – (a), (b), (c) and (d). Shade the letter that best matches the answer.

The center of the circle is point O. Labeled lines es are re straight lilin lines. Which lines represent the radius and diameter respectively? pectively? tively? B

(a) (b) (c) (d)

OB and CE AO and OB OB and AD AO and CE E

Evaluate te the e algebraic exp expression when b = 4. 36 – 9b b

(a) (b) (b (c) (d)

0 2 27 32 23

Sub-total

22 6

Express the time shown on the clock in 12-hour time.

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(a) 11 42

(b) 10:42 p.m. (c)

11:42 a.m.

(d) 11:42 p.m.

A car travels at a speed of 20 m/s for 1 minute. minute How far does it travel?

(a) (b) (c) (d)

1.2 km 120 km 20 m 120 m

What percentage of the square quare grid gri is colored?

% (a) 20% 1 (b) b)) 4 (c 25% (c) 2 (d) 75%

Sub-total

227

120 students were asked about their favorite subjects. Their responses were recorded in the pie chart below. How many students chose science as their favorite subject? ct?

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English

Science

Art 1 5

Math 2 5

(a) (b) (c) (d)

40 20 120 30

angle. le. Find the area of the triangle.

1 cm

1c cm

(a) a) (b) (c) (d)

32 2 m2 3 cm 32 m2 16 cm2 16 in2

Sub-total

22 8

Find

2 1 x . Give your answer in its simplest form. 4 7 1 14 3 11 2 28 3 28

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(a)

(b) (c)

(d)

Halle and Sophie rode their bikes to the lake. They The arrived at 13 20 and hiked around the lake until 16 10. 0. How long was their hike?

(a) (b) (c) (d)

1 h 50 min 2 h 50 min 3 h 10 min 3 h 20 min

10. What is 20% % of 360? 60? (a) (b) (c) (d))

80 20 720 18 72

Sub-total

229

A man takes 3 h to run 39 km. Find his average speed. (a) 13 km/h (b) 42 km/h (c) 13 m/s A (d) 42 m/s

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11.

12.

The pie chart below shows the different fruits ruits stocked by a fruit seller. What fraction of the fruits are mangoes? s? Give your answer in its simplest form.

Apples 8

Pears 4

(a)

(b) (c)

(d) d)

1 4 3 8 12 2 36 1 8

Mangoes 12

Melons 8

Sub-total

2 30

13.

Arrange the numbers from the smallest to the greatest.

(a) (b) (c) (d)

14.

|–8|, –3, 0, 7, –4 |–8|,–4, –3, 0, 7 –4, –3, 0, 7, |–8| –4, –3, |–8|, 0, 7

ake π = Find the circumference of the circle. Take

21 cm

(a) (b) (c) (d)

21 cm 462 cm 66 cm 33 cm

22 . 7

A school hool play ay goes for 2 hours 35 minutes. The play finished at 21 05. What hat time ime did the school scho play start? (a) (b (b) (c) (d)

18 30 17 30 18 35 18 05

15.

ed uc ati on

–3, |–8|, 0, 7, –4

Sub-total

2 31

16.

Simplify the algebraic expression.

(a) (b) (c) (d)

17.

Express 14 cm to 84 cm as a ratio in itss simplest mplest form. (a) (b) (c) (d)

18.

7m + 4n 10m + 4n 7m – 4n 8m + 4n

ed uc ati on

10m – n – m – 2m + 5n

14 : 84 14 cm : 84 cm 7 : 42 1:6

Express 24 ÷ 16 ass a mixed mixe mix number mb in its simplest form. 1 8 1 (b) 1 2 1 (c) 2 2 1 (d) 16 2

(a) 1

Sub-total

23 2

Find the area of the circle. Take π = 3.14 and round off your answer to 1 decimal place.

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19.

3 cm

(a) (b) (c) (d)

28.3 cm2 9 cm2 113 cm2 18.8 cm

20. Solve the equation. 6a – 20 = 22

(a) (b) (c) (d)

a=5 a=6 a=7 a=8

End En of Section A

Sub-total

2 33

21.

ed uc ati on

Section B – Short Answer Questions 21 – 40 carry 2 marks each. Show your working and write ite your yo answer in the space provided. A truck takes 13 h to drive 1,118 km from Miami to Nashville. shville. lle. Find the average speed of the truck.

Answer:

22. The temperature changed from m –9ºC to 2ºC. How much did the temperature ure e rise?

Answer:

23. A round table able has a radius radiu 49 cm. Find the area. Take π =

22 . 7

Answer: Sub-total

2 34

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24. Sophie takes 8 minutes 42 seconds to walk around her school. How long will it take Sophie to walk around her school 8 times? es?

Answer: r::

25. The pie chart below shows the pets kept by y class ass 6C. Half of the class kept birds or rabbits. What fraction of the class kept lizards?

Birds (35%)

Fish (25%)

Rabbits

Cats (10%)

Lizards

Answer:

26. Solve the equation. uation. on 2 100 – 12x = 52

Answer:

Sub-total

2 35

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27. Express 78% as a fraction in its simplest form.

Answer: wer:

28. Find the area of the triangle.

60 cm

40 cm

Answer:

29. A rabbit hopss at a speed of 7 m/s. m How long will it take to cross a field 462 m wide? answer in minutes and seconds. e? Give e your ans

Answer:

Sub-total

23 6

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30. Mrs. Olsen takes 12 minutes to wrap a gift. How long will it take her to wrap 23 such gifts? Give your answer in hours and minutes. s.

Answer: wer:

31.

The pie chart below shows how studentss travel school. el to schoo 45 students ride to school. How many students dents walk to school?

Car (30%)

Walk

Bus (10%)

Ride

Answer:

32. The ratio off Ethan's n's savings saving to Blake's savings to Jordan's savings is 1 : 4 : 2. They total. How much money does Jordan have? hey have $56 in tota

Answer:

Sub-total

2 37

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33. A round swimming pool has a radius of 17 m. Find its area. Take π = 3.14 and round off your answer to 1 decimal place.

nswer: er: Answer:

34. Solve the equation. 42 – 4r = 2r

Answer:

35. Jordan took 18 8 minutes inutes to walk wa from his house to the library. He studied in the library and left at 13 50. What time did y for 2 hours 27 minutes minu Jordan leave ave his house?

Answer:

Sub-total

238

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36. What is 65% of 80?

wer: Answer:

37. Divide. 6÷

2 9

Answer:

38. A triangle has a height eight that is

3 that of its base. Find the area of the 8

ven its ts base is 24 cm triangle given cm.

Answer:

Sub-total

2 39

39. Simplify the algebraic expression.

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10a + 3a – d – 2d – 3d + 5a

Answer:

40. The ratio of the mass of a watermelon mass of a mango is 12 : 5. rmelon elon to the m The mass of the mango is 700 mass of the watermelon. 0 g. Find the ma

Answer:

End of Section B

Sub-total

24 0

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Section C – Word Problems Questions 41 – 50 carry 4 marks each. Show your working and write ite your y answer in the space provided.

41.

The blue figure below is drawn in a rectangle. Find the area of the blue figure. 9 cm

3 cm

5 cm

5 cm m

1 cm c

Answer:

Sub-total

2 41

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42. A pizza chef takes 12 minutes to prepare the pizza base, 5 minutes to add the toppings and 18 minutes to bake in the oven. He needs eds to make ef should ould start sta 8 pizzas by 18 15. What is the latest time that the pizza chef making the pizzas?

Answer:

Sub-total

242

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her 43. Wyatt took 2 hours to cover 4 of a journey to his grandmother's house. He covered the remaining 31 km in 1 hour 6 minutes. s. Find his average speed for the whole journey.

Answer:

Sub-total

2 43

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44. The pie chart shows the colors of flowers spotted in a nursery. There were 720 flowers spotted in total. How many flowers of each color were spotted?

Orange

Blue

1 5

Pink

Green

1 5

Yellow

Answer :

Sub-total

244

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45. The figure below is composed of 2 semi-circles and a square. Find the area of the figure. ce. Take π = 3.14 and round off your answer to 1 decimal place.

2 cm

Answer:

Sub-total

2 45

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46. Mr. Hogan earns $m per month. Mr. Booker earns 3 times as much as Mr. Hogan. (a) Express Mr. Hogan's and Mr. Booker's total income over a period of 12 months. en m = $2,680? (b) How much does each person earn in 1 year when

Answer swer (a (a): (b):

ook computer compute is discounted by 15% and a 47. During a sale, a notebook nted ed by 10% 10%. The sale price of the notebook computer bag is discounted le pric computer is $918 and th the sale price of the computer bag is $36. ce of bo Find the regular price both items.

Answer:

Sub-total

246

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48. Find the shaded area of the figure.

m 12 cm

2 cm

16 cm

4 cm m

Answer:

Sub-total

2 47

49. A triangle has a base of b cm and a height of 2 b.

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(a) Express the area of the triangle in terms of b. (b) Find the area of the triangle when b = 32.

Answer (a): (b):

Sub-total

248

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50. Halle and Sophie took 2 hours 20 minutes to hike from their campsite m at the top of a hill down to the river at an average speed off 60 m/min. On their way back up, they hiked at an average speed of 40 m/min. How long did it take Halle and Sophie to hike from the cave ave back to the campsite? Give your answer in hours and minutes.

Answer:

End of Exam

Sub-total

2 49

End-of-year Exam Results Correct

Score

Comments

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Section

25 0

/ 20

/ 40

/ 10

/ 40

Total

/ 50 0

/ 100

Re ga le du ca tio n

This his publication lication would not have been possible without the tireless effort of our production team. Special thanks to: Daniel Cole, Matthew Matthe Cole, Col Wang Hui Guan, Kevin Mahoney, Winston Goh, Jesse Singer, Joseph eph Anderson, Anderson Halle Taylor-Pritchard, Sophie Taylor-Pritchard, Tejal Thakur, Nakapat,Varasinun Mathanattapat, Kanungnit Pookwanmuang, Saijit Lueangsrisuk Natchanuch Nak Nakapat,V

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