Measurement: Book 6 - Ages 10-11 by Teacher Superstore

Ready-Ed Publications

Book 6 r -s Ages 10/11 r o e t Bo e p ok u S

ew i ev Pr

Teac he r

Measurement in Mathematics Series © ReadyEdPubl i cat i ons

w ww

. te

m . u

Practical measuring activities the •f orr evi ew pur posesonfor l y• classroom.

o c . che e r o t r s super

Written by Gerry Westenberg. Illustrated by Rod Jefferson. © Ready-Ed Publications - 2001 Published by Ready-Ed Publications, P.O. Box 276, Greenwood ,WA, 6024 Email: info@readyed.com.au Website: www.readyed.com.au COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes. However this permission is not transferable and applies only to the purchasing individual or institution.

ISBN 1 86397 183 1

Topics/Skills Length:

measurement to nearest metre, centimetre, millimetre calculations using kilometres perimeter of polygons diameters and circumferences relate measurement of length to other measures.

Area:

r o e t s Bo r e p ok u S

Teac he r

cover surfaces using tessellations informal measurement of regions simple calculation of area - concrete experiences determine areas beyond concrete experience relate measurement of area to other measures.

Mass:

R R R R

activities based on comparing mass measure to the nearest gram and kilogram activities involving suspension and projection relate measurement of mass to other measures.

ÂŠ ReadyEdPubl i cat i ons â&#x20AC;˘f orr evi ew pur posesonl yâ&#x20AC;˘

Volume and Capacity:

R R R R

measure to the nearest millilitre and litre measure volume of solids measure volume using cubes relate measurement of volume to other measures.

Time:

calculations based on the calendar timeline with BC and AD (or common era and before common era) activities requiring rhythmic response time activities in minutes and seconds conversion of time measures read clock to the nearest minute and second (12 and 24 hour clocks) read and use simple timetables.

w ww

R R R R R R R

ew i ev Pr

R R R R R

m . u

R R R R R

Page 2

. te

o c . che e r o t r s super

Ready-Ed Publications

Contents Topics/skills

How long is a piece of string?

Are we there yet?

Measure to the nearest mL and L

r o e t s Bo r e p ok u S

Could you be an Olympic champion?

Do polygons like rulers?

Sneaky maths

Circumference

Twinkles and tessellations Tessellations to try

ew i ev Pr

Teac he r

Round and round we go!

Let’s explore area

Not area again!

The big cover-up

But what if they aren’t square?

Changing from volume to surface area

w ww

Related measurements

The elephant needs a diet

. te

Measure to the nearest kg

o c . che e r o t r s super

Measure to the nearest kg & g Suspension

m . u

Volume using cubes

Calculations based on a calendar

A timeline

More timelines

Time activities in hours, minutes and seconds 1

Time activities in hours, minutes and seconds 2

How many seconds in a year?

Clocks

Answers

35, 36

Ready-Ed Publications

Page 3

Name: ..........................

Ho w long is a piece of string? How What you need: a ruler.

Guess the lengths of the items listed below and record your guesses. Then use your ruler to find the length of each item. How close was your guess?

r o e t s Bo r e p ok u S mm

Item

guess

actual

guess

actual

guess

actual

ew i ev Pr

Teac he r

The width of your maths book

Your handspan The length of the blackboard The height of your seat

w ww

The length of this page The width of this page

. te

The height of the door of your classroom The width of the door of your classroom

m . u

The width of your desk

o c . che e r o t r s super

R Now can you work out the distance around the outside of: 1. Your desk? ...................................................................... 2. This page? ...................................................................... 3. The door of your classroom? ........................................... Page 4

Ready-Ed Publications

Name: ..........................

Are we there yet?

R Your task: The distances between the towns on the map below are measured in kilometres. Use the map to help you answer the questions. Ayville Beetown

r o e t s Bo r e p ok u S

87 km

91 km

99 km

148 km

Eeville

Deetown

127 km

80 km

Ceeville

322 km

Eltown

145 km

260 km

75 km 132 km

scale of 1 cm = 30 km

Kayville

1. What is the shortest distance to drive from:

ew i ev Pr

Teac he r

Jayton

Effton

a. Ayville to Ceeville? .................................. b. Beetown to Ceeville? .............................. c.

e. Effton to Kayville? ................................... f.

Eeville to Effton? ....................................

m . u

w ww

2. If the road from Deetown to Eeville was blocked by floods, what would your answers for question 1 be now? a. Ayville to Ceeville .................................... b. Beetown to Ceeville ................................

. te

c. Jayton to Deetown ................................ d. Ayville to Effton ....................................

o c . che e r o t r s super

e. Effton to Kayville ..................................... f.

Eeville to Effton ......................................

3. If you were to fly a direct route, the distances would be different. Use the scale on the map to find the direct route distances (to the nearest 5 km). a. Ayville to Ceeville .................................... b. Beetown to Kayville ................................ c. Jayton to Deetown ................................ d. Ayville to Effton .................................... e. Effton to Kayville ..................................... f.

Eltown to Effton......................................

Activity Draw a map of your local area and put in some of the important features/towns. Ensure that the scale is accurate. Ready-Ed Publications

Page 5

Name: ..........................

Measure tto o the nearest mL and L R What you need: a graduated mL jar and a litre jar, 10 assorted containers, e.g. milk carton, jam jar, etc. R Your task: How many mL are in a litre? I’m glad you asked. There are 1000 mL in one litre.

r o e t s Bo r e p ok u S

1. Using your litre container, fill each of your 10 containers with water one at a time. Some will use more than 1 litre, some will use less than one litre. Estimate the volume, in litres, of 6 of the containers. Estimate in L

ew i ev Pr

Teac he r

Item

1. 2. 3. 4.

5. 6.

Item

Estimate in mL

w ww

1. 2. 3. 4. 5. 6.

. te

m . u

2. Now repeat Activity 1 using the graduated mL jar.

o c . che e r o t r s super

See if you can find an easy and accurate way of actually measuring the volume of the remaining four containers.

Page 6

Ready-Ed Publications

Name: ..........................

Could you be an Olympic champion? R What you need: a tape measure or a trundle wheel and a stopwatch. R Your task: Measure out 100 m on the school sports field. 1. How many steps do you need to take to:

r o e t s Bo r e p ok u S

a. walk 100 m? ....................................................................

b. run 100 m? ......................................................................

Teac he r

2. If you could walk/run at the same rate as for 100 m, how many steps would you need to:

ew i ev Pr

a. walk 1 km? ...................................................................... b. run 1 km? ...................................................................... 3. How long does it take you to: a. walk 100 m? .................................................................... b. run 100 m? ......................................................................

4. If you could walk/run at the same rate as for 100 m, how long would it take you to: a.

b. run 1 km? ......................................................................

w ww

1 (your time for question 4b)

. te

3600 1

m . u

5. To work out your speed in km/hour, do the following calculation. .................... km/hour

For example, If it takes me 360 seconds to run 1 km, then my speed in km/hour is:

o c . che e r o t r s super

1 x 360 Now find your speed in km/hour. 1

3600 1

3600 360

10 km/hour

3600 = .................... km/hour 1 6. A cheetah can run at 80 km/hour. How long would it take to run 1km? ............................ 7. An elephant can run at 10 km/hour. How long will it take to run 1km? ............................. 8. Are you faster or slower than the elephant? By how much? ...........................................

Class discussion Why do you think people slow down when they have been running for a long time? Ready-Ed Publications

Page 7

Name: ..........................

Do polygons like rulers?

R Your task: Measure the perimeters of the polygons below using both millimetres and centimetres. When measuring in cms, go to the nearest whole number.

r o e t s Bo r e p ok u S b

ew i ev Pr

Teac he r

w ww Shape a. b. c.

. te

m . u

o c . che e r o t r s super mm

d. e. f. R Now draw 5 shapes of your own and measure the perimeter in mm and cm. Page 8

Ready-Ed Publications

Name: ..........................

Sneaky maths R Your task:

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

A sideshow alley stall gives a prize for the shape with the largest area made from a piece of string 24 cm long. On the grid below, draw shapes using a total perimeter of 24 cm, to find the shape with the largest area. Some have been done for you.

w ww

. te

m . u

o c . che e r o t r s super

1a. What did you find? ....................................................................................................... b. Which shape had the greatest area? ............................................................................ c. Is this always going to be true? ..................................................................................... 2. Try doing the same thing, but this time use a shape with a perimeter of 36 cm or 12 cm. Ready-Ed Publications

Page 9

Name: ..........................

Round and round we go! R What you need: string, bottles, or any objects that are round, e.g. a bicycle wheel, glass jar, pen top, etc. 12 12

R Your task: Measure the following:

r o e t s Bo r e p ok u S

1. The distance around the object. 2. The distance across the top.

Item

distance across D (diameter)

distance around C (circumference)

a. b. c.

C÷D

ew i ev Pr

Teac he r

Fill in the table below.

d. e. f.

m . u

w ww

1. What did you notice about the answer for C ÷ D? ......................................................... 2. See if you can work out a rule for finding the circumference of a round object using the distance across as your guide.

. te

o c . che e r o t r s super

.................................................................................................................................... ....................................................................................................................................

3. Does your rule work? ........................................ Try it out on at least 2 other objects.

If it doesn’t work, see if you can find out why it doesn’t and try and fix it. (If it still doesn’t work, talk to your teacher.) If it did work, great!

Extension What is π (pi), who discovered it, where and when? Page 10

Ready-Ed Publications

Name: ..........................

Circumference

R Your task: Calculate the circumference of the following circles. (Use π = 3.14.) Remember circumference is C = π x D or 2 x π x r. b.

a. D=4m

r o e t s Bo r e p ok u S D = 20 cm

D=3m

.....................................

ew i ev Pr

Teac he r

.....................................

D = 5 mm

..................................... ..................................... f.

90l 0i © ReadyEdPub at i ons mc m •f o..................................... rr evi ew pur poses..................................... onl y• D=

D = 32 mm

w ww

D=?

. te

Circumference = 42 m D = .................... d.

o c . che e r o t r s super

Circumference = 94 cm

C = ....................

D=?

Fred ran 157 m around this track.

D = .................... f.

15 m What is the distance around this lake?

Ready-Ed Publications

D=?

D = ....................

m . u

These are a little different. You will need to be careful and think hard!

P = .....................

5m What is the perimeter of this shape? P= ...................... Page 11

Name: ..........................

Twinkles and tessellations R What you need: scissors, glue or sticky tape, 1 cm grid paper and

paper.

What is a tessellation? A tessellation is when a shape is used to cover an area so that there are no gaps left over and no overlapping pieces. For example, bathroom tiles tessellate over a bathroom floor.

r o e t s Bo r e p ok u S

By using

I could cover an area like this:

I can cover an area like this:

R Your task:

ew i ev Pr

Teac he r

If I used this shape

1. Using your scissors and a dash of imagination, see if you can cover up ½ of a sheet of square grid paper using squares; 2. 3.

© ReadyEdPubl i cat i ons Repeat the exercise using triangles and ½ of a sheet of triangular grid paper; •f orr evi ew pur posesonl y• Now see if you can make a shape out of 3 squares that will tessellate - try it on the other half of the square grid paper;

R Once completed, colour in the tessellations.

. te

5. The 5 shapes below are made up of five 1cm squares.

m . u

w ww

4. See if you can do the same with 3 triangles and cover the other half of the triangular grid paper.

o c . che e r o t r s super

Can you trace or draw these shapes onto a piece of 1 cm squared paper so they form a square 5 x 5 cm? 6. Think up some more shapes with five 1 cm squares that are different to the ones above. Draw them on your squared paper. Page 12

Ready-Ed Publications

Name: ..........................

Tessellations to try

Tessellations can be made by cutting a piece off one side of a shape and adding it to another side. Thus, you can change the shape completely. An artist named Escher was famous for these types of drawings.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

Here is an example with a square.

w ww

. te

m . u

Here is one with a triangle.

o c . che e r o t r s super

R Now try some for yourself. You can choose either: 2 rectangle shapes, or 2 triangle shapes, or 1 rectangle, 1 triangle shape.

Can a circle tessellate? Find out if it can or not. If not, why not? .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... Ready-Ed Publications

Page 13

Name: ..........................

Let’s explore area

R What you need: scissors, a pen, pencil and glue, and 1 cm grid paper. What is area? Area is a measure of how much of a surface is covered. There are many ways of measuring and describing area. Let’s try and find some of our own. R Your task: Your objective is to cover the surface of a page. Now, draw a straight-sided figure on the grid below.

r o e t s Bo r e p ok u S

(Not too big, for example a rectangle and square

, etc.)

ew i ev Pr

Teac he r

Then cut it out and trace it onto your sheet of 1 cm squared paper (remember to cover the whole page). Does your shape fit together (tessellate) to cover the page? ................................................. If it does not, why not? ...................................................................................................... .................................................................................................................................... Change the shape to make it fit and cover the area. In groups of 3, try and come up with the best shape for covering the surface of a 1 cm squared paper.

w ww

. te

Page 14

m . u

o c . che e r o t r s super

Ready-Ed Publications

Name: ..........................

Not area again!

1. Your task: Count out the number of squares in each figure below. a. b. d.

r o e t s Bo r e p ok u S

Answer ..............

ew i ev Pr

Teac he r

Answer ..............

Answer .............. Answer ..............

Answer ..............

2. Try these! Count the number of rows of squares and the number of columns of squares, b. then count the total number of squares. a.

columns ..................

. te

columns .................. d. total number ............ (area) total number ............ rows ....................... (area) columns ..................

m . u

w ww

rows .......................

o c . che e r o t r s super total number ............ (area) rows ....................... columns .................. total number ............ (area)

rows .......................

columns ..................

total number ............ (area)

3. What is an easier way to work out the area of a rectangle? ........................................... 4. Write down your rule, and check to see if it always works. ............................................ .................................................................................................................................... Ready-Ed Publications

Page 15

Name: ..........................

The big cover-up 1. Your task: Find the area of the following shapes. a.

2m 4m

6 cm

r o e t s Bo r e p ok u S

.....................................

..................................... 9 km

16 mm

7 km

.....................................

..................................... 2. Now try these! 6 cm

Total Area ..............

w ww 1

Total Area .............. d.

. te

Total Area ..............

3. Challenge: Find the area of these 2 shapes. 3m 5

o c . che e r o t r s super 8

Total Area ..............

m . u

½ mm

ew i ev Pr

Teac he r

3 cm

b. 4 mm

5 Total Area .............. Page 16

Total Area .............. Ready-Ed Publications

Name: ..........................

But what if the y aren’ they aren’tt square? We normally can count the number of squares in a shape if it is a rectangle or square. But what happens if they aren’t shaped like this? R Your task: 1. Below are some triangle shapes. See if you can work out the areas of them.

ew i ev Pr

Teac he r

r o e t s Bo r e p ok u b. S

w ww

. te

m . u

o c . che e r o t r s super

a. ........................... b. ..........................

c. ........................... d. ............................

2. Can you see a shorter way of working out area? If so, try these harder ones.

a. ........................... b............................. c. ........................... Ready-Ed Publications

Page 17

Name: ..........................

Have you got a problem?

1. A farmer has 60 m of wire fencing. He wishes to make a pen for his sheep. On the back of this sheet draw at least 5 of the pens he could construct and calculate the area of each. 2. The farmer now decides to put the pen against a log wall, using the wall as one side of the pen. Draw at least 4 of the pens he could construct and calculate the area of each.

r o e t s Bo r e p ok u S

ew i ev Pr

Teac he r

3. A tin can has to have a label on it. The label must go all the way around the tin but not overlap. It also must cover from the top to the bottom. If the tin can is 15 cm high and it has a radius of 10 cm, what will be the area of the paper label? ....................................................................................................................................

4. If a page in a book has an area of 432 cm2 and one of the sides is 18 cm, what is the length of the other side?

....................................................................................................................................

5a. A cube is to be covered with material. If the cube is 6 m x 6 m x 6 m, how much material is going to be needed?

© ReadyEdPubl i cat i ons .................................................................................................................................... •f orr evi ew pur posesonl y• b. If the material costs $2.79 per square metre, what will it cost to cover the cube?

w ww

6. 1 litre of paint can cover an area of 12 m2.

m . u

....................................................................................................................................

a. How many litres would I need to cover 324 m2? .............................................................

. te

b. How many m2 could I cover if I had 3.6 litres of paint? ...................................................

o c . che e r o t r s super

7. A new game called “bilby” is invented. A “bilby” field has dimensions of 200 m x 40 m. Everyone who plays “bilby” needs a 100 m2 playing area to move within. All of the field is used. If all players have their own area how many players play on a “bilby” field? .................................................................................................................................... 8. A paddock needs a 3 strand wire fence around it. The dimensions of the paddock are 36 m x 48 m. If I have 180 m of wire, will I be able to make the fence? If so, how much is left over? If not, how much more do I need? ...............................................................................

Page 18

Ready-Ed Publications

Name: ..........................

Measuring the v olume of solids volume R What you need: a large container of water, a graduated jug, a tray with sides to it, string, 10 solid items. Remember that 1 litre of water is equal to 1000 cm3 and 1 mL of water is equal to 1 cm3.

r o e t s Bo r e p ok u S

Teac he r

ew i ev Pr

R Your task: Fill the container with water to the very top. Tie a piece of string around one of your objects and lower it to the bottom of the container. Water will spill out. Now take the object out and, using the graduated jug, see how much water is needed to fill the container again. The amount of water an object displaces (pushes over the side of the jug) is equal to the volume of the object.

rock

Repeat the steps for each item and fill in the table below. (Hint: If an object floats, you may need to push it under the water.)

w ww Item

1. e.g. rock 2. 3.

. te

4. 5.

Volume 400 mL

Rank

m . u

When you have finished the table, rank the items in order from the greatest volume to the least.

o c . che e r o t r s super

6. 7. 8. 9. 10. Ready-Ed Publications

Page 19

Name: ..........................

What is the volume of that? R Your task: Using 1 cm cubes, construct the following shapes. Count and record the number of cubes needed for each shape. 1a.

r o e t s Bo r e p ok u S

...........................

ew i ev Pr

Teac he r

...........................

Find the volume of the shapes below (you may build them if you need to). b.

w ww

. te

m . u

2a.

o c . che e r o t r s super ...........................

...........................

........................... Page 20

........................... Ready-Ed Publications

Name: ..........................

Volume using cubes

R Your task: Using 12 cubes, make as many different prisms as you can and draw each shape in the table below (each one must have straight sides). shape

length

area of base

height

12 cm2

r o e t s Bo r e p ok u S 12

volume 12 cm3

ew i ev Pr

Teac he r

width

w ww

. te

shape

m . u

Now make the following shapes out of cubes, and record your results in the table at the bottom of the page.

o c . che e r o t r s super

length

width

area of base

height

volume

See if you can work out a short way of getting the volume of a prism. Check that it works. If it doesn’t then check with your teacher. Ready-Ed Publications

Page 21

Name: ..........................

Changing from volume to surface area

Teac he r

Surface area is the measurement of the area of all the outside surfaces of a shape. For a shape three cubes high, two cubes long and two cubes wide, you could add the surface area up by: adding the area of the front side and the back side 6 + 6 = 12; adding the area of the left side and the right side 6 + 6 = 12 and so on to get the total surface area.

r o e t s Bo r e p ok u S

ew i ev Pr

R Your task: Make the model described above and check that the statement is correct. Count all the sides you can see (don’t forget the bottom). 1. Now construct these shapes and find the surface area.

b. ...........................

w ww

. te

c. ...........................

m . u

o c . che e r o t r s super d. ...........................

Working in pairs, make the following shapes and find out which one has the smallest surface area. Underline the smallest in each group. 2. a) 3 long, 3 high, 3 wide

b) 27 long, 1 high, 1 wide

c) 3 long, 9 wide, 1 high.

3. a) 2 long, 4 wide, 1 high

b) 8 long, 1 high, 1 wide

c) 2 long, 2 wide, 2 high.

4. What conclusion can you draw from this? ..................................................................... .................................................................................................................................... .................................................................................................................................... Page 22

Ready-Ed Publications

Name: ..........................

Related measurements

1. I have 17.4 m of string. How much string will I have left after I

wrap it once around this shape? ............................................. (Remember to use 3.14 for π.)

r o e t s Bo r e p ok u S

2. If the diameter of a circular pool is 4 m, how long will a piece of string be if it goes around the pool the number of times shown below? Write your answers in m, cm and mm.

1 x around

3 x around

3. Complete the graph below using the following measurements. a. c. D = 4 cm D = 8 cm b.

ew i ev Pr

Teac he r

Da =t 10i cmn © ReadyEdPubl i c o s •f orr evi ew pur posesonl y• d.

D = 6 cm

w ww

25 Circumference (rounded to the nearest 20 cm) 15 10

. te

5 0 1

m . u

o c . che e r o t r s super 2

Diameter (cm)

4. What do you notice about the graph? (Hint: join all the points up using a ruler.) From the graph, work out the following: What would be the approximate circumference of a circle where diameter was: a. 7 cm?..................................................

b. 2.5cm? ...................................................

c. 11 cm? ................................................

d. 9 cm? ....................................................

Ready-Ed Publications

Page 23

Name: ..........................

The elephant needs a diet It’s weighing time at the zoo! The keeper found that the elephant weighs 4 tonnes, the rhinoceros weighs 3 tonnes, the tiger weighs 340 kg and the kangaroo weighs 150 kg. 1. How many kangaroos would be needed to equal the same weight as the elephant?

r o e t s Bo r e p ok u S

.................................................................................................................................... 2. The rhinoceros weighs the same as ........................................ tigers.

Teac he r

3. What would be the total weight of 2 elephants, 5 kangaroos, 2 tigers and 1 rhinoceros? ..................................................................................................................

ew i ev Pr

4. A blue whale is said to weigh 40 tonnes. How many of the following animals would be needed to equal the total weight of the blue whale? a.

..................................... elephants

..................................... kangaroos

© ReadyEdPubl i cat i ons If a kangaroo weighs twice as much as a wallaby, how many wallabies would be •f orr evi ew pur posesonl y• needed to balance the scales with five tigers? ...............................................................

..................................... tigers

6. Write down your weight: I weigh .............................................. kg.

w ww

a. an elephant? .....................................

. te

b. a tiger? .............................................

m . u

7. How many of you would be needed to balance a set of scales with:

o c . che e r o t r s super

c. a rhinoceros? .................................... d. a blue whale? ....................................

Page 24

Ready-Ed Publications

Name: ..........................

Measure to the nearest kg

R What you need: g and kg weights, bathroom scales, kitchen scales and 10 items (including yourself!). Estimate the weight of each item in g or kg (you choose). Now measure their weights, first in kg and then in g. Put your data on this table.

r o e t s Bo r e p ok u S Estimate

Kilograms

Grams

ew i ev Pr

Teac he r

Item

w ww

Group 1 - measured in kg

. te

Ready-Ed Publications

m . u

For some items, it is more appropriate to measure in kg rather than g or in g rather than kg. Using your list above, divide the items into groups according to whether they would be measured in kg or g. Group 2 - measured in g

o c . che e r o t r s super

Page 25

Name: ..........................

Measure tto o the nearest kg & g R What you need: bathroom scales.

How much do you think your arm weighs? To find an approximate weight, put a set of bathroom scales on the desktop. Crouch down so that your shoulder is in line with the top of the bathroom scales. Rest your arm so that your elbow is fully on the scales. Record the weight. This will give you an approximate weight for your arm.

r o e t s Bo r e p ok u S

Teac he r

Fill in the table below. Item

Weight

arm leg

head

ew i ev Pr

You can also do this for your leg and your head. For example, lie on your back with your head resting on the scales. Sit with your leg resting on the scales. Have a partner note down the weights.

My torso weighed...................................

w ww

m . u

Now that you know the approximate weight of your arm, leg and head, work out the approximate weight for your torso (body).

Do you think the weight of your torso can change during the day? .......................................

. te

Why? .................................................................................................................................

o c . che e r o t r s super

..........................................................................................................................................

Thinking Cap

Why is it that somebody who is as tall as another person, and looks to be of the same build, may weigh more than the other person? Think about what makes up the body - skin, bones, muscle, etc.

Page 26

Ready-Ed Publications

Name: ..........................

Suspension

R What you need: string, a rubber band and 6 - 8 objects. Set up your materials like this:

tabletop

r o e t s Bo r e p ok u S

rubber band

string

measure

Teac he r

loop

Object

Distance

Object

ew i ev Pr

R Your task: Tie each of the objects to the loop, one at a time, and suspend as shown. Measure the distance from the top of the table to the bottom of the loop. List your findings here. Distance

m . u

Next, put the rubber band and string onto the tabletop. WARNING: Do not pull the string back too far.

w ww

Now, one at a time, attach each item to the loop. Pull it back 10 cm and let it go. How far does the object travel? List your findings here. Object

. te

Distance

Object

Distance

o c . che e r o t r s super

Compare your results. Why do you think you got the results you did? .................................. .......................................................................................................................................... Do some research on projection. You can ask your librarian for some information on Archimedes. Ready-Ed Publications

Page 27

Name: ..........................

Calculations based on a calendar JANUARY

February

Sun Mon Tue Wed Thu Fri Sat 1

9 10 11 12 13 14 15 16 17 18 5

Sun Mon Tue Wed Thu Fri Sat

March

April

Sun Mon Tue Wed Thu Fri Sat

30 31 2

4 5

6 7

7 8

9 10 11 12

9 10 11 12 13 14 15

13 14 15 16 17 18 19

19 20 21 22 23 24 25

16 17 18 19 20 21 22

20 21 22 23 24 25 26

26 27 28 29 30 31

23 24 25 26 27 28

23 24 25 26 27 28 29

27 28 29 30

r o e t s Bo r e p ok u S

May

June

July

Sun Mon Tue Wed Thu Fri Sat

Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5 6 7

Sun Mon Tue Wed Thu Fri Sat 1 2 3 4 5

6 7

9 10

9 10 11 12 13 14

7 8

August

9 10 11 12

Sun Mon Tue Wed Thu Fri Sat 31 1 2 3

4 5

6 7

13 14 15 16 17 18 19

18 19 20 21 22 23 24

22 23 24 25 26 27 28

20 21 22 23 24 25 26

10 11 12 13 14 15 16 17 18 19 20 21 22 23

25 26 27 28 29 30 31

29 30

27 28 29 30 31

24 25 26 27 28 29 30

Teac he r

September

October

Sun Mon Tue Wed Thu Fri Sat

November

Sun Mon Tue Wed Thu Fri Sat 4

5 6 7 8 9 10 11 12 13 14 15 16 17 18

21 22 23 24 25 26 27

19 20 21 22 23 24 25

16 17 18 19 20 21 22

21 22 23 24 25 26 27

28 29 30

26 27 28 29 30 31

23 24 25 26 27 28 29

28 29 30 31

Sun Mon Tue Wed Thu Fri Sat

9 10 11 12 13 14 15 16 17 18 19 20

DECEMBER

Sun Mon Tue Wed Thu Fri Sat

7 8

ew i ev Pr

15 16 17 18 19 20 21

11 12 13 14 15 16 17

1 3

4 5 6 7 8 9 10 11 12 13 14 15

1 7

8 9 10 11 12 13 14 15 16 17 18 19 20

July? ............................... © ReadyEdPubl i ca t i o ns How many weeks are there from: •f orr evi ew pur posesonl y•

1. How many days are there in April? ................................ 2.

1 6

a) April 4 to June 20 (inclusive)? ................. b) January 5 to August 24? ........................

m . u

3. How many days are there from:

w ww

a) January 5 to March 24? ......................... b) April 20 to December 25? ...................... 4. Circle today and then see how many days there are from now until Christmas Day.

. te

.......................................

o c . che e r o t r s super

5. How many months have:

a) 30 days? ...............................................

31 days? ............................................

c) Less than 30 days? .........................................................

6. How many hours are there from midnight, March 27 until midnight April 5? .................... 7. My birthday is today. I am 12 years old. How many weeks old am I? ............................. 8. My birthday is tomorrow. I am 41 years old. How many weeks old am I? ........................

Research and Repor Reportt Describe why the number of days in February vary. Page 28

Ready-Ed Publications

Name: ..........................

A timeline

The year we are in can be written with the letters ‘AD’ in front of it. AD stands for anno Domini (in the year of our Lord). It is used because our time system is taken from the birth of Jesus Christ. Any time before the birth of Jesus is said to be BC or before Christ. BC is written after dates, e.g. 200 BC. Below are some historical events. Place them in the appropriate places on the timeline.

r o e t s Bo r e p ok u S

600

Teac he r

500 400

R Julius Caesar assassinated; 44 BC.

300

R Emperor Constantine crowned emperor of Roman Empire; AD 306.

ew i ev Pr

Data Box

200 100

R Persian Invasion of Greece; 480 BC.

R Fall of the Roman Empire; AD 476.

R Beginning of the Holy Roman Empire; AD 800.

300 400

w ww

R Euclid’s Geometry is written; 300 BC.

500

. te 600 700

800

m . u

R Defeat of Hannibal; 202 BC.

R Hadrian’s Wall is completed in Britain; AD 123.

o c . che e r o t r s super

R On the timeline below, place important dates in your life.

Year

In some modern books, time BC is called Before the Common Era (BCE) and the time AD becomes the Common Era (CE). Ready-Ed Publications

Page 29

Name: ..........................

More timelines Below is a timeline of some events in history. 1918 End of WW I

1939 Start of WW II

1969 First man on the moon

r o e t s Bo r e p ok u S 1930 1929 Stock market crash

1940 1950 1960 1970 1980 1945 1959 2004 (Asia) End of Start of WW II Vietnam War

1990

2004

ew i ev Pr

1900 1910 1920 1903 1914 Wright bros WW I fly first begins powered aircraft

Teac he r

1950 Korean War begins

R Use the timeline above to answer the following questions. 1. How many years ago did the first man walk on the moon? ............................................. 2. There were ...................................... years between the end of WW I (World War One) and the start of WW II (World War Two).

© ReadyEdPubl i cat i ons This was .............................................. years before the start of WW I. •f orr evi ew pur posesonl y• How many major wars are listed on the timeline? .....................................

3. The Wright brothers flew the first powered aircraft in .................................................... .

Name the two most recent wars on this timeline. ............................................................

w ww

m . u

5. The timeline is graduated in increments (steps) of ........................................... years. 6. How many years does this timeline span? .......................................................

. te

7. There is a gap of ................................. years between the stock market crash and the

o c . che e r o t r s super

start of the Vietnam War.

8. The first man walked on the moon in ............................................................... . This is ................................. years after the beginning of the Korean War and ........................................... years after powered flight began.

9. Complete the box for 2004 to show a shocking event that happened in Asia that year. “If only the walls could speak” is a very old saying. If you could talk to the Colosseum (a building in Rome), what things might you hear about? Create a timeline of your own. Do some library research on ancient Rome and list some events on the timeline that the “walls of the Colosseum” could have seen. Page 30

Ready-Ed Publications

Name: ..........................

Time activities in hours, minutes and seconds 1

Note: all answers must be in hours, minutes and seconds.

1. In a snail race, it takes Sammy Snail 2 minutes, 34 seconds to “race” 1 metre. If he continues to travel at the same “speedy” pace, how long would it take him to complete:

r o e t s Bo r e p ok u S

a. 5 m? ...............................................

b. 7 m? ..........................................................

Teac he r

2. If a train stops in each station for 50 seconds and there are 15 stations along the line,

ew i ev Pr

what is the total amount of time spent at stations? .......................................................... The train spends an extra 6 minutes, 40 seconds waiting at the last station.

What is the total stopping time now? ..........................................................................

3. Find the total time for the following: a.

2 hours 3 minutes 15 seconds 1 hour 27 minutes 50 seconds

................................................

58 minutes 29 seconds 34 minutes 18 seconds

© ReadyEdP=ub l i cat i ons ................................................ 15• minutes 38 seconds d. r 18 minutes 4 seconds f o r r e v i e w p u p o s e s onl y• 24 minutes 29 seconds 9 minutes 38 seconds

................................................

4. How many seconds are in:

w ww

a. 3 minutes? ..........................................

. te

c. 3½ hours? ...........................................

................................................

m . u

b. 10½ minutes? ........................................ d. ¼ hour? .................................................

o c . che e r o t r s super

5. How many minutes are there in:

a. 4¾ hours? ...........................................

b. 3540 seconds? ......................................

c. 0.48 hours? .........................................

d. 570 seconds? ........................................

6. How many hours are there in:

a. 1520 minutes? .....................................

b. 72 000 seconds? ....................................

b. 845 minutes? .......................................

d. 1260 seconds? ......................................

7. I run for 40 seconds and walk for 580 seconds, then rest for 2 minutes and 50 seconds, then run back to where I started and take 5 minutes. How long have I been away from the start?....................................................................

Ready-Ed Publications

Page 31

Name: ..........................

Time activities in hours, minutes and seconds 2

R What you will need: a stopwatch. Do this activity in pairs. Estimate the time it takes you to do the following actions and fill in the table. Then, with your partner, measure each action with the stopwatch.

Teac he r

How long does it take you to: Count to 50 by ones? Draw 3 rectangles? Walk to the door? Actions

Count to 50

Draw 3 rectangles

4. Walk to the canteen and back? 5. Walk around the playing field?

Estimate

ew i ev Pr

R 1. 2. 3.

r o e t s Bo r e p ok u S

Actual Time

w ww

Walk around the playing field

m . u

Walk to the canteen and back

How many times longer did it take you to walk around the playing field than to walk to the

. te

o c . che e r o t r s super

canteen and back? (e.g. 3 times as long, 7 times as long, etc) ............................................. How many times longer did it take you to walk around the playing field than to walk to the door? (e.g. 12 times as long, 3½ times as long, etc) ............................................................ How much further is it to walk around the playing field that to walk to the canteen and back? (e.g. 4½ times as long, 2 times as long, etc) ........................................................................

Extra Time how long it takes to read a page of a novel. ..................................... Now, figure out how long it would take you to read the whole novel. ................................. Page 32

Ready-Ed Publications

Name: ..........................

Ho w many seconds in a y ear? How year? 1. There are 60 seconds in one minute and 60 minutes in one hour.

a. How many seconds are there in one hour? ............................... b. How many hours are there in one day? ....................................

r o e t s Bo r e p ok u S

c. How many days are there in one week? .................................... d. How many seconds are there in one week? ..............................

Teac he r

2. There are 52 weeks in 1 year. How many seconds are there in 1 year? ........................ a. How many years, months, weeks and days have you been alive? ...........................

b. How many hours? .................................................................... c. How many seconds? ................................................................

ew i ev Pr

4. There are 100 years in 1 century and 365 days in 1 normal year. How many days are there in a century? .........................................................................

5. a. How many weeks are there in 2 years? .................................... b.

c. How many hours are there in 2 years? .....................................

m . u

6. a. How many weeks are there in 1 century?..................................

w ww

b. How many days are there in 2½ centuries? .............................. c. How many seconds are there in 1 century? ..............................

. te

d. How many seconds old are you? ..............................................

o c . che e r o t r s super

7. Light travels at approximately 310 000 km/sec. How far will it travel in: a. 1 hour? ............................................. b

1 day? ..............................................

c. 1 week? ............................................ d. 1 year? .............................................

Ready-Ed Publications

Page 33

Name: ..........................

Clocks

1. Below are six clocks. The time is written next to each clock. Write true or false. 10 9 8

b. 9.15

2 3

6.55

c. 2.10

2 3

10 9 8

11 12 1

10 9 8

................

11 12 1

1.58

................

10 9 8

7 6

11 12 1

7 6

2. Draw the clock faces to match the digital times. a.

10 9 8

11 12 1

2 3

11 12 1

c. 2

10 9 8

................

9.10 3

11 12 1

................

10 9 8

4:05

w ww

10 9 8

11 12 1

5.40

r o e t s Bo r e p ok u S

................

Teac he r

11 12 1

10 9 8

11 12 1

ew i ev Pr

10 9 8

11 12 1

. te

11 12 1

2 3

11:20

10 9 8

11 12 1

2 3

7 6

12:50

m . u

3. Have your partner fill in the clock faces below. You do the same for your partner. Now, write the time in the digital clock face to match. a. 10 9 8

d. 10 9 8

11 12 1

2 3

11 12 1

Page 34

10 9 8

e. 2 3

o c . che e r o t r s super b.

10 9 8

11 12 1

10 9 8

f. 2 3

10 9 8

11 12 1

7 6

11 12 1

7 6

2 4

Ready-Ed Publications

Answers Page 5 1a. 167, b. 418 (A - E - D - J - C) , c. 148, d. 566 (A - J - D - C - K - F), e. 132, f. 433, (E - D - C - K - F). 2a. 167, b. 467 km, c. 148, d. 566, e. 132, f. 483 E - B - K - F. 3a. 180 km, b. 180 km, c. 120 km, d. 390 km, e. 120 km, f. 180 km. Page 7 6. 0.75 minutes, 7. 6 minutes.

r o e t s Bo r e p ok u S

Page 8 (n.b. the printing process may cause alterations in the measurements of polygons.) a. 150 mm 15 cm, b. 185 mm 18.5 cm, c. 135 mm 13.5 cm, d. 120 mm 12 cm, e. 160 mm 16 cm, f. 180 mm 18 cm.

Page 10 1. approximately 3, 2. c ≅ 3D.

ew i ev Pr

Teac he r

Page 9 1b. Which shape has the greatest area? Square of 6 x 6, 1c. yes.

Page 11 1a. 12.56, b. 62.8 cm, c. 9.42 m, d. 15.7 mm, e. 100.48 mm, f. 2826 mm. 2a. 13.38 m, b, 18.84 m, c. 29.94 cm, d. 50 m, e. 23.55 m, f. 7.85 m.

w ww

Page 15 1a. 14, b. 12, c. 10, d. 36, e. 8, 2a. rows = 3, columns = 7, area = 21, b. r = 1, c = 9, a = 9, c. r = 3, c = 6, a = 18, d. r = 4, c = 5, a = 20, e. r = 2, c = 12, a = 24, 4. area = length x width.

m . u

Page 12 5. Yes.

Page 16 1a. 8 m2, b. 18 cm2, c. 63 km2, d. 8 mm2, 2a. 24 cm2, b. 22 mm2, c. 22 m2, d. 45 m2, 3a. 39 m2, b. 128mm2.

. te

o c . che e r o t r s super

Page 17 1a. 8, b. 20, c. 8, d. 18, 2a. 24, b. 32, c. 28.

Page 18 3. 942 cm2, 4. 24 cm, 5a. 216 m2, 5b. $602.64, 6a. 27 litres, b. 43.2 m2, 7. 80 people, 8. I need 72 m more. Page 20 1a. 12 cubes, b. 16 cubes, c. 56, d. 23, 2a. 28, b. 23, c. 36, d. 36. Page 22 1a. 72cm2, b. 88 cm2, c. 54 cm2, d. 38 cm2, 2. a = 54 cm2, 3. c = 24 cm2, 4. A cube has the least surface area.

Ready-Ed Publications

Page 35

Answers Cont. Page 23 1. 1.7 m, 2a. 12.56 m, 1256 cm, 12560 mm, 2b. 37.68 m, 3768 cm, 37 680 mm, 3a. 12.56 cm, b. 18.84, c. 25.12, d. 31.4, 4. It is a straight line, a. 21.98, b. 7.85, c. 34.54, d. 28.26. Page 24 (Where required answers are rounded to the nearest whole number.) 1. 27, 2. 9, 3. 12430 kg or 12.43 tonnes, 4a. 10, b. 267, c. 118, 5. 23, 7. answers will vary.

r o e t s Bo r e p ok u S

Page 28 1a. 30, b. 31, 2a. 11 weeks, b. 33 weeks, 3a. 79 days, b. 250 days, 4. answers will vary, 5a. 5 months, b. 6 months, c. 1 month, 6. 168 hours, 7. 624 weeks, 8. 2132 weeks.

Teac he r

ew i ev Pr

Page 30 1. answers will vary, 2. 19 years, 3. 1903, 11 years, 4. 4 major wars, Vietnam and Korean War, 5. 10 years, 6. 90 years, 7. 30 years, 8a. 1969, b. 19, c. 66 years, 9. Asian Tsunami. Page 31 1a. 470 sec (or 7 minutes, 50 sec), b. 658 sec (10 minutes, 58 sec), 2a. 750 sec (12 min, 30 sec), b. 19 minutes, 10 sec, 3a. 3 hours, 31 minutes, 5 sec, b. 24 minutes, 11 sec, c. 40 minutes, 7 sec, d. 8 minutes, 26 sec, 4a. 180 sec, b. 630 sec, c. 12600 sec, d. 900 sec, 5a. 285 minutes, b. 59 minutes, c. 28.8 minutes, d. 9.5 minutes, 6a. 25.33 hours, b. 20 hours, c. 14.08 hours, d. 0.35 hours, 7. 1090 sec (18.17 minutes).

2a.

w ww

Page 34 1a. false, b. false, c. true, d. true, e. false, f. true. 10 9 8

d. 10 9 8

11 12 1

. te 2

11 12 1

Page 36

10 9 8

2 4

11 12 1

c. 2

10 9 8

11 12 1

o c . che e r o t r s super e.

3 7

m . u

Page 33 1a. 3600 sec, b. 24 hours, c. 7 days, d. 604 800 sec, 2. 31 449 600 sec, 3a. answers will vary, b. answers will vary, c. answers will vary, 4. 36 500 days + 24 leap year days, 5a. 104, b. 730 days, c. 17 520 hours, 6a. 5200 weeks, b. 91 250 days, c. 3 144 960 000 sec, d. answers will vary, 7a. 1 116 000 000 km, b. 26 784 000 000 km, c. 187 488 000 000 km d. 9 749 376 000 000 km.

10 9 8

11 12 1

3 7

10 9 8

7 6

11 12 1

3 7 6

Ready-Ed Publications