4 Unit 4

Estimating, Time and Shapes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Topic A: Estimating

 

You use numbers in your everyday life. You often use estimating in your everyday life.

 

You go shopping and you only have twenty dollars, you may need to estimate how much your groceries are going to cost before you go to pay for them.

 

You commute by bus each day to work and it takes thirty-three minutes going to work and thirty-three minutes coming home at the end of the day. You would say that it takes you about one hour on the bus.

 

These are examples of estimating.

 

You have already learned about rounding numbers. You need to be able to round numbers in order to be able to estimate.

 

When you solve math problems, it is a good idea to estimate what the answer may be. Estimating the answer means finding an answer that is close to the real answer. Estimating helps you to see if the real answer is sensible. To estimate an answer, you need to round the numbers then add or subtract the rounded numbers. Remember to round to the nearest ten.

 

Example:	23 + 45	Estimate:	20 + 50
			70
Example:	67	Estimate:	70
	─ 31		─ 30
			40
Example:	372	Estimate:	370
	+ 416		+ 420
			790
Example:	564	Estimate:	560
	─ 243		─ 240
			320

 

 

 

 

Exercise OneEstimate the following answers. Be sure to round to the

nearest 10 before adding. Check your work using the answer key at the end of the exercise.

 

 

a)27	Estimate:	b)42	Estimate:
+ 31		+ 51

 

 

 

 

c)26	Estimate:	d)14	Estimate:
+ 32		+ 52

 

 

 

 

e)44	Estimate:	f)31	Estimate:
+ 24		+ 27

 

 

 

 

 

g)65	Estimate:	h)46	Estimate:
+ 22		+ 23

 

 

 

 

 

i)23	Estimate:	j)42	Estimate:
+ 72		+ 36

 

 

 

 

 

k)64	Estimate:	l)32	Estimate:
+ 14		+ 20

 

 

 

 

 

 

 

 

m) 423	Estimate:	n) 526	Estimate:
+ 324		+ 345

 

 

 

 

o) 123	Estimate:	p) 752	Estimate:
+ 541		+ 243

 

 

 

 

 

q) 429	Estimate:	r) 324	Estimate:
+ 316		+ 115

 

 

 

 

 

s) 162	Estimate:	t)156	Estimate:
+ 531		+ 322

 

 

 

 

 

u) 302	Estimate:	v) 326	Estimate:
+ 473		+ 607

 

 

 

 

w) 312	Estimate:	x) 341	Estimate:
+ 148		+ 248

 

 

 

 

Answers to Exercise One
a)	60	b)	90	c)	60	d)	60	e)	60	f)	60	g)	90
h)	70	i)	90	j)	80	k)	70	l)	50	m)	740	n)	880
o)	660	p)	990	q)	750	r)	440	s)	690	t)	480	u)	770
v)	940	w)	460	x)	590

 

 

 

Exercise TwoEstimate the following answers. Be sure to round to the

nearest 10 before subtracting. Check your work using the answer key at the end of the exercise.

 

 

a)35	Estimate:	b)52	Estimate:
─ 16		─ 14

 

 

 

 

 

c)67	Estimate:	d)51	Estimate:
─ 19		─ 23

 

 

 

 

 

e)36	Estimate:	f)72	Estimate:
─ 17		─ 44

 

 

 

 

 

g)38	Estimate:	h)74	Estimate:
─ 19		─ 26

 

 

 

 

i)93	Estimate:	j)82	Estimate:
─ 89		─ 57

 

 

 

 

 

k)56	Estimate:	l)94	Estimate:
─ 27		─ 48

 

 

 

 

 

 

 

m) 752	Estimate:	n) 765	Estimate:
─ 342		─ 439

 

 

 

 

 

 

 

o) 673	Estimate:	p) 645	Estimate:
─ 424		─ 309

 

 

 

 

 

 

 

q) 811	Estimate:	r) 591	Estimate:
─ 502		─ 57

 

 

 

 

 

 

s) 972	Estimate:	t)178	Estimate:
─ 447		─ 152

 

 

 

 

 

 

 

u) 471	Estimate:	v) 316	Estimate:
─ 146		─ 222

 

 

 

 

 

 

 

 

w) 678	Estimate:	x) 486	Estimate:
─ 425		─ 211

 

 

 

 

 

Answers to Exercise Two
a)	20	b)	40	c)	50	d)	30	e)	20	f)	30	g)	20
h)	40	i)	0	j)	20	k)	30	l)	40	m)	410	n)	330
o)	250	p)	340	q)	310	r)	540	s)	520	t)	30	u)	320
v)	100	w)	250	x)	280

 

 

 

Exercise ThreeEstimate the following answers. Be sure to

round to the nearest ten before adding or subtracting. Remember to circle the information and underline what is being asked. Check your work using the answer key at the end of the exercise.

 

 

Example:There are 186 people living in my apartment building. If 103 are children, how many are adults?

 

 

 

103

There are186people living in my apartment building. If how many are adults?

are children,

 

 

186Estimate:190

─ 103─ 100

90

 

About 90 people are adults.

 

 

• The bus has 84 passenger seats. All the seats are filled and 39 passengers are standing. How many passengers are on the bus?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• Trisha counted 67 boxes on one shelf. She counted 78 boxes on the next shelf. How many boxes were there altogether?

 

 

 

 

 

 

 

 

 

 

 

 

 

• The library loaned out 157 books on Monday. It loaned out 118 books on Tuesday. How many book did it loan on both days?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• Ryan worked on the computer for 78 minutes. Helen worked on the computer for 54 minutes. How much longer did Ryan work on the computer?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• The Ludlow factory has 73 people working in the factory. The Watson factory has 48 people working in their factory. How many more people work in the Ludlow factory?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• Mr. Martinez needs 257 metres of fencing. He has 125 metres. How much more fencing does he need to buy?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answers to Exercise Threea)120 passengersd)30 minutesb) 150 boxese)20 peoplec)280 booksf)130 meters

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Topic B: Time

 

 

The ancient Babylonians used a number system based on 60. We still use their number system when we talk about time.

 

There are 60 minutes in an hour, and there are 60 seconds in a minute.

 

60 minutes = 1 hour

60 seconds = 1 minute

 

 

Writing Time in Standard FormatTime is written in a standard format. Hours: Minutes: SecondsExample:12 noonwould be written as 12:00:00 or 12:00 (without the seconds)Example:4 o’clockwould be written as 4:00:00 or 4:00 (without the seconds)Example:8 hours, 47 minutes, 3 secondswould be written as 8:47:03Note:When there is only one number, put in a zero to hold the tens place.Example:3 hours, 9 minutes, 3 secondswould be written as 3:09:03

 

 

 

 

 

 

 

 

Exercise OneWrite the following times in standard format. Check your

work using the answer key at the end of the exercise.

 

Example:2 hours, 7 minutes, 31 seconds

 

2:07:31

 

Note: If there is only one number, remember to put in a zero to hold the tens place.

 

 

• 3 hours, 56 minutes, 42 seconds

 

 

 

 

 

 

• 12 hours, 2 minutes, 29 seconds

 

 

 

 

 

 

• 1 hour, 23 minutes, 54 seconds

 

 

 

 

 

 

 

• 6 hours, 7 minutes, 39 seconds

 

 

 

 

 

 

 

• 11 hours, 41 minutes

 

 

 

 

 

 

 

 

• 7 hours, 14 minutes, 59 seconds

 

 

 

 

 

 

• 21 hours, 36 minutes

 

 

 

 

 

 

 

• 1 hour, 51 minutes, 41 seconds

 

 

 

 

 

 

 

• Answers to Exercise One
  5 hours, 18 minutes, 10 seconds.

 

 

 

 

 

 

 

 

 

 

a)	3:56:42	b)	12:02:29	c)	1:23:54
d)	6:07:39	e)	11:41	f)	7:14:59
g)	21:36	h)	1:51:41	i)	5:18:10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

and P.M.

 

You need to go to the dentist at 9:00 a.m. This is in the morning because of the a.m. The abbreviation a.m. means ante meridiem or before noon. We use a.m. for any times between 12 midnight and 12 noon.

 

You are meeting friends for dinner at 6:00 p.m. This is at night because of the p.m. The abbreviation p.m. means post meridiem or after noon. We use p.m. for any times between 12 noon and 12 midnight.

 

 

Example:You catch the bus at 7 o’clock in the morning.

The time would be written as 7:00 a.m.

 

 

Example:You are meeting friends to go fishing at 6:30 at night.

The time would be written as 6:30 p.m.

 

 

 

Exercise TwoWrite the following times using a.m. or p.m. Check your

work using the answer key at the end of the exercise.

 

Example:The sun rises at 7:07 in the morning.

 

7:07 a.m.

 

 

• Your shift at work starts at 8:30 in the morning.

 

 

 

 

• Your class starts at 1:00 in the afternoon.

 

 

 

 

• Your son has soccer practice at 4:00 in the afternoon.

 

 

 

 

• Answers to Exercise Two
  You catch your bus at 6:15 in the morning.

 

 

 

 

• You need to go to the doctor at 3:20 in the afternoon.

 

 

 

 

• You eat dinner at 6:30 in the evening.

 

 

 

 

• Your children go to bed at 8:45 in the evening.

 

 

 

 

• Your alarm goes off at 5:50 in the morning.

 

 

 

 

• Your friend called at 11:25 in the morning.

 

 

 

 

 

 

 

 

 

 

 

 

a)	8:30 a.m.	b)	1:00 p.m.	c)	4:00 p.m.
d)	6:15 a.m.	e)	3:20 p.m.	f)	6:30 p.m.
g)	8:45 p.m.	h)	5:50 a.m.	i)	11:25 a.m.

 

 

 

 

 

 

 

Rounding Time

 

When you round time, if the minutes are more than thirty, you round up to the next number of hours. If the minutes are less than thirty, you remain at the same number of hours.

 

Example:If it took 45 minutes to drive to school, you would round that to one hour because 45 minutes is greater than 30 minutes.

 

 

Example:If it took one hour and 15 minutes to get to school by bus, you would round that to one hour because 15 minutes is less than 30 minutes.

 

 

Example:If it took 8 hours and 37 minutes to complete the painting job, you would round that to 9 hours because 37 minutes is greater than 30 minutes.

 

 

 

Exercise ThreeRound the following times to the nearest hour. Check

your work using the answer key at the end of the exercise.

 

Example:The movie lasted 3 hours and 13 minutes.

 

3 hours

 

 

• You needed 2 hours and 15 minutes for grocery shopping.

 

 

 

• It took 1 hour and 50 minutes to cook dinner.

 

 

 

• You drove for 9 hours and 23 minutes.

 

 

 

• Your baby slept for 1 hour and 47 minutes.

 

 

 

 

 

• Answers to Exercise Three
  You visited with friends for 3 hours and 11 minutes.

 

 

 

 

• It took 2 hours and 35 minutes to play the hockey game.

 

 

 

 

• You rode on the bus for 1 hour and 28 minutes.

 

 

 

 

• You walked to work in 38 minutes.

 

 

 

 

• How long does it take you to get to school?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a)	2 hours	b)	2 hours	c)	9 hours
d)	2 hours	e)	3 hours	f)	3 hours
g)	1 hour	h)	1 hour	i)	check with your instructor

 

 

 

 

 

 

 

 

 

Topic C: Shapes

 

 

Circle

 

The circle is a shape we all know.

 

 

 

 

 

These objects suggest the idea of a circle.

 

rim of coffee cups and glassestop of lamp shades top of cans of foodcompact discs

the ends of pipes and hoses (called the cross-section) the coloured part of your eye (the iris)

 

Add some examples of your own.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Triangle

 

A triangle is a three-sided shape. Triangles have three sides and three angles.

 

 

 

 

Draw some different sized triangles here.

 

 

 

 

 

Rectangle

 

 

A rectangle is a four-sided shape. Rectangles have four sides and four right angles (square corners).

 

 

Can you think of anything that has a rectangle shape? Write it here.

 

 

 

 

 

 

 

 

Squares

 

A square is a special kind of rectangle. Squares have square corners and four sides are the same length

 

 

 

Can you think of anything that has a square shape? Write it here.

 

 

 

 

Exercise OneThe following things give the idea of a shape. Write

the nameof the shape in each blank. Then draw the shape.

 

 

Example:A cookie is a circle.

 

 

 

• A door is a .

 

 

 

 

• This page is a .

 

 

 

 

 

• A yield sign is a .

 

 

 

 

 

 

 

 

• A room is usually a .

 

 

 

 

 

• A coin is a .

 

 

 

 

 

• A ten dollar bill is a .

 

 

 

 

 

• The rim of a jar is a .

 

• This warning sign is a .

 

 

 

 

 

 

• Answers to Exercise One
  A pizza is a .

 

 

 

 

 

 

 

 

 

 

a)	rectangle	b)	rectangle	c)	triangle
d)	rectangle	e)	circle	f)	rectangle
g)	circle	h)	triangle	i)	circle

 

 

 

 

 

 

 

 

Exercise TwoLook around the room and find each of the following shapes.

Write the name on the line. Have your instructor check your answers.

 

 

Example:A rectangle door

 

 

• A circle

 

 

 

 

• A rectangle

 

 

 

 

• A square

 

 

 

 

• A triangle

 

 

 

 

 

 

Exercise ThreeCircle the correct shape in each line. Have your

instructor check your answers.

 

• A rectangle.

 

 

 

 

 

 

 

 

 

 

 

 

 

• 
  A circle

 

 

 

 

 

• A square

 

 

 

 

• A triangle

 

 

 

 

 

 

Exercise FourWhat shape are the following things? Write triangle, square, rectangle or circle on the line.

 

 

 

a)b)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answers to Exercise Four
c)d)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e)f)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g)h)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) circle	b)triangle	c)rectangle	d) square	e)rectangle or triangle
f) circle	g) square	h) rectangle

 

 

 

Unit 4 Review – Estimating, Time, Shapes

 

You will now practice all the skills you learned in Unit 4. Check your work using the answer key at the end of the review.

 

Estimate the following sums. Be sure to round to the nearest 10 before adding.

 

a)23	Estimate:	b)68	Estimate:
+ 32		+ 17

 

 

 

 

 

c)34	Estimate:	d)42	Estimate:
+ 28		+ 53

 

 

 

 

 

e)74	Estimate:	f)33	Estimate:
+ 24		+ 28

 

 

 

 

 

 

g)17	Estimate:	h)27	Estimate:
+ 42		+ 18

 

 

 

 

• Estimate the following sums. Be sure to round to the nearest 10 before adding.

 

a) 625	Estimate:	b) 432	Estimate:
+ 254		+ 325

 

 

 

 

 

 

 

 

 

c) 328	Estimate:	d) 529	Estimate:
+ 163		+ 248

 

 

 

 

 

 

 

 

e) 536	Estimate:	f)867	Estimate:
+ 137		+ 215

 

 

 

 

 

 

 

 

g) 843	Estimate:	h) 435	Estimate:
+ 107		+ 127

 

 

 

 

Estimate the following answers. Be sure to round to the nearest 10 before subtracting.

 

a)43	Estimate:	b)64	Estimate:
─ 28		─ 25

 

 

 

 

 

c)73	Estimate:	d)83	Estimate:
─ 47		─ 24

 

 

 

 

 

e)68	Estimate:	f)54	Estimate:
─ 28		─ 22

 

 

 

 

 

g)67	Estimate:	h)85	Estimate:
─ 29		─ 29

 

 

 

 

Estimate the following answers. Be sure to round to the nearest 10 before subtracting.

 

 

a) 625	Estimate:	b) 908	Estimate:
─ 407		─ 413

 

 

 

 

 

 

 

c) 976	Estimate:	d) 882	Estimate:
─ 134		─ 257

 

 

 

 

 

 

e) 572	Estimate:	f)908	Estimate:
─ 154		─ 713

 

 

 

 

 

g) 965	Estimate:	h) 988	Estimate:
─ 702		─ 254

 

 

 

 

• Write the following times in standard format.

 

 

• 10 hours, 20 minutes, 12 seconds

 

 

 

 

 

• 8 hours,45 minutes, 6 seconds

 

 

 

 

 

• 5 hour, 32 minutes, 45 seconds

 

 

 

 

 

• 1 hour, 7 minutes, 28 seconds

 

 

 

 

 

• 12 hours, 55 minutes

 

 

 

 

 

• 6 hours, 5 minutes, 39 seconds

 

 

 

Write the following times using a.m. or p.m.

 

• The movie starts at 6:45 in the evening.

 

 

 

• Your friend calls and wakes you up at 3:23 in the morning.

 

 

 

• Your dog barks at the mailman at 2:35 in the afternoon.

 

 

 

• Your morning break is at 10:15.

 

 

 

 

 

Round the following times to the nearest hour.

 

• You took a walk for 47 minutes.

 

 

 

 

• Your round trip (there and back) to the mall took 2 hours and 12 minutes.

 

 

 

 

Circle the correct shape in each line.

 

• A triangle

 

 

 

 

 

• A square

 

 

 

 

 

 

 

The following things give the idea of a shape. Write the name of the shape in each blank.

 

 

• A window is a .

 

 

 

 

 

 

 

 

• A checkerboard is a .

 

 

 

 

 

• A watch is a .

 

 

 

 

 

• A yield sign is a .

 

 

 

 

 

J.Word Problems. Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting. Remember to circlethe information and underline what is being asked.

 

 

 

 

 

 

 

• The Sears Tower is 443 metres tall. It has a 105 metre TV antenna on top.

Estimate the height of the building and the antenna.

 

 

 

 

 

 

 

 

• A restaurant used 76 kilograms of potatoes and 68 kilograms of meat.

Estimate how many kilograms of potatoes and meat the restaurant used altogether.

 

 

 

 

 

 

 

 

 

 

 

• Paolo’s father weighs 78 kilograms. Paolo weighs 29 kilograms. Estimate how much more Paolo’s father weighs.

 

 

 

 

 

 

 

 

 

 

• Chi bought 54 litres of gasoline on Tuesday. He bought 38 litres of gasoline on Friday. Estimate how many litres of gas he bought altogether.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a)50b)90c)60d)90e)90f)60g)60h)50B.a)880b)760c)490d)780e)680f)1 090g)950h)570C.a)10b)30c)20d)60e)40f)30g)40h)60D.a)220b)500c)850d)620e)420f)200g)270h)740E.a)10:20:12b)8:45:06c)5:32:45d)1:07:28e)12:55f)6:05:39F.a)6:45 p.m.b)3:23 a.m.c)2:35 p.m.d)10:15 a.m.G.a)1 hourb)2 hours
Answers to Unit 4 Review A.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H.

Have your instructor check these.

 

I. a)	rectangle	b) square	c)	circle
d)	triangle
J. a)	550 metres	b) 150 kilograms	c)	50 kilograms
d)	90 litres

 

 

 

 

 

 

 

 

 

 

 

 

 

CONGRATULATIONS!!Now you have finished Unit 4.TEST TIME!Ask your instructor for the Practice Test for this unit.Once you’ve done the practice test, you need to do the unit 4 test.Again, ask your instructor for this.Good luck!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Book 1 Review

 

You will now practice all the skills you learned in Book 1. Check your work using the answer key at the end of the review.

 

If you can‟t remember how to do a question, go back to the lesson on this topic to refresh your memory. The unit and topic for where each question came from is listed next to the question.

Example: 1-B means Unit 1, Topic B

 

1-B

• Count the number of things in each picture. Write the number and word name.

 

 

Numeral: Word Name
Numeral: Word Name
a)b)

 

 

 

 

 

 

 

 

 

 

 

●●● ● ●● ● ●
●●●●●●
c)d)

 

 

 

 

 

 

Numeral:Numeral:

Word Name:Word Name:

 

 

1-C

• Fill the blanks to make each sentence true. Draw a picture for b and d.

 

• 58 means tens and ones.

 

 

 

 

• 18 means tens and ones. Draw your picture below.

 

 

 

• 471 means hundreds, tens, ones.

 

 

• 127 means hundreds, tens, ones. Draw your picture below.

 

 

 

Write the place value name (ones, tens, hundreds) for each underlined digit.

 

a)564 b)239

 

 

c)986 d)534

 

 

 

Name the digit for the place value named from the number below.

 

5 782

 

• tens b)hundreds

 

 

Write the word names for the numbers.

 

a)17

 

 

b)342

 

 

c)625

 

 

Write numerals for these word names.

 

• seventy-five b) nineteen

 

c) seven hundred fifty d) nine hundred five

 

e) eight hundred seventy-three

 

 

1-D

• Place a box around the larger number.

a) 452245b) 678687

Arrange these numbers in order from smallest to largest.

a) 8666888668686866866

 

 

 

 

 

 

 

 

 

b) 2332322333332322232

 

 

 

 

 

Write <, > or = in each blank as needed.

 

a) 23 34	b)	118 118
c) 667 576	d)	405 450

 

 

 

1-E

• Round each number to the nearest 10.

 

a)52 b) 123

 

c)178 d) 89

 

 

 

 

Word Problems. For each problem, round the numbers to the nearest 10.

 

• The polar bear can weigh 1 002 kilograms, a koala bear can weigh 14 kilograms, a panda bear can weigh 113 kilograms, a kodiak bear can weigh 679 kilograms and a black bear can weigh 272 kilograms. Round each number to the nearest 10.

 

Bear	Number	Rounded Number
Polar bear
Koala bear
Panda bear
Kodiak bear
Black bear

 

 

 

 

How much money do you have?

 

a)

 

How much money to you have? cents

 

 

b)

 

How much money do you have? dollars

 

 

 

 

2-A

• Check out your addition facts.

 

a)0	b)2	c)8	d)1
+ 8	+ 3	+ 2	+ 4

 

 

 

 

 

 

e)5	f)9	g)6	h)3
+ 0	+ 5	+ 7	+ 6

 

 

 

 

 

 

 

Add across or horizontally.

 

a)	7	+	4	=	b)	3	+	0	=
c)	2	+	9	=	d)	9	+	8	=
e)	6	+	2	=	f)	5	+	6	=
g)	8	+	9	=	h)	4	+	2	=

 

 

• Find the sums.

 

a)4	b)2	c)4
5	7	2
+ 3	+ 8	+ 8

 

 

 

 

 

d)4	e)3	f)6
6	2	1
+ 7	+ 3	+ 5

 

 

 

 

• Find the sums.

 

a)5	b)2	c)3
2	3	0
3	4	1
+ 4	+ 7	+ 2

 

 

 

 

 

 

 

 

 

 

d)2	e)5	f)4
3	1	3
1	3	2
+ 2	+ 2	+ 6

 

 

 

 

 

Find the perimeter of the shape. Be sure to put the unit of measure in your answer. Write the name of the shape below the picture.

 

• 
  3 metres

 

2 metres

 

 

 

 

 

 

 

 

 

 

b)

 

5 metres3 metres

 

 

 

4 metres

 

 

 

 

 

 

c)

 

2 metres

 

 

 

 

 

 

 

Find the sums.

 

a)46	b)35	c)82
+ 33	+ 93	+ 56

 

 

 

 

 

d)91	e)740	f)638
+ 17	+ 859	+ 610

 

 

 

 

 

 

g)521h)970

+ 848+ 625

 

 

 

 

 

 

 

Word Problems.

 

• Seven cars were in the first row. Four cars were in the second row. How many cars are there in the first two rows?

 

 

 

 

 

 

 

• One bicycle stored ordered 56 bikes. Another store ordered 72 bikes. How many bikes did both stores order?

 

 

 

 

 

 

 

 

 

• A mail carrier walked 51 kilometres in a week. The next week she walked 48 kilometres the next week. How far did she walk in two weeks?

 

 

 

 

 

 

 

 

 

 

3-A

• Check out your subtraction facts.

 

a)9	b)6	c)17	d)14
− 5	− 3	− 8	− 7

 

 

 

 

 

 

e)14g)11g)12h)9

 

 

 

 

 

 

U.Subtract across or horizontally.   a)4 − 1 =	b)	8 − 2 =
c)17 − 8 =	d)	11 − 6 =
e)6 − 4 =	f)	11 − 3 =
g)10 − 1 =	h)	13 − 8 =

 

 

 

 

3-B

• Find the differences.

a)76b)84c)95

 

 

 

 

d)69e)852f)789

 

 

 

 

 

g)938h)959

 

 

 

 

 

Word Problems. Solve each work problem.

 

• There were 18 roses in a bouquet. Milton gave 9 roses away. How many roses were left?

 

 

 

 

 

 

 

 

• A city has 89 mail carriers. One day only 54 were at work. How many were not at work?

 

 

 

 

 

 

 

 

 

 

• Mariko and Stefan went 5-pin bowling. Mariko scored 274 points while Stefan scored 152. How many more points did Mariko score?

 

 

 

 

 

 

 

4-A

• Estimate the following answers. Be sure to round to the nearest 10 before adding.

 

a)81	Estimate:	b)53	Estimate:
+ 74		+ 39

 

 

 

 

 

c)43	Estimate:	d) 733	Estimate:
+ 68		+ 719

 

 

 

 

 

e) 907	Estimate	f)623	Estimate:
+ 448		+ 914

 

 

 

 

 

• Estimate the following answers. Be sure to round to the nearest 10 before subtracting.

 

• 82Estimate:b)67Estimate:

 

 

 

 

 

 

 

 

c)61Estimate:d) 968Estimate:

 

 

 

 

 

 

 

 

e) 577Estimatef)742Estimate:

 

 

 

 

 

 

 

Word Problems. Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting.

 

• Mr. Han worked in his store for 33 years. Before owning a store, he had worked in a bank for 24 years. How many years has Mr. Han worked?

 

 

 

 

 

 

 

 

 

 

 

• The longest span of the Lions Gate Bridge in Vancouver is 473 metres. The longest span of the Confederation Bridge in Prince Edward Island is 247 metres. What is the difference?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4-B

AA.Write the following times in standard format.

 

• 3 h, 22 min, 51 s

 

 

 

 

• 8 h, 38 min, 9 s

 

 

 

 

c) 10 h, 18 min, 23 s

 

 

 

 

d) 7 h, 43 min, 34 s

 

 

 

 

BB.Write the following times using a.m. or p.m.

 

• The movie begins at 8:30 in the evening.

 

 

 

• The coffee shop opens at 5:15 in the morning.

 

 

 

 

• The shopping mall closes at 10:00 at night.

 

 

 

 

CC.Round the following times to the nearest hour.

 

• The running time for the movie was 2 hours and 25 minutes.

 

 

 

 

 

 

 

• It took 5 hours and 53 minutes to go the hockey and return home after the game.

 

 

 

 

DD.The following things give the idea of a shape. Write the name of the shape in each blank.

 

 

• A Christmas tree is a .

 

 

 

• A swimming pool is a .

 

 

 

• A quarter is a .

 

 

 

 

 

EE.What shape are the following things. Write triangle, square, rectangle or circle on the line.

 

• b)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answers to Book 1 Review A.

• 4, fourb) 3, threec)8, eightd) 6, six

 

B.

a) 5 tens, 8 onesb) 1 ten, 8 onesc)4 hundreds, 7 tens, 1 one

d) 1 hundred, 2 tens, 7 ones

 

C.

a)tensb)onesc)tensd) hundreds

 

D.

a)8b)7

 

E.

a)seventeenb)three hundred forty-twoc)six hundred twenty-five

 

F.

a)75b)19c)750d) 905e) 873

 

452
687
G.

a)b)

 

H.

a)66 86 668 686 866 868 886b) 23 33 223 232 322 323 332

 

I.

a)<b)=c)>d) <

 

J.

a)50b)120c)180d) 90

 

K.

a)

Bear	Number	Rounded Number
Polar bear	1 002	1 000
Koala bear	14	10
Panda bear	113	110
Kodiak bear	679	680
Black bear	272	270

 

 

 

 

 

L. a)	40 cents	b)	12 dollars
M. a)	8	b)	5	c)	10	d)	5	e)	5
f)	14	g)	13	h)	9
N. a)	11	b)	3	c)	11	d)	17	e)	8
f)	11	g)	17	h)	6
O. a) 12		b) 17	c)14	d) 17		e)8	f)12

P.

a) 13b) 16c)6d) 8e)11f)15

 

Q.

• 10 metres, rectangleb) 12 metres, trianglec)8 metres, square

 

R. a)	79	b)	128	c)	138	d)	108	e)	1 799
f)	1 248	g)	1 369	h)	1 595
S.
a)	11 cars	b)	128 bikes	c)	99 kilometres
T. a)	4	b)	3	c)	9	d)	7	e)	5
f)	9	g)	7	h)	6
U. a)	3	b)	6	c)	9	d)	5	e)	2
f)	8	g)	9	h)	5
V. a)	51	b)	41	c)	21	d)	53	e)	531
f)	139	g)	137	h)	427

 

 

 

 

 

 

 

 

W.a)9 rosesb)35 mail carriersc)122 pointsX.a)80 + 70 = 150d)730 + 720 = 1 450b) 50 + 40 = 90e)910 + 450 = 1 360c)40 + 70 = 110f)620 + 910 = 1 530Y.a)d)b)e)c)f)Z.a)50 yearsb) 220 metresAA.a)3:22:51b)8:38:09c)10:18:23d) 7:43:34BB.a)8:30 p.m.b)5:15 a.m.c)10:00 p.m.CC.a)2 hoursb)6 hoursDD.a)triangleb)rectanglec)circleEE.a)rectangleb)square

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Glossary

 

addends The numbers to be added together in an addition question. In 3 + 5 = 8, the addends are 3 and 5.

 

axis Any straight line used for measuring or as a reference.

 

balance Balance has many meanings. In money matters, the balance is the amount left. It might be the amount left in a bank account (bank balance) or it might be the amount you still must pay on a bill (balance owing).

 

cancelled cheque A cheque that has been cashed. The cheque is stamped, or cancelled, so it is no longer negotiable.

 

circumference The distance around a circle; the perimeter of a circle.

 

commission Salespeople may be paid a percentage of the money made in sales. The commission is part or all their earnings.

 

common fractions eg, , ,

 

cross multiply In a proportion, multiply the numerator of the first fraction times the denominator of the second fraction. Then multiply the denominator of the first fraction times the numerator of the second fraction. In a true proportion, the products of the cross multiplication are equal.

 

denominator The bottom number in a common fraction; tells into how many equal parts the whole thing has been divided.

 

diameter The distance across a circle through its centre.

 

difference The result of a subtraction question, the answer. Subtraction gives the difference between two numbers.

 

digit Any of the ten numerals (0 to 9) are digits. This term comes from our ten fingers which are called digits. The numerals came to be called “digits” from the practice of counting on the fingers!

 

discount An amount taken off the regular cost. If something is bought “at a discount” it is bought at less than the regular price.

 

divide To separate into equal parts.

 

dividend The number or quantity to be divided; what you start with before you divide.

 

 

 

divisor The number of groups or the quantity into which a number (the dividend) is to be separated.

 

equal = The same as

 

equation A mathematical statement that two quantities are equal. An equation may use numerals with a letter to stand for an unknown quantity. 6 + Y = 9

 

equivalent Equal in value; equivalent numbers (whole or fractions) can be used interchangeably; that is, they can be used instead of each other.

 

estimate Make an approximate answer. Use the signto mean approximately equal.

 

factors The numbers or quantities that are multiplied together to form a given product.

52 = 10, so 5 and 2 are factors of 10.

 

fraction Part of the whole; a quantity less than one unit.

 

horizontal in a flat position; we are horizontal when we lie in a bed. A horizontal line goes across the page.

 

improper fraction A common fraction with a value equal to or more than one.

 

infinite Without end, without limit.

 

invert To turn upside down.

 

like fractions With the same denominators.

 

lowest terms When the terms of a common fraction or ratio do not have a common factor (except 1), the fraction or ratio are in lowest terms (also called simplest form).

 

minuend The first number in a subtraction question.

 

mixed number A whole number and a common fraction. 1

 

mixed decimal A whole number and a decimal fraction. 1.75

 

multiple If a certain number is multiplied by another number, the product is a multiple of the numbers. Think of the multiplication tables. For example, 2, 4, 6, 8, 10, 12, 14. . . are multiples

of 2.

 

multiplicand The number to be multiplied.

 

multiplier The number you multiply by.

 

 

 

negotiable Something which can be cashed, that is, exchanged or traded as money.

 

numbers Numbers represent the amount, the place in a sequence; number is the idea of quantity or order.

 

numerals The digits 1,2,3,4,5,6,7,8,9,0 are also called numerals. These ten digits are combined to make infinite numerals. Digits are like the letters, numerals are like the words and numbers are the meaning.

 

numerator The top number in a common fraction; the numerator tells how many parts of the whole thing are being considered.

 

overdrawn If the value of the cheques or money taken from a bank account is higher than the amount of money in the account, then the account is overdrawn. The account is “in the hole” or “in the red” are expressions sometimes used.

 

parallel Two objects or lines side by side, never crossing and always the same distance from each other. Railway tracks are parallel, the lines on writing paper are parallel.

 

percent % For every one hundred.

 

perimeter The distance around the outside of a shape.

 

place value We understand numbers by the way the digits (numerals) are arranged in relationship to each other and to the decimal point. Each position has a certain value. Our number system is a decimal system. The place value is based on ten.

 

prime number A number that can only be divided evenly by itself and 1.

 

product The result of a multiplying question, the answer.

 

proper fraction A common fraction with a value less than one.

 

proportion Generally, proportion is a way of comparing a part of something to the whole thing. Eg. his feet are small in proportion to his height. In mathematics, proportion is used to describe two or more ratios that are equivalent to each other.

 

quotient The result of a division question; the quotient tells how many times one number is contained in the other.

 

radius The distance from the centre of a circle to the outside of the circle.

 

ratio The relationship between two or more quantities. Eg. the ratio of men to women in the armed forces is 10 to 3 (10:3)

 

 

 

 

 

reciprocal A number, when multiplied by its reciprocal, equals 1. To find the reciprocal of a common fraction, invert it.= 1

 

reduce Write a common fraction in lowest terms. Divide both terms by same factor.

 

remainder The amount left when a divisor does not divide evenly into the dividend. The remainder must be less than the divisor.

 

sign In mathematics, a symbol that tells what operation is to be performed or what the relationship is between the numbers.

+plus, means to add

–minus, means to subtract multiplied by, “times” divided by, division

=equal, the same quantity as

not equal approximately equal

<less than

>greater than

less than or equal to greater than or equal to

 

simplify See reduce.

 

subtrahend The amount that is taken away in a subtraction question.

 

sum The result of an addition question, the answer to an addition question.

 

symbol A written or printed mark, letter, abbreviation etc. that stands for something else.

 

term a) A definite period of time, such as a school term or the term of a loan.

• Conditions of a contract; the terms of the agreement. c) In mathematics, the quantities in a fraction and in a ratio are called the terms of the fraction or the terms of the ratio. In an algebra equation, the quantities connected by a + or – sign are also called terms.

 

total The amount altogether.

 

transaction One piece of business. A transaction often involves money. When you pay a bill, take money from the bank or write a cheque, you have made a transaction.

 

unit Any fixed quantity, amount, distance or measure that is used as a standard. In mathematics, always identify the unit with which you are working. Eg. 3 km, 4 cups, 12 people,

$76, 70 books, 545 g.

 

unit price The price for a set amount. Eg. price per litre, price per gram.

 

Fundamental Mathematics257

 

unlike fractions Fractions which have different denominators.

vertical in an up and down position; we are vertical when we are standing up. On a page, a vertical line is shown from the top to the bottom of the page.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

258Book 1