u n i t
2
W h o le N u m b e r s
where shall we go?
l e a r n i n g G o a l s
recognize and read numbers from 1 to 10,000
read and write numbers in standard form, expanded form, and written form use place value to represent numbers
compare and order numbers estimate sums and
differences
add and subtract 3-digit numbers mentally add 4-digit numbers
subtract a 3-digit number from a 4-digit number
pose and solve problems
A n g e lie is a travel writer.
Sh e w rites articles for
n ew sp ap ers and m agazines.
A n g e lie visits different places all o ver th e w orld.
Gulf of S t Lawrence
Corner Brook
d eer Lak« Gander saint. Anthony
Saint John's
Distances in Kilometres
Corner Brook. Deer Lake. Gander. Saint. Anthony. Saint. John’s Corner Brook —
Deer Lake —
Gander Saint. Anthony S aint. John’s
Suppose Angelie travelled from Sa
in
t John's to
Saint Anthony through Deer Lake.
How could you find out how far she travelled?
Suppose Angelie is in Gander.
How could you find out if it's farther to Sa
in
t John's
or to Corner Brook?
W hat else do you know from this map?
K e y W o rd s
expanded form
standard form
L E S S O N
1
Whole Numbers to 10,000
The largest marching band ever assembled had
4,526 members.
There were students from 52 different school bands.
explore
How many different ways can you show 4,526? Draw a picture to record each w ay you find.
S h o w a n d S h a r e
Share your pictures with another pair of students.
How do you know each picture shows 4526?
explore
The largest marching band had 1,342 majorettes, flag bearers, and drill team members.
The rest of the band were musicians.
You can represent the number 1,342 in different ways.
Use Base Ten Blocks.
To show the number 1,342:
Use a place-value chart. To show the num ber 1,342:
Thousands Hundreds Tens Ones
1 3 4 2
1,000 300 4 2
You can w rite the num ber 1,342 as the sum of the thousands, hundreds, tens, and ones.
1,342 = 1,000 + 300 + 40 + 2
Use words.
This is
expanded form.
1,342 is one tho usan d
th re e hundred fo rty -tw o ,
The num ber 1,342 is w ritten in
standard form.
Every digit has a place value, depending on its position.
practice
1
.
The Canada - U.S border is about 8,893 km long from west to east W rite this num ber in words.2. The M ackenzie River is the longest river in Canada.
It is about 4,241 km long.
Use Base Ten Blocks to show this number. Draw pictures of the blocks.
3
.
M ount Logan, Yukon, is the highest m ountain in Canada. It is about 5,959 m high.Use expanded form to show this number.
numbers every day
Mental Math
Add.
Which strategies did you use?
20
+12
2 + 4 + 8 + 64. Write each number in standard form. a)
b)
5. Write each number in question 4 in words.
6
.
Write each number in standard form.a) 5,000 + 600 + 40 + 3 b) 9,000 + 700 + 80 c) 3,000 + 200 + 9
d) 8,000 + 20 e) 7,000 + 5 f ) 4,000 + 70 + 3
7. Write each number in standard form. a) one thousand seven hundred fifty-four b) nine thousand nine hundred ninety-nine c) four thousand seventy
d) six thousand five hundred three
8. Write each number in expanded form
a) 5,352 b) 7,056 c) 8 ,104 d) 4,370
9. a) Press: 578. Make the screen show 508. How did you do it?
b) Explain how to get each target number from each start number.
10
.
Tyler wrote 2,005 in words as tw o hundred five. Explain Tyler's error.Show your work.
Start 394 156 4,689
Target 94 106 4,009
Reflect
Write the num ber that is halfway between the two given numbers. L E S S O N
2
Rounding Numbers
T here a re a b o u t 5,000
people here today.
How did Athina estimate the number of people at the gam e?
explore
You will need a copy of these num ber lines.
Use the number lines to answer each question. • Is 57 closer to 50 or 60? • Is 331 closer to 300 or 400? • Is 6,500 closer to 6,000 or 7,000? Show your work.
S h o w
a n d
S h a r e
Share your answers with a classmate.
connect
There w ere 2,371 people at a baseball game.
The num ber 2,371 is exact because it is a count of the num ber of people. To w rite an estim ate for the num ber o f people at the game,
you can
round.
2,000 2,371 2,500 3,000
Round 2,371 to the nearest hundred. Look at the hundreds: 23 hundreds
Look at 71. It is closer to 100 than to 0; so add 1 hundred. So, 2,371 rounds to 24 hundreds, or 2,400.
2,300 2,350 2,371 2,400
Round 2,371 to the nearest ten. Look at the tens: 237 tens
Look at 1. It is closer to 0 than to 10. So, 2,371 rounds to 237 tens, or 2,370.
2,370 2,371 2,375 2,380
Look at the num ber lines above.
To round the m iddle num ber on each num ber line, you round up. To the nearest thousand, 2,500 rounds to 3,000.
To the nearest hundred, 2,350 rounds to 2,400. To the nearest ten, 2,375 rounds to 2,380.
p r a c tic e
Use a number line w hen it helps.
1
.
The longest country line dance had 6,275 people. Round this number to the nearest thousand.2. The biggest game of Pass the Parcel had 3,918 students. Round this number to the nearest hundred.
3. The biggest game of musical chairs began with 8,238 students.
Round this number to the nearest ten.
4. Round to the nearest thousand. How did you get each answer? a) 2,376 b) 7,891
c) 6,300 d) 4,735 e) 1,999 f) 3,087 g) 5,501 h) 9,498
5. Round to the nearest hundred. a) 9,876 b) 1,509
c) 3,055
e) 5,465 f ) 8,230 g) 4,811 h) 1,984
6. Round to the nearest ten. How did you get each answer? a) 2,347 b) 6,708
c) 8,973 d) 7,597
7. W rite three numbers that round to 600 w hen rounded to the nearest hundred.
8. W rite three numbers that round to 6,000 w hen rounded to the nearest thousand.
numbers every day
Num ber Strategies
Order these numbers from least to greatest.
Use this table for questions 9 to 12.
Attendance at Silver Broom Tournament.
Day Number of People
Wednesday 4,652
Thursday 5,373
Friday 5,546
9. Round each number to the nearest thousand.
10
.
Round each number to the nearest hundred.11
. Suppose a person wants to know about how many people attended each day. W ould you give her the answer to question 9 or question 10? Explain.12
.
The Saturday attendance was 5,968.a) Round this num ber to the nearest thousand and nearest hundred.
W h at do you notice?
b)
Write another number that rounds to the same number when rounded to the nearest hundred and nearest thousand.13. A number is rounded to the nearest ten, nearest hundred, and nearest thousand. All the rounded numbers are 5,000.
W hat was the number before it was rounded? How many possible numbers are there?
Show your work.
Reflect
Is it possible that a 3-digit num ber rounds to 1,000? Explain.
At Home
Look through newspapers and magazines.
Find examples of large numbers. Write each number.
L E S S O N
Comparing and Ordering Numbers
explore
Use the digits 3,5,7,8.
W rite 3 different num bers using all these digits. Order the num bers from greatest to least. Show your work.
S h o w a
n
d
S h a r e
Share your numbers and ordering with another pair of students. Take turns to describe the strategy you used for ordering.
W hat other strategies could you use to order the numbers?
To order the numbers 2 ,143, 2,413, and 1,423 from least to greatest:
Represent each number with Base Ten Blocks.
2 ,143
2,413
1,423
Both 2,143 and 2,413 have 2 th o usands.
Compare their hundred flats. 2,143 has the fewest
So. 2 ,1 4 3 less than 2,413.
Compare the thousand cubes. 1,423 has the fewest
so, 1,423 is the least number
Write each number in a place-value chart.
Thousands Hundreds Tens Ones
2 1 4 3
2 4 1 3
1 4 2 3
1,423 has the fewest
thousands, so it is the least number.
Both 2 ,143 and 2,413 have 2 thousands.
Compare their hundreds. 100 is less than 400. So, 2 ,143 is less than 2,413.
You can use less than and greater than to show order. 1,423 less than 2 ,143 means
1,423 is less than 2 ,143.
2,413 greater than 2 ,143 means 2,413 is greater than 2 ,143.
The a r r o w head
p o in ts t o the
smaller nu m b e r .
5 g
reater th
an
2
Use a number line.
Mark a dot for each number on a number line.
1,000
1,423
1,500 2,000
2,143 2,413
2,500 3,000
Read the numbers from left to right. From least to greatest: 1,423, 2,143, 2,413
practice
1
.
The Canadian Armed Forces have 80 F-18 Hornets. The US Navy has 200. W hich has more F-18's? How do you know?numbers every day
Mental Math
W hat happens when you add 5 to a number with
5 in the ones place? Add.
2. Copy and com plete. W rite greater, less, or equal.
How did you decide w hich sym bol to use?
a) 582 □ 589 b) 3,576 □ 3,476 c) 5,754 □ 5,745 d) 792 □ 6,082 e) 4 ,110 □ 4 ,101 f) 8,192 □ 8,291
3
.
W rite the num bers in order from least to greatest. a) 862, 802, 869 b) 7,656, 7,665, 6,7564
.
W rite the num bers in order from greatest to least. Explain how you did it.a) 9,006, 9,600, 9,060 b) 5,865, 895, 5,685
5
.
Replace each □ w ith a digit so the statem ent is true. How m any ways can you do this each tim e?a) 5,762 less than 5, 76 b) 7,998 greater than □ , 998 c) 6, □ 05 less than 6,604
6 Chantelle and Elena collect shells.
Chantelle has 4325 shells. Elena has 4,235. W ho has more shells? How do you know?
7
.
Katie, Urvi, and Blake collect stamps.Katie has 2,340 stamps; Urvi has 2,304 stamps; and Blake has 2,430 stamps.
W ho has the most stam ps? The few est stam ps? How do you know ?
8. Use the digits 3 , 7 , 8 , 9.
W rite all the 4-digit num bers greater than 7,000 and less than 8,000.
Order the num bers from least to greatest. Show your work.
Reflect
L E S S O N
4
Estimating Sums
W hen you don't need an exact answer, you estimate W hen would you use an estimate?
W hen you estimate a sum, you find a number that is close to the sum.
Do you think d o cto rs else an estimate when
they prescribe medicine?
e x p lo re
About how much will it cost to buy a TV set and a DVD player? W h at could you buy if you had $700 to spend?
Estimate to find out. Record your answers.
S h o w
a n d
S h a r e
Compare your answers with those of another pair of students. Are your estimates higher or lower? Explain.
W h at strategies did you use to estimate?
connect
An electronics store had 395 customers on Friday and 452 customers on Saturday.
About how many customers did the store have for those 2 days?
W hen a question asks "about how many," you can estimate. Estimate: 395 plus 452
You could round each num ber to the nearest 100. 395 rounds to 400.
452 rounds to 500.
Add the rounded numbers: 400 plus 500 = 900
Both num bers w ere rounded up; so this estim ate is high. The store had about 900 custom ers for the 2 days.
You could cluster.
Both 395 and 452 are about 400.
So, 395 + 452 is about 400 + 400 = 800.
The store had about 800 custom ers for the 2 days.
You could use front-end estim ation. Add the first digits of the numbers. 395 + 452 is about 300 -h 400 = 700.
For a better estim ate: R
Think about 95 plus 52. ^
This is about 100 plus 50 = 150.
So, 395 plus 452 is about 700 plus 50 = 850.
The store had about 850 custom ers for the 2 days.
Practice
1
.
How m any digits do you think each answ er will have? Explain.a)
7 1 4 plus 621 b) 3 7 5 plus 496 c) 265 plus 6612
.
Raji estim ated each sum. Is each estim ate high or low ? How do vou know?a)
5 1 7 plus 475 as 900 b) 3 1 6 plus 442 as 8003. Estim ate each sum.
4
.
Sam wants a lunch with less than 1,000 calories. He has a hamburger with 445 calories, an apple pie with 405 calories, and ice cream with 270 calories. a) About how many calories are in the lunch? b) Did Sam make his goal? Explain.5
.
Write a story problem where you would n o t use estimation to solve it.Explain w hy you would not estimate.
6, Look at these two addition questions:
449 + 449 451 +451
a) Round to the nearest hundred to estimate each sum.
b) Use a calculator.
Are the two sums as different as the estimates
make them seem? Explain.
c) How might you get a better estimate for each sum?
7
.
When you estimate to add, how can you tell if theestimated sum is greater than or less than the exact sum?
8
.
The estimated sum of tw o numbers is 600. W h at might the numbers be?Show your work.
9
.
Suppose you w ant to know if you have enough money to buy 3 items. W ould you estimate the priceof each item by rounding up or rounding dow n? Explain.
Reflect
When you estimate to add, how do you
decide if you should round to the
nearest ten or to the nearest hundred?
Use words and numbers to explain.
numbers every day
Num ber Strategies
Replace □ with greater than, less than, or =. 2 + 4 + 6 , 3 + 5 + 7
6 + 6 + 6 , 6 X 3
L E S S O N
Using Mental Math to Add
Explore
Students from two schools w ent on a field trip. There were 227 students in one school,
and 134 students in the other school. How many students w ent on the field trip?
Use mental math to find out. Record your answer.
S h o w
S h a r e
Share your strategies for adding with another pair of students.
co n n e ct
Use mental math to add: 137 + 298
Use the strategy of make a "friendly" number. 137 + 298
298 is 300 minus 2.
Add 300, then take away 2. 137 + 300 = 437
437 - 2 = 435 So, 137 + 298 = 435
Use mental math to add: 170 + 343 Make a friendly number.
170 + 30 = 200 343 - 3 0 = 313
So, 170 + 343 = 200 + 313 = 513
300 is a friendly
nnumber b ecau se it is
easy t o a d d 300.
I kno w
170 + 30 is 200, and
Use m ental math to add: 264 plus 323 Use the strategy of adding on.
Add on hundreds, add on tens, then add on ones. Start w ith the greater number.
323 plus 264
Think 323 + 200 + 60 + 4
Count on by 100 tw o times: 323, 423, 523
C o u n t on by 10 six times: 523, 533, 543, 553, 563, 573, 583 Then add 4: 583 + 4 = 587
So, 2 6 4 + 323 = 587
practice
Use m ental math.
1
.
Add. Try to use a different strategy each time.a) 179 + 234 b) 266 + 313 c) 348 + 434 d) 536 + 299
2. Add. For w hich questions w ould you "m ake a friendly num ber"? a) 263 + 328 b) 439 + 544 c) 691 + 180 d) 270 + 438
3. There w ere 168 children in the park on Friday morning. There w ere 273 children in the park on Friday afternoon.
How m any children w ere in the park on Friday?
4. Make up an addition problem you can solve using m ental math. Tell w hich strategy you used to solve the problem , and why.
Reflect
You know several strategies to add mentally. W hich is your favourite strategy?
Can you always use it?
Use words and num bers to explain.
numbers every day
M ental M ath
Add.
W hat patterns do you see? 12 + 21
L E S S O N
6
Adding 3-Digit Numbers
explore
M adhu uses the tw o sets of building blocks together How m any pieces does she have?
Use Base Ten Blocks to find out. Draw pictures to show your work.
S h o w
a n d
S h a r e
Share your results w ith another pair of students. Did you get the same answ er? Explain.
How could you solve the problem w ithout using Base Ten Blocks?
connect
One jigsaw puzzle has 357 pieces. Another puzzle has 275 pieces. How m any pieces are there altogether?
Add: 357+ 275
Use Base Ten Blocks on a place-value mat to add.
Hundreds Tens Ones
3 5 7
2 7 5
Make 10.
Hundreds Tens Ones
Trade 10 tens for 1 hundred.
Hundreds Tens Ones
6 hundreds 3 tens 2 ones
357
+275
=632
Use expanded form to add.
357 300 + 50 + 7
+ 275 + 200 + 70 + 5
500 + 120 + 12 = 620 +112 = 632
Use place value to add.
Add the ones: 12 ones Regroup 12 ones as 1 ten 2 ones.
357 + 275
2
Add the tens: 13 tens Regroup 13 tens as 1 hundred 3 tens.
1 1 357 + 275
32
Add the hundreds.
357 + 275
632
practice
1. Estim ate first.
Then add the num bers for w hich the sum w ill be greater than 600.
a] 503
+ 365
b)
817+ 179
c) 199
+ 52
d)
765+ 384
2
.
Estim ate first.Then add the num bers for w hich the sum will be less than 500.
a) 384
+ 765
b)
174+ 89
c) 305
+ 168
d ) 491
+ 256
3. A video store rented 165 more DVDs than video games. The store rented 258 video games.
How m any DVDs did the store rent?
4. The sum of tw o num bers is 756. W h at m ight the num bers be? How do you know?
Can you find more than one pair of num bers? Explain.
5. Each letter in this sum represents a different digit.
W h at is the value of each letter? How do you know ?
6
.
W hat is the greatest num ber you can add to 365 w ith o u t having to regroup in any place? Show your work.Reflect
You know 3 ways to add.
How are these ways the sam e? Different? Use words and num bers to explain.
numbers every day
Num ber Strateg ies
Use the numbers in the box. 34 ,22 ,11, 15 ,16, 41 Find two numbers whose:
l e s s o n
7
Adding 4-Digit Numbers
People set up dominoes in patterns.
So, w hen 1 domino topples, the rest topple.
explore
There are 1,275 dominoes in one set-up. There are 2 ,168 dominoes in another set-up.
How many dominoes are there altogether?
Use w hat you know about adding 3-digit numbers to solve this problem. Show your work.
S h o w
a n d
S h a r e
Share your solution with another pair of students. How did you add without using Base Ten Blocks?
connect
Scott Suko is a world famous "domino toppler." On his Website, there are photos of his set-ups. One of Scott's set-ups had 1,976 dominoes. Another set-up had 2,868 dominoes.
How many dominoes were there altogether?
Use expanded form to add.
1,976 1,000 + 900 + 70 + 6
+ 2,868 + 2,000 + 800 + 60 + 8
3,000 + 1,700 + 1 3 0 + 14
4,700
+
144 = 4,844Use place value to add.
Step 1
Add the ones: 14 ones Regroup 14 ones as 1 ten 4 ones.
I 1,976 + 2,868
4
Step 2
Add the tens: 14 tens Regroup 14 tens as 1 hundred 4 tens.
1,976 + 2,868
44
Step 3
Add the hundreds: 18 hundreds Regroup 18 hundreds as
1 thousand 8 hundreds.
I I I
1,976 + 2,868 844
Step 4
Add the thousands: 4 thousands
1 1 1
1,976 + 2,868
4,844
There are 4844 dom inoes altogether.
You estim ate to check that the sum is reasonable.
1,976 rounds to 2,000. 2,868 rounds to 3,000.
2,000 + 3,000 = 5,000
Since 4,844 rounds to 5,000, the sum is reasonable.
numbers every day
Calculator Sk ills
Use the digits 2 , 3, and 4. Find the product closest
5.
Find each sum. Estim ate to check,
a) 4 ,167
b)
3,974+ 2,534 + 4,382
c) 5,287 + 3,756
2. Add. How do you know each sum is reasonable? a) 7,865
+ 1,987
b)
3,198 + 6,751c) 9,999 + 324
3. Estim ate each sum, then add. a) 2,496
3,758 + 1,832
b)
1,976 2,627 3,499 + 1,863c) 1,285 352 6,007 + 128
4. a) W rite a story problem that could be solved by adding: 4,267 + 1,398
b)
Estim ate the sum. How did you get your estim ate?c) Is your estim ate high or low ? How do you know ?
d)
Find the sum. W h at strategy did you use?e) How do you know your answ er is reasonable? Show your work.
Three thousand six hundred forty-two people w ent to the Fall Fair on Friday.
Four thousand seven hundred ninety-five people w ent on Saturday.
How m any people w ent to the Fall Fair on these 2 days?
6. The sum of tw o 4-digit num bers is 3,456. W h at m ight the tw o num bers be? Explain.
Reflect
Think about the m ental math strategies you know for adding 3- digit numbers. W hich strategies could you use to add
L E S S O N
8
Estimating Differences
explore
An arena has 594 seats.
Three hundred eight tickets have been sold for a concert. About how many tickets are left?
Estimate to find out. Record your answer.
S h o w
and S h a r e
Compare your estimate with that of another pair of students. Did the strategies you used affect your answers? Explain.
connect
Estimate: 612 minus 387
Round each number to the nearest 100. 612 rounds to 600.
387 rounds to 400. Subtract:
600 minus 400 = 200 So, 612 minus 387 is about 200.
Make friendly numbers before
you s u b tra c t
Estimate: 387 minus 49
One number has only 2 digits, so round to the nearest ten. 387 rounds to 390.
49 rounds to 50.
Subtract: 390 minus 50 = 340 So, 387 minus 49 is about 340.
You get a better estimate if you round only one number. Round 387 to 400.
612 minus 400 = 212
So, 612 minus 387 Is about 212.
A better w ay to estimate is to round only the number you subtract.
387 minus 50 = 337
practice
1
.
Use roundinq to estimate each difference.a) 871 minus 263
b)
610 minus 429 c) 734 minus 591d)
990 minus 6252. Kyle estimated each difference. Is each estimate high or low? How do you know?
a) 576 minus 392 as 100
b)
911 minus188 as 800 c) 736 minus 187 as 6003. Estimate each difference by rounding.
How did you decide how to round each number? Explain.
a) 983 minus 407
b)
772 minus 695 c) 9 1 8 minus 75d)
447minus 2934. Charlotte looks at this survey.
She says, "About 300 more students chose biking over walking."
a) How might Charlotte have estimated? Explain.
b)
Is the estimate high or low? Explain.5. Write a subtraction problem that can be solved by estimating.
Solve the problem.
favorite exercise
biking
3 7 8 studentswalking124 students
6. The estimated difference of two numbers is 300. W hat might the numbers be?
Explain how you found the numbers.
Reflect
W hen does rounding to the nearest hundred not give a good estimate w hen you subtract?
Use words and numbers to explain.
numbers evry day
Mental M ath
Is each statement an equation? How do vou know?
5 + 7 = 1 + 2 + 9 20minus 3 = 19minus 2
L E S S O N
Using Mental Math to Subtract
explore
Anita used 354 cards to make a house of cards. Christopher used 198 to make his house.
How many more cards are in Anita's house than Christopher's?
Use mental math to find out. Record your answer.
S h o w
a n d
S h a r e
Share the strategy you used with another pair of students.
connect
Use mental math to subtract: 516 - 299 Use the strategy of "make a friendly number." Add 1 to 299 to make 300.
Add 1 to 516 to make 517. Write 5 1 6 minus 2 9 9 as:
5 1 7 minus300 = 217 So, 5 1 6 minus299 = 217
I use this stra te g y when the number
I
take aw ay is close to a friendly number.Use mental math to subtract: 347 minus 205 Use a friendly number.
Subtract 200 instead of 205.
3 4 7 minus 200= 147
Then subtract 5. 147minus 5 = 142 So, 3 4 7 minus 205 = 142
Use mental math to subtract: 432 minus 220 Use the strategy of "counting on."
For 432 minus 220, count on from 220.
Count:
220
,+ 100 320,
+ 100
420,
+ 10 430,
+ 2 432
=
212
So, 432 minus 220 = 212I ulse this strategy when there are not to o many steps to c o unt on.
practice
Use mental math.
1
.
Subtract. W hich strategy did you use each tim e?a) 536 minus 399 b) 635 minus 188 c) 822 minus 216 d) 423 minus 298
2. Subtract 715 minus 197 mentally as many different ways as you can. W hich strategy was easiest? Explain.
3. How much change will you get from $100 w hen you buy something that costs $68? How do you know?
4. The answer to a subtraction problem is 127.
Use mental math to find w hat the problem might be. How many different problems can you find?
Show your work.
5. Write a subtraction problem you can solve using mental math. Solve the problem.
reflect
Can you always use mental math to subtract?
Use words and numbers to explain the different strategies.
numbers every day
M ental M ath
Subtract.
W hat patterns do you see?
21 m
inus 12
L E S S O N
1 0
Subtracting 3-Digit Numbers
Explore
There are 430 students at Plym outh School. Two hundred sixty-five students are boys. How many are girls?
Use Base Ten Blocks to find out.
Draw pictures of the blocks to show your work.
S h o w
a n d
S h a r e
Share your answer with another pair of students. How could you have subtracted without using blocks?
connect
Glendale School has 400 students.
Two hundred eighty-six students are girls. How many are boys?
Subtract: 400 minus 286
Use Base Ten Blocks on a place-value mat to subtract.
H u n d re d s Tens Ones
2 8 6
You cannot take 6 ones from 0 ones.
Hundreds Tens Ones
2 8 6
Trade 1 ten for 10 ones.
Hundreds Ones
2 8 6
Take away 6 ones. Take away 8 tens. Take away 2 hundreds.
So, 400 minus 286 = 114 numbers every day
M ental M ath
Estimate each sum.
Which strategies did you use?
73 + 22 155 + 156 307 + 199
Use place value to subtract.
You cannot take 6 ones from 0 ones. There are no tens to regroup.
Regroup 1 hundred as 10 tens. Regroup 1 ten as 10 ones.
4 0 0
minus 2 8 6
Subtract the ones. Subtract the tens. Subtract the hundreds.
9
3 >{j 10
400
minus 2 8 6Use mental math to subtract. Count on from 286 to 400.
Count: 286,
+ 100
386,
+ 10
396,
+ 4 400
= 114
So, 400 minus 286 = 114
There are 114 boys.
You can check by adding.
The total number of boys and girls must equal the number of students.
4
00
m
inus
286
114
These t w o number s should a d d t o this number. A d d : 286 + 114
The sum should be 400.
Since 286 + 114 is 400, the answer is correct.
practice
1
.
Subtract. W h at patterns do you see in the questions and answers? a) 857 minus 100b)
857 minus 200 c) 857 minus 300d)
857 minus 4002
.
Estimate first. Then subtract the numbers for which the answer will be less than 200.a) 255
minus 76
b)
426minus 158
c) 678
minus 298
d ) 382
minus 192
3. Subtract. How do you know each answer is reasonable?
a) 565
minus 317
bl
700minus 189
c)
101
minus 96
d]
861minus 178
4. Sadiq read 315 pages. Laura read 248 pages.
5. The largest gorilla has a mass of about 275 kg. The largest orangutan has a mass of about 90 kg. W hat is the difference in their masses?
6. The world records for barrel jum ps are held by Canadians.
The longest barrel jum p by a wom an is 670 cm. The longest barrel jum p by a man is 882 cm.
How much farther is the man's jum p?
How do you know your answer is reasonable? Show your work.
7. a) The answer to a subtraction problem is 375. W h at might the problem be?
How many problems can you find?
b)
The answer to an addition problem is 375. W h at might the problem be?How many problems can you find?
m a th lin k H istory
The abacus is used for counting. You can add, subtract, multiply, and divide with it.
The abacus was invented in China over 800 years ago.
In North America, blind children are taught to use the abacus.
reflect
l e s s o n
11
Subtracting from a 4-Digit Number
explore
Matthew's school created a Website.
One day, the site had 1,531 visitors. The next day it had 867 visitors. How many more people visited the site the first day?
Use w hat you know about subtracting 3-digit numbers to solve this problem.
S h o w
a n d
S h a r e
Share your solution with another pair of students. How did you subtract w ithout using Base Ten Blocks?
explore
How many more people visited the Website on Friday than on Saturday?
Subtract: 2,031 minus 856
Use place value to subtract.
Day Visitors to Website
Friday 2,031
Saturday 856
You cannot take 6 ones from 1 one.
Regroup 1 ten as 10 ones.
Then, subtract the ones.
You cannot take 5 tens from 2 tens. There are no hundreds to regroup. So, regroup 1 thousand as
10 hundreds.
Then, regroup 1 hundred as 10 tens.
Then, subtract the tens. Subtract the hundreds. Subtract the thousands.
Check.
By adding
Add the answ er to the num ber you subtracted.
856 + 1,175
=
2,031 The sum is the number you started with. So. the answer is c o rre c t
By estim ating
2,031 rounds to 2,000. 856 rounds to 900. 2,000 minus 900 = 1100
1,100 is close to 1,175; so,
the answer is reasonable.
Practice
1. Estim ate, then subtract.
Is each answ er reasonable? Explain. a) 8,274
minus 96
b) 6,328 minus 937
c) 4,028 minus 639
2
.
Subtract. Check your answer. a) 3 ,102minus 428
b) 5,287 minus 931
c) 7,000 minus 476
3. Subtract. a) 7,130
minus 2,864
b) 9,345 minus 6,898
c) 6,005 minus 4,816
4. Subtract.
a) Seven thousand one minus three hundred fifty-six
5. It's 450 km from Fredericton to Halifax. It's 4,625 km from Fredericton to Edmonton.
How much closer is Fredericton to Halifax than to Edm onton?
6. Is it possible to subtract a 3-digit number from a
4-digit number and get a 4-digit number as the answer? A 3-digit number as the answer?
A 2-digit number as the answer? A 1-digit number as the answer?
Give an example for each possible answer. Show your work.
7
.
In 1215, the Magna Carta was signed. How many years ago is that?8. Use eight different digits from 1 to 9.
□ □□□
a) W hat is the greatest difference you can make?
b)
W hat is the least difference you can make? c) How do you know the answer you found inpart a is the greatest? In part b is the least?
9. Each letter in this problem represents a different digit from 0 to 9.
W h at is the value of each letter? How do you know?
reflect
W h at is the difference between checking if your answer is reasonable and
checking if your answer is correct? Use words and numbers to explain.
numbers every day
M ental M ath
Estimate each difference. Which strategies did you use?
L e s s o n
12
Strategies Toolkit
Fiona is 5 cm taller than Zac.
Together their heights total 299 cm. How tall is Fiona? How tall is Zac?
Work together to solve this problem. Use any materials you think will help.
S h o w
a n d
S h a r e
Describe the strategy you used to solve the problem.
explore
Yael and Victor collect postcards.
Yael has 10 more postcards than Victor. Together, they have 420 postcards.
How many postcards does each person have?
W h at do you know?
• There are 420 postcards in all. • Yael has 10 more postcards
than Victor.
Think of a strategy to help you solve the problem.
• You can
make an organized list.
• Find tw o numbers that add to 420.One number must be 10 more than the other.
S tra te g ie s
• Make a table. Use a model. • Draw a picture. • Solve a simpler
problem. • Work backward. • Guess and check.
Make an organized list.
Make an organized list to show the numbers.
Choose a number for Yael's postcards; such as 220. Subtract 220 from the total:
420 minus 220 is 200 postcards for Victor. Subtract the numbers of postcards: 220 minus 200 = 20 This is too high.
Yael’s postcards
Victor’s postcards
Difference
220 200 220 minus 200 = 20 Too high 219 201 219 minus 201 = 18 Too high
Try 1 less fo r Yael
and 1 more fo r
V ic to r
Continue this strategy until the difference is 10.
Could you have added and subtracted 2 or 3 instead? Explain.
practice
1
.
The Huda family drove 800 km in tw o days.They drove 20 km farther on the first day than on the second day. How far did the family drive each day?
2. Raphie has $1.75 in quarters and dimes. She has the same number of each coin. How many of each coin does Raphie have?
Choose one of the
stra te g ie s
reflect
W h at is the difference between "making a list" and "making an organized list"?
Unit
2
S
h
o
w
What You Know
LESSON
1
1.
The highest score in a Scrabble gam e is 1,049. Write this number in words and in expanded form.2. Write each number in standard form.
a) eight thousand twenty-six b) 6,0 0 0 plus 8 0 0 plus 7
2
3. The deepest a submarine has goneis 6,526 m below the surface of the ocean. Round this number:
a) to the nearest thousand b) to the nearest hundred c) to the nearest ten
3
4. W rite these numbers in order from least to greatest. 5,242, 5,232, 5,2234
-8
5. Estimate each sum or difference.a) 680 + 213 b) 276 minus 178 c) 176 + 412 d) 597minus 237 e) 276 plus 566 f ) 911 minus 499
5-9
6
.
Use mental math to add or subtract.a) 256 +172 b) 385 minus 189 c) 247 plus 338 d) 421 minus 298
4 7. For a Read-A-Thon, Natalie read 786 pages. Kevin read 815 pages. Mario read 623 pages. Altogether, they read over 2,000 pages.
a) Is 2,000 exact or an estimate? How do you know?
b) About how many more pages did Kevin read than Mario?
6 7111
8
.
Add or subtract. Check your answers. a) 2,211minus 878
b) 452 plus 348
c) 800 minus 298
LESSON
1 1 9. The tallest unicycle is 3,053 c m high.
The shortest unicycle is 20 cm high. How much taller is the tallest unicycle?
10.
Canada was founded in 1,867.W hich birthday will Canada celebrate in 2,006?
How do you know?
Use the following information to answer questions 11 to 13.
Container A holds 2,500 m l of water. Container B holds 1,875 m l of water.
A B
7
11
.
How much do the tw o containers hold together?
1
1
12
. Rhonda uses 725 m l fromcontainer A to make lemonade. Then Marilyn uses 925 m l to make juice, and Everett uses 375 m l for his water bottle. How much Is left in container A?
13. Is there enough room now in container A to pour in the water from container B? Explain.
unit 2 learning goals
recognize and read numbers from 1 to 10,000
read and write numbers in standard form, expanded form, and written form use place value to represent numbers
compare and order numbers estimate sums and
differences
Unit
Problem
Where
Shall We Go?
You will need an atlas or a map of Canada, or maps of the territories and provinces.
Plan a 7-day car trip anywhere in Canada.
Decide on the city where you will begin your trip.
You can travel up to 500 km per day.
Decide which cities you will stop at on each day of your trip. (You do n o t have to plan your return trip.)
Plan your trip. Include:
• The cities you will travel to on each day of your trip
• The distance you will travel each day • How much farther you will travel on
one day than the next
• The total distance you will travel for the w eek
Show your work.
Suppose you have $ 1,000 for the trip. Do you think you will have any m oney left at the end of the trip? Explain.
Check List
Your work should show
a plan of your trip and how you did what you were asked
your thinking in words, numbers, or pictures how you added and subtracted correctly a clear record of your
answers
Reflect on the Unit
