1 Unit 1
Number Sense
Topic A: Emotions and Learning
Emotions, or what we feel about something, play a big part in how we learn. If we are calm, we learn well. If we are afraid or stressed, we do not learn as well. Many people are afraid of math. They fear making a mistake. “Math anxiety” is the fear of math.
People who suffer from math anxiety may get headaches, sick stomachs, cold hands or they may just sweat a lot or just feel scared.
Do you suffer from math anxiety?
Read the list below and put a check mark (√) beside the ones you feel.
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Are your palms moist? |
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Is your stomach fluttering? |
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Do you feel like you can’t think clearly? |
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Do you feel like you would rather do anything else than learning math? |
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Are you breathing faster than normal? |
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Is your heart pounding? |
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Do you feel cold? |
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Add any other things you are feeling.
Math Anxiety
“Math anxiety” or the fear of math is a learned habit. If it is learned, it can be unlearned. Most math anxiety comes from bad memories while learning math. It may be from doing badly on a test or asking a question then being made fun of. These bad memories can make learning math hard.
Everyone can learn math. There is no special talent for math. There are some people who are better at math than others, but even these people had to learn to be good at math.
How to Deal with Math Anxiety
Anyone can feel anxiety that will slow down learning. The key to learning is to be the “boss” of your anxiety.
One way to be the “boss” is to relax. Try this breathing exercise.
Start by breathing in slowly to the count of four. It may help to close your eyes and count. Now hold your breath for four counts and then let your breath out slowly to the count of four. The counting is silent and should follow this pattern: “breathe in, two, three four; hold, two, three, four; breathe out, two, three, four; wait, two, three four.” With practice, the number of counts can be increased. This is an easy and good way to relax.
Now try this exercise quietly and repeat it five times slowly.
Each time you feel anxious about learning, use the breathing exercise to help calm yourself. Ask yourself if what you tried worked. Do you feel calmer?
Remember learning to deal with your math anxiety may take some time. It took you a long time to learn “math anxiety”, so it will take some time to overcome it.
Topic B: Counting
To learn to read, you first need to learn the letters of the alphabet. Once you know the alphabet, you put the letters together to make words, then sentences, then paragraphs and then stories.
Those letters become the “tools” used to write everything.
The same is true for math. In math we use digits. The digits are:
0123456789
Digits are named after our fingers. Our fingers are also called digits. The mathematics term comes from the days of counting on our fingers. We have ten fingers and there are ten digits. We use the letters of the alphabet to make up words, and we use digits to make up numbers. There are two ways to write numbers. You can write them as numerals. You can write them using word names.
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Numeral |
Word Name |
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0 |
zero |
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1 |
one |
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2 |
two |
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3 |
three |
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4 |
four |
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5 |
five |
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6 |
six |
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7 |
seven |
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8 |
eight |
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9 |
nine |
Counting is matching the number name to the things being counted. You see a bowl of apples on the table. You want to know how many apples are in the bowl. You answer that question by saying “There are one, two, three, four apples.” You are giving the number names “one”, “two”, “three,” and “four” to the apples. The last number you say is the total number of apples.
Exercise OneCount the number of shapes in each picture. Then write the
numeral and the word name. Check your work using the answer key at the end of the exercise.
Numeral:3 Word name: three
Example:
Numeral: Word Name:
Numeral: Word Name:
a)b)
Numeral: Word Name
c)
Numeral: Word Name:
d)
Exercise One – Answer Key
Numeral: Word Name:
Numeral: Word Name:
e)f)
Numeral:Word Name:
Numeral: Word Name:
g)h)
Numeral: Word Name:
i)
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a) |
2, two |
b) |
6, six |
c) |
8, eight |
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d) |
9, nine |
e) |
1, one |
f) |
5, five |
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g) |
7, seven |
h) |
4, four |
i) |
0, zero |
Need More Practice?
Ask your instructor for the dominoes to do this page. Take the dominoes zero-zero to five- five. Flip them over so you cannot see the dots. Pick a domino and flip it over. Draw the number of dots then count the number of dots. Write the numeral and word name. Have your instructor check these for you.
Example:
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● ● ● ● |
Numeral:6 Word Name: six
a)b)
Numeral:Numeral:
Word Name:Word Name:
c)d)
Numeral:Numeral:
Word Name:Word Name:
e)f)
Numeral:Numeral:
Word Name:Word Name:
Exercise Two
Here are the numerals from one to ten.
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2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Practice writing them below.
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Now practice writing the numerals from one to ten in the following. Try to do them without looking. Check your work using the answer key at the end of the exercise.
a)
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3 |
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5 |
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7 |
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9 |
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b)
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2 |
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4 |
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6 |
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8 |
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10 |
c)
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1 |
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4 |
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7 |
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d)
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3 |
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6 |
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9 |
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e)
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1 |
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4 |
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7 |
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f)
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1 |
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5 |
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9 |
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g)
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1 |
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6 |
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h)
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5 |
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i)
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Answers to Exercise Two
a)
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2 |
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4 |
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6 |
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8 |
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10 |
b)
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1 |
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3 |
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5 |
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7 |
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9 |
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c)
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2 |
3 |
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5 |
6 |
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8 |
9 |
10 |
d)
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1 |
2 |
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4 |
5 |
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7 |
8 |
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10 |
e)
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2 |
3 |
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5 |
6 |
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8 |
9 |
10 |
23467810
f)
g)
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2 |
3 |
4 |
5 |
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7 |
8 |
9 |
10 |
1234678910
h)
i)
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1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Topic B: Self-TestMark/18Aim 15/18
Count the number of things in each picture, then write the numeral and the
word name.8 marks
●●● ●● ●
b)
Numeral:Numeral:
Word Name:Word Name:
● ●● ●● ●● ●
●●●● ● ●● ● ●
c)d)
Numeral:Numeral:
Word Name:Word Name:
- Write the numerals from one to 10.10 marks
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Topic B: Self-Test – Answer KeyA:a)0, zerob) 6, sixc) 8, eightd) 9, nineB:
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2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Emotions Check
How are you feeling? Are your palms moist? How is your breathing?
Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.
Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four.
Topic C: Place Value
As you know, we count much higher than ten in our world. Each place in a number has a value.
The ones place tells how many ones there are.
3 means 3 ones
0 means 0 ones
9 means 9 ones
9 is the largest amount that we can express (write or say) with one digit.
The tens place shows how many tens there are. The ones place must have a digit in it before there can be a digit in the tens place.
Every ten is ten ones.
=
43 means 4 tens and 3 ones
20 means 2 tens and 0 ones. The zero holds the ones place.
99 means 9 tens and 9 ones. 99 is the largest amount that we can express (write or say) using only two digits.
Exercise OneFill in the blanks to make each sentence true. Draw a
picture for questions c, f, h and j like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches.
Example: 49 means 4tens and 9ones
- 37 means tens and ones.
- 65 means tens and ones.
- 56 means tens and ones.
(Draw your picture below.)
- 87 means tens and ones.
- 33 means tens and ones.
- 60 means tens and ones.
(Draw your picture below.)
- 70 means tens and ones.
- 44 means tens and ones.
(Draw your picture below.)
- 98 means tens and ones.
- 75 means tens and ones.
(Draw your picture below.)
Exercise One – Answer Key
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a) |
3 tens, 7 ones |
b) |
6 tens, 5 ones |
c) |
5 tens, 6 ones |
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d) |
8 tens, 7 ones |
e) |
3 tens, 3 ones |
f) |
6 tens, 0 ones |
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g) |
7 tens, 0 ones |
h) |
4 tens, 4 ones |
i) |
9 tens, 8 ones |
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j) |
7 tens, 5 ones |
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The place to the left of the tens place is the hundreds place. It shows how many hundreds there are. A number written using three whole digits has a hundreds place, a tens place, and a ones place.
Every hundred is ten tens – every hundred is the same as one hundred ones.
100100100
425 means 4 hundreds, 2 tens, and 5 ones.
354 means 3 hundreds, 5 tens, and 4 ones.
Exercise TwoFill in the blanks to make each sentence true. Draw a picture
for questions c, e, and h, like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches.
- 190 = 1hundreds, 9tens, 0ones
- 555 = hundreds, tens, ones
- 309 = hundreds, tens, ones
(Draw your picture below.)
- 499 = hundreds, tens, ones
- 480 = hundreds, tens, ones
(Draw your picture below.)
- 999 = hundreds, tens, ones
- 657 = hundreds, tens, ones
- 125 = hundreds, tens, ones
(Draw your picture below.)
i)212 = hundreds, tens, ones
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b) |
5 hundreds, 5 tens, 5 ones |
c) |
3 hundreds, 0 tens, 9 ones |
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d) |
4 hundreds, 9 tens, 9 ones |
e) |
4 hundreds, 8 tens, 0 ones |
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f) |
9 hundreds, 9 tens, 9 ones |
g) |
6 hundreds, 5 tens, 7 ones |
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h) |
1 hundred, 2 tens, 5 ones |
i) |
2 hundreds, 1 ten, 2 ones |
Answers to Exercise Two
Exercise ThreeCount the hundreds, tens, and ones shown in the drawings.
The pictures will help you understand the quantity of a number. Then write the numeral. The first one is done for you. Check your work using the answer key at the end of the exercise.
a)
2hundreds 0tens 3ones = 203
b)
hundredstensones =
c)
hundredstensones =
d)
hundredstensones =
e)
hundredstensones =
Answers to Exercise Threeb)4 hundreds, 3 tens, 1 one, 431d)3 hundreds, 1 ten, 6 ones, 316c)1 hundred, 8 tens, 0 ones, 180e)2 hundreds, 0 tens, 3 ones, 203
Need more practice?
Ask your instructor for some play money. Using the one, ten and hundred dollar bills practice trading ten of one type of bill for one of the next value.
Example:
ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$10Ten
equals
ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$1One
Exercise FourWrite the place value name (ones, tens, hundreds) for each
underlined digit. Check your work using the answer key at the end of the exercise.
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a) |
622 |
hundreds |
b) |
468 |
tens |
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c) |
920 |
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d) |
920 |
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e) |
648 |
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f) |
426 |
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g) |
534 |
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h) |
555 |
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i) |
451 |
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j) |
901 |
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k) |
226 |
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l) |
486 |
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c) |
ones |
d) |
hundreds |
e) |
tens |
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f) |
ones |
g) |
hundreds |
h) |
tens |
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i) |
tens |
j) |
ones |
k) |
hundreds |
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l) |
ones |
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Answers to Exercise Four
Exercise FiveUnderline the digit for the place value named. Check your work
using the answer key at the end of the exercise.
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a) |
hundreds |
416 |
b) |
tens |
368 |
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c) |
tens |
364 |
d) |
hundreds |
456 |
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e) |
ones |
206 |
f) |
ones |
634 |
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g) |
hundreds |
742 |
h) |
hundred |
543 |
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i) |
tens |
221 |
j) |
ones |
100 |
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k) |
ones |
169 |
l) |
tens |
684 |
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a) |
4 |
b) |
6 |
c) |
6 |
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d) |
4 |
e) |
6 |
f) |
4 |
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g) |
7 |
h) |
5 |
i) |
2 |
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j) |
0 |
k) |
9 |
l) |
8 |
Answers to Exercise Five
Emotions Check
How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.
Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four.
Reading and Writing Numerals
You know that the digits are 0 1 2 3 4 5 6 7 8 9 and that digits are arranged in different places so we can count larger amounts than our ten fingers!
When we use digits we call what we write the numeral.
328 is a numeral 46 is a numeral 3 is a numeral
We use numerals to represent numbers.
If we think about language instead of mathematics it will be clearer.
Letters are used to make words. We respond to the meaning of words.
Digits are the “letters” of math. Numerals are the “words” of math. Numbers are the “meaning” of math.
Now you know the place value of digits up to three places. Next you will learn to read and write numerals and number words. Some of the words to read and spell may be new to you.
The numerals from 1 to 12 have special words. These are
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0 |
zero |
7 |
seven |
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1 |
one |
8 |
eight |
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2 |
two |
9 |
nine |
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3 |
three |
10 |
ten |
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4 |
four |
11 |
eleven |
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5 |
five |
12 |
twelve |
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6 |
six |
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The number names for numerals from 13 to 19 are made up of two parts. The first part tells us how many units. The second part (“teen”) tells us there is also 1 ten.
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13 |
thirteen |
three units and 1 ten |
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14 |
fourteen |
four units and 1 ten |
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15 |
fifteen |
five units and 1 ten |
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16 |
sixteen |
six units and 1 ten |
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17 |
seventeen |
seven units and 1 ten |
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18 |
eighteen |
eight units and 1 ten |
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19 |
nineteen |
nine units and 1 ten |
Exercise SixWrite the word name for each number. Try not to look at the
list. Check your work using the answer key at the end of the exercise.
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a) |
8 |
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b) |
16 |
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c) |
7 |
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d) |
15 |
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e) |
5 |
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f) |
11 |
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g) |
9 |
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h) |
18 |
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i) |
6 |
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j) |
17 |
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k) |
4 |
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l) |
14 |
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m) |
12 |
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n) |
13 |
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o) |
19 |
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p) |
3 |
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Answers to Exercise Six a) eight |
b) |
sixteen |
c) seven |
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d) fifteen |
e) |
five |
f) eleven |
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g) nine |
h) |
eighteen |
i) six |
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j) seventeen |
k) |
four |
l) fourteen |
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m) twelve |
n) |
thirteen |
o) nineteen |
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p) three |
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The word names for the numbers 20 to 90 are also made up of two parts. The first part tells us how many groups of tens. The second part (“ty”) tells us we are counting groups of tens and not something else. The “-ty” may have come from a shortening of the word “ten”.
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20 |
twenty |
two tens |
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30 |
thirty |
three tens |
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40 |
forty |
four tens |
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50 |
fifty |
five tens |
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60 |
sixty |
six tens |
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70 |
seventy |
seven tens |
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80 |
eighty |
eight tens |
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90 |
ninety |
nine tens |
The names for the numbers between groups of tens also follow a pattern. The first number tells us how many tens. The second number tells us how many ones.
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TensOnes |
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Tens Ones |
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Tens Ones |
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20 |
twenty |
30 |
thirty |
40 |
forty |
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21 |
twenty-one |
31 |
thirty-one |
41 |
forty-one |
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22 |
twenty-two |
32 |
thirty-two |
42 |
forty-two |
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23 |
twenty-three |
33 |
thirty-three |
43 |
forty-three |
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24 |
twenty-four |
34 |
thirty-four |
44 |
forty-four |
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25 |
twenty-five |
35 |
thirty-five |
45 |
forty-five |
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26 |
twenty-six |
36 |
thirty-six |
46 |
forty-six |
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27 |
twenty-seven |
37 |
thirty-seven |
47 |
forty-seven |
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28 |
twenty-eight |
38 |
thirty-eight |
48 |
forty-eight |
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29 |
twenty-nine |
39 |
thirty-nine |
49 |
forty-nine |
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The written names for numbers that have tens and ones are written with a hyphen (-) between them. This pattern with the hyphen continues up to ninety-nine (99).
Exercise SevenWrite the word names for these numbers. Check your work
using the answer key at the end of the exercise.
a) 24 twenty-fourb) 35 thirty-five
c) 83d) 46
e) 59f)20
g) 71h) 94
i)62j)53
Answers to Exercise Sevenc)eighty-threef)twentyi)sixty-twod)g)j)forty-sixseventy-one fifty-threee)h)fifty-nineninety-four
Exercise EightWithout looking back, write the word names for these
numbers.Check your work using the answer key at the end of the exercise.
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a) |
44 |
forty-four |
b) |
97 |
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c) |
71 |
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d) |
86 |
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e) |
53 |
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f) |
25 |
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g) |
15 |
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h) |
38 |
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30 |
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Book 1 |
Answers to Exercise Eightb) ninety-sevene) fifty-threeh) thirty-eightc) seventy-onef) twenty-fived) eighty-sixg) fifteen
Exercise NineWrite the numerals for these word names. Check your work
using the answer key at the end of the exercise.
a) ninety-nine 99b) sixty-seven 67
c) eighty-oned) eighteen
e) twenty-sixf)thirteen
g) thirtyh) forty-three
i)sixteenj)twenty
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Answers to Exercise Nine c) 81 |
d) 18 |
e) 26 |
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f) 13 i)16 |
g) 30 j) 20 |
h) 43 |
When we write hundreds in words, we need two words. The first word tells us how many
hundreds. The second word tells us we are counting hundreds.
200two hundred
You now know how to write numbers in words up to 999.
Fundamental Mathematics31
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367 is made of |
3 hundreds |
6 tens |
7 ones |
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Each is written: |
three hundred |
sixty |
seven |
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Put the parts together: |
three hundred sixty-seven |
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Remember:
hyphen (-) between the tens and units no hyphen anywhere else
no “s” on the hundred
504 is made of5 hundreds0 tens4 onesEach is written:five hundredfourPut the parts together:five hundred four
no „and” between the hundreds place and the tens place Here is another example. Watch out for the empty space!
Here is another example. Watch out for the empty space!
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890 is made of |
8 hundreds |
9 tens |
0 ones |
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Each is written: |
eight hundred |
ninety |
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Put the parts together: |
eight hundred ninety |
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Here is another example. Watch out for the empty spaces!
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100 is made of |
1 hundreds |
0 tens |
0 ones |
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Each is written: |
one hundred |
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Put the parts together: |
one hundred |
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Remember: empty spaces are not written in words.
Exercise TenWrite the word names for these numerals. Check your work
using the answer key at the end of the exercise.
a)
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623 is made of |
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Each is written: |
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Put the parts together: |
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b)
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364 is made of |
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Each is written: |
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Put the parts together: |
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c)
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213 is made of |
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Each is written: |
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Put the parts together: |
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d)
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405 is made of |
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Each is written: |
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Put the parts together: |
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e)
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820 is made of |
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Each is written: |
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Put the parts together: |
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f)704
g) 470
h) 993
i)100
j)972
Answers to Exercise Ten
a)
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623 is made of |
6 hundreds |
2 tens |
3 ones |
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Each is written: |
six hundred |
twenty |
three |
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Put the parts together: |
six hundred twenty-three |
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b)
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364 is made of |
3 hundreds |
6 tens |
4 ones |
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Each is written: |
three hundred |
sixty |
four |
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Put the parts together: |
three hundred sixty-four |
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c)
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213 is made of |
2 hundreds |
1 ten |
3 ones |
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Each is written: |
two hundred |
thirteen |
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Put the parts together: |
two hundred thirteen |
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d)
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405 is made of |
4 hundreds |
0 tens |
5 ones |
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Each is written: |
four hundred |
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five |
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Put the parts together: |
four hundred five |
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e)
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820 is made of |
8 hundreds |
2 tens |
0 ones |
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Each is written: |
eight hundred |
twenty |
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Put the parts together: |
eight hundred twenty |
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f) |
seven hundred four |
g) four hundred seventy |
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h) |
nine hundred ninety-three |
i)one hundred |
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j) |
nine hundred seventy-two |
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Topic C: Self-TestMark/17Aim 14/17
Write the place value for the underlined digit.6 marks
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a) |
765 |
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b) |
903 |
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c) |
479 |
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d) |
185 |
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e) |
732 |
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f) |
397 |
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- Write the word names for these numerals.6 marks
a) 79
b) 492
c) 378
d) 820
e) 405
f) 583
Write the numerals for these word names.5 marks
- five hundred forty-seven
- three hundred eighty
- two hundred seventy-five
- four hundred sixteen
- nine hundred twenty-three
Answers to Topic C Self-testA.a) tensb) tensd) onese) onesc) hundredsf) hundredsB.a) seventy-ninec) three hundred seventy-eighte) four hundred fiveb) four hundred ninety-twod) eight hundred twentyf) five hundred eighty-threeC.a) 547d) 416b) 380e) 923c) 275
Topic D: Ordering Numerals
We arrange numerals in order from smallest to largest. Sorting numbered papers such as order forms, arranging items by the date and comparing prices are some of the ways you use this skill.
Look at two numerals and tell which one is larger. How do you do this?
Exercise OneDraw a box around the larger numeral in each pair.
48
a)43b)2721c)6463
d)2435e)9289f)7281
Answers to Exercise Oneb)27c)64d)35e)92f)81
To compare numerals, look at the place with the largest value.
Example A:Compare 63 and 59
Look at the tens place.
63 has a 6 in the tens place. 59 has a 5 in the tens place.
63 is larger than 59.
Example B:Compare 496 and 476.
Look at the hundreds – both have 4’s. Look at the tens place.
496 has a 9 in the tens place. 476 has a 7 in the tens place.
496 is larger than 476.
Note: Numerals with one digit are always less than numerals with two digits. Numerals with two digits are always less than numerals with three digits, and so on.
9 is less than 15
87 is less than 107
999 is less than 1 001
Exercise TwoDraw a box around the larger numeral in each pair. Check your
work using the answer key at the end of the exercise.
46
a)36b)58059c)8767
d)716116e)429449f)289283
g)229329h)230210i)51159
Answers to Exercise Two
j)836935k)3637l)461468
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b) |
580 |
c) |
87 |
d) |
716 |
e) 449 |
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f) |
289 |
g) |
329 |
h) |
230 |
i) 159 |
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j) |
935 |
k) |
37 |
l) |
468 |
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Exercise ThreeDraw a box around the larger numeral in each pair. Check your
work using the answer key at the end of the exercise.
151
a)148b)129132c)3437
d)325236e)11813f)489423
g)471422h)316322i)876319
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b) 132 |
c) 37 |
d) |
325 |
e) 118 |
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f) 489 |
g) 471 |
h) |
322 |
i) 876 |
Exercise Three – Answer Key
Now use the same ideas to arrange more than two numerals in order.
For example, to arrange 6, 616, 1, 66, 666, 61, and 16 in order from smallest to
largest, use the following method:
First, sort the numerals with the same number of digits into groups.
6, 166, 16, 61and616, 666
The group of one digit numerals contains 6 and 1. As 1 is smaller than 6, the list starts with 1, then 6.
The group of two-digit numerals contains 66, 61, and 16. Use your skills in ordering numerals to see that 16 is smallest, then 61, and 66 is the largest of this group. The list now reads, 1, 6, 16, 61, 66.
Finally, look at the three-digit numerals, 616 and 666. As 616 is smaller than 666, it will come first. The list now reads: 1, 6, 16, 61, 66, 616, 666.
Exercise FourArrange these numbers in order from smallest to largest.
Check your work using the answer key at the end of the exercise.
a) 323323323333222
b) 447474477447477
c) 123135152125
d) 472427452475
Answers to Exercise Foura)2, 3, 32, 33, 322, 323, 332c)123, 125, 135, 152b)7, 44, 47, 74, 77, 474, 744d)427, 452, 472, 475
Greater Than, Less Than, Equals
The sign < means “is less than” (smaller than). The sign > means “is greater than” (bigger than).
The greater than and less than signs always point to the smaller number. That is, the point or the tip of the sign is close to the small number.
- < 12means 5 is less than 12
- > 3means 6 is greater than 3
The sign = means “equals” and is used when two amounts are the same.
Exercise FiveWrite <, >, or = in each blank as needed. Check your work
using the answer key at the end of the exercise.
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a) c) |
3 <5 12 9 |
b) d) |
8 >7 28 28 |
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e) |
48 84 |
f) |
376 376 |
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g) |
520 530 |
h) |
582 521 |
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i) |
674 296 |
j) |
214 251 |
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k) |
879 900 |
l) |
784 784 |
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Answers to Exercise Five |
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c) |
> |
d) |
= |
e) |
< |
f) = |
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g) |
< |
h) |
> |
i) |
> |
j) < |
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k) |
< |
l) |
= |
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Topic D: Self-TestMark/12Aim 10/12
Box the larger number of each pair.6 marks
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a) |
978 |
789 |
b) |
566 |
556 |
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c) |
120 |
142 |
d) |
701 |
710 |
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e) |
430 |
403 |
f) |
879 |
987 |
- Arrange these numerals in order from smallest to largest.2 marks
a) 7575447547747574775
b) 1823742982437994112
Write >, <. or = in each blank to make a true statement.4 marks
a) 678 768b) 102 100
Answers to Topic D Self-Test
c) 463 846d) 101 101
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978 |
b) 566 |
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c) 142 |
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d) |
710 |
e) 430 |
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f) 987 |
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B. a) |
< |
b) > |
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c) < |
d) = |
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C. a) |
47, |
75, 475, 574, 747, |
754, |
775 |
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b) |
18, |
37, 112, 237, 429, |
824, |
994 |
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Topic E: Rounding Numbers
We use numbers a lot in our everyday lives. List some of the ways you use numbers.
You may have written money, shopping, time, and counting as part of your answer.
Think about time. Let’s say it takes eight minutes to walk to the bus. If someone asks you how long it takes, you will probably say, “About ten minutes.”
If you buy a sweater that cost $29, you may say, “Oh, it was around thirty dollars.”
How far is it from Vancouver to Prince George? The map says 796 km, but we would probably say, “About 800 kilometres.”
You have just read examples of rounding numbers.
We round numbers for many reasons:
We may not know the exact number.
The exact number may not be important for what we are doing.
We may need a quick way to figure something out.
When you are rounding numbers, use zeros to hold the places at the end of the number. Work through the following examples and exercises carefully. Rounding is an important skill.
Rounding to the Nearest Ten
A number rounded to the nearest ten will have a zero in the ones place. The number will end with 0, 10, 20, 30, 40, 50, 60, 70, 80, or 90.
When rounding to the nearest 10, we are looking for the closest group of 10.
Example:20, 23 and 30.
202330
Is 23 closer to 20 or 30? It is closest to 20.
Which gives a better estimate of 23…..2 tens or 3 tens. 2 tens
If we round 23 to the nearest ten, the result would be 20.
Remember: The rounded number has a zero in the ones place.
Example:40, 46 and 50
404650
Is 46 closer to 40 or 50? it is closest to 50.
Which gives a better estimate of 46……4 tens or 5 tens? 5 tens
If we round 46 to the nearest ten, the result would be 50.
Example:60, 65 and 70
606570
Is 65 closer to 60 or 70? It is closer to 70.
Which gives a better estimate of 65…… 6 tens or 7 tens? 7 tens
When we have a number which ends in 5, we always round up to the next ten. If we round 65 to the nearest 10, the result would be 70.
Example: Round 32 to the nearest 10.
32 is between 3 tens and 4 tens.
32 is closest to 3 tens. Rounded number is 30 .
Exercise OneRound each number to the nearest 10. Check your work using
the answer key at the end of the exercise.
- 47 is between tens and tens.
47 is closest to tens. Rounded number is .
- 81 is between tens and tens.
81 is closest to tens. Rounded number is .
- 14 is between tens and tens.
14 is closest to tens. Rounded number is .
- 26 is between tens and tens.
26 is closest to tens. Rounded number is .
- 98 is between tens and tens.
98 is closest to tens. Rounded number is .
- 57 is between tens and tens.
57 is closest to tens. Rounded number is .
- 73 is between tens and tens.
73 is closest to tens. Rounded number is .
- 2 is between tens and tens.
2 is closest to tens. Rounded number is .
- 39 is between tens and tens.
39 is closest to tens. Rounded number is .
- 65 is between tens and tens.
65 is closest to tens. Rounded number is .
- 18 is between tens and tens.
18 is closest to tens. Rounded number is .
Fundamental Mathematics47
Answers to Exercise One
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a) |
4 tens, 5 tens 5 ten 50 |
b) |
8 tens, 9 tens 8 tens 80 |
c) |
1 ten, 2 tens 1 ten 10 |
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d) |
tens, 3 tens tens 30 |
e) |
tens, 10 tens tens 100 |
f) |
tens, 6 tens tens 60 |
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g) |
7 tens, 8 tens 7 tens 70 |
h) |
0 tens, 1 ten 0 tens 0 |
i) |
tens, 4 tens tens 40 |
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j) |
tens, 7 tens tens 70 |
k) |
ten, 2 tens tens 20 |
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Now look at a shorter method to round to the nearest ten.
When rounding to the nearest ten, do this:
Step 1: Underline the tens digit.
83
Step 2: Look at the digit following in the ones place.
83
Step 3: If the digit in the ones place is less than 5,
write a 0 in the ones place. leave the tens digit as it is.
42rounds to 40 (42 is nearer to 40 than to 50)
14rounds to 10
83rounds to 80
Step 4: If the digit in the ones place is 5 or more,
write a 0 in the ones place.
add one more ten to the tens place.
36rounds to 40 (36 is nearer to 40 than to 30)
25rounds to 30
98rounds to 100 (one more ten than nine tens is ten tens)
Note: If you are rounding to the nearest ten, single digits are rounded like this: 0, 1, 2, 3, 4 all round to 0.
5, 6, 7, 8, 9 all round to 10.
When you round a number, use the sign that means “approximately equal”
Exercise TwoRound each number to the nearest ten. Check your work using
the answer key at the end of the exercise.
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22 |
20 |
b) |
86 |
90 |
c) |
31 |
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96 |
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84 |
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55 |
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88 |
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70 |
m) |
40 |
n) |
50 |
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90 |
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Answers to Exercise Two
Numbers of any size can be rounded to the nearest ten using the method you have just learned.
238 240883 880297 300
Answers to Exercise Three
Exercise ThreeRound each number to the nearest ten. Check your work using
the answer key at the end of the exercise.
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a) |
424 |
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b) |
867 |
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c) |
499 |
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d) |
132 |
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e) |
278 |
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f) |
617 |
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g) |
208 |
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h) |
851 |
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i) |
124 |
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j) |
576 |
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k) |
315 |
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l) |
742 |
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m) |
397 |
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n) |
952 |
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o) |
639 |
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a) |
420 |
b) |
870 |
c) 500 |
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130 |
e) |
280 |
f) 620 |
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210 |
h) |
850 |
i) 120 |
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j) |
580 |
k) |
320 |
l) 740 |
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m) |
400 |
n) |
950 |
o) 640 |
Exercise FourFor each problem, round the numbers to the nearest ten.
Check your work using the answer key at the end of the exercise.
Example: Mei Ling has just moved into a new apartment. She bought the following items. Round each amount to the nearest ten.
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Item Towels |
Cost $14 |
Rounded to nearest ten $10 |
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Dishes |
$32 |
$30 |
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Saucepan |
$43 |
$40 |
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Microwave |
$109 |
$110 |
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Carving Knife |
$18 |
$20 |
- Akkul walked 12 kilometres on Monday, 26 kilometres on Tuesday and 6 kilometres on Wednesday. Round each number to the nearest ten.
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Day |
Number |
Rounded Number |
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Monday |
12 |
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Tuesday |
26 |
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Wednesday |
6 |
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- Werner is a keen bird watcher. On Monday, he saw 57 birds, on Tuesday he saw 124 birds, on Wednesday he saw 31 birds and on Thursday he saw 75 birds. Round each number to the nearest ten.
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Rounded Number |
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Thursday |
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Jamir drove 678 kilometres. 493 kilometres, 387 kilometres and 914 kilometres in one week. Round each mileage to the nearest ten.
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Rounded Number |
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#2 |
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#4 |
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- Koho Industries canned 281 cans of salmon last week and 392 cans of salmon this week. They plan to can 438 cans of salmon next. Round each number of cans to the nearest ten.
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Rounded Number |
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Last week |
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Next week |
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- During one week at the movie theatre there were 423 people on Monday, 328 people of Tuesday, 148 people on Wednesday and 523 people on Thursday. Round each number to the nearest ten.
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Rounded Number |
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Answers to Exercise Four a) 10, 30, 10 |
b) 60, 120, 30, 80 |
c)680, 490, 390, 910 |
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d) 280, 390, 440 |
e)420, 330, 150, 520 |
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Topic E:Self-TestMark/12Aim10/12
Round your answer to the nearest ten.8 marks
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a) |
47 |
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b) |
123 |
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c) |
4 |
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d) |
945 |
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e) |
329 |
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f) |
481 |
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g) |
865 |
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h) |
916 |
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- Round each number to the nearest ten.4 marks
- Mary scored 78, 91, 79, 67 and 102 on her arithmetic test. Round her scores to the nearest ten.
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Score |
Rounded Score |
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Answers to Topic E Self-TestA.a) 50b)d) 950e)g) 870h)120330920c) 0f) 480B.a) 80, 90, 80, 70, 100
Topic F: More Counting
Practice your counting by filling in the counting chart. Have your instructor check your chart when you are done.
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If you had a pile of pennies or loonies, you would count by ones in order to find out how much money you have.
Use your counting chart and start at 1. Write down every second number.
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The numbers above are called odd numbers.
Use your counting chart and starting at 0. Write down every second number.
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The numbers above are called the even numbers. If you had a pile of toonies, you could count by two’s to find out how much money you have.
Use your counting chart and start at 0. Count five and write down that number.
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5 |
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If you had a pile of nickels or five dollar bills and wanted to know how much money you have, you would count be 5’s.
Use your counting chart and starting at 0. Count ten and write down that number.
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0 |
10 |
20 |
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If you had a pile of dimes or ten dollar bills and wanted to know how much money you have, you would count by 10’s.
Exercise OneCount how much money you have. Check your work using the
answer key at the end of the exercise.
Example:
51015
How many nickels? 3
How much money do you have? 15 cents
a)
How many twonies do you have?
How much money do you have? dollars
b)
How many dimes do you have?
How much money do you have? cents
c)
How many nickels to you have?
How much money do you have? cents
d)
How many dimes do you have?
How much money do you have? cents
e)
How many nickels to you have?
How much money do you have? cents
f)
How many twonies do you have?
How much money do you have? dollars
g)
How much money do you have? cents
h)
How much money do you have? dollars
i)
How much money do you have? cents
Answers to Exercise One
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a) |
4 twonies, $8 |
b) |
7 dimes, 70 cents |
c) |
9 nickels, 45 cents |
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d) |
4 dimes, 40 cents |
e) |
10 nickels, 50 cents |
f) |
3 twonies, $26 |
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g) |
90 cents |
h) |
$36 |
i) |
70 cents |
Topic F: Self-TestMark/16Aim 13/16
Write the first 10 odd numbers starting with 1.5 marks
- Write the first 10 even numbers starting at 2.5 marks
How much money do you have?6 marks (2 marks each)
i)
How much money do you have? cents
ii)
How much money do you have? dollars
iii)
How much money do you have? cents
Answers to Topic F Self-Test A. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19B. 2,4,6,8,10,12,14,16,18, 20C. i) 75 centsii) 38 dollars iii) 80 cents
Emotions Check
How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.
Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four.
Unit 1 Review – Number Sense
You will now practice all the skills you learned in Unit 1. Check your work using the answer key at the end of the review.
Count the number of things in each picture. Write the number and word name.
Numeral:Word Name:
a)
- Numeral: Word Name:
Numeral:Word Name:
c)
d)e)
Numeral:Numeral:
Word Name:Word Name:
- Fill in the blanks to make each sentence true. Draw a picture for questions b and e.
- 46 means tens and ones.
- 25 means tens and ones.
Draw your picture below.
c)
means tens and ones
- 138 = hundreds, tens, ones.
- 231 = hundreds, tens, ones.
Draw your picture below.
f)
hundredstensones =
Write the place value name (ones, tens, hundreds) for each underlined digit.
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a) |
821 |
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b) |
294 |
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c) |
638 |
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d) |
417 |
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e) |
346 |
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f) |
573 |
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Underline the digit for the place value named.
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a) |
hundreds |
164 |
b) |
tens |
892 |
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c) |
tens |
250 |
d) |
hundreds |
371 |
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e) |
ones |
485 |
f) |
ones |
743 |
- Write the word names for the numbers.
a) 73 b) 14
c) 5 d) 39
e) 52 f)496
g) 803 h) 640
Write the numerals for these word names.
- forty-seven b) nineteen
c) sixty-fived) thirty-eight
e) twenty-four f)five hundred thirty-five
g) three hundred sixty h) two hundred four
Arrange these numbers in order from smallest to largest.
a)2583223282345534
b)15527635208452335
Write <, >, or = in each blank as needed.
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a) |
37 52 |
b) |
4 0 |
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c) |
349 394 |
d) |
67 67 |
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e) |
86 68 |
f) |
732 751 |
- Round each number to the nearest ten.
a) 37 b) 344 c) 68
d) 25
e) 51
f)876
How much money do you have?
a)
How much money do you have? cents
70Book 1
b)
How much money do you have? dollars
c)
How much money do you have? cents
Word Problems
- Hussein’s fruit stand sold 114 watermelons, 287 honeydew melons and 345 cantaloupes. Round each number to the nearest ten.
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Melon |
Number |
Rounded Number |
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Watermelons |
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Honeydew Melons |
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Cantaloupes |
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- Yi-Min drove her delivery van 106 kilometres on Saturday, 187 kilometres on Sunday and 285 kilometres on Monday. Round each number to the nearest ten.
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Kilometres |
Number |
Rounded Number |
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Saturday |
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Sunday |
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Monday |
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Answers to Unit 1 Review A.
a) 9, nineb) 7, sevenc) 6, sixd) 8, eighte) 5, five
B.
a) 4 tens, 6 onesb) 2 tens, 5 onesc) 63, 6 tens, 3 ones
d) 1 hundred, 3 tens, 8 onese) 2 hundreds, 3 tens, 1 one
f) 3 hundreds, 2 tens 5 ones, 325
C.
a) hundredsb) tensc) onesd) hundreds
e) tensf) ones
D.
a) 164b) 892c) 250d) 371e) 485f) 743
E.
a) seventy-three b) fourteenc) fived) thirty-nine
e) fifty-twof) four hundred ninety-sixg) six hundred forty
F.
a) 47b) 19c) 65d) 38e) 24f) 535
g) 360h) 204
G.
a) 23, 32, 258, 282, 345, 534b) 27, 155, 208, 335, 452, 635
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H. a) < |
b) > |
c) < |
d) = |
e) > |
f) < |
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I. a) 40 |
b) 340 |
c) 70 |
d) 30 |
e) 50 |
f) 880 |
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J. a) 70 cents |
b) 26 dollars |
c) 90 cents |
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K. a) |
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b) |
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MelonNumberRounded NumberWatermelons114110Honeydew Melons287290Cantaloupes345350
DayKilometresRounded NumberSaturday106110Sunday187190Monday285290
CONGRATULATIONS!!Now you have finished Unit 1.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 1 test.Again, ask your instructor for this.Good luck!