Ontario Grade 4 Mathematics - Chapter 1: Number Concepts PDF

# Ontario Grade 4 Mathematics ## Chapter 1: Number Concepts ### Exercises 1.1 1. Fill in each blank in the table below: | thousands | hundreds | tens | ones | |---|---|---|---| | 9 | 0 | 5| 2 | | 2 | 0 | 6 | | | 6 | 3 | 0 | 0 | | 5 | 1 | 0 | 6 | | 3 | 1 | 0 | | | 0 | 4 | 2 | | | 7 | 0 | 0 | 7...

# Ontario Grade 4 Mathematics ## Chapter 1: Number Concepts ### Exercises 1.1 1. Fill in each blank in the table below: | thousands | hundreds | tens | ones | |---|---|---|---| | 9 | 0 | 5| 2 | | 2 | 0 | 6 | | | 6 | 3 | 0 | 0 | | 5 | 1 | 0 | 6 | | 3 | 1 | 0 | | | 0 | 4 | 2 | | | 7 | 0 | 0 | 7 | 2. Write each of the following numerals in expanded notation. The first one is done for you. * a. 3257 = 3000 + 200 + 50 + 7 * b. 4433 * c. 8056 * d. 8506 * e. 9990 3. Write the numeral for each description below: * a. 2 thousands, 9 hundreds, 7 tens, and 5 ones = 2975 * b. 2 hundreds, 5 tens, and 6 ones = 256 * c. 8 hundreds and 5 ones = 805 * d. 9 thousands, 9 hundreds, 9 tens and 9 ones = 9999 * e. 2 thousands, 7 hundreds and 3 ones = 2703 * f. 6 thousands and 5 tens = 6050 * g. 4 thousands, 5 tens and 4 ones = 4054 * h. 3 thousands and 3 ones = 3003 * i. 27 thousands and 8 ones = 27008 * j. 38 hundreds and 20 ones = 3820 4. The word numbers below combine some of the place values. Three examples are done for you. Write the correct numeral for each of those that follow: | Examples | Solution | |---|---| | (i) five hundred twenty seven | 527 | | (ii) twelve hundred sixty five | 1265 | | (iii) twenty six hundred eight | 2608 | | a. eight hundred twelve | 812 | | b. six hundred twenty one | 621 | | c. eighteen hundred seven | 1807 | | d. eleven hundred sixty eight | 1168 | | e. twenty five hundred forty two | 2542 | | f. one thousand two hundred five | 1205 | | g. twenty nine hundred six | 2906 | | h. nine thousand twenty | 9020 | | i. ten thousand six | 10006 | 5. Write the word number for each numeral listed below: * a. 106 = one hundred six * b. 67 = sixty seven * c. 235 = two hundred thirty five * d. 610 = six hundred ten * e. 501 = five hundred one * f. 1034 = one thousand thirty four * g. 1528 = one thousand five hundred twenty eight * h. 5202 = five thousand two hundred two 6. Match the word number in the left column with the numeral in the right column (draw an arrow between them). The first is done for you. * a. six hundred seventy -> 670 * b. twenty three hundred two -> 2320 * c. forty two thousand sixty five -> 42 065 * d. ten thousand ten -> 10 010 * e. twenty three hundred twenty -> 2320 * f. eleven thousand eleven -> 11 101 * g. ten thousand one hundred one -> 10 101 * h. forty two thousand six hundred five -> 42 605 * i. six hundred seven -> 607 * j. eleven thousand one hundred one -> 11 101 7. Use numerals to write each of the following numbers: * a. two hundred greater than twenty one = 221 * b. one thousand greater than five hundred nine = 1509 * c. two hundred less than one thousand three hundred = 1100 * d. three hundred less than twenty five hundred = 2200 * e. one hundred seventy two more than seven hundred = 872 * f. twelve hundred less than twenty five hundred = 1300 * g. seventeen more than fifteen hundred = 1517 * h. five hundred less than seventeen hundred = 1200 8. Use words to write each of the following numbers: * a. 28 more than 500 = five hundred twenty eight * b. 200 more than 750 = nine hundred fifty * c. 300 less than 2575 = two thousand two hundred seventy five * d. 100 more than 890 = nine hundred ninety * e. 1250 more than 1005 = two thousand two hundred fifty five * f. 210 more than 530 = seven hundred forty * g. 1400 less than 1750 = three hundred fifty ### Extra for Experts 9. I have 6 thousands, no hundreds, 2 tens and 3 ones = 6023 10. I have 3 hundreds, twice as many tens as hundreds, and no ones = 360 11. I have 11 ones and 2 tens = 211 12. I have 12 tens and 3 ones = 123 13. I have 13 hundreds, 5 tens and 15 ones = 1355 14. I have twice as many hundreds as tens, twice as many tens as ones, and 2 less than 3 ones = 842 15. I have 8 thousands, half as many tens as thousands, and one more ones than tens = 8405 16. I have the same number of thousands, hundreds, tens and ones. My number of ones is two more than three = 1111 ## 1.2 Comparing and Ordering Numbers ### Comparing Numbers When two numbers are compared to each other based on size (or magnitude), one of the following relationships exists between them: * They can be equal to each other. * The first can be less than the second. * The first can be greater than the second. We use the following symbols to represent each of these comparisons: | Symbols | Examples | |---|---| | "=” means is equal to | 125 is equal to 125. | | "<" means is less than | 2100 is less than 2200. | | “>” means is greater than | 500 is greater than 100. | Location on the number line can also be used to compare numbers. * Numbers that lie to the right of a given number are greater than (>) that number. * Numbers that lie to the left of a given number are less than (<) that number. **Examples with Solutions** 1. Use <, = or > to compare each pairs of numbers: * a. 120 > 102 * b. 2105 < 2109 * c. 219 < 227 * d. 1150 = 1150 * e. 21 - 10 = 9 + 2 * f. 38 < 41 * g. 15 x 10 < 15 x 12 * h. 223 + 5 > 225 + 1 * i. 130 - 7 > 120 + 2 * j. 412 + 7 > 413 + 5 2. What is higher or heavier, and by how much? * a. A bridge 122 m high or a building 110 m high: The bridge is 12 m higher (or the building is 12 m shorter). * b. A cat with a mass of 4 kg or a dog with a mass of 12 kg: The dog is 8 kg heavier (or the cat is 8 kg lighter). * c. A tree 15 m high or a house 9 m high: The tree is 6 m higher (or the house 6 m shorter). * d. A motorcycle with a mass of 50 kg or a car with a mass of 1500 kg: The car is 1450 kg heavier (or the motorcycle is 1450 kg lighter). ### Ordering Numbers Sometimes it is important to order numbers from the smallest to the largest or from the largest to the smallest. **Examples** * 1. The following numbers are ordered from smallest to largest: 205, 215, 221, 300, 309, 31, 1001 * 2. The same numbers are ordered from largest to smallest: 1001, 310, 309, 300, , 221, 215, 205 Use the following rules when ordering numbers in terms of size: * 1. First, look at the values of the numeral in the highest place value location. * 2. Next, look at the value in the second highest place value location, and so on. * 3. Order from smallest to largest or largest to smallest based on these results. **Example 1:** Order the following numbers from largest to smallest: 6019, 5819, 5822, 5918 * 1. 6019 is the largest since the 6 in the thousands place is the largest of the digits in the thousands place. * 2. Each of the other numbers have a 5 in the thousands place, so look for the hundreds place next. The highest digit in the hundreds place is 9, so 5918 is next. * 3. Since the remaining numbers each have an 8 in the hundreds place look at the tens place next. 5822 has a 2 in the tens place while 5819 has only a 1, so 5822 is next. * 4. The correct answer, ordering the numbers from largest to smallest is: 6019, 5918, 5822, 5819. **Example 2:** Order the following numbers from smallest to largest: 4213, 3999, 4220 * 1. 3999 is the smallest since the 3 in the thousands place is the smallest. * 2. Both 4213 and 4220 have a 2 in the hundreds place, so go to the tens place next. * 3. 4213 has a 1 in the tens place & 4220 has a 2 in the tens place, s 4213 is the smaller of the two. * 4. The correct answer from smallest to largest, is: 3999, 4213, 4220. **Examples with Solutions** 1. Which number is the largest: 6498, 6509, 6099? * 1. All three numbers have a 6 in the thousands place value location, so go to the hundreds place next. * 2. 6509 has a 5 n the hundreds place compared to a 4 and a 0 with the other numbers. * 3. 6509 is the largest number. 2. Which number is the smallest: 7519, 7545, 7538? * 1. All three numbers have 7 in the thousands place and a 5 in the hundreds place value locations, so go to the tens place. * 2. The smallest digit in the tens place is 1 in 7519. * 3. 7519 is the smallest number. 3. Order the following numbers from largest to smallest: 948, 3079, 3165, 899. * 1. Both 3079 and 3165 have a 3 in the thousands place, which makes them both larger than the other two numbers. Of these, 3165 is larger since it has a 1 in the hundreds place compared to a 0 for the other number. * 2. 948 is larger than 899 since it has a 9 in the hundreds place compared to an 8. * 3. Ordered from largest to smallest, the numbers are 3165, 3079, 948, 899. 4. Order the following numbers from smallest to largest: 5412, 5438, 4980, 4895. * 1. 4980 and 4895 are the smallest two numbers since they have a 4 in the thousands place. Of these, 4895 is the smaller since it has an 8 in the hundreds location. * 2. The next 2 numbers, that are larger than the first two, are 5412 and 5438. * 3. Of these last two numbers 5412 is the smaller since it has a 1 in the tens place, compared to a 3. * 4. Ordered from smallest to largest, the numbers are 4895, 4980, 5412, 5438. ### Exercises 1.2 1. Find the largest numeral in each of the following sets of numbers: * a. 450, 540, 539, 499, 509 = 540 * b. 2101, 2110, 2109, 1999 = 2110