Introduction to Numbers
This lesson introduces the main number terms needed before beginning a Year 6 mathematics programme. The tasks become gradually more difficult and repeatedly use ideas introduced earlier.
Fill in the gaps with terms. The hints help you to remember.
1. Ways of Writing Numbers
1. A is one of the ten symbols used to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
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1. How many digits are there in 48,306?
2. Which digit is in the tens place in 7,284?
3. True or false: 10 is a digit.
4. Which number contains exactly six digits?
5. Write the greatest four-digit number.
2. A is a written symbol or group of symbols used to represent a number.
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6. Write “four thousand and nineteen” as a numeral.
7. Which is a numeral?
8. Write the numeral made from 6 thousands, 4 hundreds, 2 tens and 9 ones.
9. True or false: “12,508” and “twelve thousand five hundred and eight” represent the same number.
10. Write the smallest numeral that can be made using 7, 0, 4 and 2 exactly once.
3. shows the value of every digit as an addition statement.
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11. Write 5,406 in expanded form.
12. Write 70,205 as an addition statement.
13. Which expanded form equals 9,081?
14. Write 400,000 + 20,000 + 700 + 9 as a numeral.
15. Complete the expanded form: 63,418 = 60,000 + 3,000 + 400 + ___ + 8.
4. is the value of a digit according to its position in a number.
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16. What is the value of 7 in 47,312?
17. Which digit is in the hundreds place in 96,843?
18. What is the value of 3 in 503,721?
19. Which number has 6 in the ten-thousands place?
20. A number has 4 hundred-thousands, 2 ten-thousands, 7 hundreds, 5 tens and 1 one. Write it as a numeral.
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2. Main Types of Numbers
1. are the numbers used for counting: 1, 2, 3, 4, ... . Some textbooks also include 0.
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1. Which is certainly a natural number?
2. True or false: -8 is a natural number.
3. Write the first five positive natural numbers, separated by commas.
4. Which number comes immediately after 999 in the natural-number sequence?
5. How many natural numbers are there from 7 to 12 inclusive?
2. are 0 and all positive counting numbers: 0, 1, 2, 3, ... .
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6. Which number is whole but may not be treated as natural in every textbook?
7. True or false: Every natural number is a whole number.
8. Which is not a whole number?
9. Write the whole number represented by 8 thousands + 3 tens + 4 ones.
10. What is the smallest whole number?
3. are negative whole numbers, zero and positive whole numbers.
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11. Which is an integer?
12. Write the integer immediately before -4.
13. Which is greater: -3 or -8?
14. The temperature rises from -6°C to 2°C. By how many degrees does it rise?
15. Put -2, 4, 0 and -7 in ascending order.
4. A represents part of a whole or a division of one number by another.
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16. What fraction of four equal boxes is shaded if three are shaded?
17. Which number is a fraction?
18. Write one half as a fraction.
19. True or false: 4/4 is equal to one whole.
20. Which is greater: 3/4 or 2/4?
5. A is a number written using a decimal point to show whole units and parts of a unit.
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21. Write seven tenths as a decimal.
22. Which digit is in the hundredths place in 4.386?
23. Write 3/10 as a decimal.
24. Which is greater: 0.6 or 0.56?
25. Put 0.9, 0.09 and 0.99 in ascending order.
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3. Properties of Whole Numbers
1. An is a whole number divisible by 2.
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1. Is 48 even?
2. Which is even?
3. Write the next even number after 198.
4. True or false: 0 is even.
5. Find the missing even number: 34, 36, ___, 40.
2. An is a whole number that is not divisible by 2.
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6. Is 75 odd?
7. Write the next odd number after 999.
8. Which description fits 17?
9. What is the sum of two odd numbers: odd or even?
10. Which number is odd and composite?
3. A is a whole number that divides another whole number exactly.
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11. Is 5 a factor of 30?
12. Which is not a factor of 24?
13. Write all positive factors of 10.
14. What is the greatest factor of every positive whole number?
15. Find the common factors of 12 and 18.
4. A is the result of multiplying a number by a whole number.
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16. Which is a multiple of 7?
17. Write the first five positive multiples of 6.
18. Is 1 a multiple of 8?
19. Write the least common multiple of 4 and 6.
20. A number is a multiple of both 3 and 5 and lies between 20 and 40. Write it.
5. A is a positive whole number with exactly two positive factors: 1 and itself.
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21. Which number is prime?
22. True or false: 1 is prime.
23. What is the only even prime number?
24. Which description fits 2?
25. Write all prime numbers between 10 and 20.
6. A is a positive whole number with more than two positive factors.
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26. Which number is composite?
27. True or false: 1 is composite.
28. Which description fits 9?
29. Write the smallest composite number.
30. A number is even, composite and has exactly three positive factors. What is it?
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4. Number Patterns and Powers
1. A is the result of multiplying a whole number by itself.
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1. Which is a square number?
2. Write the square of 9.
3. Complete the sequence: 1, 4, 9, 16, ___.
4. True or false: Every square number is even.
5. Which number is both a square number and an odd composite number?
2. A is the result of multiplying a whole number by itself twice.
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6. Write the cube of 4.
7. Which is a cube number?
8. Complete the sequence: 1, 8, 27, 64, ___.
9. True or false: 8 is both a cube number and a composite number.
10. Which number is both a square number and a cube number?
3. A is a compact way of showing repeated multiplication.
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11. Write 3 × 3 × 3 × 3 as a power.
12. Calculate 2⁵.
13. In 7³, what is the base?
14. In 7³, what is the exponent?
15. Which is equal to 5² + 2³?
4. follow one another without gaps.
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16. Write the number after 406.
17. Which set contains consecutive numbers?
18. Three consecutive numbers have 31 as the middle number. Write them.
19. The sum of three consecutive numbers is 36. What is the middle number?
20. Write the next consecutive prime number after 5.
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5. Fractions, Decimals and Percentages
1. The is the number above the fraction line. It shows how many parts are being considered.
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1. What is the numerator of 7/12?
2. In 9/10, which number counts the selected parts?
3. Write a fraction with numerator 4 and denominator 9.
4. True or false: In 5/8, 8 is the numerator.
5. Which fraction has a numerator of 6?
2. The is the number below the fraction line. It shows how many equal parts make one whole.
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6. What is the denominator of 11/15?
7. A cake is divided into 8 equal slices. What denominator should be used?
8. Write a fraction with numerator 3 and denominator 10.
9. Which fraction has the greatest denominator?
10. True or false: Fractions with the same denominator are divided into the same-sized number of parts.
3. A has a numerator smaller than its denominator, so its value is less than 1.
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11. Which is a proper fraction?
12. True or false: 9/10 is less than 1.
13. Write a proper fraction with denominator 7 and numerator 3.
14. Which is greater: 4/9 or 7/9?
15. How many proper fractions with denominator 5 have a positive whole-number numerator?
4. An has a numerator equal to or greater than its denominator, so its value is 1 or more.
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16. Which is an improper fraction?
17. Write 1 1/2 as an improper fraction.
18. Convert 11/4 to a mixed number.
19. True or false: 6/6 is an improper fraction equal to 1.
20. Which is greater: 9/5 or 7/5?
5. A contains a whole number and a proper fraction.
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21. Which is a mixed number?
22. Convert 5/2 to a mixed number.
23. Convert 3 2/5 to an improper fraction.
24. Which is greater: 1 3/4 or 1 2/4?
25. Add 1 1/2 and 2 1/2.
6. have different numerators and denominators but the same value.
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26. Complete: 1/3 = ___/6.
27. Which fraction is equivalent to 3/4?
28. True or false: 4/10 = 2/5.
29. Complete: 5/8 = 15/___.
30. Which pair is not equivalent?
7. A fraction is in its when its numerator and denominator have no common factor greater than 1.
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31. Simplify 8/12.
32. Simplify 15/20.
33. Is 5/7 already in simplest form?
34. Simplify 18/24.
35. Simplify 42/56.
8. A is a denominator shared by two or more fractions.
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36. Give the least common denominator of 1/2 and 1/3.
37. Rewrite 1/4 with denominator 12.
38. Rewrite 2/3 with denominator 12.
39. Add 1/4 + 2/4.
40. Add 1/2 + 1/3.
9. A expresses a number as a fraction of 100.
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41. Write 50% as a decimal.
42. Write 3/4 as a percentage.
43. Write 0.2 as a percentage.
44. Which is greatest?
45. A class has 20 students, and 5 are absent. What percentage are absent?
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6. Comparing, Ordering, Rounding and Estimating
1. means larger than. Its symbol is >.
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1. Complete with >, < or =: 38 ___ 29.
2. Which is greater: -2 or -7?
3. Complete: 3/4 ___ 2/4.
4. Complete: 0.8 ___ 0.75.
5. Which is greatest: 60%, 0.65 or 5/8?
2. means smaller than. Its symbol is <.
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6. Complete: 17 ___ 71.
7. Complete: -9 ___ -4.
8. Which is less: 2/3 or 3/4?
9. Complete: 0.09 ___ 0.9.
10. Which is least: 45%, 0.4 or 1/2?
3. means having the same value. Its symbol is =.
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11. Complete: 6 × 5 ___ 30.
12. Complete: 0.5 ___ 50%.
13. Complete: 3/5 ___ 6/10.
14. Which is equal to 0.25?
15. Complete: 2³ ___ 4².
4. means arranging values from smallest to largest.
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16. Arrange 8, 3, 11 and 1 in ascending order.
17. Arrange -2, 5, -7 and 0 in ascending order.
18. Arrange 0.5, 0.05 and 0.55 in ascending order.
19. Arrange 1/4, 3/4 and 1/2 in ascending order.
20. Arrange 40%, 0.35 and 3/8 in ascending order.
5. means arranging values from largest to smallest.
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21. Arrange 4, 19, 7 and 13 in descending order.
22. Arrange -1, -6, 2 and 0 in descending order.
23. Arrange 0.4, 0.04 and 0.44 in descending order.
24. Arrange 2/3, 1/6 and 1/2 in descending order.
25. Arrange 70%, 0.68 and 3/4 in descending order.
6. means replacing a number with a nearby number that is easier to use.
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26. Round 43 to the nearest ten.
27. Round 3,678 to the nearest hundred.
28. Round 58,499 to the nearest thousand.
29. Round 6.47 to the nearest whole number.
30. Round 3.786 to two decimal places.
7. means close in value but not exactly equal. Its symbol is ≈.
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31. Which symbol means “approximately equal to”?
Open the virtual mathematical keyboard , select the required symbol, and copy and paste it into the gap.
32. Complete: 49 + 31 ___ 50 + 30.
33. True or false: 3.14 = π exactly.
34. Round 198 to the nearest hundred.
35. Complete with = or ≈: 1/3 ___ 0.33.
8. An is a sensible approximate answer rather than an exact one.
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36. Estimate 198 + 304 by rounding each number to the nearest hundred.
37. Estimate 49 × 21 by rounding to the nearest ten.
38. Estimate £4.95 + £2.10 to the nearest pound.
39. A bus holds 49 people. About how many people can 8 buses hold?
40. Is 6,000 a reasonable estimate for 198 × 31?
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