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Stage 6 Mathematics: The Number System and Sequences

Worksheet
Primary Stage 6
English

Stage 6 Mathematics: The Number System and Sequences

Stage 6 Mathematics: Checkpoint-Style Revision

Name: ____________________________ Date: _____________________________ Class: ____________________________

Instructions:
  • Answer all questions.
  • Use a pen for writing and a pencil for any drawings.
  • Calculators are not allowed.
  • Pay attention to the marks available for each question.


Section 1: Place Value

  1. Write the value of the digit 7 in the number 213.807. [1 mark]

  1. Write the number Twelve thousand and forty-five point zero six in figures. [1 mark]

  1. What is the value of the digit 9 in the number 809.46? [1 mark]

  1. Complete the number sentence:
    
    ________________ [1 mark]
  1. Write down the number that is ten times bigger than 0.01. [1 mark]

  1. Write the terms of this partition in order of size, starting with the highest place value:
    
    [2 marks]

  1. Look at the digit cards below:
[ 2 ] [ 4 ] [ 6 ] [ 0 ] [ . ]
What is the smallest number, greater than 1, that you can make using all five cards? [2 marks]

  1. Use the place value grid below to show the number made of: 3 Tens, 1 One, 5 Tenths, and 8 Thousandths.
fig 1: Place value grid for decimals
fig 1: Place value grid for decimals

[2 marks]
  1. Find the 'odd one out' from these four values. Explain your answer.
  • 1.234
  • 1234 thousandths
  • 12.34
  • 123.4 hundredths
Odd one out: ____________________________________ Explanation: ____________________________________ [2 marks]
  1. Petra is regrouping decimal numbers. She spills ink on her work. What number is under the ink blot?
    
    💧 [2 marks]

  1. Fill in the missing numbers to complete the calculations: a)
    
    ____________ b)
    
    ____________ [2 marks]
  1. Fill in the missing numbers: a)
    
    ____________ b)
    
    ____________ [2 marks]
  1. Mira divides a number by 10, then by 10 again, and then by 10 again. Her final answer is 0.005. What number did she start with? [2 marks]

  1. Work out the value of
    
    in this number sentence:
    
    [2 marks]

  1. Look at these number cards: [ A: 1200 ] [ B: 1.2 ] [ C: 12000 ] [ D: 0.12 ]
Write the letter of the card that is: a) One thousand times bigger than 12: ________ b) One hundredth of 12: ________ [2 marks]
  1. Write down a number with three decimal places where the value of the thousandths digit is half the value of the tenths digit. [2 marks]

  1. Circle the calculation that has the same answer as
    
    .
    
    |
    
    |
    
    |
    
    [2 marks]


Section 2: Rounding Decimal Numbers

  1. Round 6.2 m to the nearest whole metre. [1 mark]

  1. Round 12.36 cm to the nearest tenth. [1 mark]

  1. Round
    
    to the nearest dollar. [1 mark]

  1. Circle the number that rounds to 5 when rounded to the nearest whole number. 4.35 | 4.05 | 5.5 | 5.05 [1 mark]
  1. Write down the smallest number with one decimal place that rounds to 100 when rounded to the nearest whole number. [2 marks]

  1. Tick (✓) the numbers that round to 7.5 when rounded to the nearest tenth. [ ] 7.49 [ ] 7.55 [ ] 7.51 [ ] 7.56 [2 marks]
fig 2: An athlete finishing a race
fig 2: An athlete finishing a race
  1. 
  1. An athlete runs a race in 13.9 seconds (measured to one decimal place). What is the slowest time the athlete could have run if their time was originally measured to two decimal places? [2 marks]

  1. Jasper says, "7.97 is 8 when rounded to the nearest whole number and is also 8 when rounded to the nearest tenth." Is Jasper correct? Show your working or explain. [2 marks]

  1. Correct the following false statement: "3.04 is 3 when rounded to the nearest whole number and 3.1 when rounded to the nearest tenth." Corrected version: _________________________________________________ [2 marks]
  1. A rectangle has sides measuring 5.4 cm and 6.7 cm. Round each measurement to the nearest whole centimetre and then estimate the perimeter. Rounded sides: ________ and ________ Estimated perimeter: ________ cm [2 marks]
  1. Choose the smallest number from this list that rounds to 1: 0.55 | 0.99 | 1.9 | 1.45 | 0.5 | 1.05 | 0 [2 marks]

  1. Round these measures to the nearest tenth: a) 55.55 litres -> ________ b) 12.22 metres -> ________ [2 marks]
  1. Round 456.702 to: a) the nearest whole number: ________ b) the nearest tenth: ________ [2 marks]
  1. A bag of flour weighs 1.45 kg. What is this weight to the nearest whole kilogram? [1 mark]

  1. Which of these numbers rounds to 3.9 when rounded to the nearest tenth? 3.84 | 3.95 | 3.86 | 4.0 [1 mark]

  1. Write down a number with two decimal places that rounds to 10 when rounded to the nearest whole number AND to the nearest tenth. [2 marks]



Section 3: Number and Sequences

  1. Find the missing numbers in this sequence which increases by equal amounts each time: 3, [ ], [ ], 15 [2 marks]
  1. A sequence starts at 15 and counts back in steps of 0.4. Write the next three terms: 15, 14.6, 14.2, _____, _____, _____ [2 marks]
  1. Samira counts on from 20 in steps of 1.001. 20, 21.001, 22.002, 23.003... What is the first number Samira says that is bigger than 30? [2 marks]

  1. Look at the position-to-term table below:
fig 3: Position-to-term table
fig 3: Position-to-term table

a) What is the position-to-term rule? ______________________ b) What is the 10th term in this sequence? ________________ [2 marks]
  1. Hassan counts back from 0 in steps of
    
    . Circle the numbers that Hassan would say: -1 | -1.2 | -2 | -2.5 | -4 [2 marks]
  1. Pablo counts up in quarters. He starts at
    
    . Write the missing numbers in his sequence:
    
    ,
    
    ,
    
    , 1, _____, _____, 2 [2 marks]
  1. A sequence has the rule: multiply the position by 4 and then add 2. What is the term for position 5? [2 marks]

  1. Ollie says, "In my sequence 15, 14.6, 14.2, 13.8..., the number 1.5 cannot be in the sequence." How do you know Ollie is correct without counting back? [3 marks]


  1. Complete the table for a sequence where the term is three times the position plus one.
Position
Term
1
4
2
____
5
____
____
31
[3 marks]
  1. A sequence of constant size has a first term of 1 and a fifth term of 1.04. Work out the second, third, and fourth terms. 1, ________, ________, ________, 1.04 [3 marks]
  1. Draw the next pattern in this sequence:
  • Pattern 1: 1 dot
  • Pattern 2: 4 dots (in a 2x2 square)
  • Pattern 3: 9 dots (in a 3x3 square)
(Draw Pattern 4 below)
How many dots will be in Pattern 10? ________ [3 marks]
  1. A sequence increases by 0.25 each time. The 4th term is 2. What is the 1st term? Show your working. [3 marks]

  1. Write the position-to-term rule for the sequence: 6, 12, 18, 24... Rule: ___________________________________________ Find the 50th term: __________________________ [3 marks]
  1. Match each sequence to its term-to-term rule:
  • 2, 4, 6, 8... • Add 0.5
  • 10, 9.5, 9, 8.5... • Multiply by 2
  • 1, 2, 4, 8... • Subtract 0.5
  • 0.5, 1, 1.5, 2... • Add 2 [3 marks]
  1. Look at this pattern of triangles:
  • Shape 1 uses 3 straws.
  • Shape 2 uses 5 straws.
  • Shape 3 uses 7 straws.
How many straws are needed for Shape 20? Explain your method. [3 marks]

  1. Jodi makes a sequence where the 10th term is 30. Give two possible position-to-term rules Jodi could be using. Rule 1: _________________________________________ Rule 2: _________________________________________ [3 marks]
  1. In the Northumberland Woods, there are 10 trees. Each tree has 10 branches. Each branch has 10 twigs. Each twig has 10 flowers. Each flower has 10 petals.
Sofia takes 1 petal, 1 flower, 1 twig, and 1 branch. How many petals are left in the woods? [3 marks]