Maths Year 5/6 Autumn Place Value

Each unit has everything you need to teach a set of related skills and concepts. 'Teaching for Understanding' provides whole-class teaching and fully differentiated adult-led group activities. ‘Problem-solving and Reasoning’ develops these skills, and includes questions to enable you to assess mastery. Practice sheets ensure procedural fluency. Extra support activities enable targeted work with children who are well below ARE.

‘UNIT PLAN’ gives you a text version of all parts of the unit to use in your school planning documentation. ‘DOWNLOAD ALL FILES’ gives you that unit plan plus all of associated documents. These bulk downloads are available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

Unit 1 PV and +/- in 5-digit and 6-digit numbers (suggested as 3 days)

Objectives

Place value in 5- and 6-digit numbers: place on lines, add and subtract
Unit 1: ID# 56110

Y5: Place value in 5-digit numbers, place on lines, add and subtract using place value.
Y6: Place value in 6-digit numbers, place on lines, add and subtract using place value.

National Curriculum
Y5: Num/PV (i) (ii) Add/Sub (ii)
Y6: Num/PV (i)

Y5 Hamilton Objectives
1. Read, write and locate 5- and 6-digit numbers on a landmarked line; use this to compare/order numbers; recognise the value of each digit.
3. Count forwards or backwards in steps of powers of 10 for any given number < 1,000,000.
7. Add/subtract mentally with confidence, where numbers are less than 100 or the calculation relies upon simple addition/subtraction and place value

Y6 Hamilton Objectives
1. Locate numbers up to 10 million on a landmarked line; use this to compare/order numbers.
5. Consolidate: Add /subtract mentally with confidence, where numbers are < 100 or it relies upon simple addition/subtraction and place value.

Teaching and Group Activities for Understanding

Day 1 Teaching
Use vertical place value charts to make 5-digit and 6-digit numbers, including using fewer than five cards. Work out what to subtract to ‘zap’ digits – change them to zero with one place value subtraction.
Group Activities
Y5 -- Identify the value of digits and ‘zap’ digits using subtraction … or … Add and subtract using place value.
Y6 -- Explore place value additions and subtractions in 6-digit numbers, based on a dice roll, or by changing digits to give an answer of 555,555.

Day 2 Teaching
Add and subtract 1s, 10s, 100s, 1000s and 10,000s to/from 5-digit numbers, using a calculator.
Further Teaching with Y6
Children form a counting machine with digit cards then count on in 1s, 10s and 100s.
Group Activities
Y5 -- Work out what to add and subtract, one step at a time, to make 55,555 or 99,999 from a starting number.
Y6 -- Work out what to add and subtract, one step at a time, to make 555,555 or 999,999 from a starting number.

Day 3 Teaching
Use digit cards to make smallest and largest 5-digit and 6-digit numbers possible and place approximately on landmarked lines.
Group Activities
Use one of the in-depth problem-solving investigations in ‘Activity Set A’ from NCETM as today’s group activity.
Or, use this activity:
Whole class activity using digit cards to make 5-digit or 6-digit numbers; compare and place on landmarked lines.

You Will Need

  • Vertical place value charts 1 and 2 (see resources)
  • Whiteboards and pens
  • 1–6 dice
  • 0–9 dice
  • Number cards 0–9
  • Flipchart and pens
  • Calculators
  • IWB calculator
  • 0–100,000 landmarked line (see resources)
  • 0–1,000,000 landmarked line (see resources)

Short Mental Workouts

Day 1
Place value in 4-digit numbers

Day 2
Count on and back in steps of 100

Day 3
Decimal pairs to 100

Procedural Fluency

Day 1
Y5: Use knowledge of place value to complete number sentences (5-digit numbers).
Y6: Use knowledge of place value to complete number sentences (6-digit numbers).

Day 2
Y5: Add and subtract 1, 10, 100, 1000 and 10,000. Add and subtract 1s, 10s, 100s, 1000s and 10,000s.
Y6: Add and subtract 1s, 10s, 100s, 1000s. 10,000s and 100,000s.

Day 3
Y5: Place 5-digit numbers on landmarked lines and compare them. Use given digits 1–5 to make numbers in given ranges.
Y6: Place data (6-digit numbers) on lines and compare.

Mastery: Reasoning and Problem-Solving

Y5

  • Sketch a line from 0–100,000. Mark on the line a mystery number (e.g. 5000). What number have I marked? Children ask questions to find the number, e.g. Is it 6000? Repeat.
  • How many numbers between 19,000 and 20,000 contain just one zero?

Y6

  • Sketch a line from 0–1,000,000. Mark on the line a mystery number (e.g. 400,000). What number have I marked? Children ask questions to identify the number. Repeat.
  • What is the smallest number between 800,000 and 900,000 which has just four digits all the same (no zeros allowed)?
  • How many numbers between 100,000 and 200,000 contain exactly four 9s?

Y5 and Y6

  • Add 1, 10 or 100 each go. How many goes to turn 98,089 into 99,999?

In-depth Investigation: Activity Set A
Choose an activity to explore place value in 5- and 6-digit numbers. Activity Set A from ncetm.org.uk

Extra Support

Y5: Digit Doom/Digit Delight
Understanding place value in 4-digit numbers

Y6: Pick 'n' Mix My Digits
Place value in 5-digit numbers; Adding and subtracting 1, 10, 100, 1000, 10,000

Unit 2 Numbers on a line; round to powers of 10 (suggested as 2 days)

Objectives

Place numbers on a line and round to powers of 10
Unit 2: ID# 56126

Y5: Place 4-digit and 5-digit numbers on lines and round to the nearest 10, 100, 1000 or 10,000.
Y6: Place 5-digit and 6-digit numbers on lines and round to nearest 10, 100, 1000, 10,000 or 100,000.

National Curriculum
Y5: Num/PV (i) (iv)
Y6: Num/PV (i) (ii)

Y5 Hamilton Objectives
1. Read, write and locate 5- and 6-digit numbers on a landmarked line; use this to compare/ order numbers; recognise the value of each digit.
2. Round any number up to 1,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000.

Y6 Hamilton Objectives
1. Locate numbers up to 10 million on a landmarked line; use this to compare/ order numbers.
2. Round to ten, a hundred, a thousand, ten thousand, one hundred thousand or a million, as appropriate.

Teaching and Group Activities for Understanding

Day 1 Teaching
Round distances between cities around the world to the nearest 10, 100 or 1000 miles, placing distances between neighbouring multiples of 10, 100 and 1000 to help.
Group Activities
Y5 -- Mark 4-digit distances between adjacent multiples; round to nearest 10, 100 and 1000. Some children will plan a world tour.
Y6 -- Mark 5-digit distances between adjacent multiples; round to nearest 10, 100 and 1000. Some children will plan a world tour.

Day 2 Teaching
Place 6-digit numbers between neighbouring multiples of 100,000; round to the nearest 100,000. Place 6-digit numbers between neighbouring multiples of 10,000; round to the nearest 10,000.
Further Teaching with Y5
Place 5-digit numbers between neighbouring multiples of 10, 100, 1000 and 10,000 to round to nearest 10, 100, 1000 and 10,000.
Group Activities
Use the problem-solving game/investigation ‘Nice or Nasty’ from NRICH as today’s group activity.
Or, use these activities:
Y5 -- Place 4-digit, then 5-digit numbers on landmarked lines; round to nearest 10, 100 and 1000, then to nearest 10,000.
Y6 -- Use number lines to support understanding of place value for marking numbers; round to nearest 10, 100, 1000, 10,000 or 100,000.

You Will Need

  • Whiteboards and pens
  • ‘Distances around the world’ (see resources)
  • ‘Marking and rounding distances’ (see resources)
  • Globe or world map
  • 3000–4000 landmarked lines (see resources)
  • Several sets of number cards 0–9
  • 0–1,000,000 landmarked lines (see resources)

Short Mental Workouts

Day 1
Place value in 5-digit numbers

Day 2
Times tables

Procedural Fluency

Day 1
Y5: Place 4-digit numbers on lines and round to the nearest 10, 100 or 1000.
Y6: Round distances and areas to the nearest 100 and 1000. Round areas of islands to nearest 10, 100, 1000, 10,000 or 100,000.

Day 2
Y5: Place 5-digit numbers on lines and round to the nearest 10, 100, 1000 or 10,000.
Y6: Round population numbers of UK cities to the nearest 10, 100, 1000, 10,000, 100,000.

Mastery: Reasoning and Problem-Solving

Y5

  • How many numbers round to 50,000 as the nearest 1000 and to 50,500 as the nearest 100?
  • Sketch a line from 67,000 to 68,000. Mark the 100s. Write two consecutive numbers between each pair of marks – one must round up to the nearest 100 and the other down. Say the numbers aloud .

Y6

  • How many numbers round to 550,000 as the nearest 10,000 and to 555,000 as the nearest 1000? [Hint: Sketch a number line to help visualise where these two ranges overlap.]
  • Sketch a line from 680,000 to 690,000. Mark the 1000s. Write two consecutive numbers between each pair of marks – one must round up to the nearest 1000 and the other down to the nearest 1000. Say the numbers aloud.
  • My answer has six digits. Four of the digits are identical and the other two are both 9. It rounds to 560,000 as the nearest 10,000. Write two different possible answers.

In-depth Investigation: Adapt Nice or Nasty (Game 3)
Work out the difference between two 5-digit numbers and an agreed target number. Keep a running total. The first player to 100,000 loses! Adapt Nice or Nasty (Game 3) from nrich.maths.org.

Extra Support

Y5: Astounding Rounding
Placing 3-digit numbers on a line and rounding to the nearest 10 and 100;
Placing 4-digit numbers on a line and rounding to the nearest 1000

Y6: Ring and Ring and Rounding!
Placing 4-digit numbers on a line and round to the nearest 10, 100 and 1000

Unit 3 Properties of numbers, including primes (suggested as 3 days)

Objectives

Properties of numbers, including prime numbers
Unit 3: ID# 56134

Y5: Find common multiples, factors and prime numbers.
Y6: Find common multiples, highest common factors and prime factors.

National Curriculum
Y5: Multi/Div (i) (ii) (iii)
Y6: Multi/Div (v)

Y5 Hamilton Objectives
12. Know and recite all times tables including division facts; identify multiples and factors, including common factors of two numbers.
13. Identify prime numbers up to 100 and know primes up to 19; understand the vocabulary of prime and composite numbers; identify prime factors.

Y6 Hamilton Objectives
9. Know all multiplication and division facts up to 12 ×12; identify common factors, common multiples, square numbers to 144 and prime numbers up to 20.

Teaching and Group Activities for Understanding

Day 1 Teaching
Identify multiples of given numbers on a grid. Discuss divisibility tests. Identify common multiples of two numbers. Identify the lowest common multiple.
Group Activities
Y5 -- Explore common multiples, either using a Venn diagram for sorting, or by playing a 4-in-a-row dice game.
Y6 -- Explore common multiples, either by playing a 4-in-a-row dice game or a card game.

Day 2 Teaching
Find factors of 2-digit numbers. Play a game to help children understand that bigger numbers don’t necessarily have more factors.
Further Teaching with Y6
Find common factors; then the highest common factor.
Group Activities
Use the ‘Long as you like’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y5 -- Investigation: Find the number less than 50 with the greatest number of factors; explore numbers which have an even or odd number of factors.
Y6 -- Play games finding common factors and then highest common factors.

Day 3 Teaching
Play a game which encourages children to think which numbers have fewest factors, introduce prime and composite numbers.
Group Activities
Y5 -- Investigation: Find all the prime numbers to at least 50.
Y6 -- Investigation: Find which numbers from 10 to 50 can be made by multiplying two prime numbers together.

You Will Need

  • ITP: Number Grid
  • Whiteboards and pens
  • IWB calculator
  • Flipchart and pen
  • Sticky notes
  • 12 × 12 multiplication grid (see resources)
  • 0–9 dice
  • Coloured pencils
  • Several sets of number cards 2–12
  • Large number cards 1–10
  • ‘Common factors’ grid (see resources, enlarge to A3)
  • ‘Common factors’ grid (see resources)
  • 1–6 dice

Short Mental Workouts

Day 1
Divisibility

Day 2
Stand up – sit down squares

Day 3
Times tables

Procedural Fluency

Day 1
Y5: Place numbers into a Carroll diagram, depending on divisibility by 3 and 4.
Y6: Find common multiples.

Day 2
Y5: Find factors of 2-digit numbers.
Y6: Find common factors of 2-digit numbers.

Day 3
Y5: Identify prime numbers to 100.
Y6: List prime numbers in a given range. Identify numbers with a pair of prime factors. Reduce a composite number to a list of its prime factors.

Mastery: Reasoning and Problem-Solving

Y5

  • Are there more or fewer common multiples of 2 and 3 under 30 than of 3 and 5? Explain your answer.
  • Write the common multiples of 2, 3 and 4 up to 50. Write the common multiples of 3, 4 and 5 up to 200. Which is the bigger group?
  • True or false?
    5 is a factor of 20 and a factor of 40.
    3 is a factor of 7 numbers less than 20.
    15 is a factor of 100.
  • Prime numbers are often one more or less than a multiple of 6. Write two prime numbers for which this is not true.
  • Write the following as the product of 2 or more prime numbers: 30, 35, 42, 56.

Y6

  • Which pair of numbers under 20 have the largest number of common factors? What is the highest common factor of these numbers?
  • Write common multiples of 4 and 6 up to 60. What is the lowest common multiple? Use this information to find the lowest common multiple of 8 and 12.
  • True or false?
    The lowest common multiple of two prime numbers, a and b is always a × b.
    The highest common factor of two multiples of 6 is always 6.

In-depth Investigation: Long as You Like
Children create chains of numbers by finding factors and multiples. Their aim is to create the longest chain possible.

Extra Support

Y5: Array or Disarray
Making different arrays using a given number as an introduction to factors.

Y6: Factor Hunt
Finding factors of numbers within times tables.