Maths Year 5 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 Place value in 5-digit numbers (suggested as 3 days)

Objectives

Writing 5-digit numbers and understanding the value of each digit
Unit 1: ID# 5107

National Curriculum
Num/PV (i)

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
5. Solve number problems and practical problems involving place value.

Teaching and Group Activities for Understanding

Day 1 Teaching
Model writing numbers dictated in words and show the place value of each digit using a place value chart. Write place value additions and subtractions, e.g. 43,561 – 3000.
Group Activities
-- Work out what to add to a number with one zero, e.g. 50,555 to make all digits the same.
-- Identify numbers with digits of given value.
-- Create 5-digit numbers from given digits.

Day 2 Teaching
Start with a 5-digit number and add/subtract 1s, 10s, 100s, 1000s, 10,000s to get a number with all the digits the same, e.g. 44,444. Discuss how to do this, letting children have a go first. Agree the place value of each digit.
Group Activities
Use the in-depth problem-solving investigation ‘Space Distances’ from NRICH as today’s group activity.
Or, use these activities:
-- Play a game adding 1s, 10s, 100s, 1000s, and 10,000s.
-- Work out what to add and subtract, one stage at a time to make the number 55,555.
Day 3 Teaching
Generate 5-digit numbers using cards, then place these on a line and compare pairs of numbers. Ensure children know which digits are most important when ordering or comparing numbers.
Group Activities
-- Play a game creating and comparing 5-digit numbers.

You Will Need

  • Vertical place value chart (see resources)
  • Calculators
  • Mini-whiteboards and pens
  • IWB calculator
  • 1–6 dice per pair
  • Blank dice & wipe-off marker pen per pair
  • 0–9 digit cards
  • 0–100,000 landmarked line (see resources)

Mental/Oral Maths Starters

Day 1
Place value in 4-digit numbers (pre-requisite skills)

Day 2
Add/subtract 100 or 1000 to/from 4-digit numbers (pre-requisite skills)

or
Count on/back in 10s from 3-digit numbers (pre-requisite skills)

Suggested for Day 3
Pairs to 100 (simmering skills)

Procedural Fluency

Day 1
Use knowledge of place value to complete number sentences.

Day 2
Add/subtract 1, 10, 100, 1000 and 10,000.

Day 3
Place 5-digit numbers on landmarked lines and compare them.
Use given digits 1–5 to make numbers in given ranges.

Mastery: Reasoning and Problem-Solving

  • Sketch a line 0–100,000. Teacher marks a mystery number (e.g. 5000). What number have I marked? Children ask question to guess. Repeat.
  • Add 1, 10 or 100 each go. How many goes to turn 98,089 into 99,999.


In-depth Investigation: Space Distances
This task focuses on distances travelled by the asteroid 'Florence', providing the opportunity to add and subtract powers of 10. Space Distances from nrich.maths.org.

Extra Support

Digit Doom/Digit Delight
Understanding place value in 4 digit numbers

Unit 2 Place 5-digit numbers on a line; round (suggested as 2 days)

Objectives

Place 4- and 5-digit numbers on a line
Round numbers
Unit 2: ID# 5113

National Curriculum
Num/PV (i) (iv)

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.

Teaching and Group Activities for Understanding

Day 1 Teaching
Display a table of distances between places around the world and then place these 4-digit numbers on number lines. Look at what is the nearest 10 miles, or 100 miles or 1000 miles. Use these to round numbers to nearest 10, 100 and 1000.
Group Activities
- -Mark distances between places around the world on lines between adjacent multiples of 10, 100 and 1000; round to nearest 10, 100 and 1000.
-- Plan a world tour, round to find approximate total distance.

Day 2 Teaching
Children sketch a line from 55,700 and 55,800 and think of a number between 55,700 and 55,800 to mark on the line. Discuss the lines drawn, numbers marked and which is the nearest multiple of 100. Repeat with other lines/numbers.
Group Activities
Use the in-depth problem-solving investigation ‘Adapt Nice or Nasty (Game 3)’ from NRICH as today’s group activity.
Or, use these activities:
-- Mark 5-digit numbers between adjacent multiples of 10, 100, 1000 and 10,000; round to nearest 10, 100, 1000 and 10,000.
-- Place 4-digit numbers on landmarked lines; round to nearest 10, 100 and 1000.

You Will Need

  • Table of distances between places (see resources)
  • Globe (optional)
  • Mini-whiteboards & pens
  • 0–9 digit cards
  • 3000–4000 landmarked lines, 100s labelled (see resources)

Mental/Oral Maths Starters

Day 1
‘Zap’ digits in a 4-digit number (pre-requisite skills)

or
Count on/back in 10s, 100s, 1000s from 4-digit numbers (pre-requisite skills)

Suggested for Day 2
Times tables (simmering skills)

Procedural Fluency

Day 1
Place 4-digit numbers on lines and round to the nearest 10, 100 or 1000.
Draw lines between adjacent multiples of 10, 100 and 1000; round 4-digit numbers to nearest 10, 100 and 1000.

Day 2
Place 5-digit numbers on lines and round to the nearest 10, 100, 1000 or 10,000.

Mastery: Reasoning and Problem-Solving

  • How many numbers round to 50,000 as the nearest 1000 and to 50,500 as the nearest 100?
  • Sketch a line from 67,000–68,000 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.


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

Extra Support

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

Unit 3 Place 6-digit numbers on a line; round (suggested as 3 days)

Objectives

Place value in 6-digit numbers
Placing on a line and rounding
Unit 3: ID# 5119

National Curriculum
Num/PV (i) (ii) (iv)

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.
3. Count forwards or backwards in steps of powers of 10 for any given number > 1 000 000

Teaching and Group Activities for Understanding

Day 1 Teaching
Talk about how we write 6-digit numbers with a comma or thin space to indicate a break between the 1000s and 100s. Build numbers from the 1s upwards, writing spoken numbers in turn. Generate 6-digit numbers by rolling a dice.
Group activities
-- Compare and use place value to subtract from 6-digit numbers.
-- Use place value subtraction to ‘zap’ each digit in a 6-digit number.

Day 2 Teaching
Use the IWB calculator’s constant function to repeatedly add then subtract 1, 10, 100, 1000, 10,000 and 100,000 to 6-digit numbers. Check that children can cross the place value boundaries when adding powers of ten.
Group activities
-- Add 1, 10, 100, 1000, 10,000 and 100,000 to 6-digit numbers.
-- Add and subtract 1, 10, 100, 1000, 10,000 and 100,000 to/from 6-digit numbers.
-- Find mystery numbers following addition or subtraction of 1, 10, 100, 1000, 10,000 and 100,000.

Day 3 Teaching
Draw a 0–1,000,000 line and mark the 100,000s. Children place given 6-digit numbers on the line and round them to the nearest multiple of 100,000. Write 6-digit numbers between 125,000 and 126,000 and ask children for the nearest multiple of 1000.
Group activities
Use the in-depth problem-solving investigation ‘Adapt Nice or Nasty (Game 5, Nasty Version)’ from NRICH as today’s group activity.
Or, use these activities:
-- Mark 6-digit numbers between adjacent multiples of 100 and 1000; round to the nearest 100 and 1000.
-- Place 6-digit numbers on landmarked lines; round to the nearest 100 and 1000.
-- Estimate a mystery 6-digit number marked on a 200,000–300,000 line.

You Will Need

  • Vertical place value chart (see resources)
  • 0–9 dice
  • Calculators
  • IWB calculator
  • 1–6 dice
  • Landmarked lines (see resources)
  • Post-it notes
  • 0–9 digit cards

Mental/Oral Maths Starters

Day 1
Place value in 5-digit numbers (pre-requisite skills)

Day 2
Count on/back in 10s, 100s, 1000s from 4-digit numbers (pre-requisite skills)

Suggested for Day 3
Double 2-digit numbers (simmering skills)

or
Pairs to 100 (simmering skills)

Procedural Fluency

Day 1
Write 6-digit numbers with digits of given values.
Write missing digits in numbers to create ascending/descending list of 6-digit numbers.

Day 2
Add/subtract 1, 10, 100, 1000, 10,000 and 100,000; preserve inequalities.

Day 3
Place 6-digit numbers on lines and round to the nearest 100 or 1000.

Mastery: Reasoning and Problem-Solving

  • How many palindromic 6-digit numbers can be written using only 7 and 0? Read each number aloud.
  • Write the missing digits in this sequence of numbers:
    449,998, 44☐,9☐9
    4☐☐,☐☐0
    4☐☐,☐☐1
  • True or false?
    11 more than a number ending in 9 is always a multiple of 10.
    11 less than a number ending in 11 is always a multiple of 100.
    111 more than a number ending in 999 is never a multiple of 1000.


In-depth Investigation: Adapt Nice or Nasty (Game 5, Nasty Version)
Work out the difference between two six-digit numbers and an agreed target number. Keep a running total. First player to 1,000,000 loses! Adapt Nice or Nasty (Game 5, Nasty Version) from nrich.maths.org.

Extra Support

Back to the Start
Adding/subtracting 1, 10, 100 and 1000 to/from 4-digit numbers (not crossing 10s, 100s or 1000s)

Line ‘em Up
Placing 4-digit numbers on landmarked lines

Unit 4 Deepen understanding of 6-digit numbers (suggested as 2 days)

Objectives

Order, compare, round 6-digit nos
Place value additions and subtractions
Unit 4: ID# 5147

National Curriculum
Num/PV (i) (v)

Hamilton Objectives
3. Count forwards or backwards in steps of powers of 10 for any given number > 1 000 000
5. Solve number problems and practical problems involving place value.

Teaching and Group Activities for Understanding

Day 1 Teaching
Read out numbers for children to write in numerals. Add 10,000 to and subtract 1000 from each number. Encourage children to say numbers of thousands aloud so they understand crossing a PV boundary, e.g. 420 thousand subtract 1 thousand equals 419 thousand. Children then add 2030 to and subtract 200,002 from different numbers.
Group activities
-- Add/subtract 1, 10, 100, 1000, 10,000 and 100,000 to/from 6-digit numbers.
-- Find starting numbers when given answers 101, 1001, 10,001 and 100,001 have been added to 6-digit numbers.
-- Investigate how many digits change when numbers are added to a 6-digit starting number.

Day 2 Teaching
Round 427,789 to the nearest 10, 100, 1000, 10,000 and 100,000. Use digit cards to make three 6-digit numbers and write an inequality to show them. Make numbers close to 500,000.
Group activities
Use the in-depth problem-solving investigation ‘Activity Set A’ from NCETM as today’s group activity.
Or, use these activities:
-- Write digits to create a chain of ascending 6-digit numbers.
-- Place 6-digit numbers on landmarked lines and round populations to the nearest 100,000.

You Will Need

  • Mini-whiteboards and pens
  • 0–9 digit cards
  • Paper and pens
  • Populations of UK cities table (see resources)
  • 0–1,000,000 landmarked line (see resources)

Mental/Oral Maths Starters

Suggested for Day 1
Change from £1 (simmering skills)

or
Revise subtraction facts to 20 (simmering skills)

Day 2
Round 3-digit numbers to the nearest 10 or 100 (pre-requisite skills)

Procedural Fluency

Day 1
Use place value to add and subtract (2 versions).

Day 2
Round populations to the nearest 10,000 and 100,000.
Use digits to make 6-digit numbers less than, more than or equal to given numbers.

Mastery: Reasoning and Problem-Solving

  • 234,500, 275,500 and 290,900 are clearly marked on a number line. What two hundred-thousands numbers mark the beginning and end of the line?
  • How many times must Fred add 202,020 to 30,303 to get over 1 million?
  • Write 5 different numbers that round to 500,000 as the nearest thousand, hundred and ten.


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

Extra Support

Guess my Number
Understanding place value in 5-digit numbers