Short Blocks

Maths Year 3/4 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 added value for Hamilton Friends and School Subscribers.

Unit 1 Numbers on a line; compare and order (suggested as 3 days)

Objectives

Place numbers on a line; compare and order numbers
Unit 1: ID# 34110

Y3: Place 2-digit and 3-digit numbers on lines; compare and order.
Y4: Place 3-digit and 4-digit numbers on lines; compare and order.

National Curriculum
Y3: PV (iii) (iv)
Y4: PV (iv) (v) (vi)

Y3 Hamilton objectives
1. Read, write and locate any 3-digit number on a landmarked line from 0–1000 and use this to order and compare numbers.
2. Estimate quantities and represent numbers in different ways.

Y4 Hamilton objectives
1. Locate 4-digit numbers on a landmarked line and use this to compare and order numbers.

Teaching and Group Activities for Understanding

Day 1 Teaching
Mark 2-digit numbers on 0–100 beaded, landmarked and empty lines. Mark 3-digit numbers on 0–1000 landmarked lines and place numbers between multiples of 100.
Group Activities: T with Y3
Y3 -- Place 2-digit numbers on empty and landmarked lines.
Y4 -- Place 3-digit numbers on empty and/or landmarked lines.

Day 2 Teaching
Use skills learned to place numbers between 0 and 100 to place numbers between 100 and 200, then on 0–1000 landmarked lines.
Further Teaching with Y4
Place 4-digit numbers on 0 to 10,000 landmarked lines.
Group Activities: T with Y4
Use the in-depth problem-solving investigation ‘Round the Three/ Four Dice’ from NRICH as today’s group activity.
Or, use these activities:
Y3 -- Mark numbers on 100–200, or 0–1000, landmarked lines.
Y4 -- Place multiples of 50 on 0–10,000 landmarked lines, find the number halfway between them; order 4-digit numbers.

Day 3 Teaching
Play a game comparing 3-digit numbers (Y3) and 4-digit numbers (Y4) and place them on landmarked lines.
Whole Class Activity: T to circulate
-- Play a game comparing 3-digit numbers (Y3) and 4-digit numbers (Y4) and place them on landmarked lines. The winner of each round wins a digit card, which they use to try to make the larger number once the game has finished.

You Will Need

  • 0 to 100 beaded line (see resources)
  • 0 to 100 landmarked line (see resources)
  • 0 to 100 empty number line (see resources),
  • Additional activity sheets (see resources)
  • A4 paper
  • 0–9 dice, or 10s and 1s place value dice
  • Washing line/string, multiples of 100 (0–1000) on cards, blank cards, pegs
  • 0–9 digit cards
  • Flipchart and pens
  • 0-100 bead bar with tags for 0, 100, 200 and multiples of 10 (10–90)
  • A3 paper

Short Mental Workouts

Day 1
In between

Day 2
Count on and back

Day 3
Compare

Procedural Fluency

Day 1
Y3: Place 2-digit numbers on landmarked or empty 0–100 lines.
Y4: Place 3-digit numbers on landmarked or empty 0–1000 lines.

Day 2
Y3: Place numbers on 100–200 landmarked lines. Place numbers on 0–1000 landmarked lines.
Y4: Place 4-digit numbers on 0–10,000 number lines.

Day 3
Y3: Compare 3-digit numbers and place them on lines between 100 and 200/ 0 and 1000.
Y4: Order 4-digit numbers and place them on lines.

Mastery: Reasoning and Problem-Solving

Y3

  • Sketch a line 0–1000. Mark 500. Draw arrows to 250, 350 and 850.
  • True or false?
    - There are always four numbers between two multiples of 5.
    - There are always nine numbers between two multiples of 10.
    - The number before a multiple of 10 always ends in 9.
  • What number will be marked halfway between 125 and 151 on the number line?

Y4

  • Sketch a line 0–10,000. Mark 5000. Draw arrows to 7500, 3200, 8700 and 5500.
  • Count in 1s. Work out what digits a and b are. Write the next number: 54aa, 54ab, 54b0, _____

In-depth Investigation
Round the Three Dice

Which 100s number is your 3-digit number closest to? Round the Three Dice from nrich.maths.org.

Round the Four Dice
Which 1000s number is your 4-digit number closest to? Round the Four Dice from nrich.maths.org.

Extra Support

Y3: Bigger or Beaten
Partitioning and comparing 2-digit numbers

Y4: Walk the Line
Placing 3-digit numbers on a 100 to 200 line, then a 0 to 1000 landmarked line

Unit 2 PV in 3-/4-digit nums; amounts of money (suggested as 4 days)

Objectives

Place value in 3-digit and 4-digit numbers and amounts of money
Unit 2: ID# 34126

Y3: Place value in 3-digit numbers and amounts of money.
Y4: Place value in 4-digit numbers and amounts of money.

National Curriculum
Y3: PV (ii) (iv) (v) (vi) Measures (iii)
Y4: PV (iv) (vi) (viii)

Y3 Hamilton objectives
2. Estimate quantities and represent numbers in different ways.
3. Understand place value in 3-digit numbers; add and subtract 1, 10 or 100 without difficulty.
5. Solve number problems and practical problems involving place value.
32. Add and subtract amounts of money and give change by counting up; use both £ and p in practical contexts.

Y4 Hamilton objectives
3. Understand the numbers of 1s, 10s, 100s, 1000s in a 4-digit number and the use of zero as a placeholder.
9. Solve number and practical problems involving place value.

Teaching and Group Activities for Understanding

Day 1 Teaching
Explore place value in 3-digit numbers using place value cards and grids, and worded place value charts.
Further Teaching with Y4
Explore value in 4-digit numbers using place value cards and grids, and worded place value charts.
Group Activities: T with Y4
Use the ‘No zero’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
Y3 -- Read 3-digit numbers in words and numerals, or use digit cards to create 3-digit numbers, then write corresponding place value additions. Order numbers.
Y4 -- Read 4-digit numbers in words and numerals, or use digit cards to create 4-digit numbers, then write corresponding place value additions. Order numbers.

Day 2 Teaching
Use place value cards to help solve and write place value additions and subtractions (3-digit numbers).
Further Teaching with Y4
Use place value grids to help solve and write place value additions and subtractions (4-digit numbers).
Group Activities: T with Y4
Y3 -- ‘Zap’ digits in 3-digit numbers using a calculator.
Y4 -- ‘Zap’ digits in 4-digit numbers using place value subtractions.

Day 3 Teaching
Use a place value grid to support ‘zapping’ two digits in 3-digit and 4-digit numbers.
Further Teaching with Y3
Write amounts between £1 and £10 using £p notation and in PV grid.
Group Activities: T with Y3
Y3 -- Identify a given amount of money and write it in £ and p notation … or … Identify two coins from clues and explore zero as a placeholder in money amounts.
Y4 -- Find missing numbers and functions in place value additions and subtractions.

Day 4 Teaching
Write amounts of money in place value grids. Write place value additions and subtractions for these amounts.
Group Activities: T with Y3
Y3 -- Solve word problems or missing number problems involving place value additions and subtractions of money.
Y4 – Explore place value calculation with money, adding and subtracting multiples of £10, £1, 10p and 1p.

You Will Need

  • Mini-whiteboards and pens
  • 1000s, 100s, 10s and 1s place value cards
  • ‘Worded place value chart: 3-digits’ (see resources)
  • ‘Worded place value chart: 4-digits’ (see resources)
  • Flipchart and pens
  • Counters
  • 0–9 number cards
  • 0–9 digit cards, with extra 0 card (1 set of cards per pair)
  • large 100s, 10s and 1s place value cards
  • Calculators
  • Mobile keypad (see resources)
  • Additional activity sheets (see resources)
  • Real coins: £1s, 10ps and 1ps
  • Sticky notes

Short Mental Workouts

Day 1
Place value

Day 2
Place value 2

Day 3
Count in steps of 25

Day 4
Place 2-digit numbers on an empty 0–100 line

Procedural Fluency

Day 1
Y3: Place value additions, words and numerals (3-digit numbers).
Y4: Place value additions, words and numerals (4-digit numbers).

Day 2
Y3: Place value subtractions (3-digit numbers).
Y4: Place value subtractions (4-digit numbers).

Day 3
Y3: Money place value additions (3 digits).
Y4: Money place value additions (4 digits).

Day 4
Y3: Solve money problems.
Y4: Money place value additions and subtractions.

Mastery: Reasoning and Problem-Solving

Y3

  • Rings slide down onto the rods on a counting frame to make 3-digit numbers (see images on download). How many different 3-digit numbers can you create with three rings? Four rings? Five rings? Describe any patterns you notice.
  • ☐ + 108 = 148
    238 – ☐ = 38
    ☐ + 40 = 846
  • Jo has more than £1.50 and less than £2. She has three coins, all different. None are brown. How much could she have?
  • £2 – ☐ = £1.55
    ☐ + £1.23 = £2.30
    £4 + ☐ = £4.51
    £6.02 – ☐ = £5.00

Y4

  • Draw a place value grid. Use digits 9 and 0 (must use both) and create the largest and smallest 4-digit numbers possible. Use the same digits to write 2 numbers in between.
  • What is the largest possible 4-digit number that has digits which add to 10? It must not contain a 0 and no two digits are the same. What is the smallest possible number like this?
  • Write the missing numbers:
    ☐ + 4040 = 9099
    6166 – ☐ = 6001
    £45.79 – ☐ = £39.99
    ☐ – £4.07 = £40.30
  • Megan has an amount between £10 and £30. She has one note and three coins. What is the most she could have? And the least?

In depth Investigation: No Zero
Children investigate how many numbers between one and ten thousand have a zero. They use their understanding of place value in numbers with up to 4-digits.

Extra Support

Y3: Coin Count Up
Writing amounts of money in pounds and pence

Y4: Digit Do-it
Partitioning 3-digit numbers, and combining 100s, 10s and 1s to make 3-digit numbers

Unit 3 +/- 1, 10, 100 and 1000, and multiples (suggested as 3 days)

Objectives

Add and subtract 1, 10, 100 and 1000, and multiples of these
Unit 3: ID# 34142

Y3: Add and subtract 1, 10, 100 and multiples of these to/from 3-digit numbers.
Y4: Add and subtract 1, 10, 100, 1000 and multiples of these to/from 4-digit numbers.

National Curriculum
Y3: Num/PV (i) (ii), AS (i) (iv)
Y4: Num/PV (i) (ii) (iv)

Y3: Hamilton objectives
3. Understand place value in 3-digit numbers; add and subtract 1, 10 or 100 without difficulty.
9. Mentally add and subtract multiples of 1s, 10s and 100s to/from 3-digit numbers.

Y4: Hamilton objectives
3. Understand the numbers of 1s, 10s, 100s, 1000s in a 4-digit number and the use of zero as a placeholder.
6. Add multiples of 1, 10, 100, 1000 without difficulty, e.g. 5,347 + 3000, 434 + 300 and 648 – 220.

Teaching and Group Activities for Understanding

Day 1 Teaching
Add/subtract 1, 10, 100 to/from 3-digit numbers using place value cards (Y3) and to/from 4-digit numbers (Y4), then also add/subtract 1000 (Y4). Calculations do not 10s, 100s, or 1000s.
Group Activities: T with Y3 or Y4
Y3 -- Play a dice game, or complete an investigation, adding and subtracting 1, 10 and 100.
Y4 -- Play a dice game, or complete an investigation, adding and subtracting 1, 10, 100 and 1000.

Day 2 Teaching
Write 3-digit numbers (Y3) or 4-digit numbers (Y4) in place value grids. Add/subtract 1, 10 and 100, crossing 10s and 100s.
Further Teaching with Y4
Add and subtract 100, crossing through multiples of 1000.
Group Activities: T with Y3
Y3 -- Play a choice of games, adding and subtracting 1, 10 and 100.
Y4 -- Play a choice of games, adding and subtracting 1, 10, 100 and 1000.

Day 3 Teaching
Write 3-digit numbers (Y3) or 4-digit numbers (Y4) in place value grids. Add/subtract 2, 3, 20, 30, 200 or 300. Add/subtract using place value to end up with 555 or 5555.
Group Activities: T with Y3 or Y4
Y3 -- Use an inverse operation to work out what multiple of 1, 10 or 100 has been added/subtracted.
Y4 -- Use an inverse operation to work out what multiple of 1, 10, 100 or 1000 has been added/subtracted.

You Will Need

  • Mini-whiteboards and pens
  • 1000s, 100s, 10s and 1s place value cards
  • Flipchart and pens
  • 1–6 dice
  • 0–9 cards, one set per pair
  • Tug of war: 495 to 505, 495 to 615, 150 to 950 number lines (see resources, copy onto A3 paper)
  • Tug of war: 4995 to 5005, 5495 to 5615, 1850 to 3050 and 62 to 10,062 number lines (see resources, copy onto A3 paper)
  • Counters
  • Coins
  • +/– 2, 3, 20, 30, 200 and 300 cards (see resources)
  • +/– 2, 3, 20, 30, 200, 300, 2000 and 3000 cards (see resources)

Short Mental Workouts

Day 1
Count on and back in 1s

Day 2
Count on and back in steps of 10

Day 3
Time quiz

Procedural Fluency

Day 1
Y3: Add/subtract 1, 10 and 100, not crossing 10s or 100s.
Y4: Add/subtract 1, 10, 100 and 1000, not crossing 10s, 100s or 1000s.

Day 2
Y3: Work out what has been added/ subtracted.
Y4: Count through 10s, 100s and 1000s in steps of 1, 10 and 100.

Day 3
Y3: Complete addition and subtraction grids, adding/subtracting multiples of 1, 10 and 100.
Y4: Complete addition and subtraction grids, adding/subtracting multiples of 10, 100 and 1000.

Mastery: Reasoning and Problem-Solving

Y3

  • Add sequences of 1s, 10s, and 100s: 473 + 1 – 10 + 100. Use different starting numbers. Look for patterns.
  • Start at 375. Add a multiple of 10 which only changes one digit. Add a multiple of 10 which changes two digits.
  • Do three identical subtractions to get from 285 to 225. What number are you subtracting?

Y4

  • Write the missing digits in this sequence of numbers:
    4865, 48☐5, 4☐85, 48☐5, 4☐☐5
  • True or false? If you start with a 4-digit number and subtract 10 nine times, you will always have to change the hundreds digit.
  • Complete this sequence by adding 30 each time.
    2467, ______, ______, ______, 2587
  • Do 3 identical subtractions to get from 3265 to 2365. What number are you subtracting?

In depth Investigation
Complete the Day 1 or Day 2 Group Activities.

Extra Support

Y3
Spider Sums

Adding 10s to 2-digit numbers (answers less than 100); Subtracting 10s from 2-digit numbers

Y4
Flipping Fun

Place value in 3-digit numbers. Adding and subtracting 1, 10 and 100

Tens Chains
Adding and subtracting 10s to and from 3-digit numbers