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# Maths Year 4 Summer 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 Place and round 4-digit numbers on lines (suggested as 2 days)

### Objectives

Place 4-digit numbers on land-marked lines and round
Unit 1: ID# 4937

National Curriculum
Num/PV (iv) (v) (vi) (vii)

Hamilton Objectives
1. Read, write and locate any 3-digit number on a landmarked line from 0-1000; use this to locate 4-digit numbers on a landmarked line and use this to compare/order numbers.
2. Round to ten, a hundred and a thousand.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Two children stand at either end of the room. One holds 4600; the other holds 4700. Quietly support a third child to stand where 4654 might be between these two multiples of 100. Children discuss, in groups, what the number might be. Then they say what two multiples of 10 they would like on the line, then revise guesses. Round 4654 to the nearest 10. What is 4655 rounded to the nearest 10?
Group Activities
-- Create 4-digit numbers to mark on a number line. Then round to nearest 10.
-- Create 4-digit numbers. Mark the numbers on a section of number line between neighbouring multiples of 10. Circle the nearest 10.
-- Quick-fire rounding to nearest 10.

Day 2 Teaching
Two children stand at either end of the room. One holds 5000; the other holds 6000. A third child stands where 5579 belongs. In groups, children guess the number. Children choose two multiples of 100 to ‘zoom in’ on, to replace the end numbers on the line; groups then revise their estimates. Round 5579 to the nearest 100 (5600). Agree a number between 5500 and 5600 which rounds to 5500. Ask a child to hold this number in approximately the right place. Which 100s number would we round 5550 to? (5600)
Group Activities
-- Create 4-digit numbers to mark on a number line. Then round to nearest 100.
-- Create 4-digit numbers. Mark the numbers on a section of number line between neighbouring multiples of 100. Circle the nearest 100.
-- Quick-fire rounding to nearest 100.

Day 3 Teaching
Show children a 0–10,000 line marked in 1000s, with three numbers marked but not labelled. Children work out which of the six numbers written underneath the line each number on the line might be. Reason about positions on the line. Round each marked number to the nearest 1000. Write a number between 3000 and 4000 which rounds down to 3000/ up to 4000.
Group Activities
Use the in-depth problem-solving investigation ‘The Thousands Game’ from NRICH as today’s group activity.
Or, use these activities:
-- Create 4-digit numbers to mark on a number line. Then round to nearest 1000.
-- Play a game, rounding numbers 0 to 10,000 to the nearest 1000.

### You Will Need

• Mini-whiteboards and pens
• Number cards 0–9
• ‘Round to the nearest 10’ (see resources)
• Number cards 2–6
• Random number generator
• ‘0–10,000 line’ (see resources)
• ‘5000 to 6000 lines’ (see resources)
• Flipchart and coloured pens
• 1000s cards (e.g. from place value cards)

### Mental/Oral Maths Starters

Day 1
Compare 4-digit numbers (pre-requisite skills)

Day 2
Place 3-digit numbers on an empty number line (pre-requisite skills)

Day 3
Order 4-digit numbers (pre-requisite skills)

### Procedural Fluency

Day 1
Mark 4-digit numbers on landmarked lines and round to the nearest 10.

Day 2
Mark 4-digit numbers on landmarked lines and round to the nearest 100.

Day 3
Mark 4-digit numbers on landmarked lines and round to the nearest 1000.

### Mastery: Reasoning and Problem-Solving

• Estimate the number shown by the arrow on this number line:
 | ↑ | 2000 3000
• Circle the number which is closer to 2000:
1997, 2007
Explain how you know.
• Round 7483 to the nearest 10, nearest 100 and nearest 1000.
• Round these numbers to the nearest 100: 127, 1272, 12,727.

In-depth Investigation: The Thousands Game
Each child in Class 4 took four numbers out of the bag. Who had made the highest even number? The Thousands Game from nrich.maths.org.

### Extra Support

100s Neighbours
Placing 3-digit numbers on landmarked lines.

## Unit 2 Negative numbers in temperature (suggested as 2 days)

### Objectives

Recognise negative numbers in the context of temperature
Unit 2: ID# 4951

National Curriculum
Num/PV (iii)

Hamilton Objectives
5. Recognise negative numbers in relation to number lines and temperature.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Use Thermometer ITP. Choose a range of −10 to 20. At what temperature does water freeze? On a cold night the temperature might fall 1 degree below 0 degrees Celsius (0°C). What is the temperature then? Say this is called ‘minus 1’. Show how this is written as ‘−1°C’. Count from 0 down to −10°C. Say that numbers less than zero are called negative numbers, and numbers more than zero are called positive numbers. Use the ITP to show and calculate temperature differences – both rises and falls – either side of 0°C.
Group Activities
Use the in-depth problem-solving investigation ‘Sea Level’ from NRICH as today’s group activity.
Or, use these activities:
-- Order positive and negative numbers. Investigate temperatures in a range of locations and solve problems relating to temperature differences.

Day 2 Teaching
Count back in ones from 5 at the top of a vertical counting stick. 5, 4, 3, 2, 1, 0, what comes next? Continue, minus one, minus two…. Write 0, −2 and −4 on sticky notes and ask children where they belong on the stick. Repeat for a horizontal stick.
Give each pair of children some cards/ sticky notes with −5, −4, −3… 5 in random order and ask them to put them in order.
Choose pairs of numbers between −10 and 10. On whiteboards, children write < or > between the numbers to complete inequalities, e.g. 3 > −7, −9 < 8, etc.
Group Activities
-- Practise ordering cards −10 to 10. Write three consecutive negative numbers, given the ‘middle’ number. Complete inequalities using < or > symbols.
-- Practise ordering numbers −10 to 10. Complete inequalities using < or > symbols. Answer and create subtractions with negative answers.

### You Will Need

• ITP: Thermometer (see resources)
• Sticky notes
• Internet access
• Counting stick
• Cards/sticky notes for numbers −5 to 5 (in random order) for each group
• Number cards −10 to 10

### Mental/Oral Maths Starters

Suggested for Day 1
Compare pairs of 4-digit numbers and give one number in between (simmering skills)

Suggested for Day 2
Add/subtract 1, 10, 100 or 1000 (simmering skills)

### Procedural Fluency

Day 1
Children mark on missing numbers on the scale of a thermometer, and then find differences in temperature.

Day 2
Mark negative numbers on a number line, then compare and order.

### Mastery: Reasoning and Problem-Solving

• Put these temperatures in order, starting with the lowest:
19°C, −9°C, −18°C, 0°C, 21°C
• Estimate the number shown by the arrow on this number line:
 | ↑ | -10 20
• What temperature is 10 degrees less than 4°C?
• Alfie says ‘20 degrees higher than −5°C is 25°C’. Do you agree with him?

In-depth Investigation: Sea Level
Can you work out the depths between some of the underwater creatures? Sea Level from nrich.maths.org.

### Extra Support

Temperature Differences
Work together on Day 1’s group activity. Use a number line to support finding the difference between positive and negative numbers.

## Unit 3 Count in 25s/1000s; Roman numerals (suggested as 2 days)

### Objectives

Count in steps of 25/1000; Roman numerals
Unit 3: ID# 4957

National Curriculum
Num/PV (i) (viii) (ix)

Hamilton Objectives
4. Count in multiples of 25 and 1000.
8. Read Roman numerals to 100 (I to C).

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show the first four numbers in a sequence starting with 356, increasing in steps of 1000. How will you work out the last two numbers? Discuss reasoning before revealing the last two numbers.
Take 25 as start number, increasing in steps of 25. Repeat with 4, then 17. Discuss patterns in the last two digits of the numbers. Repeat with 1017, 1004, 1021 and 1018. Do children use the pattern of digits to help them?
Group Activities
-- Whole class investigation: Count back in 25s to find the smallest positive number that started a sequence of counting in 25s.

Day 2 Teaching
Write the numerals 1 to 9 and point out how these numerals can be used to write any number that we can think of, from tiny numbers to huge numbers. Show a picture of a clock with Roman numerals. Point out how 9, 11 and 12 are written. Challenge children to write 13 to 18. Explain that 20 is written as XX. How do you think we might write 19? 21? 25? Together, write the multiples of 10 from X, through L, to C, explaining that C is the symbol for 100. Have children seen these symbols anywhere else, e.g. at the end of TV programmes/ films, or elsewhere?
Discuss the history of numbers, including the use of zero as place holder (see teaching and group activities download for information).
Group Activities
Use the ‘Roman numeral teaser’ in-depth problem-solving investigation below as today’s group activity.
Or, use this activity:
-- Whole class investigation: Write a times-table using Roman numerals. Reason about patterns in sequences of Roman numerals.

### You Will Need

• ‘Step counting’ sheets 1 to 5 (see resources)
• ‘Roman numeral clock’ (see resources)
• Mini-whiteboards and pens

### Mental/Oral Maths Starters

Suggested for Day 1
Count on and back in steps of 6 (simmering skills)

Suggested for Day 2
Round 4-digit numbers to the nearest 10, 100 and 1000 (simmering skills)

### Procedural Fluency

Day 1
Fill in missing numbers in ascending and descending sequences with 1000, then 25 as the step size.

Day 2
Write the number before and number after given numbers using Roman numerals.

### Mastery: Reasoning and Problem-Solving

• Here is part of a number sequence.
25, 50, 75, 100, 125 …
Circle all of the numbers below that will appear in the sequence.
235, 300, 865, 450, 795
• The numbers in this sequence decrease by the same amount each time.
14,507 13,507 12,507 …
What are the next three numbers in the sequence?
• Write these numbers in Roman numerals: 39, 1001, 49.
• Write these Roman numbers in figures: XLI, LIX, CXLIX
• Looking at the calculation
XC – X, Polly says ‘That’s easy… you just take away the X from XC to leave C!’ Is she correct? Explain your ideas.

In-depth Investigation: Roman Numeral Teaser
Children apply their knowledge of place value to a different number system.

### Extra Support

Number Forum
Writing Roman numerals 1 to 100