Short Blocks

# Maths Year 5/6 Spring Place Value

Each unit has everything you need to teach a set of related skills and concepts.

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The PowerPoint incorporates step-by-step teaching, key questions, an in-depth mastery investigation, problem-solving and reasoning questions - in short, everything you need to get started.

All the other resources are there to support as-and-when required. Explore at your leisure - and remember that we are always here to answer your questions.

## Unit 1 Place value (suggested as 4 days)

### Objectives

Place value
Unit 1: ID# 56412

Y5: Place value in 6-digit numbers.
Y6: Place value in 7-digit numbers.

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

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

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 and a thousand, ten thousand, one hundred thousand or a million, as appropriate.
4. Solve number and practical problems involving place value, rounding and negative numbers.

### Planning and Activities

Day 1 Teaching
Discuss how to write and say 6-digit numbers. Build numbers using place value chart. Generate 6-digit numbers by rolling a dice and create an inequality. Discuss how to write 7-digit numbers. Write a number between two 7-digit numbers.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Lost Digit’ as today’s group activity.
Or, use these activities:
Y5 -- Compare and use place value to subtract from 6-digit numbers; Use place value subtraction to ‘zap’ each digit in a 6-digit number.
Y6 -- Use dice rolls to construct and subtract from 7-digit numbers. Order 7-digit numbers with consecutive digits.

Day 2 Teaching
Use the Interactive Whiteboard 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.
Further Teaching with Y6
As above but beginning with 7-digit numbers.
Group Activities: T with Y6
Y5 -- Subtract and/ or add 1, 10, 100, 1000, 10,000 and 100,000 to 6-digit numbers.
Y6 -- Use dice rolls to add/subtract 1, 10, 100, 1000, 10,000, 100,000 or 1,000,000 from 5,000,000. Turn a 7-digit number into 5,555,555 by adding and subtracting multiples of 1, 10, 100, 1000, 10,000, 100,000 and 1,000,000.

Day 3 Teaching
Place 6-digit numbers on landmarked lines and round to the nearest 100,000, 1000 and 100.
Further Teaching with Y6
Place 7-digit numbers on lines and round to the nearest 1,000,000, 100,000 and 10,000.
Group Activities: T with Y6
Y5 -- Place 6-digit numbers on landmarked or empty lines; round to the nearest 100 and 1000.
Y6 -- Mark numbers on a 2,000,000 to 3,000,000 landmarked line and round them. Round 7-digit numbers to the nearest 100, 1000, 10,000, 100,000 and 1,000,000.

Day 4 Teaching
Demonstrate how to use ‘add and adjust’ strategies to add ‘nearly numbers’, such as 4735 + 203, 4735 + 197, 4735 + 1995, 465 + 299, 4.65 + 2.99. Repeat to ‘subtract and adjust’ for subtraction of nearly numbers, e.g. 4735 – 705, 4735 – 197, 4735 – 1995, 6.25 – 1.98, 4.21 – 3.02.
Group Activities: T with Y5
Y5 -- Use place value to add and subtract multiples and near multiples of 100 and 1000.
Y6 -- Choose pairs of numbers to add and subtract, using an ‘add/subtract and adjust’ strategy, including some decimals.

### You Will Need

• Vertical place value chart (see resources)
• 1–6 and 0–9 dice
• Calculators
• Interactive whiteboard calculator
• Landmarked lines (see resources)
• Sticky notes
• 0–9 digit cards
• 250,000–260,000 landmarked lines with 1000s labelled (see resources)
• Landmarked line from 2,000,000 to 3,000,000 (see resources)
• Mental addition and subtraction activity sheets 1 and 2 (see resources)

### Short Mental Workouts

Day 1
Double 2-digit numbers

Day 2
Count on/back in 10s, 100s, 1000s and 10,000s from 5-digit numbers

Day 3
Place value in 6-digit numbers

Day 4
Add and subtract near multiples of 10, 100 and 1000 to/from 4-digit numbers

### Worksheets

Day 1
Y5: Write 6-digit numbers with digits of given values.
Write missing digits in numbers to create ascending/descending lists of 6-digit numbers.
Y6: Compare and order numbers, including use of > and <.

Day 2
Y5: Add and subtract 1, 10, 100, 1000, 10,000 and 100,000; preserve inequalities.
Y6: Use place value to add and subtract from large numbers.

Day 3
Y5: Place 6-digit numbers on lines and round to the nearest 100 or 1000.
Y6: Round numbers to the nearest 1,000,000, 100,000, 10,000 and 1,000.

Day 4
Y5: Add and subtract from 4- and 5-digit numbers:
- using place value;
- recognising near multiples of 100, 1000 and 10,000.
Y6: Add and subtract from whole numbers and decimals:
- using place value;
- recognising near multiples.

### Mastery: Reasoning and Problem-Solving

Y5

• True or false?
10 more than 99,999 is 100,090.
100 less than 202,020 is 201,920.
Add 10,000 to 105,432 five times to get 150,432.
• Sketch a line between two multiples of 100,000. Mark the appropriate 10,000s. Choose an adjacent pair of numbers and mark the midpoint between them.
• Write a number that rounds to 40,000 as the nearest 10,000 and to 35,000 as the nearest 1000.
• Round 49,949 to the nearest:
-- ten thousand
-- thousand
-- hundred
-- ten
• What is the smallest number between 800,000 and 900,000 which has just four digits all the same and no zero?

Y6

• Fill in the missing digits:
384,☐79 < 384,0☐9
1,0☐0,841 > 1,040,996
• Complete the place value subtractions.
(a) 1,249,541 – [_____] = 1,240,501
(b) 673,890 – [_____] = 70,090
(c) 2,951,159 – [_____] = 2,050,050
• Draw a line from 3,000,000 to 4,000,000. Mark the halfway point. Mark two numbers that round to 3,000,000. Mark two numbers that round to 3,500,000 as the nearest 100,000.

In-depth investigation: Lost Digit
Children explore place value in 6-digit numbers through finding digit sums and ‘casting out nines’.

### Extra Support

Y5: 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.

Y6: Dicey Decisions
Understanding place value in 4-digit and 5-digit numbers; Comparing 4-digit numbers and 5-digit numbers.

Zoom Zoom
Rounding 5-digit numbers to the nearest 100, 1000 and 10,000.

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

### Objectives

Negative numbers
Unit 2: ID# 56428

Y5: Temperature and negative numbers.
Y6: Understand/calculate negative numbers.

National Curriculum
Y5: Num/PV (iii)
Y6: Num/PV (iii)

Y5 Hamilton Objectives
41. Begin to read scales of different types; solve scaling problems involving measures.
4. Interpret negative numbers in context, counting backwards and forwards through zero.

Y6 Hamilton Objectives
3. Use negative numbers in context, calculate intervals across zero.
4. Solve number and practical problems involving place value, rounding and negative numbers.

### Planning and Activities

Day 1 Teaching
Use negative numbers in the context of temperature. Using the ITP Thermometer, label some temperatures and calculate rises/falls in temperature.
Group Activities: T with Y5
Y5 -- Calculate rises and falls in temperature, drawing own vertical number lines or using a thermometer image.
Y6 -- Compare day and night temperatures across a 5-day period. Find temperature differences. Use a web-based resource to compare temperatures in different places around the world.

Day 2 Teaching
Display a table showing the temperatures recorded at a school weather station. Discuss the differences between temperatures. Find how much the temperature rose and fell during the day and night.
Further Teaching with Y6
Show a line from –20 to 20, with multiples of 5 labelled. Discuss contexts for negative numbers. Make up additions and subtractions with positive and negative answers.
Group Activities: T with Y6
Use the in-depth problem-solving investigation ‘Noughts and negatives’ as today’s group activity.
Or, use these activities:
Y5 -- Find pairs of temperatures with a difference of 10°C. One temperature must be above freezing and one below. Add and subtract numbers to/from -5 to give one answer >0 and one answer <0.
Y6 -- Investigate the difference between a positive and a negative number and two negative numbers.

### You Will Need

• ITP: Thermometer
• 'Temperature' activity sheet (see resources)
• –9°c to 9°C cards
• 2 cut-out card arrows
• Sticky-tack
• PCs/laptops/tablets
• Atlas
• –20 to 20 number line with 0 and multiples of 5 labelled (see resources)
• Calculators (optional)

### Short Mental Workouts

Day 1
Pairs to 100

Day 2
Place negative and positive numbers on lines

### Worksheets

Day 1
Y5 Order temperatures and calculate rises and falls in temperature.
Y6: Calculate temperature differences.

Day 2
Y5: Calculate differences on a bar chart of temperatures in a range of cities.
Y6: Add and subtract with negative numbers.

### Mastery: Reasoning and Problem-Solving

Y5

• Sketch a line –20 to +20. Mark 0. Teacher marks a mystery number (e.g. –8). What number have I marked? Children ask questions to guess. Repeat.
• Count on in steps of 4 from –27. How many steps to reach or pass 20?
• Count in steps of –5. Start at +3. How many steps to get to –42?
• Order these temperatures, starting with the lowest: 12°C, –6°C, –11°C, 0°C, 27°C

Y6

• The temperature at 6pm is given first; then the fall during the night until 5am. Write the night temperatures for each weekday.
Monday: 5°C Falls 9°
Tuesday: 3°C Falls 8°
Wednesday: 8°C Falls 10°
Thursday: 3°C Falls 7°
Friday: 2°C Falls 3°
• On which night was the temperature lowest?
• On Saturday, the temperature fell 15° overnight to −6°C. What was the temperature at 6pm?
• On Sunday, the temperature was 13°C at 6pm and −5°C at 5am. How much did it fall overnight?

In-depth investigation: Noughts and negatives
Children play an adapted game of noughts and crosses, aiming to get negative number answers.

### Extra Support

Y5: Out at Sea
Understanding negative numbers.

Y6: Sea Level
The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures? Sea Level from nrich.maths.org.