Short Blocks

Maths Year 5 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 Negative numbers; count through zero (suggested as 2 days)

Objectives

Understand negative numbers; count back and forward through 0
Unit 1: ID# 5711

National Curriculum
Num/PV (iii)

Hamilton Objectives
4. Interpret negative numbers in context, counting backwards and forwards through zero.

Teaching and Group Activities for Understanding

Day 1 Teaching
Discuss contexts in which we use negative numbers: temperature, depth, debts, etc. Launch the ITP Number Line. Choose –20 to 20 range. Click so that the numbers are not displayed on the tags. Children identify numbers. Mark –2 and –8. What numbers are in-between? Repeat with +3 and –4. Ask children to write a number between –15 and 15 on a whiteboard. Gradually create a human number line, with children negotiating their position in the line.
Group Activities
-- Practise ordering number cards –10 to 10.
-- Order sets of three –15 to 15 number cards using < and >. Play a team game.

Day 2 Teaching
Show a horizontal counting stick. Identify the end as –10. Count from this to +10. Then start at –40 and count in steps of 5. Start at –100 and count in 10s. Start at –200 and count in 25s. Repeat, counting back and forth across 0 in different size steps. Discuss situations in ‘real life’ where these sorts of subtractions are possible, e.g. falls in temperature, descending below sea level, or being overdrawn at the bank.
Group Activities
Use the in-depth problem-solving investigation ‘First Connect Three’ from NRICH as today’s group activity.
Or, use these activities:
-- Play a game to practise counting back through zero to -20 and beyond.
-- Repeatedly subtract from the first number in a given pair to exactly reach the second.

You Will Need

  • ITP Number Line (see resources)
  • Mini-whiteboards and pens
  • –10 to 10 cards
  • –15 to 15 cards
  • Counting stick
  • –20 to 20 number lines (see resources)
  • 1–6 dice

Mental/Oral Maths Starters

Day 1
Count back through zero (pre-requisite skills)

Suggested for Day 2
Count on and back in steps of 25 (simmering skills)

Procedural Fluency

Day 1
Compare pairs of positive and negative numbers, order groups of numbers, write a number between given pairs of numbers.

Day 2
Continue sequences counting on and back through zero. Solve challenge problems.

Mastery: Reasoning and Problem-Solving

  • 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

In-depth Investigation: First Connect Three
A game to add or subtract the two numbers on a dice and cover the result on a grid, trying to get a line of three. First Connect Three from nrich.maths.org.

Unit 2 Place value in 6-digit numbers (suggested as 3 days)

Objectives

Understand place value in 6-digit numbers; place on a number line
Unit 2: ID# 5717

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
Write 457,849. In pairs, one child writes the number 1 less, and the other child writes the number 1 more. Repeat with 10 more/less, 100 more/less, 1000 more/less, 10,000 more/less and 100,000 more/less. Then repeat with 230,193 then 352,605.
Group Activities
-- Recognise which digit will change during a series of place value additions and subtractions.
-- Write pairs of 6-digit numbers with a difference of 1, 10, 100, 1000, 10,000, 100,000 and multiples of those powers of 10.
-- Fill in blank 100-grids that count across and down in higher powers of 10, e.g. 10s, 100s, 1000s, 10,000s, 100,000s.

Day 2 Teaching
Show a 0 to 1,000,000 line marked in multiples of 100,000. Choose numbers to mark so that children have to identify and label. Then ask one child to mark a number. The rest of the class guess it, asking careful questions. Children repeat with a partner to place numbers on a 100,000 to 200,000 line. Repeat for groups of numbers, using a number line bounded by appropriate adjacent multiples of 100,000.
Group Activities
-- Estimate a number marked on a 0 to 1,000,000 line to the nearest 10,000.
-- Play a game marking 6-digit numbers on landmarked number lines.
-- Play a game marking 6-digit numbers on empty number lines.

Day 3 Teaching
Sketch a line from 200,000 to 300,000. Mark a number, then ‘zoom in’ and draw a line to show that number between two multiples of 10,000. Repeat for two multiples of 1000. Round to nearest 100,000, 10,000 and 1000. Repeat with a new child and a line between 500,000 and 600,000. Then play ‘100k Bingo.’
Group Activities
Use the in-depth problem-solving investigation ‘Lost digit’ as today’s group activity.
Or, use these activities:
-- Sketch number lines to help round population figures to the nearest 100,000 and 10,000.
-- Play bingo games rounding 6-digit numbers to the nearest 100,000, 10,000, then 1000.

You Will Need

  • Mini-whiteboards and pens
  • Flipchart and pens
  • ‘1–100 grid’ (see resources)
  • ‘Guess the number’ (see resources),
  • ‘0 to 1,000,000 landmarked line’ (see resources) [copy onto A3]
  • Additional activity sheets (see resources)
  • 0–9 digit cards
  • A3 paper

Mental/Oral Maths Starters

Day 1
Place value in 6-digit numbers (pre-requisite skills)

Day 2
Compare pairs of 6-digit numbers (pre-requisite skills)

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

Procedural Fluency

Day 1
Add/subtract 1, 10, 100, 1000, 10,000 and 100,000, then multiples of these, to and from 6-digit numbers.

Day 2
Mark 6-digit numbers on landmarked number lines with different scales.

Day 3
Round population figures to the nearest 100,000, 10,000 and 1000.

Mastery: Reasoning and Problem-Solving

  • True or false?
    10 more than 99,999 is 100,090.
    100 less than 202,020 is 201,920.
    199,009 add 1000 is 201,009.
    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

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

Extra Support

Is That Your Final Answer?
Understanding place value in 5-digit numbers; Adding and subtracting 1, 10, 100, 1000 and 10,000.

Unit 3 Identify and write Roman numerals (suggested as 2 days)

Objectives

Identify and write Roman numerals
Unit 3: ID# 5737

National Curriculum
Num/PV (v) (vi)

Hamilton Objectives
5. Solve number problems and practical problems involving place value.
6. Read Roman numerals and recognise years written in Roman numerals.

Teaching and Group Activities for Understanding

Day 1 Teaching
Make a list with children of Roman numerals from 1 to 10. Then extend to discuss how we write the 10s numbers to 100. Then show children how to write numbers greater than 100, demonstrating use of new letters for 100, 500 and 1000 (C, D, M). Children discuss other Roman numbers.
Group Activities
-- Derive Roman numbers 0 to 300.
-- Derive Roman numbers 0 to 1000. Attempt addition of Roman numbers.

Day 2 Teaching
Point out that on TV or at the end of films, the year is sometimes given in Roman numerals. Tell history of zero: Persian mathematician Muhammad ibn Ahmad al-Khwarizmi is widely credited with suggesting using a circle ‘to keep the rows’ in a calculation. This was called ‘empty’ in Arabic and later called zero. Write Roman numbers using the ‘Dates’ resource sheet.
Group Activities
Use the in-depth problem-solving investigation ‘Martian numbers’ as today’s group activity.
Or, use these activities:
-- Investigate all possible numbers between 500 and 2000 that only need two Roman numerals.
-- Collaborate to write Roman numbers, using a fixed number of numerals, within a given range.

You Will Need

  • Mini-whiteboards and pens
  • ‘Dates’ (see resources)
  • ‘Roman numeral fact sheet’ (see resources)

Mental/Oral Maths Starters

Day 1
Read the time on a clock with Roman numerals (pre-requisite skills)

Day 2
Write numbers less than 100 using Roman numerals (pre-requisite skills)

Procedural Fluency

Day 1
Write the next two numbers in a sequence of Roman numerals.

Day 2
Choose at least 8 notable dates, written as Roman numerals, and rewrite them using Hindu-Arabic numerals.

Mastery: Reasoning and Problem-Solving

  • Write the current year in Roman numerals. Write next year and the year after in Roman numerals.
  • Write the missing letters in this sequence of numbers:
    LXIX, LXXIX, LXXXIX, ☐☐IX, CIX, ☐☐IX,
    ☐☐☐IX, ☐☐☐☐IX, ☐☐☐☐☐
  • Do this calculation using Hindu Arabic numbers:
    3,496 + 5,514
  • Now do it using Roman numbers. What do you notice?
  • Which Roman number <100 uses the most numerals? Is this the same as the amount of money <£1 that uses most coins?

In-depth Investigation: Martian Numbers
Children explore the fact that Hindu-Arabic numbers use a base of 10, we can write numbers using a base of 3, and Roman numbers have no base.

Extra Support

Roman Rules
Use the NRICH activity ‘Roman Numerals’ to support children in deriving a set of rules for creating Roman numbers. Roman Numerals from nrich.maths.org.