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# Maths Year 3 Spring 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 Partition 3-digit numbers; place on a line (suggested as 5 days)

### Objectives

Place 3-digit numbers on a line; partition into 1s, 10s 100s
Unit 1: ID# 3533

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

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.
3. Understand place value in 3-digit numbers; add/subtract 1, 10, 100 without difficulty.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Discuss how we mark 2-digit numbers on a line 0–100. Then mark 275 on a line 200–300. Discuss halfway, and where 275 goes. Repeat, marking numbers on a 400–500 line.
Group Activities
-- Create a game placing hidden 3-digit numbers between hundreds on a landmarked line.
-- Mark 3-digit numbers on landmarked lines.

Day 2 Teaching
Review the top tips written yesterday. Model how to think about half and quarter to help place 3-digit numbers on a 0–1000 line.
Group Activities
-- Place 3-digit numbers on 0–1000 landmarked lines.
-- Make and use a 0–1000 number line.
-- Play a game to find mystery numbers string ‘number line’.

Day 3 Teaching
Play the Nasty Game. Show a place value grid (100s, 10s and 1s). Write different numbers on the grid, discussing their place value.
Group Activities
-- Play the ‘Nasty Game’ to make and compare 3-digit numbers.

Day 4 Teaching
Compare and order numbers using the place value grid. Discuss which digit to look at when the hundreds digit is the same. Find 3-digit numbers which fall between two given 3-digit numbers.
Group Activities
-- Order numbers using number lines and place value.
-- Find numbers between pairs of 3-digit numbers.
-- Ask questions to determine a mystery 3-digit number.

Day 5 Teaching
Challenge children to write the largest 3-digit number using digits 0–9 only once each. Repeat for other target numbers.
Group activities
Use the in-depth problem-solving investigation ‘Counter Place Value’ as today’s group activity.
Or, use this activity.
-- Investigate making 3-digit numbers with given criteria.

### You Will Need

• Mini-whiteboards and pens
• Blank landmarked line (see resources)
• Sticky notes
• ‘Placing 3-digit numbers on a landmarked line’ sheet (see resources)
• Pot containing a range of 3-digit numbers on cards
• ‘0–1000 landmarked lines’ sheet (see resources)
• Strips of paper, counters and felt tip pens
• Place value cards
• String and pegs
• 0–9 cards and sticky tack
• 2- and 3-player Nasty Game sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Place 2-digit numbers on a 0–100 line (pre-requisite skills)

Day 2
Place value in 3-digit numbers (pre-requisite skills)

Suggested for Day 3
Tell the time to the nearest 5 mins (simmering skills)

Day 4
Compare pairs of 3-digit numbers (pre-requisite skills)

Suggested for Day 5
Round 2- and 3-digit numbers to nearest 10 (simmering skills)

### Procedural Fluency

Day 1
Place 3-digit numbers between hundreds on a number line.

Day 2
Place 3-digit numbers on a number line.

Day 3
Make and order 2- or 3-digit numbers using a range of starting digits.

Day 4
Order a series of 3-digit numbers. Find numbers between pairs of 3-digit numbers.

Day 5
Place value challenge: create 3-digit numbers according to given criteria.

### Mastery: Reasoning and Problem-Solving

• Sketch a 0–1000 line.
Mark 500.
Mark 350, 700 and 990.
How can you demonstrate that you have marked these accurately?
• True or false?
Between any pair of next-door multiples of 100, there are always 98 whole numbers.
The middle of a 500–1000 line is 800.
There are ten numbers ending in 3 between 300 and 400.
The digit 0 is used 18 times between 600 and 700.
• Write numbers to make the sentences true:
100 < ☐ < 110
304 > ☐ > 302
999 > ☐ > 888
0 < 101 < ☐
459 < ☐ < 461
• Write the value of the 5 digit in these numbers:
(i) 652
(ii) 591
(iii) 905

In-depth Investigation: Counter Place Value
Children place counters on a place value grid to make 3-digit numbers and then use logic to ensure they have made all the combinations.

### Extra Support

In-betweenies
Placing numbers on a 0 to 100 landmarked line

Make the Number
Knowing the value of each digit in 3-digit numbers

## Unit 2 Understand x 100 and ÷ 100 as inverses (suggested as 3 days)

### Objectives

Understand multiplying and dividing by 10 and 100 (3-digit numbers) as inverse operations
Unit 2: ID# 3539

National Curriculum
Num/PV (iv) (v)

Hamilton Objectives
2. Estimate quantities and represent numbers in different ways.
3. Understand place value in 3-digit numbers; add/subtract 1, 10, 100 without difficulty.
5. Solve number problems and practical problems involving place value.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Children copy a place value grid from the board to their whiteboards. They use digit cards to show 30 on it. Demonstrate multiplying by 10 and dividing by 10. Repeat to multiply 25 by 10 and to divide 270 by 10. Continue with other examples.
Group Activities
-- Create 2-digit numbers and multiply and divide them by 10. Record these calculations.
-- Challenge others to guess the starting number by giving the answer to × 10 questions.

Day 2 Teaching
Children write 4 on a place value grid on their whiteboards, they show 4 × 10 then 4 × 100. Point out that the digits are shifting two places to the left when we multiply by 100. Repeat with 7 × 10 and 7 × 100. Then divide by 100.
Group Activities
-- Play a divide by 10 and multiply by 10 card game.

Day 3 Teaching
Show a function machine (see resources). Children think what is happening inside the machine. Use the machine to multiply by 10 or 100, and then to ‘undo’ this by dividing by 10 or 100. Use the machine to demonstrate these inverse operations.
Group Activities
Use the in-depth problem-solving investigation ‘Lost Logic’ as today’s group activity.
Or, use this activity.
-- Use function machines to multiply and divide in single and double steps through inversion.

### You Will Need

• Place value grid (see resources)
• Mini-whiteboards and pens
• Interactive Whiteboard calculator
• 0–9 digit cards
• Place value grid (see resources)
• ÷ and x card game function cards and number cards (see resources)
• Additional activity sheets (see resources)

### Mental/Oral Maths Starters

Day 1
Division facts for 10 times table (pre-requisite skills)

Suggested for Day 2
Division facts for 5 times table (simmering skills)

Suggested for Day 3
Doubling and halving (simmering skills)

### Procedural Fluency

Day 1
Multiply and divide numbers by 10.

Day 2
Multiply and divide by 100. Find the missing number or function.

Day 3
Complete the function machines that include single and double steps.

### Mastery: Reasoning and Problem-Solving

• Describe in words what happens to a number when we multiply by 10. Now explain why it happens. You may draw a picture if it helps.
• Write the missing numbers
(a) ☐ × 10 = 550
(b) 100 × 39 = ☐
(c) ☐ ÷ 10 = 60
(d) 17 × ☐ = 170
(e) 500 ÷ ☐ = 5
(f) ☐ × 10 = 990
• Write the result number in each chain:
5 × 100 ÷ 10 × 10 ÷ 100 = ?
300 ÷ 10 ÷ 10 × 10 × 10 = ?
40 × 10 ÷ 100 × 10 = ?
Invent your own chain where you end up with the number you started.

In-depth Investigation: Lost Logic
Children use their knowledge of inverse operations to solve a logic problem.

### Extra Support

Treasure or Trap
Multiplying and dividing by 10