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# Maths Year 2 Summer Puzzles and Problems

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 available to friends and School Subscribers. These bulk downloads are added value for Hamilton Friends and School Subscribers.

## Unit 1 Maths games (suggested as 5 days)

### Objectives

Maths games
Unit 1: ID# 2801

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

Hamilton Objectives
4. Locate any 2-digit number on a landmarked line; use this to order/compare numbers with <, > and = signs.
7. Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15 (7+8, 6+9, 5+10, 4+11, 3+12, 2+13, 1+14, 0+15).
8. Know different unit patterns when adding or subtracting, first when not crossing a 10 and then when crossing a 10, in numbers up to 100.
9. Add 2 or 3 single-digit numbers, using number facts and counting up.
10. Add a 2-digit number and 10s; add two 2-digit numbers which total less than 100 by counting on in 10s and 1s.
11. Count back in 1s or 10s or use number facts to take away, e.g. 27-3 = or 54-20 =.
12. Begin to count up to find a difference between two numbers with a small gap, e.g. 20 – 14.
13. Show that addition of 2 numbers can be done in any order (commutative) and subtraction cannot.
15. Solve problems involving addition and subtraction of numbers, using recall of number facts and appropriate models and images.
27. Combine amounts, find different combinations of coins with same total.
28. Solve simple problems in a practical context; add and subtract pence, including finding and giving change.
33. Identify/describe common 2-D shapes.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Keep this part of the lesson short so that children have time to play 2 games. Introduce Skittles and Roll a penny, modelling these games in front of the class with a group of children. Talk through the calculation strategies that might be needed for each game.
Group Activities
-- Children play Tug of War and Can Knock Down.
-- Children play Skittles and Roll a Penny.

Day 2 Teaching
Play ‘Traffic lights’. Each pair chooses 3 numbers on their sheet and rings them. Roll two 0 to 9 dice. If the total is one of children’s 3 numbers, they colour the top light in red. Continue until 1 pair has completely coloured one of its 3 lights red, orange and green. Which numbers appear to be good to choose? Why? Which numbers were not so good to choose?!
Group Activities
-- Play Make 10.
-- Play Stick or Roll.
-- Play Turn the Cards.

Day 3 Teaching
Play Avoid the 10s. Place a counter on a number. A child moves the counter to a neighbouring number. They add this number to the previous number. Record the running total. Continue taking turns with the class. If the class get past 50 without you making a total of a multiple of 10, they win. If not, you win!
Group Activities
-- Play Spot on.
-- Play Avoid the 10s, but with subtraction.

Day 4 Teaching
Shuffle 1 to 9 digit cards. Ask an ‘assistant’ to use the cards in that order to mark a 2-digit number on a 0 to 100 landmarked line. Repeat. Children work in pairs to shuffle 1 to 9 digit cards, and take two to try to make a number between your two numbers. Repeat.
Group Activities
-- Children play Inbetweenies in pairs on 0 to 100 lines.
-- Children play Inbetweenies with 3-digit numbers on a 0 to 1000 line.

Day 5 Teaching
Two children help you to demonstrate the game Banned. Write 35 on a whiteboard, with tens and more written alongside. Show the class, but NOT the two children helping you. A child from each table gives a clue without using the two banned words. Continue until the children guess the number. Repeat for rectangle with rectangle and sides as the banned words.
Group Activities
-- Children play Banned using given cards with numbers/pictures and banned words.

### You Will Need

• ‘Skittles’ - small plastic water/pop bottles labelled 1, 2, 3, 4, 5 or 6, containing 1, 2… or 6 egg cups of sand and a ball capable of knocking them down
• ‘1 to 100 grids’ (see resources)
• ‘Roll a penny’ grids on A3 paper (see resources)
• Pennies and plenty of replica coins
• Long strip of paper (for Tug of War number line)
• Counters and a coin
• Empty cans labelled 10, 20, 30, 40, 50 and 60
• Bean bag
• ‘Traffic Lights’ sheet (see resources)
• IWB 0 to 9 dice
• Red, orange and green colouring pencils
• ‘Make 10’ sheet (see resources)
• 1-6 dice and 1 to 12 digit cards
• Additional activity sheets (see resources)
• Flipchart paper
• Mini-whiteboard and pens

### Mental/Oral Maths Starters

Day 1
How many to the next 10? (pre-requisite skills).

Day 2
Identify numbers on a line (pre-requisite skills).

Suggested for Day 3
Recognise multiples of 5 (simmering skills).

Suggested for Day 4
Compare numbers (simmering skills).

Suggested for Day 5
5 times tables (simmering skills).

### Procedural Fluency

Day 1
Add three or four multiples of 10 in a game of Skittles.
Add many multiples of 10 to a string of 1s numbers to find a grand total for games of Skittles and Hoopla.

Day 2
Play ‘Make 10’ to practise adding several 1-digit numbers.
Play ‘Down the snake’ to practise subtracting 1-digit numbers from 2-digit numbers.

Day 3
Play ‘Tens frustration!’ to practise adding 1-digit numbers to 2-digit numbers.

Day 4
Write numbers between given pairs of 2-digit numbers; place them on a line.
Make all possible 2-digit numbers using three different digit cards.

Day 5
Write descriptions of at least 3 number/ picture cards without using ‘banned’ words.

### Mastery: Reasoning and Problem-Solving

This unit has no separate problem-solving activities or investigations.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 2 Number puzzles (suggested as 2 days)

### Objectives

Number puzzles
Unit 2: ID# 2819

National Curriculum
Num/PV (vi)

Hamilton Objectives
6. Use place value and number facts to solve problems, e.g. 60 -  = 20.
7. Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15 (7+8, 6+9, 5+10, 4+11, 3+12, 2+13, 1+14, 0+15).
9. Add 2 or 3 single-digit numbers, using number facts and counting up.
13. Show that addition of 2 numbers can be done in any order (commutative) and subtraction cannot.
15. Solve problems involving addition & subtraction of numbers, using recall of number facts and appropriate models and images.
17. Understand equivalence in simple calculations: 3 x 4 = 6 x ☐.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Show the ‘Number lines’ puzzle. Explain that that each line adds up to 16. Which would be a good number to work out first? Why? Children find the total of the 3 numbers in the top line, and work out what needs to be added to make 16. Continue to solve the puzzle.
Group Activities
-- Arrange counters on 5 plates to make given totals.
-- Create balancing sums using cubes and a bucket balance.
-- Solve, and then make up number puzzles.

Day 2 Teaching
Display the first arithmagon. Explain how it works. Write 4 and 1 in the top and bottom right circles. Children work out the number in the bottom left circle. Ah, a problem! We need 5 to add to 1 make 6, but we need 3 to add to 4 to make 7! Through experimentation, trial and improvement, agree the solution.
Group Activities
-- Solve addition or multiplication arithmagons.

### You Will Need

• ‘Number lines’ (see resources)
• 15 paper plates
• Counters
• Bucket balance (rocker scales)
• Cubes
• ‘Number puzzles’ sheet (see resources)
• ‘Arithmagons’ sheet 1 (see resources)
• ‘Solve these arithmagons’ sheets 2 and 3
• Additional activity sheets (see resources)
• 1-9 digit cards

### Mental/Oral Maths Starters

Day 1

Suggested for Day 2
Pairs of multiples of 10 adding to 100 (simmering skills).

### Procedural Fluency

Day 1

Day 2
Arithmagons: Solve missing number addition puzzles, using logic.

### Mastery: Reasoning and Problem-Solving

This unit has no separate problem-solving activities or investigations.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 3 Logic and shape puzzles (suggested as 3 days)

### Objectives

Logic and shape puzzles
Unit 3: ID# 2833

National Curriculum
Meas (iii) (iv)
PoS (i)
P&D (ii)

Hamilton Objectives
15. Solve problems involving addition and subtraction of numbers, quantities and measures, using recall of number facts and appropriate models and images.
27. Recognise/use symbols for pounds (£) & pence (p); combine amounts, find different combinations of coins to give same amount.
28. Solve simple problems in a practical context; add and subtract pence and pounds, including finding and giving change.
33. Identify/describe common 2-D shapes.
36. Order and arrange combinations of mathematical objects in patterns.
37. Use mathematical vocabulary to describe position.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Display ‘Teddy bears’ birthday tea’. The four bears are going to sit at this table for a birthday tea. Your task is to sit them in the correct places according to some clues. Together work out how to sit them in the correct places.
Group Activities
-- Move the bears to find solutions to the logic puzzles.
-- Arrange bears, then make up and test their own clues.
-- Choose a number on the 1-100 grid; give clues for others to identify the mystery number, or have others ask number property questions.

Day 2 Teaching
Display one of each of the following coins on the IWB: 1p, 2p, 5p and 10p. Say that these four coins need to be arranged in a line according to the given rules. Take suggestions about coin order, with reasoning, from the class, moving the coins around to try out their ideas until the arrangement matches all four rules.
Group Activities
-- Work as a group to solve logic puzzles involving coins.
-- Work together to solve Queen Esmerelda’s coins challenge.

Day 3 Teaching
Explain that tangrams are an ancient Chinese puzzle made from seven 2-D pieces. Give each pair of children a set of tangram pieces, ask them to cut them up and then mix them up. Their first challenge is to try and rearrange them as a square! Repeat for other shapes, as suggested in an online activity.
Group Activities
-- Whole class: Children use tangram pieces to recreate pictures.

### You Will Need

• ‘Teddy bears’ birthday tea’ sheets 1 and 2 (see resources)
• Coloured counting bears (or counters)
• ‘Write your own clues’ sheet (see resources)
• ITP: Number Grid
• Interactive 100 grid (Splat from www.primarygames.co.uk requires Flash)
• IWB coins and 1p, 2p, 5p and 10p coins
• Additional activity sheets (see resources)
• 20 identical coins for each pair
• Online tangrams game at www.ejectamenta.com

### Mental/Oral Maths Starters

Day 1
Positional vocabulary (pre-requisite skills).

Day 2
Coin totals (pre-requisite skills).

Suggested for Day 3
Ordering numbers (simmering skills).

### Procedural Fluency

Day 1
Work in pairs to solve ‘Bear birthday party’ logic puzzles, using bears or counters.

Day 2
Solve coin logic puzzles, moving coins around to help.

Day 3
None

### Mastery: Reasoning and Problem-Solving

This unit has no separate problem-solving activities or investigations.

### Extra Support

This unit has no separate Extra Support activities.

## Unit 4 Problem solving and investigations (suggested as 5 days)

### Objectives

Problem solving and investigations
Unit 4: ID# 2843

National Curriculum
PoS (i)

Hamilton Objectives
7. Know securely number pairs for all the numbers up to and including 20.
8. Know different unit patterns when adding or subtracting, first when not crossing a ten and then when crossing a ten, in numbers < 100.
9. Add 2 or 3 single-digit numbers, using number facts and counting up.
10. Add a 2-digit number and 10s; add two 2-digit numbers which total less than 100 by counting on in 10s and 1s.
13. Show that addition of 2 numbers can be done in any order (commutative).
14. Recognise that addition and subtraction are inverse operations; use addition to check subtractions and solve missing number problems.
15. Solve problems involving addition and subtraction of numbers, quantities and measures, using recall of number facts and appropriate models and images.
33. Identify/describe common 2-D shapes, referring to properties including on the surface of 3-D shapes; compare/sort 2-D shapes.

### Teaching and Group Activities for Understanding

Day 1 Teaching
Draw a 4 by 4 rectangle anywhere on a calendar. Children add the number in the top left corner to the number in the bottom right corner, then double it. Circle a number. Cross out all the numbers in the same row and column as your circled number. Repeat until 4 numbers are circled and the rest crossed out. Add the 4 circled numbers. What do you notice? Does this always happen? Investigate other months and choose other numbers to find out…
Group Activities
-- Whole class investigation: Investigate totals of four 2-digit numbers in a 4 by 4 grid placed on a calendar month.

Day 2 Teaching
Read ‘Sandcastles’ carefully together. Let’s recap the facts. And what do we need to find out? How we might make a start? Hear children’s ideas. If necessary, model thinking: Let’s pick a number to try for day 1 and see how we get on. Write a child’s suggestion (even if it clearly isn’t going to work) under a ‘Day 1’ heading. If Lisa made this many on Day 1, how many would she have made on Day 2? And Day 3/ 4/ 5? How many is this altogether? That’s too many/ few. How shall we change the starting number?
Group Activities
-- Whole class investigation: Work in pairs on the Sandcastles problem.

Day 3 Teaching
Think of a 2-digit number less than 70. Add 30. Subtract 20. Add 10. Subtract 20. Add 3. Write down this final answer. Ask several children to tell you the number they first thought of. Quickly add 3 to this number and say: Your answer is… Children discuss how you are working out their answers so quickly…!
Group Activities
-- Create ‘magic chains’ of numbers.
-- Solve multi-step ‘age’ problems. Create your own similar puzzles.

Day 4 Teaching
Show the triangle of circles. Write 1 to 6 in any order in the circles around the triangle. Ask children up to the board to write the total of each side of the triangle in the squares. Ask children to suggest how you might move numbers around to make each side have a total of 9.
Group Activities
-- Whole class investigation: Arrange digit cards 1 to 6 in a triangle such that each side has the same total. Find the range of possible different totals.

Day 5 Teaching
Show a picture of triangles on the board. 1 person says this picture has 2 triangles, and another person says that she can see 3! What do you think? Use different coloured pens to draw round each triangle. So there are 3 triangles! Repeat with the picture of squares.
Group Activities
-- Reason about the number of triangles and squares that can be counted in different pictures.
-- Use Tangram pieces to create 2-D shapes.

### You Will Need

• Calendar on the IWB
• Mini-whiteboards and pens
• ‘Calendar capers’ sheet (see resources)
• Photocopies of calendars
• ‘Sandcastles’ sheet (see resources)
• ‘Magic chain’ writing frame (see resources)
• Additional activity sheets (see resources)
• 1-6 digit cards
• Coloured IWB pens
• Coloured pencils

### Mental/Oral Maths Starters

Day 1
Double numbers to 50 (pre-requisite skills).

Day 2
Count on and back in 4s (pre-requisite skills).

Suggested for Day 3
Add 1-digit numbers to 2-digit numbers (simmering skills).

Day 4
Trios with a total of 10 (pre-requisite skills).

Suggested for Day 5
Describe numbers (simmering skills).

### Procedural Fluency

Day 1
Use addition of pairs of 2-digit numbers in solving a calendar-based puzzle.

Day 2
Solve a puzzle involving number sequences, using logic, trial & improvement and reasoning.

Day 3
Work backwards/ use inverse operations to find start numbers in number chains and age-based word problems.

Day 4
Solve ‘mystery triangles’ and ‘magic squares’, by applying addition skills and using logic, trial & improvement and reasoning.

Day 5
Solve shape-based ‘find all possibilities’ problems.

### Mastery: Reasoning and Problem-Solving

This unit has no separate problem-solving activities or investigations.

### Extra Support

This unit has no separate Extra Support activities.