Short Blocks

Maths Year 2 Summer Investigations

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

Problem solving and investigations (suggested as 5 days)

Planning and Activities

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).


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.


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

Extra Support

This unit has no separate Extra Support activities.