Year 2 Reasoning
Many schools are using some of the ideas of the ‘mastery programme’ as used in Singapore and other parts of the Far East. The aim of this programme is to give children a deep understanding and fluency in the fundamentals of maths. Because this understanding is deep it will not have to be re-taught at a later time; something which happens all too often at the moment.
This new approach needs new resources, especially geared towards reasoning and problem solving. Thankfully we have always considered reasoning to be a key part of the maths curriculum and many of our resources in all categories are designed for this. But we also have a separate category in each year group called, ‘Reasoning and Problem Solving’ where you will find a rich source of material.
In Year 2 we have a large selection of ‘How many ways ….’ type of practical exercises (e.g. How many different ways can you score 12 with 3 dice?) These encourage children to think logically and order their results so that they can be sure that they have all possible answers. A favourite of mine is the ‘Two Coin Challenge’.
Progressing from these practical tasks are the more abstract challenges such as making 2-digit numbers from a set of number cards.
Finally, take some time out to play the maths games such as Nim which originated in China. They are great at developing logical thinking and developing a winning strategy. You should never lose if you go first!
These pages really are not to be missed and we thoroughly recommend them.
Money and shopping
Solving problems involving money and shopping.
I've got three coins. They are all different. What possible totals could I have?
Solving problems about shopping: quite tricky.
More solving problems about shopping: quite tricky.
More solving problems about shopping: quite tricky.
Buy shapes which are priced according to the number of sides.
'How many ways' investigations
Challenges which ask how many possible ways there are to solve a problem.
Three boxes and 20 buttons. How many different ways can the buttons be put in the boxes so that each box has an even number?
How many presents could each of the three girls have got from a total of 20. They all got an even number of presents!
How many ways can the apples be put in the boxes so that there is an even number of apples in each box?
How many ways can the balloons be coloured? A logical thinking exercise.
How many different addition, subtraction and multiplication questions can be made with the cards shown?
How many different addition sentences can be made using the numbers shown?
Create a number plate for the gorillas new car: but you can only use the digits 1, 2 or 3!
How many different ways can various jars be filled with jam?
How many different ways can various buckets be filled with water?
How many different ways can various containers be filled with shampoo?
How many different ways can various containers be filled with bubble bath?
Investigating combinations of packs of toy farm animals.
Investigating combinations of groups of children.
Three very athletic runners sharing a 19 mile relay. They each run an odd number of miles. How could they do this?
Mini investigations into how many different ways totals can be made from three numbers.
A mini investigation for superbrains. How many ways can you make 100, just using the numbers and signs shown?
Can you find 10 different ways of making 12 with 3 cards? (One card is zero, which makes it trickier!)
A variety of number problems and challenges
Using only the numbers 3 and 2 and the + and - signs, can all the numbers up to 20 be made?
A colourful set of number problems involving beads.
Colourful pages on solving number problems involving buttons.
Roll two dice and add the totals. Record and sort the results. What do you notice?
How many different ways can you score a total with two dice?
Using grids to reason about place value of numbers.
Use three dice to see how many different ways a score of 12 can be made.
Solve number problems with dice (1)
More number problems with dice.
Find as many ways as possible to complete the number sentence.
Make and order 2-digit numbers from a selection of number cards.
Number sentences with missing digits using addition, subtraction, multiplication and division.
Recognising that subtraction is the inverse of addition and the relationship between multiplication and division.
All the signs are missing. Find the correct signs to complete the number sentences.
Put the addition or subtraction signs in to make the number sentences correct. Hard, as there is more than one sign!
Problem solving: finding the right sign.
How many patterned tiles are there altogether?
Further challenges and investigations
More great investigations and challenges for children in Year 2.
Use the balance scales to work out which shelves the items go on.
These pages are all to do with sequencing.
Finding the lengths of pencils in a line.
Finding more than the given numbers.
Monsters and legs problems.
Writing addition statements as multiplication.
Put the numbers in the boxes so that the total of the row across adds up to the same as the total of the column down. Several ways to do this, leading to further investigations.
How long will it take to complete a page of addition, subtraction, multiplication and division questions?
Find a route through the maze from IN to OUT adding the numbers as you go.
Dominoes are a great resource for sorting. Try these ideas to begin with.
Roll two dice and add the totals. Record and sort results.
Sam's got a great aim but how many can he score with four beanbags?
Use knowledge of maths to solve problems written in words.
Addition and subtraction related to the six digits shown.
A selection of mathematical games for one or more players.
An easy version of the game of Nim. Great for logical thinking and you can always win (if you know what you are doing!)
The very simplest forms of magic squares and some ideas on how to turn them into colour patterns.
How many counters can you place on the grid without getting 3 in a row?