Developing Mathematical Thinking in Addition and

Subtraction

Pupils discussing mathematics

Homework“Homework provides rich opportunities for children and

young people to demonstrate, extend and explore learning

through a variety of exciting and enjoyable activities.

Homework is one piece of the teaching- learning picture and

in best practice is connected to what happens in the

classroom. Quality homework tasks allow learners to

practise or process information, introduce them to material

that will be discussed in the future, or provide feedback to

teachers so they may check for understanding.”

HMIE, Learning Together in Mathematics, 2010

Talking the talk

“Talking is central to teaching mathematics

formatively and providing opportunities for

students to express, discuss and argue is

essential. Through exploring and ‘unpacking’

maths, students can begin to see what they know

and how well they know it.”

Jeremy Hodgen and Dylan Wiliam, Mathematics inside the black

box, 2006

6 + 4 = 10

10 take away 9 makes 1

1…….

Score the numbers out you use. Circle the numbers you end on. Then score these out as you start with them for the next calculation

Competitive aim – stop your partner from going

Collaborative aim – cross off as many as possible

How could this be adapted to be less / more challenging?

What mathematical

skills, knowledge are

being developed here?

Challenging Able Young Mathematicians Pack (CAYM)

Section 2a, Page 4 (MNU 1-02a) CAYM available on Glow

Embedding problem solving

What number will be in the units column in this calculation ?1 + 2 + 3 + 4 + ... + 95 + 96 +97

How have you gone about

tackling this? Explain your

approach.

Explain your colleagues approach.

Have you all the same

solution?

Used by Mike Askew, Kings College, during CPD sessions in Scotland

Embedding problem solving

How many cans if 10 in base?How many cans if 100 in base?Rule?

What are possible

contexts?

Any similarity with the previous

question?

Find the rule – what approach?

Embedding problem solving

How many lines between 6 points?

How many lines between 1000 points?Rule?

Mystic Rose

Number of points

Number of Lines

2 1

3 3 (2+1)

4 6 (3+2+1)

5 10 (4+3+2+1)

6 ?

n ?

Any similarity with the previous

questions?

Is there a link between the

number of points and number of

lines

Embedding problem solving

How many games are there if there are 6 teams in a league ?How many lines between 20 teams?Rule?Number of teams

Games Played Number of games

2 a v b 1

3 a v b b v ca v c

3 (2+1)

4 a v b b v c c v d a v c b v d a v d

6 (3+2+1)

5 10 (4+3+2+1)

20 ?

n n x (n-1) 2

Any similarity with the previous

questions?

What if the teams play home and

away?

Triangular NumbersAny similarity

with the previous

questions?

What other number patterns can you investigate?

Supporting mathematical thinkingTo what extent are your pupils encouraged to ...

pursue their own ideas and strategies?

explore their own ways of expressing and recording their findings in a variety of ways?

explain and illustrate their approach and their thinking?

pose further questions and look for further challenges linked to the original problem?

Next stepsWhat

informationwillyou

share with

colleagues?

What might you or your

staff do differently in

the classroom?

What else can you do as to improve learning and

teaching about number

What impact will this have on your

practice?