Structuring numeracy lessons to engage all students: R – 4

Peter Sullivan

Overview

• We will work through three lessons I have taught this year as part of classroom modelling in years R – 4.

• The lessons are structured to maximise engagement of all students, especially those who experience difficulty and those who complete the work quickly.

• I will ask you to examine the commonalities and differences between the lessons and identify key teacher actions in supporting this lesson structure.

• I will ask you to reflect upon the implications for leading whole school Numeracy improvement.

Assumptions

• We do not want to tell the students what to do before they have had a chance to explore their own strategy

• We want to step back to allow ALL students to engage with the task for themselves

• We want them to see new ways of thinking about the mathematics

• There is no need to hurry• We want them to know they can learn (as distinct

from knowing they can be taught)

GROWING PATTERNS(Intended for Reception)

Copy the pattern and draw the group that would come next

From the Australian Curriculum

The AC for Foundation year includes the following:

• Sort and classify familiar objects and explain the

basis for these classifications. Copy, continue and

create patterns with objects and drawings

(ACMNA005)

For the students

You can copy a pattern by looking at what is there. Sometimes the pattern is growing bigger.

As an introduction

Enabling prompt(s) for students experiencing difficulty

Students who are having difficulty can look at the pattern again.

For others, you might have the pattern on a sheet of paper and they can copy it onto their mini whiteboards.

Extending prompt(s) for those that finish quickly

Students who finish can be asked to continue

the pattern to the next group (and so on).

Maybe some students can write the number of

objects in each group.

Consolidating task

Only looking for a short time, the students can copy and continue these patterns

finding difference

Lesson 2Finding a difference

Years 1 - 2

finding difference

Basketball scores

Parrots 106Galahs 97

How much did the Parrots win by?

(Work out the answer in two different ways)

finding difference

Basketball scores

Wombats 26Possums 18

How much did the Wombats win by?

(Work out the answer in two different ways)

finding difference

Enabling prompt

finding difference

Basketball scores

Eels 18Carp 13

How much did the Eels win by?

(Work out the answer in two different ways)

finding difference

Basketball scores

Cats 8Dogs 3

How much did the Cats win by?

(Work out the answer in two different ways)

finding difference

Extending prompt

finding difference

Darts scores

Parrots 1005Galahs 988

How much did the Parrots win by?

(Work out the answer in two different ways)

finding difference

Football scores

finding difference

Football scores

Seagulls 63Kingfishers 55

How much more did the Seagulls score?

(Work out the answer in two different ways)

finding difference

Football scores

Seagulls 72Kingfishers 55

How much more did the Seagulls score?

(Work out the answer in two different ways)

finding difference

Football scores

Seagulls 83Kingfishers 47

How much more did the Seagulls score?

(Work out the answer in two different ways)

Lesson 3Finding ways to add numbers in

your headYears 3 - 4

FINDING WAYS TO ADD IN YOUR HEAD

Work out how to add 298+35 in your head.

What advice would you give to someone on

how to work out answers to questions like this

in their head?

How might you run that class?

• How much would you tell the students?• What approach do you recommend to

doing this task?• How much confusion can you cope with?• When is challenge and uncertainty

productive?• What is meant by “cognitive activation”?

From the Australian CurriculumThis lesson addresses the following descriptor from the AC for year 1:• Represent and solve simple addition and subtraction problems

using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)

The lesson addresses the following descriptor from AC for year 3 (year 4 is similar):• Apply place value to partition, rearrange and regroup numbers to

at least 10 000 to assist calculations and solve problems (ACMNA053)

• There is also potential for students to build Understanding of number relationships, to be more Fluent with the mental calculations, to find their own solution by Problem Solving, and to develop Reasoning by explaining their thinking.

For the students

You can work out efficient strategies for adding

numbers in your head for yourself. You can also explain

your thinking to others.

Enabling prompt(s) for students experiencing difficulty

Work out the answer to 28 + 7 in your head.

Work out the answer to 98 + 7 in your head.

Extending prompt(s) for those that finish quickly

Work out how to add 98 + 97 + 67 in your head.

Consolidating task

The consolidating task is a set of similar questions on the attached worksheet.

Your answer Show how you did it1.

195+68

1.

496+36

1.

195+47

1.

997+27

Shepp Neighbourhood Cluster new staff visit 2

Shepp Neighbourhood Cluster new staff visit 2

Shepp Neighbourhood Cluster new staff visit 2

Shepp Neighbourhood Cluster new staff visit 2

Shepp Neighbourhood Cluster new staff visit 2

Shepp Neighbourhood Cluster new staff visit 2

Shepp Neighbourhood Cluster new staff visit 2

Shepp Neighbourhood Cluster new staff visit 2

What is your reaction to those lesson?

What might make it difficult to teach like that in your school?

In what ways were those lessons similar?

What actions might you take to encourage teachers to adopt such approaches, at least sometimes?