# Consecutive Sums

### Task 7 ... Years 4 - 8

#### Summary

Problem: Given number discs from 0 to 25, how many ways can you build addition equations with consecutive number as addends and the total among the discs?
• How many with two addends?
• How many with three addends?
• How many with four addends?

#### Materials

• Discs numbered 0 - 25

#### Content

• basic arithmetic skills in addition, multiplication and division with whole numbers
• number patterns
• algebraic notation
• generalisation and the concept of proof

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

1. Are there any similar equations which can be made for addends greater than 4?
2. For each part of the problem ask the mathematician's question:
How do you know when you have found all the solutions?
3. Look more deeply at the situation with three addends. In each case the total can be divided by 3 and one third of the total is the middle number. What can the students find out about the total and the list of addends in the other cases?
4. What happens if we investigate sums of numbers which are 2 apart, 3 apart, 4 apart, ... p apart?
Note: There is a strong link between Consecutive Sums and Task 4, Window Frames.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

The whole class lesson for this task is detailed in Maths300 Lesson 139, Consecutive Sums. To convert the task to a whole class lesson each student cuts or tears a piece of paper into 16 sections. This is easy folding and gives enough pieces per pair for the numbers 0 - 25 with some left over for + and = signs. You will find that with most classes these are soon abandoned in favour of scrapbook work with written numbers, but without the pieces some students may not become engaged in the problem in the first place.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 139, Consecutive Sums, which also includes a Poster Puzzle to stimulate the investigation.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Consecutive Sums task is an integral part of:

• MWA Number & Computation Years 3 & 4
• MWA Number & Computation Years 7 & 8

The Consecutive Numbers lesson is an integral part of:

• MWA Number & Computation Years 9 & 10