# Row Points

### Task 9 ... Years 2 - 8

#### Summary

Thirteen counters are placed on a board with 25 spaces. Points are scored according to the length of the counter lines created - 3 points for 3 in a row, 4 points for 4 in a row, 5 points for five in row - in any direction. Counters must be side be side (no empty spaces between) and the longest line is the one that scores, ie: 5 in a row doesn't also mean 4 and 3 in a row.
• What is the highest score which can be made?
This cameo has a From The Classroom section which outlines the thoughts of one Year 6 class about how to find the highest possible score.

#### Materials

• 13 counters and 1 playing board per student

#### Content

• basic arithmetic skills
• mental arithmetic
• spatial perception
• average
• problem solving strategies

#### Iceberg

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

Note

• Row is a word with a self-referenced meaning. A row 'goes across your tummy' as for an actor on stage performing to the audience who are seated in rows. Rightfully, many teachers make a point of using this language when using arrays to develop multiplication concepts. In this task the word row adopts the more general meaning of 'in a line'. If this causes any inconsistency for any student, simply encourage them to turn the board 'so the line does go acrosss your tummy'. This will also help to include all directions when counting the score.

Several iceberg questions are suggested on the card. To these could be added:

1. Can you prove that the highest score is ...?
2. In how many ways can the highest score be made?
3. In how many ways can the lowest score be made?
4. In either case, how many of these ways are (a) symmetric, (b) rotationally symmetric?
5. Investigate symmetric and rotationally symmetric solutions for any score between the highest and lowest.
6. Create a '5/4/3 in a row' scoring system for the task so that the highest possible score is zero.
7. If the investigation became a game with one board and a total of 13 counters (in two colours) used between two players, investigate possible winning placement strategies, ie: strategies which would give you the highest 'in a row' total of your colour.

#### 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 78, Row Points. The task can be converted to a whole class lesson with plenty of counters and multiple game boards, but by far the easiest way is to use Poly Plug. If you are not a member of Maths300 (why not?) you can read an outline of the whole class investigation in the Menu Maths link below. Follow the link through and you will also find a contribution from Wangaratta Primary School which includes several excellent student suggestions.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 78, Row Points, which includes a Working Mathematically self-assessment sheet.

Visit Row Points in Menu Maths Pack D.

#### 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 Row Points task is an integral part of:

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

The Row Points lesson is an integral part of:

• MWA Number & Computation Years 7 & 8

## From The Classroom

#### Immaculate Heart of Mary School

Lance Rooney
Year 6
Doug,
I just completed Row Points with the Grade 6 children and they were fully engrossed with the investigation. We did come up with a rule that we decided needed further scrutiny and I said I would pass it along to you and you could do with it what you will.

The rule is: When you add an extra counter, your maximum score will go up by four. Remove a counter and your maximum score will reduce by four.

Now we did not investigate the validity of this claim to any extent. We found that 14 counters will give you a maximum of 44 and 12 counters will give you a maximum of 36 and formed our hypothesis from that. It's over to you to see what you and the rest of the maths community can make of it.

Smile and enjoy,
Lance