# Lining Up

### Task 11 ... Years 2 - 8

#### Summary

You are told where you are in a line, ie: which position from each end. How many people are in the line?

This cameo has a From The Classroom section which offers a unique view of the problem that helps to explain the difference of two squares formula.

Lining Up also appears on the Picture Puzzles Pattern & Algebra B menu where the problem is presented using one screen, two learners, concrete materials and a challenge.

#### Materials

• Objects, such as counters, as pretend people and one distinctly different object to be you.

#### Content

• arithmetic practice
• problem solving strategies
• number patterns
• algebra, including:
• concept of a function
• generalising
• equivalence of algebraic expressions
• multiple representations

#### Iceberg

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

1. Ask the mathematicians question Can I check this another way?. In fact, in how many different ways can you work out the number of people in the line?
(See below for some ideas.)
2. What happens if you are not the same number from each end?
3. What happens if you are told your fractional position from one end? Can you work out the total in the line?

#### 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 21, Lining Up. To convert the task to a whole class lesson first involve the students in acting out some examples. Then ask them to model some problems with counters and something special for 'you'. Poly Plug is excellent for this task because a yellow/blue plug can be you and the red ones can be everyone else. See the Poly Plug & Tasks link below.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 21, Lining Up, which includes and Investigation Guide.

Visit Lining Up in Menu Maths Pack A.

#### 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 Lining Up task is an integral part of:

• MWA Pattern & Algebra Years 3 & 4
• MWA Pattern & Algebra Years 7 & 8

The Lining Up lesson is an integral part of:

• MWA Pattern & Algebra Years 3 & 4
• MWA Pattern & Algebra Years 7 & 8

## From The Classroom

#### Högskolan Malmö, Sweden

Teachers in Training
 Ameli's explanation on the right is absolutely correct. Can you see how she was thinking?