TUTOR GUIDE

Title:PLANNING A ROOMLevelONE

MATHS CONCEPTS COVERED:
Standards Ref:
C5
C8
C10 / Solve simple problems involving ratio, where one number is a multiple of the other
Convert units of measure in the same system
Construct geometric diagrams, models and shapes
PROCESS SKILLS COVERED:
Representing /
  • Understand the practical problem of planning a room
  • Identify and obtain necessary information to tackle the problem
  • Select mathematics in an organised way to find solutions

Analysing /
  • Apply mathematics in an organised way in order to plan a room
  • Use appropriate checking procedures at each stage

Interpreting /
  • Interpret and communicate room plans, drawing simple conclusions and giving explanations

FUNCTIONAL MATHS BARRIERS ADDRESSED:
  • Sorting out which pieces of information are needed
  • Disregarding irrelevant information
  • Thinking through a plan for solving a problem
  • Selecting appropriate mathematical procedures to solve a problem
  • Applying mathematical procedures correctly
  • Choosing how to check answers
  • Communicating solutions to practical problems, either verbally or by writing answers down so that they make sense
  • Interpreting solutions to make a recommendation

TASK BRIEF:
  • Description of task
This set of three activities is designed to help your learners develop skills in using simple scales and scaled diagrams in the context of planning a room.
Each activity requires learners to plan a given room by:
  • Choosing an appropriate scale to use
  • Selecting items of furniture which have been scaled down correctly using this scale
  • Deciding where to position each item of furniture in the room.
The three activities are differentiated as follows:
Activity 1 - planning a bedroom
Appropriate for learners who are working between Entry 3 and Level 1:
  • All measurements and scales are given in centimetres, eliminating the need to convert from metres to centimetres or vice versa.
  • There is only one set of actual room dimensions given.
  • There are no requirements to place specific items of furniture within given measurements in the room.
  • There are no obstacles present in the room.
Activity 2 - planning a lounge
Appropriate for learners who are working at Level 1:
  • Scales are given in centimetres only whereas room and furniture measurements are given in metres.
  • There are two sets of actual room dimensions given.
  • One item must be placed within a given range of another.
  • There are two obstacles present in the room.
Activity 3 - planning a play room
Appropriate for learners who are already comfortable at tackling Level 1 problems and who wish to stretch themselves further:
  • Scales and furniture measurements are given in centimetres or metres throughout.
  • There are two sets of actual room dimensions given.
  • Three items must be placed within a given distance from others.
The process of completing each activity is identical.
Learners should work in pairs or small groups.
The first stage is to select a scale to use from the options given. There is only one correct scale to use which is appropriate for the room size and scaled diagrams given: if students choose an inappropriate scale, this should lead to a change in decision following discussion at a later point.
Having chosen a scale, groups then decide which furniture items have been drawn correctly to this scale (they may ask to use a ruler for this task). There are multiple options given, in order to give groups the opportunity to discuss why some options areincorrect/inappropriate for the room size etc.
Groups should be encouraged tocheck at each stage whether their chosen scale and chosen furniture diagrams fit correctly with actual room and furniture sizes. How groups decide to check this is an open task: for example, they may decide tomeasure scaled diagrams first and then to apply their chosen scale, or they may decide to count squares on the room planand apply scales.
Once groups have selected a scale and a set of furniture diagrams which they believe corresponds withtheir room plan and set of room measurements, tutors may then canvass results, using this as an opportunity to explore misconceptions arising and to ensure all groups have the correct set of furniture diagrams.
Stage two of the activity may now begin: this involves groups deciding where to position scaled items of furniture in the room plan. Tutors should give out the stage two cards for each activity and facilitate groups discussing how to place items.
Activities 2 and 3 impose restrictions such as ‘The TV table must be at least 2m away from the sofa’. Groups must first cut out their scaled furniture items in order to decide where to specifically place them.
Once groups have glued the furniture into their chosen positions, tutors may facilitate comparing different resulting room plans between groups. This presents an ideal opportunity to evaluate the activity with learners; discussion points include:
  • How did the activity help you to use scales?
  • When did you need to convert from centimetres to metres or the other way around?
  • How did you decide on which scale to use?
  • What problems did you encounter when using the scale you have chosen?
  • Teaching and Learning Strategies
This activity provides an opportunity to maximise collaborative learning.
Groups must make a series of decisions together based on matching scales to scaled diagrams and planning rooms based on given actual measurements and restrictions.
During the process of decision-making, tutors should use open questions to prompt learners into constructing their own understanding of e.g. whether to multiply or divide when using a scale. Possible questions include:
  • If you choose ‘1cm represents 25cm’ rather than ‘1cm represents 50cm’, what effect will that have on the actual length of the room?
  • Show me how you find the actual room measurements using the room plan with the scale you have chosen
  • Show me how you have checked that the table is at least 100cm from the sofa.
The process of eliminating different scaled furniture options enables learners to think about how the dimensions of a scaled drawing relate to the actual dimensions by means of a simple scale. Having the opportunity to discuss how to use scales as part of this process with other learners is less threatening. Tutors should also maximise the opportunity for learners to explain to each other how to use scales; explaining how to use a scale to other learners has been shown to lead to more transferable learning.
Once learners have made their decisions, tutors have the option of asking them to present their room plans to other groups at the end of the activity. This gives them the opportunity to revise any decisions they have made and to reinforce anyunderstanding they have constructed for themselves. The activities have been designed to allow for differentiation: tutors may select a single activity for groups according to their differentiated level or may choose to ask groups to work on a combination of activities as their skills progress.
Tutors should avoid correcting any decisions learners make or telling them how to use a particular scale: the emphasis should be on giving learners time to construct their own understanding, whether they be correct or incorrect. Once groups have made their decisions, tutors will have the opportunity to expose errors and misconceptions through class discussion or by enabling groups to compare their solutions with each other.

Level One