How does Exploring maths cover Assessing pupils’ progress (APP)?
The Secondary National Strategy Assessing Pupils’ Progress Handbook states that APP
should help teachers to:
 strengthen their feel for National Curriculum levels;
 use information from focused assessments to improve teaching and learning
and secure pupils’ progress in mathematics.
Exploring maths has a number of features that support Assessing Pupils’ Progress.
Strengthening teachers’ understanding of and feel for levels
 Exploring maths’ tiered approach, which covers narrow bands of the NC levels is
ideal for helping Teachers and pupils identify their levels.
 Learning objectives for units as a whole and for individual lessons are shown on
slides and in the class book for discussion with pupils.
Promoting the use of planned and unplanned assessments as part of everyday
maths lessons drawing on a range of evidence including mathematical dialogue
 Each unit includes SATS questions in its How well are you doing? section and Check
up tests which are included on the Teacher Book CD-ROM. SATS questions are also
included in the two Revision units.
 Each number unit of the teacher’s book includes an optional mental test of 12
questions for teachers to read to the class.
 Key questions for teachers to ask informally are identified in the lesson notes.
 The review that concludes every lesson allows the teacher to judge the effectiveness
of the learning and to stress the learning points that pupils should remember.
Planning for specific, focused assessments to inform both judgements about
pupils’ levels for each attainment target and to provide diagnostic information
about pupils’ strengths and weaknesses (using new materials)
 Results Plus Progress, a series of stimulating on-line computer-mediated
assessments offers an entry test for Year 7 to guide teachers on placing pupils in an
appropriate tier at the start of the course.
 For each KS3 year, there are two end-of-term assessments for the autumn and spring
terms, and an end-of-year assessment.
 Results Plus Progess offers instant marking and analysis tools to identify strengths
and weaknesses of individuals or groups of pupils.
Using information on weaknesses to set curricular targets to inform future
teaching and strengthen learning

Future units from Exploring maths that are dependent on the same skills are
identified in the books and Results Plus Progress so that teachers are aware of the units
that they may need to adapt, perhaps by adding in extra revision or support lessons
How does Exploring maths cover Personal learning and thinking skills
(PLTS)?
QCA states that pupils should have opportunities across the curriculum to:
1. plan and complete tasks in real settings or environments sometimes outside of the
classroom
2. take on new responsibilities and work flexibly as situations change as well as
organise their own time and resources in relation to their work
3. think and reflect on what they are doing and what they want to find out
4. work in groups so that they can share and refine ideas, evaluate each other's work
and ideas, and question the assumptions behind particular ideas
These objectives are covered in the Enquiry units and Functional Skills pages. Pupils
are required to work in pairs and groups, to discuss their findings and to decide how best
to approach a task. For examples, see the following examples from Tiers 4 and 5.
Tier 4 Enquiry 2 Exercise 1B
Work in a group of six, sharing a copy of S4.3 Resource sheet 1.1.
For each person in your group, measure and record on the resource sheet their:
•
hand span;
•
foot length;
•
reaction time;
•
standing jump distance;
• height.
You should already have decided as a class how you will make each
measurement and how accurate it needs to be.
When you have finished measuring, give your completed resource sheet to your
teacher, who will put together all the class data for you to use later in this unit.
Exercise 3
Work with a partner. Your teacher will give you a copy of the data to use.
The data shows:
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hand span;
•
foot length;
•
reaction time;
•
standing jump distance;
•
height.
Your teacher will help you to choose one of these questions to investigate,
or will suggest that make up your own question.
1 Do taller people jump further?
2 Do most people have similar reaction times?
3 Is there a relationship between foot length and hand span?
4 How does hand span vary in the class?
As part of your investigation, you will need to analyse and organise the data,
draw a graph, come to some conclusions, and put together a short report. You
may use graph plotting software for statistical diagrams to plot your graphs for
this work. You will have some time in this and the next lesson to do all this.
Before you begin, think about these points.
Questions 2 and 4 are about the distribution of the data.
•
What type of data is it – continuous or discrete?
•
Do you need to group the data? If so, what class intervals will you choose?
• What type of chart or diagram will you draw?
Questions 1 and 3 are about looking for a relationship between two
quantities.
• What type of chart or diagram will you draw?
You can now start to work on your investigation.
Points to remember
•
Scatter graphs are useful for showing connections
between two quantities.
•
Frequency diagrams are useful for showing how a set of
data is distributed.
Tier 5
Functional skills 5.1
Should you buy or rent a TV set?
This group activity will help you to:
•
model a situation;
•
select the mathematical information to use;
•
change values to see the effects on answers in the
model;
•
interpret results and draw conclusions.
Background
Let’s say your family wants a new large screen high density
television.
Some of the factors that you will need to consider are:
• what a high density set costs to buy;
• loss of interest on the money you spend on a new set;
• the depreciation of the value of the TV set;
• cost of repairs;
• monthly rental charges;
• how long you will keep the TV set before you get a
better model.
General information
If you buy a TV set, you can ignore the cost of any repairs
in the first year, since the guarantee covers them.
Rental charges include the cost of repairs.
Some costs are the same regardless of whether you buy or
rent, so you can ignore them, e.g.
•
the cost of electricity to run the set;
•
the cost of a TV licence.
Problem
To rent or buy?
Suppose the high density TV you want costs
£1200 to buy.
The monthly rental charge is £33.
Should you buy the TV or rent it?
Make some assumptions about:
•
how many years you will keep the TV set;
•
the annual interest rate on money in a
savings account;
•
the annual depreciation rate on a TV set;
•
the cost of repairs after the first year.
Work out the annual costs for s suitable number
of years and come to a conclusion.
Here are some other things to think about.
•
What happens if the repair costs go up each year?
•
What happens if the monthly rental charge goes down?
•
What happens if the interest rate changes?
Be prepared to justify your assumptions and conclusions to other groups.