First pre assess + teach one topic per lesson, until some learners are fully pre assessed.
Then learners who are fully pre assessed can then learn 2 topics in most lessons, whilst their peers continue with pre assess + learn one topic.
Finally once all learners are fully pre assessed most learners can learn 2 topics per lesson but some slower paced learners will only learn one topic per lesson.
most low prior attainment learners have ingrained “I can’t do this” beliefs about learning integer skills - so the very learners we want to prepare for learning other topics, by teaching integer skills, are the learners who are least likely to learn - if we teach these skills first because:
integer is the most shaming topic theme not to be able to learn - so most learners will prefer not to compare what integer skills they have with their peers - this is easier if pre assess of integer is staggered,
once learners have begin to trust that maths teaching is very likely to become embedded maths learning, then teaching integer skills is most likely to be effective.
The lowest attainers will finish pre assess first (perhaps within 3 weeks) because the less learners, know the quicker the pre assess process is. These learners they can learn a second topic each lesson, whilst the other learners are doing longer assignments, meaning the teacher will be able to give more teaching time to “fix misconceptions”. Once the whole class is learning integer through timely practice for the first time, the lowest attaining learners may already on their second spiral of learning integer skills.
Topic Theme: FDPR
Before lesson: The teacher will make the best use of their time in the first two lessons, by doing assessment during this lesson, since no new teaching is taking place. Hence create 3 assignments per learner, ready for the first lesson (and we have no idea of the learners pace of learning).
Add learners (recommend ordered by First Name) add the First and Family Names but consider using an anonymised Known as Name e.g. the letter A to Z (we want to share the process, but not personal data)+ give best estimate of Level for Learner
Add the SOL for the first curriculum cycle see the “expand” below.
Create all of the class a 8Q (today’s date) then a 10Q (Saturday’s date) and then a 10Q assignment (Sunday’s date) - because we have no idea how fast learners can answer pre assess questions, and so want to assess at least the first few questions at the end of the lesson - or even better in the lesson.
Gather some extra time filler worksheets - just in case any learners - despite our best efforts, finish all 3 assignments.
Prepare your pep talk re difference between tests/exams versus assessment with timely practice
Tests and exams
Assessment with timely practice
Tests and exams
Assessment with timely practice
Data collected
Score e.g. 12/20
Teacher can do time consuming data analysis to find out e.g. who already knows a particular skill
Which skills you
have learned and remembered
are best learned later
What the data can be used for
Score - to compare you with your peers
Teacher data analysis - what to teach the class soon, providing the teacher has time to look through past papers.
To decide what
to skills to assess next e.g. harder/easier skills
to teach each learner next at “goldilocks' difficulty
skills to double check that you really have already learned and remembered and/or that you have remembered the skills you learned last lesson which will
make the skills easier to remember
means the teacher can help you learn to remember or be more accurate or read the questions better
means the teacher might, by helping you, sometimes find out which other skill you need to learn first.
All in all the data will be used to make sure that learning is as efficient as possible.
In the lesson
You the teacher will need their android device, so that they can assess some assignments - instead of twiddling thumbs while the learners complete their assignments.
Pep talk - see above and
What to do when you can’t answer a question → Learner may try or may cross it out or write a ? in the answer space.
What to do when learner has finished their assignment → Learner hand up and ask for next assignment. Teacher will collect completed assignments, give the learner another to do (and the teacher may assess some assignments in the lesson).
Why not copy? → Learners will have different questions (so they can’t copy) + learner will make it harder for themselves to learn in future lessons + there is no point, because there is no score.
Give out the 8Q assignment (today’s date) and sort the Saturday and Sunday assessments by first name (to make it easier to find them). Keep a list of all the Saturday assignments you give out. TOP TIP keep 3 piles of assignments today’s/Saturday/Sunday (with the assessed assignments reversed at the back of each pile).
Once learners ask for a second assignment, the teacher can begin to assess the first assignment (on the android device, remember tap with your non-writing hand and tick/bell with your writing hand).
FYI keep the completed assignments in a pile for use in lesson 5
Some topics won’t be added to the SOL until most of the first cycle of the curriculum has been taught. Remember that this assessment process will help embed learning more deeply, learning which is gradually being forgotten.
FDPR
decimalFraction
decimalXdiv
fractionADDsub
fractionINTRO
fractionOF
numberDIV10etc
orderFDP
ratio
Algebra
algebraGraph
inequality
sequenceArithmetic
sequenceOther
simplifyPQ (product/quotient i.e. x or ÷)
simplifySD (sum/difference i.e. + or -)
solvingReady
Geometry/Measure
2D
3D
area
changeUnits
coordinate
enlarge
reflect
rotate
scaleInterpret
translateANDvector
volume
Integer
10bond
base10add
base10skills
correctTOnearest
factor
givenADDsign
givenDIVsign
givenSUBsign
givenXsign
multiple
negative
numberX10etc
orderInteger
place100value9999
prime
sequenceMultiple
Probability/Statistics
discreteGraph
frequencyTable
MMMRQseparate
probabilitySingle
proportionalGraph
stemLeaf
Venn
Before lesson: Time spent getting the learners pace for practice (P4P)approximately correct is worthwhile and making sure learners complete a recently created assignment every lesson, will make planning easier and teaching more efficient.
Create a spreadsheet (see below) and if the assignments not already in 3 piles (first lesson/Saturday/Sunday) sort them like this.
Write the names of any absent learners in the correct row of the L1 8Q (lesson 1, 8 question assignment column).
Assess all remaining L1 8Q assignments
hopefully almost all learners who were present completed their L1 8Q assignment
but if any learners (were really slow working/late) and did have time to complete this assignment: assess all missed questions with reset symbol (3rd assessment choice) and write the number of missed out for lack of time questions in the correct row of the L1 8Q (lesson 1, 8 question assignment column) FYI this is because the app will be able to use this data, to move on to pre assess more on the first few topics they will teach.
Check that there is a paper assignment for each of the L1 8Q remaining assignments shown in the P&P session and no others - keep these in one pile.
Cross out the names of all the assessed assignments from Saturday and Sunday in the table.
Look at each un-assessed Saturday assignment
If the assignment is complete: assess it and cross out the learners name in the Saturday column of the table.
If there are only 1/2/3 (missed out for lack of time) questions left in the assignment, assess these with reset (if they are missed out because the learner couldn’t do them, then assess with bell) + in the correct row of the Saturday 10Q column: cross out the learner’s name + write in the number of missed out for lack of time questions + assess the rest of the questions. Write these learners names in the L2 8Q column (they will do the new 8Q assignment and the Sunday assignment next lesson).
If the are 4 or more questions still to do, do NOT assess but write their name in the L2 8Q column (they will do the new 8Q assignment first and then complete this Saturday assignment, and have the Sunday assignment as back up, if needed).
Look at the Sunday assignments: are there any that learners have
finished? - assess the assignment and write the learners name in the L2 25Q column and the L2 8Q column (they will do the 25Q assignment first, the 8Q assignment is spare in case they finish the 25Q assignment early);
less than half finished? - write their name in the L2 20Q column (they will do the 20Q assignment first and then finish the Sunday assignment),
more than half finished? - write their name in the L2 25Q column (they will do the 25Q assignment first and then finish the Sunday assignment).
Create the new assignments - first the 25Q assignment, then the 20Q assignment and finally the 8Q assignment. NB whenever possible learners will start with the assignment dated for next lesson (except learners absent last lesson: they will have no assignment dated for L2, but will do the L1 8Q assignment, and then the Saturday and then the Sunday assignments if they finish early).
Gather some extra time filler worksheets - just in case any learners finish early - see lesson 1 - or use your own.
Screen shot the topic dashboard for decimalFraction, decimalXdiv and fractionINTRO and prepare to display these on the whiteboard. FYI if you can, screenshot the dashboard so the learners “known as” name is hidden.
Name
L1 8Q
Saturday 10Q
Sunday 10Q
L2 8Q
L2 25Q
L2 20Q
2 lesson total
P4P
L3 8Q
L3 l2Q
Name
L1 8Q
Saturday 10Q
Sunday 10Q
L2 8Q
L2 25Q
L2 20Q
2 lesson total
P4P
L3 8Q
L3 l2Q
Learner 1
Learner 1
Learner 1
Learner 2
Learner 2
Learner 2
Learner 3
Learner 3
Learner 3
etc
etc
etc
In the lesson
Explaining the purpose of the second lesson: finding more about what learners know in the topic theme FDPR (fraction, decimal, percentage ratio) + doing revision - so that the teacher can teach on firm learning foundations and the timely practice app can ensure that learners retain their learning. Ask some questions, “hands up if you…”
found some questions too easy?
found some questions too hard?
couldn’t answer some questions that you’ve learned before?
Reassure this is what you expect. Continue to explain: “If you answered a question correctly last lesson, you will get a similar question to answer this lesson (or next), which will help the timely practice app be sure of what skills you already know of on a topic. Next lesson I (your teacher) will start using this data to make teaching and learning easier”
Show the decimalFraction dashboard, explain that the learners are anonymised and you won’t be saying who is which letter, but they can see what the app has found out so far about the class' learning on the topics (low number = easier, high number = harder; white = needs to learn, grey = might need to learn). Explain that next lesson, when you look again, there may be some blue squares = the app has found out all the skills the learner has already learned and remembered on the topic, but that for learners who know more on a topic, this might take 4 lessons.
Learners should start with the assignment dated today (except absent learners, who will start with the L1 8Q assignment).
The teacher may want to cross out from the table, assignments that they assess during the lesson (again keep the assignments in piles: L1 8Q/L2 20Q/L2 25Q/L2 8Q/Saturday/Sunday (don’t worry it won’t get exponentially more piles of assignments, as part of the preparation for next lesson, is to estimate the learners Pace for Practice, and the teacher will work towards having 2 assignments for each learner - one they will just finish in the lesson (weekday) and a spare (weekend) in case the learner needs more practice.
FYI keep the completed assignments in a pile for use in lesson 5
Before lesson:
Some assignments will have been assessed in the lesson, assess any complete but un-assessed assignments, cross these out from the table from lesson 2.
Begin Old Assignments list
Write lesson 1 date as a subheading: write below a list of any learners who were absent lesson 1 and 2 - put these assignments to one side and shade out the 2 appropriate squares in the L3 column of the table (they won’t need new assignments created).
Assess any complete/partially complete assignments:
assess any assignments dated L1 - unless they are on the Old Assignments list - if there are any questions not completed because the learner ran out of time: assess with reset - third option - and write the number of missed out for lack of time questions in the correct row of the L1 8Q (lesson 1, 8 question assignment column),
assess Saturday/L2 25Q/L2 20Q assignments - if there are any questions not completed because the learner ran out of time: assess with reset - third option - and write the number of missed out for lack of time questions in the correct place in the table,
for learners who were absent in lesson 2: put aside the L2 8Q/L2 25Q/L2 20Q assignments, they will complete these next lesson - write in the Old Assignments list under the appropriate subheadings L2 8Q/L2 25Q/L2 20Q, the learner's name - put these assignments to one side and shade out the 2 appropriate squares in the L3 column of the table.
look through all the remaining L2 8Q assignments
for learners who didn’t have an L2 25Q/L2 20Q assess the assignment whether finished or not - if there are any questions not completed because the learner ran out of time: assess with reset - third option - and write the number of missed out for lack of time questions in the correct place in the table,
assess any other partially complete assignments, as above, but put aside the L2 8Q assignments (in the Sunday pile) of learners who did a L2 25Q/L2 20Q assignment this lesson - this is their spare assignment
look at the Sunday assignments:
if they have not been begun - write 10 beside the learners name in the Sunday column of the table,
assess them if they are complete - and cross out the learners name in the Sunday column of the table,
if they are mainly incomplete, write the number of questions still to do in the Sunday column of the table,
if they are almost complete, assess the last few questions with reset, and write this number beside the learners name in the Sunday column of the table and cross out the learners name.
Now, for learners who have been present for both lessons, calculate their 2 lesson total number of questions (This assumes approximately 40 out of 60 minutes of the past two lessons was spent completing assignments, i.e. 80 minutes, at a rate of 1 question every 2 minutes).
Remember the number inside each column is the number of questions NOT completed
Adjust the learners P4P (Pace for Practice - found in the learners tab), using the table below:
For learners who have been present for one lesson, if they have completed 14 or fewer or more than 24 questions, adjust their P4P (Pace for Practice).
2 lesson total
12Q
16Q
20Q
24Q
28Q
32Q
36Q
40Q
44Q
48Q
52Q
P4P
30%
40%
50%
60%
70%
80%
90%
100%
120%
130%
140%
1 lesson total
6Q
8Q
10Q
12Q
14Q
24Q
26Q
5. Prepare teaching of decimalFraction by taking a new snapshot of decimalFraction dashboard (see Plan Teaching).
Look on the decimalFraction dashboard for learners who will learn layer 1 or 2 from decimalFraction
if decimalFraction layer 1 is blue, then teach layer 2 - add by tapping the blue (2) and Teach button
if decimalFraction layer 1 is white, then teach layer 1 - add by tapping the blue (1) and Teach button
if decimalFraction layer 1 is grey - learners are not sufficiently assessed, the layers won’t be added (when pressing the Teach button) - these learners will continue with pre assess throughout most of the lesson
If there are any learners who won’t be learning decimalFraction layer 1 or 2
make a seat plan so they are are sitting further away from the whiteboard/flip chart
have their assignments ready to give out at the start of the lesson.
6. If the learner
is to learn decimalFraction and has a Sunday assignment left: shade out the L3 12Q square in the table (so will get 8Q assignment and then the Sunday’s assignment)
is to learn decimalFraction and has NO Sunday assignment left: shade out the L3 8Q square in the table (so will get 12Q assignment)
is not to learn decimalFraction but has a Sunday assignment left: shade out the L3 8Q square in the table (so will get 12Q assignment and then the Sunday’s assignment to do)
is not to learn decimalFraction and has NO Sunday assignment left: do no shading (so will get 8Q and 12Q assignments - start with the 12Q assignment).
7. Create the assignments
a 12Q assignment dated for L3 - for all the learners not shaded out in the L3 12Q column
an 8Q assignment dated for L3 - for all the learners not shaded out in the L3 8Q column
In the lesson
Show the snapshot of decimalFraction dashboard to the class - explain what it shows (if layer 1 is: white - learn layer 1, if blue - learn layer 2, if grey - do more pre assess). Explain that the app is continuing to build up information for other topics every time the teacher assesses the assignments and that the class is likely to learn this topic three times during the year, so learners who were absents for a pre assess lesson, or who need to do more pre assess will learn more on this topic next term if not before.
Give out assignments to those who won’t be learning layer 1 or 2 and mini-white boards and pens to those that will. Encourage learners with assignments to ignore the teaching, if they can.
Teach layer 1 and give out the practise-learn worksheet for layer 1 (to the appropriate learners) and continue to teach layer 2 to those who are to learn layer 2. Encourage imagining shading in a 100 square to help them if they get stuck - perhaps cut up some 2cm graph paper which they can use as an aid memoire?.
Ask learners to ask for the answers when they have finished their practise-learn worksheet, they should self-assess and then continue with their assignments as before. During the second part of the lesson, the teacher is likely to have time to assess some completed assignments, remember to cross them off from the table.
Some topics from FDPR have been excluded for the first curriculum spiral. This is done to make teaching and learning easier - guidance is given about when to introduce these is given below, under the heading “Second Curriculum Spiral”
Teach Topic Theme: Algebra
This is a good topic theme to teach first or second as
its quick to pre assess with low attaining learners,
feels to learners like starting on “grown up maths”,
generally avoids ingrained “I can’t do this” opinions from learners.
It contains many quick to fully pre assess topics, as learners below the 15 percentile will have mastered no/few layers from many topics.
With the timely practice teach one layer per topic per learner per curriculum spiral approach, almost all learners will find it easy to learn a new layer from each of the suggested topics.
Topic Theme: Geometry/Measure
Suggested teaching order (NB perimeter is deliberately omitted form the first teaching cycle - as it can interfere with mastering area in the first curriculum spiral)
Topic Themes: Probability/Statistics and Integer
integer topics
probability and statistics topics
Second curriculum spiral
FDPR again
Add these topics to be pre assessed only if any learner has mastered the stated layers from the topics indicated below:
percentOF only if fractionOF (8) is mastered
correctDP and estimateSIGfig only if correctTOnearest (7) is mastered
decimalXdiv may want to wait until numberDIV10etc (8) is mastered
fractionXdiv until at least fractionINTRO (3) and givenXsign (4) are mastered
simplestForm until at least prime (3) is mastered
standardForm perhaps until numberX10etc (10) but definitely until numberX10etc (4) is mastered
everybody learns
only faster pace for practice learners
NOTES
everybody learns
only faster pace for practice learners
NOTES
decimalFraction
fractionOF
fractionADDsub
simplestForm
low attaining learners learn extra integer or nothing extra**
fractionINTRO
orderFDP
numberDIV10etc
standardForm
low attaining learners learn extra integer or nothing extra**
fractionXdiv
moreIndex
low attaining learners learn extra integer or nothing extra**
ratio
correctDP
low attaining learners learn extra integer or nothing extra**
decimalXdiv
estimateSIGfig
skip this lesson if no one is ready for these topics
** faster learning low attaining learners can have an additional timely practice assignment - ideally with a weekend date
Geometry/Measure again
Add these topics to be pre assessed only if any learner has mastered the stated layers from the topics indicated below:
perimeter in KS3 only if area (3) is mastered by ALL learners, in KS4 add this topic now
shapeProblem NC only if givenSUBsign (3) is mastered
angle only if scaleInterpret (5) is mastered
everybody learns
only faster pace for practice learners
NOTES
everybody learns
only faster pace for practice learners
NOTES
2D
3D
reflect
angle
alternate topic order after most master scaleInterpret (5)
area
rotate
scaleInterpret
changeUnits
alternate topic order after most master scaleInterpret (5)
coordinates
enlarge
alternate topic order after most master coordinates (5)
volume
perimeter
don’t teach perimeter until area (3) mastered
translateANDvector
shapeProblem NC
low attaining learners learn extra integer or nothing extra**
** faster learning low attaining learners can have an additional timely practice assignment - ideally with a weekend date
Algebra again
Add these topics to be pre assessed only if any learner has mastered the stated layers from the topics indicated below:
expandLinear only if simplifyPQ (1) is mastered
expandQuadratic only if simplifyPQ (2) and expandLinear (4) are mastered
factorise only if expandLinear (4) is mastered
solve only if solvingReady (3) is mastered
Here are suggested pairs of topics to teach in a lesson
everybody learns
faster pace of practice learners
NOTES
everybody learns
faster pace of practice learners
NOTES
sequenceArithmetic
algebraGraph
when all master sequenceArithmetic (4), OK to swap priority
simplifyPQ
fill with an integer topic until ready for valueAlgebra
inequality
expandLinear
simplifySD
writeAlgebra
when most master simplifySD (5), OK to swap priority
solvingReady
solve
fill with an integer topic
expandQuadratic
only if some learners are ready to learn expandQuadratic
fill with an integer topic
factorise
only if some learners are ready to learn expandQuadratic
The layer sequenceOther(4), can accessed at different levels of differentiation, side steps the topic not fully pre assessed problem.
make the patterns with manipulatives (such as centicubes or counters) or trace the patterns,
complete as a “copying the drawings” and doing the “adding on” activity (possibly with some support),
if learners are able to do the practise-learn worksheets independently, this layer should be added within the Plan Teaching section of the lesson BUT if this topic is taught within the same lesson as the first pre assess assignment, it can’t be added in plan teaching (and hence go into retrieval practice) until the second lesson, (because it is being pre assessed). Only add the layer within Plan Teaching + verify in Edit Taught for learners who engage with it as described with this, the 3rd level of differentiation
Integer again
Add these topics to be pre assessed only if any learner has mastered the stated layers from the topics indicated below:
beginXfacts only if givenXsign (1) is mastered
base10skills only if numberX10etc (4) is mastered
beginDIVfacts only if fractionOF (4) is mastered
factor and BiDMAS only if givenXsign (3) is mastered
everybody learns
only faster pace for practice learners
NOTES
everybody learns
only faster pace for practice learners
NOTES
10 bond or BiDMAS
correctTOnearest
swap priority once mastered 10bond
base10add or givenSUBsign
multiple
swap priority once mastered givenSUBsign (10)
place100value9999 or factor
base10skills
givenADDsign or prime
givenDIVsign
swap priority once mastered givenADDsign
sequenceMUltiple or givenXsign
beginXfacts or improveXfacts
negative
orderInteger or beginDIVfacts or improveDIVfacts
numberX10etc
practice times table facts learned this spiral
Probability/Statistics again
Add these topics to be pre assessed only if any learner has mastered the stated layers from the topics indicated below:
groupedGraph and scatter only if discreteGraph (4) or algebraGraph (4) is mastered
MMMRQgrouped only if MMMRQ (2) and (3) and (5) are mastered by at least one learner
probabilityTree only if fractionINTRO (4) is mastered
everybody learns
only faster pace for practice learners
NOTES
everybody learns
only faster pace for practice learners
NOTES
discreteGraph
Venn
frequencyTable
nothing else
this topic tends to be time consuming to learn
MMMRQseparate
groupedGraph or probabilityTree
proportionalGraph
scatter
probabilitySingle
stemLeaf
extra FDPR topic
MMMRQgrouped
skip this lesson if no one is ready to learn MMMRQgrouped
Third curriculum spiral
If there is time for this spiral and perhaps a fourth curriculum spiral (or if there is not enough time for a complete third curriculum spiral in the year) use this spiral to skip out less important topics and/or topics with fewer layers (such as enlarge).
e.g. integer is more important than algebra but no topic can be taught within 6-8 weeks of the last teaching. If possible try to teach an extra spiral of integer relative to the other topic themes. Depending on where holidays fall, teach one or two of the topic themes listed below, then teach integer. It is recommend not to miss out any integer topics unless all learners have mastered them. See below extra integer topics which might be pre assessed. Add these topics to be pre assessed only if any learner has mastered the stated layers from the topics indicated below:
improveXfacts only if beginXfacts (11) is mastered
improveDIVfacts only if beginDIVfacts (8) is mastered
e.g. within algebra prioritise: sequenceArithmetic, simplifyPQ and solvingReady until everybody has mastered solvingReady (6). All other topics are less important than most integer topics
e.g. within FDPR prioritise: decimalFraction, fractionINTRO, fractionOF and numberDIV10etc. All other topics are fine to miss out.
e.g. within geometry/measure prioritise: area, changeUnits, coordinates, volume and angle once angle (5) is mastered. All other topics are fine to miss out.
e.g. within probability/statistics prioritise: discreteGraph, MMMRQseparate and proportionalGraph. All other topics are fine to miss out.
4th curriculum spiral
If time teach a 4th curriculum spiral with integer prioritised.