This SOL enables classes to begin benefitting from timely practice as quickly as possible.
This page will need to be updated once the word problems topic theme is ready. |
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.
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. |
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).
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
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
Algebra
Geometry/Measure
Integer
Probability/Statistics
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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.
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…”
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:
5. Prepare teaching of decimalFraction by taking a new snapshot of decimalFraction dashboard (see Plan Teaching).
If there are any learners who won’t be learning decimalFraction layer 1 or 2
6. If the learner
7. Create the assignments
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. |
Before lesson
In the lesson Show the snapshot of decimalXdiv dashboard to the class - explain what it shows
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 a second time time this 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. Give out assignments to those who won’t be learning decimalXdiv and mini-white boards and pens to those that will. Encourage learners with assignments to ignore the teaching, if they can. Teach layer 7 and give out the practise-learn worksheet for layer 7 (to the appropriate learners) and continue to teach layer 8 or higher to those who are to learn layer 8 or higher. Encourage writing out all steps e.g. 7 x 6 = 42; 0.7 x 6 = 4.2; 0.07 x 6 = 0.42 etc Ask learners to ask for the answers when they have finished their worksheet, 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. |
Before the lesson: Look at the last page of each weekday assignment, and decide:
Did any learners do some work on their (weekend dated) Spare Assignment?
In the lesson Start with a timely practice assignment, as learners enter welcome them, indicate their assignment and say that a timer will go off before the end of the lesson for a different activity. Filler activity When the timer goes off, ask learners to hand in their assignments, they may be able to continue in a little while, but first they will look at the work they’ve completed to date (your going to get the learners to put their assessed assignments in their folder, and you don’t want their current assignment to get lost amongst the others!). Depending on the type of folder you have, you may want to hole punch the assignments in advance with the kind of hole-punch which has a bar, to help centre the holes).
Engage the class in questions about pre assess e.g. hands up if you had (or point on a page to)
Ask if learners are finding their questions
Take in the folders. Then give out the assignments learners to see how many of the remaining questions in their assignment they can finish before the end of the lesson (if there is time). |
This lesson can be tricky: ideally the teacher will continue to teach some new learning, but sometimes, especially if poor attendance is an issue, allocating lesson 6 to completing assignments and doing no new teaching will make
The best topic to teach this lesson is the topic with the highest proportion of blue/white/very light grey showing and the lowest proportion of darker grey/swirling blue circle showing. FDPR topics likely to be ready to teach to the class are:
Also why not look at these algebra topics which might be ready (because most learners may not know much/anything, so pre assess can be very quick)
If the teacher is going to
Before the lesson
During the lesson It is helpful to split the lesson into a sandwich: start with timely practice, do the teaching, continue with timely practice. If the topic you will teach has a large spread of attainment, you may like to make the lesson into a club sandwich: timely practice, teach some learners, timely practice, teach other learners, timely practice/practise-learn worksheets. If attendance was so poor that no topic is ready to teach, you may decide to teach a topic to just the lowest attaining learners (who will be fully pre assessed), and you may decide to have a filler activity for the other learners e.g. a “spot the difference”, a number puzzle, a complete some gaps in the times table grid, a very easy word search etc. |
Learners are likely to be either ready to learn layer 1 or 2. Teach these simultaneously, but emphasise that some learners won’t get an example as the first part of the question. |
Layer 3 is the most critical layer - do learners know how to write a fraction, from a diagram? Learners who don’t know how to do this, should probably be taught in a small group (but there is no reason, why they can’t “watch” the teaching of layer 4 or higher layers). Some learners can answer questions on harder layers, but not layer 3 (because they confuse the standard fraction notation, with e.g. a “bookies way of describing fractions e.g. writing 2/3 instead of 2/5”), learning layer 3 is, in these cases, even more important. |
Many learners can answer layer 3 questions, without knowing why, but this can be addressed through think aloud or asking probing questions when teaching other layers. In the very unlikely event that a learner has mastered layers 1 to 7 (this is unlikely for learners below the 15th percentile) there is a problem because simplestForm has not been pre assessed, its easiest to not teach this topic to this/these learner(s). |
Focus on correctly repeating “we say nought point four three, which is forty three hundredths” when a learner says “nought point forty three”, but otherwise don’t be worried about place value for this topic, it will be dealt with in decimalFraction and numberDIV10etc |
With timely practice this is “just as hard to teach a spread of attainment” as with traditional maths teaching, but with timely practice the learning will stick, so each cycle of the curriculum this will get easier. The teacher might like to teach
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With timely practice this is “just as hard to teach a spread of attainment” as with traditional maths teaching, but with timely practice the learning will stick, so in each cycle of the curriculum this will get easier. The teacher might like to teach fractionOF which is halfOF in one lesson and fractionOF layers 10, 11 and 16 in a different lesson. There are likely to be some learners who have several “firm learning foundations, so it might be sensible to avoid teaching 10, 11 and 16 for the first curriculum spiral. |
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” |
This is a good topic theme to teach first or second as
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. |
Learners below the 15 percentile often haven’t retained learning on this topic, so it can be really quick to pre assess, hence its suggested as lesson 1. Layer 1 is easy to learn, and learners are often engaged by the concept that “mathematicians are so lazy they can’t be bothered to write 2 x p so they miss out the times sign” |
This is deliberately made simple in layer 1 - learners don’t need to plot coordinates, nor continue tables of values - they merely need to draw a line segment through the given points across the full width of the graph paper. So don’t discount this topic as “too hard”. For layer 2, the learner doesn’t need to be able to plot coordinates, better that they use “go right one square and up (or down) … squares”. This helps the learner to get a natural sense of gradient, and find errors in their plotting of graphs later. |
This helps learners get a sense of negative number, so is valuable to teach this topic. |
With timely practice this is “just as hard to teach a spread of attainment” as with traditional maths teaching, but often there isn’t a wide spread of attainment, in the below 15th percentile classes. The teacher might like to teach layer 1 to the whole class (or all the class that haven’t yet mastered layer 4) as
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This topic may take some time to pre assess completely, hence teacher will probably want to leave this topic until most other algebra topics are taught. Teaching simplifySD may muddle some learners with their recently learned simplifyPQ skill - if this happens - its best to remove the simplifySD layer, as simplifyPQ has many more layers than simplifySD. |
This topic may take some time to pre assess completely, hence teacher will probably want to leave this topic until most other algebra topics are taught. With timely practice this is “just as hard to teach a spread of attainment” as with traditional maths teaching, but often there isn’t a wide spread of attainment. (The teacher can remember that with timely practice the learning will stick, so each cycle of the curriculum, teaching this topic will get easier). If there is a wide spread of attainment, it may be easier to teach to groups at their table or clustered around a flip chart, rather than teaching to the whole class. FYI If learners have mastered layer 2 and layer 4, no need to teach layer 3. |
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)
If everyone is still doing pre asses, select a teaching order which maximises topics where most learners are pre assessed
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For low attaining learners its worth taking a screenshot of the numberX10etc dashboard - to see what learners already know - although learners may be able to learn without the skills listed below: layer 1: no need to multiply by 10 layer 2: will find easier if numberX10etc layer 4 is mastered layer 3 and 4: will find easier if numberX10etc layer 10 is mastered |
There may be quite a bit of shame attached to not being able to do these skills. The first 3 layers, avoid the learner having to place the ruler accurately, so make good scaffold to layer 5. |
Have tracing paper ready + be ready to show how to use it (using a flip chart rather than a whiteboard may help). Share strategies on how to tell left from right? The common misconception is counting the squares between the two shapes. |
Have tracing paper ready + be ready to show how to use it (using a flip chart rather than a whiteboard may help). Encourage slowly turning the page to check if diagrams are correct |
Perhaps start with practise-learn layer 1 worksheet as a warm up? Make sure you pronounce the shape names, and then get learners to parrot them back. |
It is quite helpful if only the lowest attaining learners are learning volume together, as far more learners than one expects don’t know how to visualise in 3D from an isometric drawing. Having multlink available and colouring the cubes in the diagram to match might help. |
FYI perimeter is saved for next term. There are a number of layers building up to “area of rectangle = width** times height”, this is partly because low attaining learners don’t know many times table facts, but also IMHO one can’t remain a low attaining learner if one can use the power of multiply (and v.v.) ** FYI I find that using the length times width adds unnecessary confusion for many learners, as it muddles with width, depth and height measurements of furniture and the generic us of length. |
It is quite helpful if only the lowest attaining learners are learning layer 1 and 2 without teaching harder layers - using scale factor has a high working memory load, so encourage learners to show their workings out. |
“oh, here we go, along the xylophone and up or down the yoyo” is useful - whereas - “along the corridor and up the stairs” has many misconceptions waiting to trap the unwary! |
Make sure you pronounce the solid names, and then get learners to parrot them back. |
Have tracing paper ready + be ready to show how to use it (using a flip chart rather than a whiteboard may help). |
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NB those still doing pre assess will NOT be taught a second topic
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Primary schools are excellent at teaching this, so if there are problems with this skill - the small bite approach will hopefully help fix them. |
Sorry this topic isn’t well developed, but the 2 layers that currently exist are really helpful for improving place value skills. Please do request extra layers from this topic, or the easier topic place1value99 and the harder topic place10000valueUP |
There are many layers which lead the learner gently towards traditional prime questions. For learners with poor division skills, gently learning these skills helps with learning so many harder topics, so do give this topic a go - check out how easy layer 1 is. |
Imagine how hard learning maths would be without these skills. Usually this needs to be paired with another skill, as many find this topic easy. |
These questions tend to engender a lot of shame, as learners may have been failing at these for many years. The small bite approach really helps fix this. |
This is really helpful for improving accuracy and checking. |
Helps fix ordering accuracy. |
Accessible even to learners who can’t write a fraction correctly yet |
Important grounding in proportion |
Excellent for fixing place value issues which counting hasn’t resolved |
Good for logic, checking accuracy and possibly easy marks in GCSE - so do teach this topic |
Most learners will be better off only learning one new topic in the last maths lesson of the week + given a slightly longer assignment - so some of these topic pairs will need to be split up. However it is sometimes possible to use the last lesson of the week as an opportunity to teach a harder topic as the second topic to more highly attaining and faster working learners.
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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 |
|---|---|---|
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
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 |
|---|---|---|
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
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 |
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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.
The 3 levels of differentiation for the practise-learn worksheet are:
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
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 |
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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 |
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 |
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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 |
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).
The more learners know, the more new topics they can learn, so the longer each spiral of the curriculum will take, so don’t worry if only 2 curriculum spirals are possible in a year. |
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.
If a class has a wide spread of ability in the second and subsequent years of teaching with timely practice, a bespoke curriculum which balances the key topics that the higher attaining learners should learn with the needs of low attaining learners might mean that e.g. integer and algebra topic themes are taught together in a block and this block is taught more frequently than the other topic themes. Here is an example of such a SOL
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If time teach a 4th curriculum spiral with integer prioritised.