KS3 and KS4 quick start with timely practice

• 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 2 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.

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

1. decimalFraction

2. fractionINTRO

3. ratio

Algebra

1. algebraGraph

2. inequality

3. solvingReady

Geometry/Measure

1. 3D

2. area

3. changeUnits

4. coordinate

5. enlarge

6. reflect

7. rotate

8. translateANDvector

9. volume

Integer

1. 10bond

2. correctTOnearest

3. factor

4. givenDIVsign

5. givenXsign

6. multiple

7. negative

8. numberX10etc

9. orderInteger

10. prime

11. sequenceMultiple

Probability/Statistics

1. discreteGraph

2. probabilitySingle

3. stemLeaf

Before lesson: The teacher will make the best use of their time in the first lesson, by doing assessment during this lesson, since no new teaching is taking place.

Create 2 assignments per learner (as we have no idea of the learners pace of learning).

1. 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

2. Add the SOL for the first curriculum cycle see the “expand” above.

3. Create a planning and preparation session, and change the date to L1

4. Create t.p. for all learners with 10Q and only include pre assess questions

5. Create a planning and preparation session, and change the date to Saturday’s date

6. Create t.p. for all learners with 15Q (Saturday’s date). and only include pre assess questions

7. Download and print the L1 and Saturday assignments.

8. Print out the maths motivation survey (a copy for all learners and a few spares)

9. Gather some extra time filler worksheets - just in case any learners - despite our best efforts, finish both assignments.

   1. beginXfacts begin X facts (4) and (14)

   2. improveXfacts improve X facts (3w) and (11)

10. Make sure you’ll have the tablet to take into the lesson, so you can do some assessment

Maths motivation survey

Introduce the maths motivation survey purpose: to find out if learners can become more motivated in maths, if learners can remember more maths.

Instructions: it is important learners first decide which answer is best (left or right) and then colour in 1, 2 or 3 boxes to say how strongly they agree with each answer.

When the first learner has finished their survey, check they’ve not answered only in the left hand column (a sign they didn’t fully understand the instructions), if so show them how they might need to change it. If correctly filled out, interrupt the class to explain what they will all do when they have finished.

Pep talk before doing timely practice assignment

• Purpose 1: to find out the “goldilocks” place to begin teaching them each topic - it’s not a test, there are no scores, and the teacher will explain more about this over the next few lessons. That’s why the heading is learned and remembered?

• Purpose 2: to revise skills and knowledge that you already know, to help you remember for longer.

• What to do when you can’t answer a question → Learner may “have a go” 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) + because learner will make it harder for themselves to learn in future lessons + there is no point, because there is no score.

Doing personalised timely practice assignments

Give out the L1 assignment (L1 date) and sort the Saturday assignments by first name (to make it easier to find them).

TOP TIP keep 2 piles of assignments L1 and Saturday (with the assessed assignments reversed at the back of each pile).

Note the time the learners start their assignments.

Note how long it takes for the majority of learners finish the first 10Q assignment - this will set Pace for Practice of 100%

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).

Finish the lesson

A few minutes before the end of the lesson, note the time again and calculate the total time the learners had to complete both assignments.

Encourage learners to check through their assignment for any questions they have missed out which they forgot to write a ? in the answer space - and write the ? in. Tell them that they needn’t do this for questions which they “haven’t had time for” as you know you gave them more questions than you thought they could answer.

If you have time, you can scan through the assignments and divide them into 3 piles as you collect them in, according to the proportion of questions “complete” i.e. answered or with a ? (or indeed any other comment) written in the answer space.

• not started,

• up to “about half”

• “well over half”

FYI keep the completed assignments for use in lesson 5

In the app, in the planning and preparation session for lesson 1 (yes lesson 1, for assessing the L1 assignments)

1. Assess t.p. all remaining L1 assignments (some may have been assessed in the lesson). Hopefully almost all learners who were present completed their L1 assignment

   • If any learners were really slow working and did have time to complete this assignment: assess all missed questions with reset symbol (3rd assessment choice)

   • use the number of minutes taken for most learners to complete the 10Q assignment you noted from lesson 1 to calculate the Pace for Practice for the class (see the expand box below for how to do this)

   • put all the assessed L1 assignments aside (dump them in a big pile ready for lesson 5)

2. Get a piece of coloured card (so you can easily find it later!) and write the title Absent Learner List, write down the date of L1 as a subheading and then write down the names of any learners who were absent. (If all has gone well, you’ll have 2 assignments a L1 and a Saturday assignment for these learners).

3. Sort the Saturday assignments into 3 piles, according to the proportion of questions “complete” i.e. answered or with a ? (or indeed any other comment) written in the answer space.

   • not started - no need to assess, but calculate and change these learner’s Pace for Practice + write these learners under Saturdays date on the absent learner card + keep these ready for next lesson

   • “well over half” - assess the assignments (select the Planning and preparation session for Saturday’s date and select Assess t.p. ) Assess any not attempted questions with reset symbol (3rd assessment choice) and change these learners Pace for Practice + put all the assessed Saturday assignments aside (dump them in a big pile ready for lesson 5)

   • up to “about half” - just calculate the Pace for Practice, and record it, you’ll use it next lesson, but don’t bother assessing these + write these learners under Saturdays date on the absent learner card + keep these assignments ready for next lesson

   • Order these and the other un-assessed Saturday assignments, by first name (so they are easy to find) to the next lesson and put with your resources for next lesoon

4. In the app create a new planning and preparation session and change the date, to the date of L2

5. Go to the Create t.p. and uncheck all the learners in the Absent Learner list for L1 (they already have an assignment, so shouldn’t have another created) then click to create a new assignment (either 15Q or use the “nominal minutes per question of the 100% Pace for Practice” to calculate the “nominal number of questions”, for the time you’ll allocate - expect the calculator skills and explanations to take 30 minutes)

6. Download these and print them out.

7. For the teaching part of the lesson, you will need at least 1 scientific calculator per pair of learners, source these

8. Print out these worksheets as follows:

   • calculatorSkills: pre assess sheet, 1&2&3, 5&6&7 (1 of each for every learner)

   • FDPRproblemYC1 (enough for one between two)

9. Gather some extra time filler worksheets - just in case any learners finish early - see lesson 1 - or use your own.

The Pace for Practice (P4P) is a percentage

• faster answering learners should have over 100% - so they will be set more questions than their peers

• slower answering learners should have less than 100% - so they will be set fewer questions than their peers.

Here is a how to calculate (and when not to bother calculating) the Pace for Practice:

In the first lesson, you were asked to note how long it takes for the majority of learners finish the first 10Q assignment. It’s likely that many students will finish within a minute or two of each other (this gives us our nominal question rate, which corresponds to a Pace for Practice of 100%)

FYI by “complete” we mean try to answer the question or write ?, if the learner doesn’t understand the question, can’t remember the method etc

FYI We’ve found it takes about as long for a learner to not be able to answer a question, as answer it.

It takes up to 4 create/”complete”/assess rounds to fully pre assess a topic. Some learners need to answer more questions on a topic than others (the more they know the more questions they need to answer). The app works it way through the topics in the teaching order suggested. Some learners will be fully pre assessed on

In the first 4 lessons, we’ll look to assess each assignment completely - with questions that the learner didn’t get time to answer, being assessed as “reset”. This will mean:

1. we can quickly assess everybody (who is in class) on the topics we plan to teach soon,

2. we won’t have to faff about with “finish assignment and then start this assignment” which with disorganised and disaffected learners leads to “lost” assignments.

Since all the questions are pre assess, learners can just write ? on the answer line (or indeed any other message) they needn’t answer any questions they are not sure about. However some learners are not comfortable with this, so they may need a bit of guidance.

Teach some calculator skills

1. Put the learners in pairs, if they need to share a scientific calculator.

2. Students complete the pre assess sheet - move around classroom, showing any students the S-D (surds to decimals) button if necessary for the scientific calculator you have.

3. Students self assess the pre assess sheet and decide which worksheet to complete next

4. Students then complete one of the following: calculatorSkills1&2&3, calculatorSkills5&6&7 or FDPRproblemYC1 - again show the students where any “hard to find buttons are” on their scientific calculator

As soon as one student finishes, stop the class and explain the purpose of the second half of the lesson:

Reminder pep talk about doing timely practice assignments

• Purpose 1: to find out the “goldilocks” place to begin teaching them each topic - it’s not a test, there are no scores, and the teacher will explain more about this over the next few lessons. That’s why the heading is learned and remembered?

• Purpose 2: to revise skills and knowledge that you already know, to help you remember for longer.

• What to do when you can’t answer a question → Learner may “have a go” 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) + because learner will make it harder for themselves to learn in future lessons + there is no point, because there is no score.

Doing personalised timely practice assignments

Students complete the assignment dated for L2 (or L1 if they were absent last lesson)

If learners finish early, some will have a Saturday assignment they can try next (others should have a longer assignments because of their higher Pace for Practice).

If too many have finished early and have nothing else to do, use the filler activity

Finish the assignments

Encourage learners to check through their assignment for any questions they have missed out which they forgot to write a ? in the answer space - and write the ? in. Tell them that they needn’t do this for questions which they “haven’t had time for” as you know you gave them more questions than you thought they could answer.

End of lesson filler activity

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?

• recognised some questions which were very similar to questions from last lesson?

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 next lesson. This will help the timely practice app be sure of what skills you already know from each topic. Next lesson I (your teacher) will start using this data to make teaching and learning easier”

In the app,

In the planning and preparation session for L2

1. Put aside L2 assignments for any learners absent this lesson - add the L2 date to the Absent Learner List (it’s on coloured card) and write these learners names below

2. Assess t.p. all L2 assignments, assess all missed questions with reset symbol (3rd assessment choice) + dump them in a big pile ready for lesson 5

Are there any learners who were absent for L1, but in last lesson? - if so: cross their names off the Absent Learner List for both L1 and Saturday + select the planning and preparation session for L1 and Assess t.p. these assignments, remembering to assess all missed questions with reset symbol (3rd assessment choice)

Are there any learners who were absent for L1 and L2 ? Put aside the L1 and Saturday assignments ready to take to the next lesson.

Are there any other assignments with Saturday’s date on? - if so, select Saturday’s Planning and Preparation session and Assess t.p. these now, remembering to assess all missed questions with reset symbol (3rd assessment choice) + cross out these names from the Saturday section of the Absent Learner List + adjust the Pace for Practice (calculated after last lesson) + dump them in a big pile ready for lesson 5.

For Saturday’s Planning and preparation session, check Assess t.p. the list in the app should only contain learners who were absent for L1 and L2, check that the physical assignments for Saturday match with these and edit the Absent Learner List if it doesn’t match.

Now prepare for calculator skills review 1

1. Print out review questions for calculator skills you’ll need.

2. Get the scientific calculators out ready for the lesson.

3. Prepare how you will show the self-assessment answers (perhaps show them on a whiteboard?)

4. Decide how long you think this activity will take in the lesson.

Now prepare for L3 pre assess and timely practice demonstration

1. Create a new planning and preparation session and change the date to L3’s date

2. In the Plan Teaching section, choose the topic ratio, this is likely to be most advanced in the assessment process. Take a snapshot of ratio’s dashboard (try to take it without the learners' names showing, but showing the layer numbers).

3. Next lesson you’ll show the class this and explain what it means. So here’s what you might say/ draw a key on the whiteboard etc

   • White squares show where the app has found a layer (a bite of learning) which the learner doesn’t know well enough to be able to answer questions independently and accurately

   • Blue squares show where the app has found a layer (a bite of learning) which the learner can answer questions independently and accurately

   • Medium and darker grey squares show layers where the app needs to find out more.

   • Light grey squares show layers which the app hasn’t decided on what to do yet

4. Now think of some questions you can ask the learners e.g.

   • How many learners can definitely answer layer 1 questions? (it’s the number of blue squares in row 1)

   • How many learners definitely need to learn how to answer layer 1 questions? (it’s the number of white squares in row 1)

   • How many learners have answered one question correctly from layer 1, but the app still needs to ask another question? (it’s the darkest grey squares in row 1)

   • Describe to me how I could find which learners will have a ratio question in this lesson’s assignment: (it’s the ones with the dark or medium grey squares in row 1)

5. You may want to use/summarise the table below for this demonstration too.

6. Repeat 2. but with the topics decimalFraction, and fractionINTRO no need to think up any questions for this though.

7. Guess how much time this activity will take.

8. Calculate how many minutes, and therefore the nominal number of questions which should be in the L3 assignment.

9. Adjust the Pace for Practice for any learners who it seems wrong for

10. Now go to Create t.p. + deselect any learners who are still on the L1 or L2 Absent Learner List, they still have an assignment, enter the “nominal number of questions + create + download + print these assignments

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 mini-white boards and pens.

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.

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).

• Ask learners to give out old assessed assignments to their peers.

• Give out the learners folders.

• Ask learners to look at their assessed assignments - and be pleased with questions they got correct (tell them this will help them remember better)

Engage the class in questions about pre assess e.g. hands up if you had (or point on a page to)

• a question in the retrieval practice section? (discuss what this means, next lesson they might get feedback if they need it)

• a question with algebra (letters or shapes that stand for numbers)?

• a question with a decimal point?

• a question with a graph?

• a question with a fraction?

• a similar question to a question you had last lesson?

• a question with a shape?

• a question with a ruler?

Ask if learners are finding their questions

• “more goldilocks” (not too easy, not too hard) or “less goldilocks” than the first lesson?

Take in the folders.

Review2 of calculator skills

If time, 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. Else do a whole class filler activity.

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.

This is deliberately made far simpler than the teacher might expect

For 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

• it gets the sense of why inverse operations can be useful, and avoids all poor numeracy skills. Model the function diagram as well as the block diagram, if any learners have mastered layer 3 or above, and encourage learners to solve the questions if they can BUT they must write the 3 possible equations.

• it makes teaching the topic easier in the first curriculum spiral.

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

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

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).

Primary schools are excellent at teaching this, so if there are problems with this skill - the small bite approach will hopefully help fix them.

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.

Accessible even to learners who can’t write a fraction correctly yet

Excellent for fixing place value issues which counting hasn’t resolved

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

• algebra and integer

• geometry/measure

• probability/statistics

• algebra and integer

• FDPR

• reduced geometry/measure

• algebra and integer

• reduced FDPR

• reduced probability/statistics