Quadratic sequences rich tasks

Quadratic sequences rich tasks

At least a lesson’s worth of activities on the theme of quadratic sequences. Designed to come after pupils have learnt the basics (how to use and find an nth term rule of a quadratic sequence). Gives pupils a chance to create their own examples and think mathematically. There are four activities included: Activity 1 - given sets of four numbers, pupils have to order them so that they form quadratic sequences. Designed to deepen pupils understanding that the terms in a quadratic sequences don’t necessarily always go up or down. Activities 2 and 3 - on the same theme of looking at the sequences you get when you pick and order three numbers of choice. Can you always create a quadratic sequence in this way? What if you had four numbers? Could be used to link to quadratic functions. Activity 4 - inverting the last activity, can pupils find possible values for the first three terms and a rule, given the fourth term? A chance for pupils to generate their own examples and possibly do some solving of equations in more than one variable. Where applicable, worked answers provided.
danwalker
GCSE 9-1 Maths TRICKY Exam Paper (Grade 7+)

GCSE 9-1 Maths TRICKY Exam Paper (Grade 7+)

A GCSE Maths exam paper which is designed to be more challenging than your average GCSE Maths paper and is aimed at students who are aiming for grades 7/8 or 9 (MODEL SOLUTIONS ARE ALSO INCLUDED) And as a thank you for downloading this I will email you another resource for free :) There are 15 questions with a total of 60 marks and it can be used as either an exam paper for revision or as a worksheet in class or on your own to tackle trickier grade7-9 questions. The questions have been picked from topics such as: Circles and the equation of the centre and finding the radius Surds and Rationalising The Quadratic formula Completing the Square Quadratic & Geometric series Algebraic Proofs Quadratic Inequalities Transformations of graphs Functions I hope this resource is helpful for you in your studies, If there are any questions or emails regarding the questions and paper please leave me a message/comment and i’ll get to it ASAP. Please be sure to leave a review and feedback as it helps me improve my resources!
alastairj123
Gauss's formula

Gauss's formula

A complete lesson on the theme of the formula for 1+2+3+…+n, looking at how the rule emerges in different scenarios. Activities included: Starter: A classic related puzzle - counting how many lines in a complete graph. After the initial prompt showing a decagon, two differing approaches to a solution are shown. These will help pupils make connections later in the lesson. This is followed by a prompt relating to the handshaking lemma, which is the same thing in a different guise. Pupils could investigate this in small groups. Main: A prompt for pupils to consider the question supposedly put to Gauss as a child - to work out 1+2+3+…+100. Gauss’s method is then shown, at which point pupils could try the same method to sum to a different total. The method is then generalised to obtain Gauss’s rule of n(n+1)/2, followed by a worksheet of related questions. These include some challenging questions requiring pupils to adapt Gauss’s method (eg to work out 2+4+6+…+100). Plenary: A final look at the sequence Gauss’s rule generates (the triangle numbers). Please review if you buy as any feedback is appreciated!
danwalker
Quadratic shape sequences

Quadratic shape sequences

A complete lesson on patterns of growing shapes that lead to quadratic sequences. See the cover image to get an idea of what I mean by this. Activities included: Starter: A matching activity relating to representation of linear sequences, to set the scene for considering similar representations of quadratic sequences, but also to pay close attention to the common sequences given by the nth term rules 2n and 2n-1 (ie even and odd numbers), as these feature heavily in the lesson. Main: A prompt to give pupils a sense of the intended outcomes of the lesson (see cover image). An extended set of examples of shape sequences with increasingly tricky nth term rules. The intention is that pupils would derive an nth term rule for the number of squares in each shape using the geometry of each shape rather than counting squares and finding an nth term rule from a list of numbers. A worksheet with a set of six different shape sequences, for pupils to consider/discuss. The nth term rules have been given, so the task is to justify these rules by considering the geometry of each shape sequence. Each rule can be justified in a number of ways, so this should lead to some good discussion of methods. Plenary: Ideally, pupils would share their differing methods, but I’ve shown a few methods to one of the sequences to stimulate discussion. Printable worksheets (2) included. Please review if you buy as any feedback is appreciated!
danwalker
Finding the nth term rule of a quadratic sequence

Finding the nth term rule of a quadratic sequence

A complete lesson on finding the nth term rule of a quadratic sequence. This primarily focuses on one method (see cover slide), although I’ve thrown in a different method as an extension. I always cover linear sequences in a similar way and incorporate a recap on this within the lesson. Starter: To prepare for the main part of the lesson, pupils try to solve a system of three equations with three unknowns. Main: A recap on finding the nth term rule of a linear sequence, to prepare pupils for a similar method with quadratic sequences. Examples on the core method, followed by a worksheet with a progression in difficulty for pupils to practice. I’ve included two versions of the worksheet - a simple list of questions that could be projected, or a much more structured worksheet that could be printed. Worked solutions are included. A worked example of an alternative method, that could be given as a handout for pupils who finish early to try on the questions they’ve already done. Plenary: A proof of why the method works. I’d much rather show this at the start of the lesson, but in my experience this usually overloads students and puts them off if used too soon! Please review if you buy as any feedback is appreciated!
danwalker
Generating quadratic sequences

Generating quadratic sequences

A complete lesson on using an nth term rule of a quadratic sequence. Starter: A quick quiz on linear sequences, to set the scene for doing similar techniques with quadratic sequences. Main: A recap on using an nth term rule to generate terms in a linear sequence, by substituting. An example of doing the same for a quadratic sequence, followed by a short worksheet for pupils to practice and an extension task for quick finishers. A slide showing how pupils can check their answers by looking at the differences between terms. A mini-competition to check understanding so far. A set of open questions for pupils to explore, where they try to find nth term rules that fit simple criteria. The intention is that this will develop their sense of how the coefficients of the rule affect the sequence. Plenary: A final question with a slightly different perspective on generating sequences - given an initial sequence and its rule, pupils state the sequences given by related rules. No printing needed, although I’ve included something that could be printed off as a worksheet. Please review if you buy, as any feedback is appreciated!
danwalker
Recognising and extending quadratic sequences

Recognising and extending quadratic sequences

A complete lesson for introducing quadratic sequences. Rather than go straight into using or finding nth term rules, the focus is on looking at differences between terms to identify and extend given sequences. Activities included: Starter: A related number puzzle Main: Slides/examples to define quadratic sequences A set of sequences, some quadratic, for pupils to determine whether they are quadratic or not. A more challenging, open-ended task, where, given the first, second and fourth terms of a quadratic sequence, pupils form and solve an equation to find the third term. Having solved once for given numbers, pupils can create their own examples. Plenary: A comparison between linear and quadratic sequences. No printing required, please review if you buy as any feedback is appreciated!
danwalker
GCSE Maths 9-1 Exam Tips And Revision Help! (GRADE 7-9)

GCSE Maths 9-1 Exam Tips And Revision Help! (GRADE 7-9)

This is a revision sheet/exam helpsheet aimed at students aiming for grade between 7 to 9 and to help push grade 6 students to a 7. The sheet alone won’t magically push their grades up but features examples for certain topics and things to remember during the exam and other information regarding certain formulae that has to be remembered and the grade boundaries and what to aim for. Certain topics covered: Surds and Rationalising Algebraic Fractions Quadratic Sequences Geometric Sequences Circles Algebraic Proofs Completing the square and finding the turning point I hope this revision sheet will be useful for you in your study or for any students doing their GCSE’s PLEASE review and leave me feedback if you do download my sheet! If you notice any mistakes please contact me and i’ll amend anything ASAP.
alastairj123
GCSE Maths 9-1 Practise Paper 2H

GCSE Maths 9-1 Practise Paper 2H

A GCSE Maths paper designed to help you practise like a full exam by following the typical exam style and design. This paper features questions on topics such as: Surds and rationalising Simultaneous Equations Inequalities (Linear and Quadratic) Compound Interest Perpendicular Lines and Gradients Expanding Triple Brackets Pythagoras Theorem Indices Ratios I hope this is helpful in your exam practise, Paper 1 and 3 will be available soon also! Feel free to use in classrooms as extra practise if needed or as a private tutor, I would appreciate any feedback and rating my paper if you found it useful!
alastairj123
Factors - Mastering Mathematics

Factors - Mastering Mathematics

This PowerPoint presentation by Mastering Mathematics is designed to support learners in their journey to mastering the concept of ‘factors’. Within the PowerPoint Mastering Mathematics guides learners through questions which explore the different learning stages from application, fluency, reasoning to problem solving. Mastering Mathematics have included a review section so that learners can ensure they are confident they have mastered ‘factors’. Mastering Mathematics have designed this PowerPoint to be effective at supporting learners from KS2 - KS4, providing stretch and challenge to those learners developing Mastery whilst also supporting learners at the beginning of this journey.
crocker710
Nth term

Nth term

A presentation to support the teaching of the nth term with objectives, examples and differentiated student tasks with answers.
wrighte
Position in a sequence using the nth term

Position in a sequence using the nth term

Codebreaker activity, deciding whether a number is in a sequence or not. Pupils chose yes or no then rearrange the letters to give a capital city, The other side is a worksheet where pupils are given the nth term of a sequence and have to either find the term given the term number or vice versa. 3 sequences progressively harder, (positive/negative/quadratic). Easily adaptable and the answers are given.
pmmb8
Sequences Quizzes

Sequences Quizzes

Powerpoint files designed for use with Quizdom remotes, but works just as well as Powerpoint quiz. Used it with KS3 to reinforce understanding. Could use as plenary for linear sequence lesson. If have weak KS4 class they would benefit from it too.
SFairfield
Year Six - Autumn, Spring and Sum 1 (Follows order of White Rose)

Year Six - Autumn, Spring and Sum 1 (Follows order of White Rose)

All teaching slides for Autumn and Spring and Sum 1. Influenced by recent maths hub CPD training and mastery/CPA approach to teaching mathematics. Includes reasoning and problem solving activities to explore, model and discuss in order to teach the underlying mathematical concepts. Follows ORDER of White Rose teaching guidance. Join the Facebook group ‘mastering primary maths’ for preview lessons in the files section :)
xkarenx
Next Door Neighbour Numbers - 8 Lesson Activities.

Next Door Neighbour Numbers - 8 Lesson Activities.

This resource contains 8 lesson activities using next door neighbour or consecutive numbers on a number line. It could be used as eight separate lesson ideas or could be used to challenge different groups within the same class. Answer sheet included. The only apparatus needed is a number line. I recommend that younger children be given a number track so that they can cut these into different sections.
JMEducation
Quadratic Sequences 2 (Loop Cards)

Quadratic Sequences 2 (Loop Cards)

I love to start one-to-one tutorials/interventions with a loop card activity. They are also excellent when working with small groups or as a starter or plenary for a whole class. To see all the available loop-card topics click 👉 tes.com/…/More Loop Cards….<hr>This particular set of cards allows students to practise finding the nth term formulae for quadratic sequences. Note that the questions have been carefully selected so that they provide good coverage of this sub-topic and so that the opportunities for students to guess answers are minimised.<hr>Colour coding: All my loop cards are colour-coded to indicate the approximate level of the questions: KS2 – red and orange KS3/GCSE Foundation – orange and green GCSE Higher – green, blue and purple<hr>Further information: In this download there are four sets of similar cards and a student chooses one of the sets and sorts them into order by answering the questions. Then they try to do it faster using a different set, which has the same questions, but a different sort order 😃 My favourite use of loop cards is for two students to have different versions of the cards and race each other. They then check their answers, shuffle, swap packs and race again (quickest overall time wins). More instructions are included in the download. Cut out card size is approx. 65 x 90 mm.<hr>👍If you like this resource, then please rate it and/or leave a comment💬. If the rate-resource button on this page doesn’t work, then go to your ratings page by clicking 👉 www.tes.com/…/rate-resources…
Maths4Everyone
11 Plus Non-Verbal Make Your Own

11 Plus Non-Verbal Make Your Own

We have had great progress with pupils and non-verbal when they have used this sheet to create their own pattern. Worksheet includes example to work from. The final question allows the pupil to recap and explore new patterns. A must for any child taking the 11 Plus.
Hugostrange
KS2 Maths Investigations Bundle

KS2 Maths Investigations Bundle

2 packs of KS2 Maths Investigations - one set includes 5 investigations around a ‘Chinese New Year’ theme (Could also be used as part of a topic on China), the other set includes 5 investigations with a World Cup theme (football). These investigations allow children to explore possibilities, work systematically, find patterns, predict results and analyse outcomes. Children will be able to show their reasoning and problem solving skills through a range of interesting activities. Every investigation also includes a challenge activity to extend higher attaining children. An answers document is also included to support teaching. Leave a review for this resource and get a FREE resource with three easy steps: STEP 1: Leave a review for this resource on TES. STEP 2: Email us at: learndbresources@gmail.com , saying which resource you’d like to get for FREE! STEP 3: We’ll email you any single paid resource from our shop for FREE!
MrBallard23
Year 6 Maths SAT Final Test

Year 6 Maths SAT Final Test

Do you want to assess your students achievements in Mathematics and see whether they are ready to move up to Secondary? Then this is the perfect resource, which determines whether students have met the end of year expectations for Year 6.
NextWeekSorted
Median Maths Centre selected worksheets

Median Maths Centre selected worksheets

Various worksheets made by “Median maths centre” who no longer seem to exist. Some of these are great. Contents of each pdf listed below: Number: Missing Zero (place value) 2, 5, 10 (simple multiplication) Which times table? (multiplication) Which numbers? (multiply/add) Divisorgrams 1, Divisorgrams 3a (factors/multiples) Power Problems 1 (powers) Alg-Expressions (algebraic expressions): Building expressions 1 (“flow diagrams” is the topic name given, but it’s really more function machines) Fairly long worms (“flow diagrams” or function machines) Five two (“flow models” or function machines) Spider (substitution) Writing expressions (notation / symbols) Translation (notation / symbols) Linear eqns (linear equations): The Game Solve it (bar models) Equation steps Unjumbling Seq (sequences): Stick Patterns 3 Bracketneed (brackets) 4 in a line (coordinates) Probability: Different Red/yellow balls Area: Thirds 2 congruent halves
pingleby
Sequences Observation Lesson

Sequences Observation Lesson

Full sequences lesson on calculating the term-to-term rule of a sequence, finding the the nth term rule of a sequence and working out the first five terms of a sequence when given the nth term. This pack also includes differentiated worksheets, learning objectives, hint sheets and exit pass.
minop
QUADRATIC SEQUENCES - 55101

QUADRATIC SEQUENCES - 55101

The matter consists of quadratic sequences a) when a, b and c are not equal to zero, and b) when b is equal to zero and is good to students of year 8 onwards. The answers to the questions are also provided in the worksheet for your confirmation. The matter is also good to the teachers to give it to their students for a good practice work.
jo55kk
Simple quadratic sequences for KS3

Simple quadratic sequences for KS3

This is an introduction to simple quadratic sequence formula. Copy and past the questions to make a worksheet so you can display the answers using the p.pt slide.
sesma1
Special Sequences Introduction Lesson

Special Sequences Introduction Lesson

Introductory lesson to sequences, including an engaging starter showing students an optical illusion involving the Fibonacci spiral. Additional card sort activities included, for visual learners (ideal engagement tool for SEN classes), where students sequence their daily routine and also sequence the square numbers. All activities are fully differentiated, with the opportunity for students to explore Fibonacci sequences.
lively10
KS3 and KS4 Sequences

KS3 and KS4 Sequences

4 Extensive worksheets on all that you will need on sequences up to GCSE level. LINEAR SEQUENCES 1 - 10 questions on arithmetic progressions, the nth term and the algebraic approach. LINEAR SEQUENCES 2 - 6 questions over 4 pages of pattern building with matchsticks and tiles etc to develop an arithmetic sequence. OTHER SEQUENCES - questions on other sequences including squares, cubes, primes, fibonacci and a geometric sequence, in each case simply give the next two terms - no nth term here as it is aimed at KS3 and foundation level. QUADRATIC SEQUENCES - 20 sequences with answers that are quadratic - just for practice. ANSWER SHEETS
happymathematician
Unit 2H Algebra - Non-Linear Sequences 2-6

Unit 2H Algebra - Non-Linear Sequences 2-6

Hi folks, firstly I just wanted to say thanks to TES and all those who are sharing their fantastic resources. All I have done is utilised some of these resources and made a flipchart with a humble contribution from myself. Some of you will recognise parts of your resources embedded in the flip. I have TEEPED the lesson as well. The lesson has been created with reference to the new edexcel GCSE 9-1 grade boundaries.Please feel free to ameliorate it further.
patelv
Huge Bank of KS3 Algebra Starters

Huge Bank of KS3 Algebra Starters

A huge bank of 13 KS3 starters on KS3 Algebra Topics. Topics included are: Solving Equations, Simplifying and Writing Expressions, Formulae and Sequences/Nth term. Excellent to help students make a good start to the lesson and as a plenary activity. I also used these with my form group as brain teasers and a check of their Maths skills.
jcoulter62
Unit 2H Algebra - Linear Sequences 2-5

Unit 2H Algebra - Linear Sequences 2-5

Hi folks, firstly I just wanted to say thanks to TES and all those who are sharing their fantastic resources. All I have done is utilised some of these resources and made a flipchart with a humble contribution from myself. Some of you will recognise parts of your resources embedded in the flip. I have TEEPED the lesson as well. The lesson has been created with reference to the new edexcel GCSE 9-1 grade boundaries.Please feel free to ameliorate it further.
patelv
Year 7 Revision Booklet

Year 7 Revision Booklet

This Year 7 revision booklet is suitable for low and middle ability students and has a range of questions which cover elements of the following topics: Number skills e.g. addition, division etc. Analysing and displaying data e.g. pictograms, dual bar charts etc. Algebra e.g function machines, collecting like terms, finding the next term in a sequence and finding the nth term Line and angles e.g. angles on a straight line, angles in a triangle wtc. Decimals and measures e.g. converting ml to litres Probability Fractions and percentages - including percentage of amount Ratio and proportion Transformations e.g. reflection, scale factors etc.
CSR2016
Multiple Choice combined the first 15

Multiple Choice combined the first 15

15 little activities for AFL, revision, starter or a plenary. Works well with mini whiteboards and adaptable to voting systems Aimed at KS3 and KS4 although some topics do go to KS5 especially if you have a resit group all are available as individual resources, Have uploaded them here to save finding and separate downloads. Topics covered include Surds, expanding brackets, factorising, equation of a line, sequences, quadratic sequences, completing the square, solving equations, solving quadratic equations , using discriminants and others. hope you find it useful please leave feedback let me know if you would like one making for a particular topic (I have plenty more lined up) thanks
commuter
Algebra: Sequences (nth term rule) Exam Questions (with Answers)

Algebra: Sequences (nth term rule) Exam Questions (with Answers)

These are exam questions on sequences. I predominantly use these for either homework or revision. Do view my excellent lessons / bundle on sequences. https://www.tes.com/teaching-resource/algebra-sequences-bundle-6-lessons-perfect-for-gcse-igcse-11602553 NOTE: Feel free to browse my shop for more excellent free and premium resources, and as always please rate and feedback, thank you.
ajf43
AQA Best Guess Paper 2 Summer 2018 HIGHER

AQA Best Guess Paper 2 Summer 2018 HIGHER

Here is a revision best guess paper for AQA Paper 2 Exam. It is not 80 marks but more a combination of topics that have not been tested yet on the AQA Spec. I hope people find this very useful and please feel free to share. PLEASE find my latest resource for topic revision for everything not on Paper 1 at : https://www.tes.com/teaching-resource/not-on-paper-1-higher-gcse-key-topic-revision-sheets-11913602?theme=0
Yougoteach