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25.01.2022 Another example of how data can be misleading. What do you notice about this graph? Does the mathematics match the message the author seems to want portrayed?

24.01.2022 The Proof is in the Pudding . Its always nice to here from teachers who are involved in Learning Through Doing! . Our goal has always been to give students the best possible mathematics experiences through our hands-on inquiry based approach.... . To achieve this we know that supporting teachers with their approach and understanding of maths is the key (and saving them time from searching for good ideas and resources- theyre time poor already). . If you havent tried our 7 Day FREE Trial yet head over to our website and give it a go! What do you have to lose . Big thanks to Patrick for letting me know how the lessons are going See more

24.01.2022 Part of the challenge in starting a new business is building an awareness of your product. . One of the purposes of Multiplication Masterclass was to give teachers access to our content so they could experience what teachers all over Australia (and some in New Zealand ) are experiencing. . Thank you to all of the new teachers that have signed up to the Masterclass, purchased the Multiplication Lesson Bundle or tried our 7 Day Free Trial!... . AND THANK YOU to all the teachers who continue to use our content and support Jude and I to keep developing new content! See more

24.01.2022 What does the start of your lesson like? Is there anything worse than setting a task - thinking you have nailed it and then within a couple of minutes a flurry of hands go up! Let me guess what happens next... You get a bit frustrated and cant believe that your detailed instructions or modelling of the requirements hasnt hit the spot...... Some students start to become disengaged and off task... You stop the lesson and try to reword your instructions and set them back to work with little improvement... You give an exasperated sigh (blame the kids listening skills) and stop the activity... How did I go? The way we structure our lessons at Learning Through Doing allows the teacher to get a clear insight into what students know and dont know and these clues are perfect for informing what the students are ready for next. Oh and one more thing... learning is meant to be fun and creative... a teacher standing in front of a white board barking instructions is as enjoyable as sitting on an ants nest.

23.01.2022 What is a rectangle? What are the geometric features that a rectangle MUST have? How many rectangles are there in the picture below?

22.01.2022 I am working on some quick assessment check ups for early Maths concepts..with checklists for quick meaningful data collection.... interested??

21.01.2022 We are working on a bunch of data lessons right now including ones specifically for Interpreting Data. This is a great example of how data can be presented to be misleading... we will have lesson specifically teaching these ideas.

21.01.2022 What does this mean to you? . Teachers can have a huge impact on the progress a student makes with mathematics. Encourage failure as a natural step in learning. Build students who have a belief they can learn.... As a teacher have a deep understanding of what, why and WHO you are teaching. AND ONE MORE THING... Make learning exciting #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy See more

20.01.2022 Do your students know their Times Tables? As promised - your FREE short concise MASTERCLASS is ready for viewing! We all know that engaged, inquisitive children learn better than bored, frustrated ones. Get your free step-by-step guide to teaching times tables effectively. The Masterclass provides:... Structured, hands-on models & strategies for teaching multiplication basic facts Detailed, inquiry-based lesson plans FREE RESOURCES Do you know the three visual mathematical models that are used to support learning? Do you know the order and strategies in which you teach multiplication facts? Fine tune your teaching methods and engage your students - click on the link and get started!

20.01.2022 Todays class... What Im going to tell you isnt done to try and impress you but rather IMPRESS ON YOU how much of an impact your approach (pedagogy) has on students engagement and learning outcomes. I worked with a class of 12-13 year old students today for the first time and my intent was to check what they knew, and introduce them to operations (+-) with positive and negative integers.... When I stated 5 minutes left before we need to stop what we are doing a sea of meerkats popped their heads up... The responses ranged: What and thats the 70 minute lesson over This has been the best maths lesson This is the fastest lesson ever Im not joking one child even looked over to another and stated I love maths I had used the 3-step approach like I use in all my lessons, students labelled and paced out operations on a number line on the floor (we reversed the activity by getting students to pace out their own operations and students identified what the operation was *side note: this is a good one for differentiation). We shared understandings on where we see negative numbers in the real world and created an environment where the teachers were also the students. The students then used number lines and counters to model operations/word problems before finalising their learning with 10 questions (consolidate learning and check for understanding). By chunking the lesson and using movement, peer conversation, visual models and hands-on activities you are able to engage (it improves students behaviour soooooo much) the learners easier (variety) and of course create strong connections with their learning through movement and visual models! P.S. If you havent had the chance to watch our FREE Masterclass (Teaching Times Tables) or take advantage of our 7 Day Trial head over to our homepage learningthroughdoing.com.au and see how we approach teaching mathematics!

20.01.2022 How do you inform your teaching focus? Jude has been putting her years of experience to the test by designing these short precise Check Ups! They are absolutely brilliant! Check out how she structures her questions! Here are her thoughts from a recent LTD Newsletter: Teachers are often urged to be data-informed in their practice. Collecting data that reflects not just what students can do but what they understand and that is directly related to what you are teaching is a chal...lenge. The LTD Check-Ups provide a quick and easy way for teachers to check student understanding of particular Maths topics. They can be used as a pre-test or post-test or both. We also provide a checklist that is prepopulated with possible responses for quick marking and a teacher guide that links the items to particular concepts so areas of need can be identified for small groups or across the whole class. We have a series of these available to all of our members- if you would like to know how to get your hands on all of these - email me: [email protected]

18.01.2022 A quick example of multiplicative thinking vs additive thinking

17.01.2022 Guess what these are for? . All of my maths resources fit into 1 small suitcase and some of them are 10 years old! If you put in the time and effort early it pays a off down the track for you and the students . Whats your favourite mathematics resource? #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy

17.01.2022 Using Units and Measurement . Hands-on learning at its best! So many great ways to engage students in rich mathematical thinking! AND the links to fundamental understandings in number are endless! . Checkout the new lessons and get involved #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy

17.01.2022 Matching cards are a simple but effective tool for consolidating learning. Can you see anything interesting that this child has done? Equivalent fractions

16.01.2022 I thought I would share some of my recent lesson writing and resource making for LTD. These worksheets are Independent tasks each from a different lesson. All of these have a Whole Class and Hands On activity that comes before the Independent worksheet . Access these lessons via our website www.learningthroughdoing.com.au. Judy H

15.01.2022 Look for Maths investigations /questions from real life contexts. Heres one from my real life. Off road racing last weekend. - The track is 15km long. Race will be 6 laps. How far will the race car drive this weekend? - Race car uses 1 litre of fuel per 2km. How much fuel should we take to the race?... - The fastest cars are doing 1 lap in 12 mins. Slowest cars take about 17 mins. How many heats can we fit in one day? BTW we won our class Judy

15.01.2022 This is a great quote..

15.01.2022 An example showing the importance of zero, not just as a number representing a collection with no objects but as a starting point for number lines. Rulers and Measuring Tapes are practical examples of number lines. Learning Through Doing lessons link measurement tools with number lines explicitly. You can access our lessons via a free 7 day trial via our website.

15.01.2022 WHAT WOULD YOU PREFER? . If a student was a wizard at reciting their multiplication basic facts which they had learnt through ROTE learning or a student that learnt through strategy and knew some of their facts automatically but when they didnt they had a strategy to help them get there? . Which one??... . I wonder why the student (who doesnt know all their facts off by heart- and wasnt taught through rote learning) always out performs the wizard student when working with mathematical problems that involve multiplicative thinking (place value, division, fractions, scale, percentage, rate, ratio, decimals... get the picture)? . Dont get me wrong the end goal is always automaticity! BUT, the journey to getting there has to be one of learning through strategy as it gives a deeper understanding of multiplicative thinking and a fall back to when you just dont remember 7x8... . 7x8= hmmmm 5x8 + 2x8 (this is where developmental sequencing of teaching is also important ) or an extension of a strategy: 5x37= hmmmm 10x37=370 half of 370 equals 185. . Next week we are releasing a FREE short concise MASTERCLASS (yes it will be like being zapped... as we all know that our attention spans arent the best... ) that will explore this idea and give you the tools to successfully teach multiplication and transform your students understanding. See more

14.01.2022 A chuckle for your weekend ;)

13.01.2022 Ill let the picture doing the talking...

12.01.2022 Time to reflect... When you have a chance to look at how many new lessons have been written, fully resourced and recorded in just over 6 months! Jude and I cant wait to get back in front of teachers and students #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy

12.01.2022 Finally Cracked it . 2 kilometres in under 8 minutes! The amount of mathematics that went into ensuring I didnt miss it by 5 seconds like last time... . This is just a little finisher I do at the end of my workouts - it started at trying to get under 9 minutes and then things got competitive (@davidgoggins your voice was in my head ).... . Now back to the maths side of it... I bet you can state- yep he used rate to figure that out but leave a comment on what prerequisite mathematical knowledge I needed! . This is how we need to think before teaching a concept! So leave a comment and then Ill put the list together and share #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy

11.01.2022 What equations can you see in these Part-Part-Total (Bar Model)? Can you see/write more than one ? Can you write an equation that has the unknown alone on one side? Does the bar model help work out a path to find the unknown? I am working on 3 LTD lessons today exploring equivalent number sentences.. ... Australian Curriculum links ACMNA083 (+ and -), ACMNA121 (x & ) and ACMNA134 (All ops). Post your equations please and comments most welcome :) Judy See more

10.01.2022 This kid gets current affairs :)

10.01.2022 Number Lines are an important model for many Maths concepts. The LTD lesson Representing Numbers - Introduction to Number Lines lesson has the Whole Class work to construct a phsyical number line and place number cards between multiples of ten represented using ten frames and numeral cards. Then students work together in the Hands On section to make a number line using straws and place numbers themselves. The benefit of using straws is they create evenly spaced graduations. The Independent task is a worksheet for them to write numbers on number lines. This can be done straight away or left for a later check for understanding. If you havent done it yet.. Sign up for a free 7 day trial of all our current lessons. Go to www.learningthroughdoing.com.au and scroll down...

09.01.2022 Multiplication Check Up! . How do you identify what your students know about their multiplication basic facts aka times tables? . And Im not just talking about surface knowledge... have they transitioned from additive thinkers to multiplicative thinkers? Do they have strategies they draw on? Which ones? What facts do they know and dont know and why is this?... . We have created a double sided Check Up (with a teacher guide) to help you figure this out! Flick me an email and Ill send you a copy [email protected] #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy See more

09.01.2022 A sneak peak of an activity I made today. In memory of Professor Tom Cooper who believed sorting and a focus on attributes could lead to success in Maths through logical reasoning. Not sure if this will be a Hands On activity done in pairs or an Independent activity... hmm 48 shape pictures to place in the grid so there is always 1 attribute the same across and 2 attributes the same up and down.. Can you spot my error in the third photo?

08.01.2022 Hi LTD followers, I have just finished writing a set of Place Value Check-Ups with Teacher Guides and Response checklists (for easy marking and insight into conceptual understandings I hope). I would like to find some schools in Brisbane (Qld Australia) to try them out with real students. I will come and collect them and mark them for you as I am keen add other possible responses to the checklists based on what real kids do with them. If you are interested either reply to this post or send us a message. Thanks in Advance Judy H :)

08.01.2022 A quote supporting the approach we take to focus on conceptual understanding rather than memorisation and algorithms.. The concept mentioned below is inverse (the smaller the parts the more you will need). Many of our fraction, division and measurement lessons (so far) specifically focus on teaching inverse. In their research, Richland and her collaborators highlighted the stunning degree of reliance community college students... 41% of all undergraduate students [18 year olds] in the United Stateshave on memorized algorithms. Asked whether a/5 or a/8 is greater, 53% of students answered correctly, barely better than guessing. Asked to explain their answers, students frequently pointed to some algorithm. Students remembered that they should focus on the bottom number, but a lot of them recalled that a larger denominator meant a/8 was bigger than a/5 Others remembered that they should try to get a common denominator, but werent sure why. There were students who reflexively cross-multiplied, because they knew thats what you do when you see fractions, even though it had no relevance to the problem at hand. Only 15% of the students began with broad, conceptual reasoning that if you divide something into five parts, each piece will be larger than if you divide the same thing into eight parts. Every single one of those students got the correct answer. Source: Why Generalists Triumph in a Specialized World by David J. Epstein

07.01.2022 Always learning... . What a huge morning of SIGN UPS for our Multiplication Masterclass! In the last 48 hours there have been HUNDREDS of people enrol! . Jude and I were very particular in planning this Masterclass - we wanted teachers to walk away with a deep understanding of how they can make changes to students learning.... . The feedback has been terrific so far - so thank you for trusting us! The other feature of this Masterclass is accessing the 14 inquiry-based lessons packed with hands-on learning activities and support resources. . The purpose of giving access to these lessons is to give teachers an insight into how we approach teaching mathematics and to give you a taster of how we can support your teaching in the future! . So if you havent gotten your hands on the 14 lesson bundle please dont hesitate the lessons are EPIC See more

06.01.2022 Rote Counting . Willow (nearly 2) has been nailing her counting lately! She is obviously at the earliest of developmental stages (Rote Counting) and can associate some meaning with numbers 1-3 (Point Counting & Rational Counting). . She has learnt how to do this through nursery rhymes and everyday interactions (e.g. cracking eggs for scrambled eggs). The next step for her is to build a deeper understanding of the numbers 1-10 before exploring larger numbers. If this can be na...iled it will set her up for success (base 10 number system). Teen numbers are tricky little buggers! . Just a side note... imagine if your child/student had a deep understanding of numbers from 0-100... they could count, represent, add, subtract, multiply and divide them with confidence (of course this would be achieved through an inquiry approach using visual models and hands-on learning). With our number system structure this would set them up just perfectly! . Think about how you link maths to your child/students reality as it might just create stronger connections #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy See more

06.01.2022 Starting . One of the biggest challenges with STARTING a new business from scratch is getting people to give it a go. . TO TRUST YOU.... . The focus for this year was to consolidate what we had created, build HEAPS of new content and ensure the schools and teachers who had already taken the leap were 100% satisfied! . Next Year we are looking to take on another 11 schools in Australia . If you want to change the way you approach teaching mathematics I would love to explore what we can do for your school (and students) [email protected] #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy See more

06.01.2022 Filming some lessons today Here is one of the sections where students are building their awareness around the basic facts! Can you guess what strategy this one is? I love how multilayered this task is and if ‘set up’ correctly it gives students the opportunity to explore in their learning rather than be dictated too! #mathematics #automaticity #basicfacts #inquiryapproach

05.01.2022 Never use a resource just once... . If you take the time to organise your resources you will save time down the road! These strategy matching cards were used in an earlier lesson and now can be reused to reinforce the learning! Some ideas: Turn it into a race (a little bit of competition never hurt anyone). Give the students a card on entry after lunch and they have to QUIETLY find and match.... Give them several cards and ask them to identify/write the cards that could go with it. Use some of the cards for the game MEMORY. Use them in Mathematics Rotations as the students are familiar with the process so it allows you to focus on the group you may be working with. . And just a quick comment... I have learnt that using strategies to build mathematical understanding is so critical! Even if a student might understand a concept its still important to get them to look at it through a different lens! This engages critical thinking skills and makes stronger connections. #ltdmathematics #teachersofinstagram #teachersfollowteachers #teacherlife #learnmathematics #mathsonline #mathstutoring #homeschooling #pedagogy

05.01.2022 Another lesson today.. Yr 6 Percent lesson. Whole class we used sports marker domes to investigate proportional relationships..e.g. 2 per 5, 4 per 10.. 20 per 50.. 40 per 100. Hands On we looked at the sugar in drinks... How can Iced Tea have more sugar than Energy drinks or lemonade? When the drink bottle is larger. So we need the same amount of drink to compare.. how much?.. 100mL was a good suggestion.. wow per 100 that seemed familar. Then an independent worksheet to consolidate.

05.01.2022 Games . If you have a clear intent, games can be a great motivator and a way to practice repetition of a certain skill! . This multiplication activity reinforces understanding of arrays, commutativity, basic fact strategies and recall .... . Another great one for multiplication is BOOM... Do you know what this game is? See more

03.01.2022 Today I taught the Place Value - Multiplicative structure x10 10 (Decimals) in a Yr 5 classroom. Whole Class on the tarp, Hands On with cut out digits on a persona pv chart. We kept the Independent task (game) for the class teacher to do another day. Great to be back in a classroom trying the lessons I have written.

02.01.2022 What do they say about making assumptions... . This is an image of part of a multiplication lesson I did on commutativity (thats a fancy maths word for your multiplication turn arounds ). I was working with 14 year olds who have found mathematics challenging for many years. . As youre all aware by now... I harp on about how important multiplicative thinking is (and this is because I have seen over and over again the implications of this lack of knowledge). ... . I had used the Check Up (you get access to this from our website when you do our FREE Masterclass) for multiplication and saw that many of my students didnt use this strategy to solve unknown basic facts. . I started the lesson with a length model (and set model to reinforce) to check for understanding... and it was a great eye opener to see the confusion and new connections being made. . The visual models added a great layer of critical thinking and enabled the to SEE THE MATHEMATICS . . Im glad I didnt assume that my students understood commutativity... See more