Think Mentals — Maths Strategies and Practice: Year 1 — Firefly Education Educational Resources and Supplies
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- Think Mentals — Maths Strategies and Practice: Year 1
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Part of the series Think Mentals — Maths Strategies and Practice.
View all products in this series
Book 1 includes:
- Preparatory units that teach early maths concepts and friendly number facts
- 9 modelled computation strategies for addition and subtraction
- Over 30 weeks of carefully structured and differentiated mental computation questions
- Strategy revision and core maths skills questions
- Weekly assessment and a Student Assessment Profile
- End of unit higher-order thinking activities
- Content written for the Australian Curriculum.
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View Think Mentals 1 Sample Pages
The Think Mentals series is the ‘how-to’ guide for making mental maths calculations friendly. By learning and practising Think Mentals’ clever strategies students can train their brains to solve maths problems quickly and easily. From Day 1 students learn mental computation strategies to use when solving addition, subtraction, multiplication and division problems. Once students learn how to use these simple strategies the rest is just practice – and there are plenty of opportunities for practice. Think Mentals Student Books are divided into carefully structured weekly units. Each book contains:
- 18 modelled computation strategies for addition, subtraction, multiplication and division
- A fun and easy introductory unit to show students how to find, make and fix ‘friendly’ numbers
- Over 30 weeks of carefully structured and differentiated mental computation questions
- Content written for the Australian Curriculum.
What’s in a week?
Day 1: Strategy The week begins with a new strategy. A friendly explanation is followed by worked examples and practice questions. Days 2–4: Practice The focus strategy is consolidated with more practice questions, then previous strategies are reinforced with revision questions. Next, students tackle a variety of question types from across the ACARA content strands. Day 5: Assessment The weekly test combines focus, revision and core content questions. Results are recorded in the Student Assessment Profile to give a weekly snapshot of progress. Students can also record scores and times daily.
Think inside the box!
After students have learnt the most effective strategies for mental computation, they can top off the unit with a Think Box activity. These engaging problem solving exercises are great brain training, whether they’re solved individually or in groups.
|Product Type||Student Books,|
|Year Level||Year 1,|
|Author(s)||Chris Linthorne, Sandra Williams, Peter Williams|
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Mental Math, Gr. 1-2, eBook – Creative Teaching Press
**THIS IS A DOWNLOADABLE PRODUCT!**
Mini Mental Workouts to Improve Computation Skills
Over 100 quick mental math workouts that encourage students to compute quickly in their headsÑno paper or pencil required! Use the math challenges as a fun way to begin a math lesson or as sponge activities throughout the day. Mental Math problems will increase students listening, problem solving, and basic computation skills.
Mental Math features over 100 quick mind challenges that encourage students to compute quickly in their head – no paper or pencil required! use the math challenges as a fun way to begin a math lesson or as sponge activities throughout the day. Mental Math problems will increase your students’ listening, problem-solving, and basic computation skills. These book pages can be turned into handy math «cards» by cutting them in half. The cards are perfect for classroom and partner games and can be easily stored in a file box. This must-have resource also includes timesaving assessment ideas and tips for encourgaing students to explain and justify their computation strategies. Designed to challenge young minds, these stimulating problems will enrich any math program.
|Weight||5. 0 oz|
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Mathematics of Ramzan Kadyrov’s demarche › Articles › 47news from the Leningrad region
The Russia-10 project has been suspended. Over the last day of the second round, 50 million messages were received. Checking possible computer cheats. Ramzan Kadyrov made a scandal and withdrew «The Heart of Chechnya» from the competition. 47News has its own mathematical version of what happened.
TV channel «Russia» together with the Geographical Society from March 25 to September 29, 2013 holds the contest «Russia-10». The goal of the project is to show that there are hundreds of unique places in our country and they should be of interest to our own and foreign tourists. The most important task is to promote the image of Russia.
A popular vote should determine the top ten. They will reflect the mentality and image of the state. At the same time, «they will form a new wave of geopatriotism.» For five months now, the choice has been coming from more than seven hundred proposed historical sites.
Voting is carried out by sending SMS messages and from personal computers.
Starting from Friday, August 30, the website of the contest welcomes visitors with an announcement about the suspension of voting. According to the organizers, in 24 hours, from 29to August 30, the project received about 50 million SMS and Internet messages — a third of all received since the beginning of the project. The site also reports that due to the wide public outcry, the management of the TV channel decided to conduct a technical audit to identify possible technical errors and computer cheating.
Recall that a few hours before the suspension of voting, the head of the Chechen Republic Ramzan Kadyrov demanded from the mobile operators Beeline and Megafon, as well as the Russian Geographical Society, to return the money spent by the inhabitants of the republic in the process of voting for the mosque «Heart of Chechnya» at the competition «Russia-10». Kadyrov said that telecom operators deliberately did not take into account «hundreds of thousands» of votes for the object put up by the republic for the competition — the «Heart of Chechnya» mosque, built in Grozny in 2008 in honor of Akhmat Kadyrov. By «not taken into account», the head of the Chechen Republic apparently means refusals to register SMS messages, in the following wording: «The service is temporarily unavailable, please repeat the request later.»
47News took a look at the rules and suggested that, as always, Ramzan Akhmatovich’s emotional statement was due more to mathematical knowledge and political foresight than concern for the cleanliness of operators.
The rules of the competition provide for three rounds. In the first, which ended on June 30, ten objects are selected among the Subjects of the Federation within one Federal District. At this stage, voting was possible only through the project website. Each user could vote for 24 hours no more than three times. What is characteristic — for the same object, it was possible to vote all three times. The organizers emphasized that the votes received through computer technology will not be counted.
After the first round, Pskov Krom won in the Northwestern Federal District. In the North Caucasian district, the mosque named after Akhmat Kadyrov «Heart of Chechnya» was predictably chosen. And in the Central — the Kolomna Kremlin.
In total, over 17.5 million votes were cast for all objects in Russia in the first round.
In the second round, from July 1 to August 30, 80 objects took part — ten from each federal district. At the same time, the votes cast in the first round were reset to zero. The ability to send SMS has been added to voting on the Internet.
When voting, it was necessary, without fail, in contrast to the first round, to choose three different objects that you liked. It was still possible to vote on the Internet no more than three times (for three different places). But the number of SMS was unlimited and also for three different objects.
30 objects reached the final, and more than 128 million votes were received in the voting box. On the last day before the end of the second round, the first two positions were reversed and received approximately 21 million votes each. The Kolomna Kremlin scored the largest number, followed by the Heart of Chechnya.
After that, Kadyrov’s demarche followed. The head of Chechnya removed the mosque from further participation in the competition. In his opinion, the operators deliberately did not take into account «hundreds of thousands» of votes for the «Heart of Chechnya», and thus did not allow the mosque to take first place.
According to the rules of the third round, which was supposed to start on September 1 and end at the end of the month, the votes of the previous stages are reset. The choice will be made from 30 objects that won in the second round. Only this time, it will be necessary to vote for five objects at once. And still no more than three times on the Internet, but no more than 30 times from one SIM card.
So, in the case of the first round, using SMS and goodwill, it was possible to get the number of votes, limited only by the voting time. Recall that at this stage, when sending, it was possible to specify three identical objects.
In the second case, it was necessary to specify three different positions. In this case, for example, the Chechens could count on the support of fellow tribesmen from neighboring republics and the Muslim part of Tatarstan.
In the third round, the rules of the competition prescribe to choose five different objects. Here a simple statistical fact intervenes. There are no more than 20 million Muslims in Russia. And simple arithmetic shows that under no circumstances, the object, which is a modern shrine in Grozny, could not become the first.
It is difficult to assume that Ramzan Kadyrov, distinguished by political far-sightedness, did not understand this. Then, perhaps, claims against operators are just an elegant Machiavellian move. As a result of which, two targets were hit — it is loudly emphasized that the «Heart of Chechnya» was the first and only the uncleanliness of third parties did not allow victory to happen. And secondly, the demarche, as it were, hints at the legitimacy of all further results and gestures of the other participants.
In addition, Kadyrov deftly raised the question of distrust of MegaFon and Beeline in general, which could lead to difficulties for them in Chechnya and leaving this region. Of course, in this case, no one will be left without a cellular connection. Their place can be taken, for example, by a local company.
As for the «not taken into account» SMS, as a result of a survey of colleagues from different regions of Russia, 47News found out that all voters received such messages, despite the fact that they were far outside the Chechen Republic. But the indignation followed only from the mountainous region.
Victor Smirnov, 47News
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These are the «gray cardinals» of the best mathematicians in Russia — the director of Lyceum No. 239Maxim Pratusevich and teacher Kirill Sukhov
Science and education
Physmatlyceum No. 239 is a phenomenon among educational brands not only in St. Petersburg, but throughout Russia. For more than 40 years, students of the school have been winning medals at international math olympiads every year. In 2023, the 239th school topped the ranking of the best physics and mathematics schools in the country, and three of its students took gold at the international Romanian Master of Mathematics tournament. For the last 14 years, the lyceum has been headed by Maxim Pratusevich, in this position he was recognized as the best school director in Russia. And 5 years ago, Kirill Sukhov, a lyceum teacher, headed the Russian team in mathematics Olympiad. Under his leadership, our Olympiads are regaining their leading positions after a decline in the late 2010s. This year, teachers became laureates of the TOP50. The most famous people of St. Petersburg» — 2023 in the nomination «Science and Life».
Director of the Presidential Physics and Mathematics Lyceum No. 239
Let’s start with the building we are in. What is its history?
The school has existed on this site since 1736, when, by order of Anna Ioannovna, the Annenschule school was formed at the Church of St. Anna (Annenkirche). The current building was erected by the architect Dutak in 1865. Later, according to the project of Leonty Benois, the assembly hall was rebuilt, which is now an architectural monument. Even later, a sports hall was added — the first gym in the schools of the Russian Empire. He, by the way, is the birthplace of domestic basketball, here at 19In 08, the country’s first basketball game was held.
But the history of the 239th school began, as far as I know, not here?
Yes, the first address is Chernomorsky Lane, building 1. There, in 1918, a school was founded for the children of employees of the People’s Commissariat of Food. In 1922, the school, then a seven-year school, moved to the Lobanov-Rostovsky house, the famous house with lions from The Bronze Horseman.
It was in this building that the school, already ten years old, worked throughout the blockade. Many famous graduates studied here, for example, Alisa Brunovna Freindlich, whose father, by the way, graduated from Annenshule. Left the house with lions 239- me in the 1960s. She changed two more addresses until she moved here in 1975 to the Annenschule building.
How did the former seven-year school turn into the country’s best gymnast?
It all started in the 1960s. School education was made 11 years old to add work experience to the program. Schools arose on this wave, where computer work was such a practice. One of them was the 239th, its graduates received the working specialty «computer programmer».
Trained IT people before it became mainstream?
Yes! We had our own computer at school already in 1963. And since machine time was then in short supply, the school even carried out contractual work: it calculated something for the collective farms. Mathematics was needed for this work, so here they began to study it in depth.
Our student won the first diploma of the International Olympiad in Mathematics in 1964. The 239th became a recognizable brand, then it only remained not to “sink”, which, probably, we succeed. From 19On the 81st, every year at our school there was at least one medalist of the International Olympiad in Mathematics. I think that there are few schools in the world that can boast of this.
When did you first come here?
In 1987, when I entered the 9th grade. My brother graduated from this school before me, he was a classmate of Perelman. I was going to become a historian or a chemist, but my parents said that after this school I would go anywhere.
It was here that our teacher Vladimir Vasilievich Bakrylov instilled in me a love for mathematics, who had been working at the school since the winter of 1941 years old. He was then specially recalled from the front so that he would release the class of his father, who died in the blockade.
Why, after the 239th, did you decide to enter the Pedagogical Institute named after. Herzen? Any doors were open for you…
Well, yes, I even successfully passed the entrance exams for mathematics and mathematics at Leningrad State University, I had already received an invitation, but I still wanted to teach. Therefore, between the university and Herzen, I chose pedagogical.
To return to 239 latera teacher?
Look, no. I had great-hearted plans for going to the people. It’s funny to remember. I read the memoirs of the great ballerinas of the Soviet era: Vecheslova, Karsavina, they all wrote that they did not understand mathematics at the Vaganov School and tried their best to dodge. And for this it was necessary to dance very well, because those who danced very well were taken to rehearsals of the corps de ballet of the Kirov Theater, removing them from mathematics lessons. Thus, the poor teaching of mathematics served the national ballet in good stead.
And I thought that I would come to Vaganovskoye and show them how wonderful mathematics is. But my classmate dissuaded me, he taught mathematics to young dancers and explained that no one needs it. Meanwhile, I did not lose connections with the 239th, in 1991 I was called to lead a mathematical circle, and in April 1992 an order was issued for my employment as a teacher.
“Since 1981, every year we have had at least one medalist in the International Mathematics Olympiad”
Early nineties! You came to school at a difficult time…
Everything was easier here — salaries were not delayed, teachers were fed, they were given vouchers for lunch in the canteen. But most importantly, no one bothered, everyone could do what they wanted. It was then that I came up with many pedagogical techniques that I still use today.
But you didn’t have your own computer yet?
Why? Were! In 1988, a Yamaha PC was brought here, colored, with floppy disks and mice. Actually, it was a miracle! The Internet was dug here at 1994 year.
Then the teachers complained not only about poverty, but also about the motivation of students. Like, they often said that more teachers would earn at the car wash without any studies…
Then we didn’t have such problems. This argument does not work for people who are used to thinking two or three steps ahead. Paradoxically, the problem appears now when students say they will become bloggers or will mine cryptocurrency. I even had to write a book about cryptocurrency to explain to them what it is and why it should not be done.
This is a lottery, and the lottery brings profit only to its organizers.
In 2009, you became a director and first of all opened in the 5th-6th grades, although earlier you were admitted to the school from the 7th. Why did you do it?
The level of training in ordinary schools has dipped. And the 5-7th grades are a very important thing, if you didn’t learn math well then, it will be very difficult to become a programmer in the 11th grade.
I read that in the 239th they teach well not only mathematics, but also humanities. Why bother a programmer with history?
We don’t train programmers, we train those who can become programmers… Or maybe an actor or a composer.
Are all these graduates equally valuable to you?
Of course. I have many students that I can be proud of, and not all of them are mathematicians. There is a restaurateur, and another of my graduates became a rabbi.
“We [at 239] do not train programmers, we train those who can become programmers… Or maybe an actor or a composer”
And the last question: they say you have a whole collection of toy pigs… Unexpectedly!
Yes, there is one. It began with the fact that in 2003 the children brought one large pig to the office, and then they began to bring “children” to it. So they bred, now, probably, about a hundred have accumulated. Where does such an idea come from? Don’t know. One could ask the 2003 students, but I guess they don’t remember. Maybe something to do with «put the pig on».
The most unusual item in my collection is a lego pig. She was brought by the president of the Lego Corporation. In the summer of 2018, he was at our school, I was in the Tver forests, and he communicated with me via Skype from my office.
The next year, impressed by what he saw, he brought all the regional vice presidents to the 239th and said that the last time he understood what I should give, he gave me a pig made of Lego pieces. It now hangs the gold medal of the World Robotics Competition.
Lyceum No. 239 teacher, head coach of the Russian school team in mathematics
How did you get into the world of mathematical Olympiads?
In the 5th grade, my mother brought me to my first Olympiad, as a result of which I ended up in the district mathematical circle. In the 6th I got to the city Olympiad, from where I was taken to a circle, which was in the 239th school. And so it rolled … In 1998, I entered the 8th grade here, and in the spring of 1999 I got to my first «Vseros» (All-Russian Olympiad in mathematics. — Approx. ed.).
I remember that before him I was kicked out of the math circle for a couple of months for my behavior. But I had more time, and I took it to solve Olympiad problems. As a result, if before the expulsion I was the fifth or sixth in the circle, then after I became the first. Therefore, when I was driving the Vseros, I had mixed feelings. On the one hand, I was confident in myself, on the other hand, I understood that I was in the 8th grade, and I would have to compete with ninth graders. I didn’t sleep for half the night before the first round and in the end I got only a prize, then I took it as a handout. But in the 10th grade I won, after which in the 11th I went to the international Olympiad in Glasgow.
This was my first trip abroad, and with the feeling that I represent my Motherland. Plus, I was worried that if I didn’t win, but brought silver or bronze, then everyone would point fingers at me. In the end, everything was fine and I got my gold, but I remember the feeling of nervousness well. And now my job as a coach is, among other things, to ensure that children go to the Olympics without this feeling.
“To learn hockey, you have to play hockey. To win at the Olympiads, you need to solve Olympiad problems. Four hours twice a day0005
Very similar to classic sports…
This is sport! It’s just that the muscles are more complicated!
Who comes to it?
Various children. It is clear that there are those who are kissed by God, who could not be prevented from being at the international Olympiad. In any case, if they were born in St. Petersburg. But there are very few of them, even among the winners. The rest is a healthy balance of talent and work.
How do Olympiads train?
Trivial — to learn hockey, you have to play hockey. To win at the Olympiads, you need to solve Olympiad problems. Four hours twice a day.
We have classical topics: algebra, geometry, combinatorics, number theory. It’s like different sports skills that are needed at the Olympics all at the same time. We meet regularly and solve problems on each of these topics. When working at the training camp, there are also classes “about something else”. For example, what to do if there is half an hour left before the end of the Olympiad, but you have not solved the problem. Or what to do in the first half hour of the competition.
And this training is the same in all countries? Or are there national schools?
Of course, there are features. For example, this year 160 tenth-graders from Russia and three from China took part in Vseros. The last problem in algebra — an inequality with several variables — was not solved by any of ours, the Chinese solved all three.
They know how to solve such problems where technical methods are needed, when you write a lot and think at the same time. We do not like this, they prefer combinatorics, where, ideally, nothing needs to be done. You just sit, think — and the problem seems to be solved by itself. Or if technique, then without much thought. I don’t know where this comes from, maybe we have such a mentality, to wait for it to work out on its own.
What is the secret of our Olympiad school? Yet not every country has so many awards?
If we talk about Russia, then we have a cult of the Olympics, unlike, for example, in France, where it is completely out of fashion.
If you go down one level and talk about the 239th school, then this is a combination of strong school preparation and long-standing traditions of the mathematical circle, which support each other. Parents bring their children to this school because they are sure that they will not be disappointed with the result. And then these strong children get into the circle, from where they go to the Olympiad, which further strengthens the reputation of the school.
“My job as a coach is, among other things, to ensure that children go to the Olympics without feeling nervous”
How did you lead the Russian team?
I have been going to the training camp with the team since 2012, and in 2016 I became an assistant to the team leader. Then in 2015-2017 we had three unsuccessful performances (in 2017 we were 11th in the team standings), and it became obvious that something needed to be changed, which I was offered to do.
And what did you change?
Almost everything! We increased the number of classes, introduced additional fees, created a formalized system where the composition of the team determines only the number of points scored by applicants. Neither my nor anyone else’s opinion matters.
It seems to work! In any case, in March, all participants received gold at the Romanian Master of Mathematics Olympiad. What do you expect from the International Mathematical Olympiad?
What am I waiting for or what would I like? Looking forward to a decent performance. And I would like all six members of the team to score maximum points at the International Olympiad. Last year, only one of ours succeeded. If everyone reaches the maximum, it will be possible to retire.